Source code for skrf.network

# -*- coding: utf-8 -*-
"""
.. module:: skrf.network
========================================
network (:mod:`skrf.network`)
========================================


Provides a n-port network class and associated functions.

Much of the functionality in this module is provided as methods and
properties of the :class:`Network` Class.


Network Class
===============

.. autosummary::
    :toctree: generated/

    Network

Building Network
----------------

.. autosummary::
    :toctree: generated/

    Network.from_z

Network Representations
============================

.. autosummary::
    :toctree: generated/

    Network.s
    Network.z
    Network.y
    Network.a
    Network.t

Connecting Networks
===============================

.. autosummary::
    :toctree: generated/

    connect
    innerconnect
    cascade
    cascade_list
    de_embed
    flip



Interpolation and Concatenation Along Frequency Axis
=====================================================

.. autosummary::
    :toctree: generated/

    stitch
    overlap
    Network.resample
    Network.interpolate
    Network.interpolate_self


Combining and Splitting Networks
===================================

.. autosummary::
    :toctree: generated/

    subnetwork

    one_port_2_two_port
    n_oneports_2_nport
    four_oneports_2_twoport
    three_twoports_2_threeport
    n_twoports_2_nport
    concat_ports



IO
====

.. autosummary::

    skrf.io.general.read
    skrf.io.general.write
    skrf.io.general.network_2_spreadsheet
    Network.write
    Network.write_touchstone
    Network.read
    Network.write_spreadsheet

Noise
============
.. autosummary::
    :toctree: generated/

    Network.add_noise_polar
    Network.add_noise_polar_flatband
    Network.multiply_noise


Supporting Functions
======================

.. autosummary::
    :toctree: generated/

    inv
    connect_s
    innerconnect_s
    s2z
    s2y
    s2t
    s2a
    s2h
    z2s
    z2y
    z2t
    z2a
    y2s
    y2z
    y2t
    t2s
    t2z
    t2y
    h2s
    h2z
    fix_z0_shape
    renormalize_s
    passivity
    reciprocity

Misc Functions
=====================
.. autosummary::
    :toctree: generated/

    average
    two_port_reflect
    chopinhalf
    Network.nudge
    Network.renormalize

"""
from typing import (Any, NoReturn, Optional, Sequence,
    Sized, Union, Tuple, Callable, TYPE_CHECKING, Dict, List)
from numbers import Number
from functools import reduce

import os
import warnings
from io import StringIO
from pathlib import Path
import pickle
from pickle import UnpicklingError

import sys
import re
import zipfile
from copy import deepcopy as copy
from numbers import Number
from itertools import product

import numpy as npy
from numpy.linalg import inv as npy_inv
from numpy import fft, gradient, ndarray, reshape, shape, ones, std
from scipy import stats, signal  # for Network.add_noise_*, and Network.windowed
from scipy.interpolate import interp1d  # for Network.interpolate()
from scipy.ndimage.filters import convolve1d
import unittest  # fotr unitest.skip

from . import mathFunctions as mf
from .frequency import Frequency
from .util import get_fid, get_extn, find_nearest_index, slice_domain
from .time import time_gate

from .constants import NumberLike, ZERO, K_BOLTZMANN, T0
from .constants import S_DEFINITIONS, S_DEF_DEFAULT

if TYPE_CHECKING:
    import pandas as pd

#from matplotlib import cm
#import matplotlib.pyplot as plt
#import matplotlib.tri as tri
#from scipy.interpolate import interp1d

[docs]class Network(object): """ A n-port electrical network. For instructions on how to create Network see :func:`__init__`. A n-port network [#TwoPortWiki]_ may be defined by three quantities * network parameter matrix (s, z, or y-matrix) * port characteristic impedance matrix * frequency information The :class:`Network` class stores these data structures internally in the form of complex :class:`numpy.ndarray`'s. These arrays are not interfaced directly but instead through the use of the properties: ===================== ============================================= Property Meaning ===================== ============================================= :attr:`s` scattering parameter matrix :attr:`z0` characteristic impedance matrix :attr:`f` frequency vector ===================== ============================================= Although these docs focus on s-parameters, other equivalent network representations such as :attr:`z` and :attr:`y` are available. Scalar projections of the complex network parameters are accessible through properties as well. These also return :class:`numpy.ndarray`'s. ===================== ============================================= Property Meaning ===================== ============================================= :attr:`s_re` real part of the s-matrix :attr:`s_im` imaginary part of the s-matrix :attr:`s_mag` magnitude of the s-matrix :attr:`s_db` magnitude in log scale of the s-matrix :attr:`s_deg` phase of the s-matrix in degrees ===================== ============================================= The following operations act on the networks s-matrix. ===================== ============================================= Operator Function ===================== ============================================= \+ element-wise addition of the s-matrix \- element-wise difference of the s-matrix \* element-wise multiplication of the s-matrix \/ element-wise division of the s-matrix \*\* cascading (only for 2-ports) \// de-embedding (for 2-ports, see :attr:`inv`) ===================== ============================================= Different components of the :class:`Network` can be visualized through various plotting methods. These methods can be used to plot individual elements of the s-matrix or all at once. For more info about plotting see the :doc:`../../tutorials/Plotting` tutorial. ========================= ============================================= Method Meaning ========================= ============================================= :func:`plot_s_smith` plot complex s-parameters on smith chart :func:`plot_s_re` plot real part of s-parameters vs frequency :func:`plot_s_im` plot imaginary part of s-parameters vs frequency :func:`plot_s_mag` plot magnitude of s-parameters vs frequency :func:`plot_s_db` plot magnitude (in dB) of s-parameters vs frequency :func:`plot_s_deg` plot phase of s-parameters (in degrees) vs frequency :func:`plot_s_deg_unwrap` plot phase of s-parameters (in unwrapped degrees) vs frequency ========================= ============================================= :class:`Network` objects can be created from a touchstone or pickle file (see :func:`__init__`), by a :class:`~skrf.media.media.Media` object, or manually by assigning the network properties directly. :class:`Network` objects can be saved to disk in the form of touchstone files with the :func:`write_touchstone` method. An exhaustive list of :class:`Network` Methods and Properties (Attributes) are given below References ---------- .. [#TwoPortWiki] http://en.wikipedia.org/wiki/Two-port_network """ PRIMARY_PROPERTIES = ['s', 'z', 'y', 'a', 'h'] """ Primary Network Properties list like 's', 'z', 'y', etc. """ COMPONENT_FUNC_DICT = { 're': npy.real, 'im': npy.imag, 'mag': npy.abs, 'db': mf.complex_2_db, 'db10': mf.complex_2_db10, 'rad': npy.angle, 'deg': lambda x: npy.angle(x, deg=True), 'arcl': lambda x: npy.angle(x) * npy.abs(x), 'rad_unwrap': lambda x: mf.unwrap_rad(npy.angle(x)), 'deg_unwrap': lambda x: mf.radian_2_degree(mf.unwrap_rad( \ npy.angle(x))), 'arcl_unwrap': lambda x: mf.unwrap_rad(npy.angle(x)) * \ npy.abs(x), # 'gd' : lambda x: -1 * npy.gradient(mf.unwrap_rad(npy.angle(x)))[0], # removed because it depends on `f` as well as `s` 'vswr': lambda x: (1 + abs(x)) / (1 - abs(x)), 'time': mf.ifft, 'time_db': lambda x: mf.complex_2_db(mf.ifft(x)), 'time_mag': lambda x: mf.complex_2_magnitude(mf.ifft(x)), 'time_impulse': None, 'time_step': None, } """ Component functions like 're', 'im', 'mag', 'db', etc. """ # provides y-axis labels to the plotting functions Y_LABEL_DICT = { 're': 'Real Part', 'im': 'Imag Part', 'mag': 'Magnitude', 'abs': 'Magnitude', 'db': 'Magnitude (dB)', 'db10': 'Magnitude (dB)', 'deg': 'Phase (deg)', 'deg_unwrap': 'Phase (deg)', 'rad': 'Phase (rad)', 'rad_unwrap': 'Phase (rad)', 'arcl': 'Arc Length', 'arcl_unwrap': 'Arc Length', 'gd': 'Group Delay (s)', 'vswr': 'VSWR', 'passivity': 'Passivity', 'reciprocity': 'Reciprocity', 'time': 'Time (real)', 'time_db': 'Magnitude (dB)', 'time_mag': 'Magnitude', 'time_impulse': 'Magnitude', 'time_step': 'Magnitude', } """ y-axis labels to the plotting functions """ noise_interp_kind = 'linear' """ Default interpolation method. """ # CONSTRUCTOR
[docs] def __init__(self, file: str = None, name : str = None, comments: str = None, f_unit: str = None, s_def: str = S_DEF_DEFAULT, **kwargs) -> None: """ Network constructor. Creates an n-port microwave network from a `file` or directly from data. If no file or data is given, then an empty Network is created. Parameters ---------- file : str or file-object file to load information from. supported formats are: * touchstone file (.s?p) * pickled Network (.ntwk, .p) see :func:`write` name : str Name of this Network. if None will try to use file, if its a str comments : str Comments associated with the Network s_def : str -> s_def : can be: 'power', 'pseudo' or 'traveling' Scattering parameter definition : 'power' for power-waves definition, 'pseudo' for pseudo-waves definition. 'traveling' corresponds to the initial implementation. Default is 'power'. NB: results are the same for real-valued characteristic impedances. \*\*kwargs : key word arguments can be used to assign properties of the Network, such as `s`, `f` and `z0`. Examples -------- From a touchstone >>> n = rf.Network('ntwk1.s2p') From a pickle file >>> n = rf.Network('ntwk1.ntwk') Create a blank network, then fill in values >>> n = rf.Network() >>> freq = rf.Frequency(1, 3, 3, 'ghz') >>> n.frequency, n.s, n.z0 = freq, [1,2,3], [1,2,3] Directly from values >>> n = rf.Network(f=[1,2,3], s=[1,2,3], z0=[1,2,3]) See Also -------- from_z : init from impedance values read : read a network from a file write : write a network to a file, using pickle write_touchstone : write a network to a touchstone file """ # allow for old kwarg for backward compatibility if 'touchstone_filename' in kwargs: file = kwargs['touchstone_filename'] self.name = name self.comments = comments self.port_names = None self.deembed = None self.noise = None self.noise_freq = None self._z0 = npy.array(50, dtype=complex) if s_def not in S_DEFINITIONS: raise ValueError('s_def parameter should be either:', S_DEFINITIONS) else: self.s_def = s_def if file is not None: if isinstance(file, Path): file = str(file.resolve()) # allows user to pass StringIO, filename or file obj if isinstance(file,StringIO): self.read_touchstone(file) else: # open file in 'binary' mode because we are going to try and # unpickle it first fid = get_fid(file, 'rb') try: self.read(fid) except UnicodeDecodeError: # Support for pickles created in Python2 and loaded in Python3 self.read(fid, encoding='latin1') except (UnpicklingError,TypeError): # if unpickling doesn't work then, close fid, reopen in # non-binary mode and try to read it as touchstone filename = fid.name fid.close() self.read_touchstone(filename) if name is None and isinstance(file, str): name = os.path.splitext(os.path.basename(file))[0] if self.frequency is not None and f_unit is not None: self.frequency.unit = f_unit # allow properties to be set through the constructor for attr in PRIMARY_PROPERTIES + ['frequency', 'f', 'z0', 'noise', 'noise_freq']: if attr in kwargs: self.__setattr__(attr, kwargs[attr])
# self.nports = self.number_of_ports
[docs] @classmethod def from_z(cls, z: npy.ndarray, *args, **kw) -> 'Network': """ Create a Network from its Z-parameters Parameters ---------- z : Numpy array Impedance matrix. Should be of shape fxnxn, where f is frequency axis and n is number of ports \*\*kwargs : key word arguments can be used to assign properties of the Network, `f` and `z0`. Returns ------- ntw : :class:`Network` Created Network Examples -------- >>> f = rf.Frequency(start=1, stop=2, npoints=4) # 4 frequency points >>> z = np.random.rand(len(f),2,2) + np.random.rand(len(f),2,2)*1j # 2-port z-matrix: shape=(4,2,2) >>> ntw = rf.Network.from_z(z, f=f) """ s = npy.zeros(shape=z.shape) me = cls(s=s, *args, **kw) me.z = z return me
# OPERATORS def __pow__(self, other: 'Network') -> 'Network': """ Cascade this network with another network Returns ------- ntw : :class:`Network` Cascaded Network See Also -------- cascade """ # if they pass a number then use power operator if isinstance(other, Number): out = self.copy() out.s = out.s ** other return out else: return cascade(self, other) def __floordiv__(self, other: Union['Network', Tuple['Network', ...]] ) -> 'Network': """ de-embedding 1 or 2 network[s], from this network :param other: skrf.Network, list, tuple: Network(s) to de-embed :return: skrf.Network: De-embedded network Returns ------- ntw : :class:`Network` See Also -------- inv : inverse s-parameters """ if isinstance(other, (list, tuple)): if len(other) >= 3: warnings.warn( "Number of networks greater than 2. Truncating!", RuntimeWarning ) other_tpl = other[:2] else: other_tpl = (other, ) for o in other_tpl: if o.number_of_ports != 2: raise IndexError('Incorrect number of ports in network {}.'.format(o.name)) if len(other_tpl) == 1: # if passed 1 network (A) and another network B # e.g. A // B # e.g. A // (B) # then de-embed like B.inv * A b = other_tpl[0] result = self.copy() result.s = (b.inv ** self).s # de_embed(self.s, b.s) return result else: # if passed 1 network (A) and a list/tuple of 2 networks (B, C), # e.g. A // (B, C) # e.g. A // [B, C] # then de-embed like B.inv * A * C.inv b = other_tpl[0] c = other_tpl[1] result = self.copy() result.s = (b.inv ** self ** c.inv).s # flip(de_embed(flip(de_embed(c.s, self.s)), b.s)) return result def __mul__(self, other:'Network') -> 'Network': """ Element-wise complex multiplication of s-matrix Returns ------- ntw : :class:`Network` """ result = self.copy() if isinstance(other, Network): self.__compatable_for_scalar_operation_test(other) result.s = self.s * other.s else: # other may be an array or a number result.s = self.s * npy.array(other).reshape(-1, self.nports, self.nports) return result def __rmul__(self, other: 'Network') -> 'Network': """ Element-wise complex multiplication of s-matrix Returns ------- ntw : :class:`Network` """ result = self.copy() if isinstance(other, Network): self.__compatable_for_scalar_operation_test(other) result.s = self.s * other.s else: # other may be an array or a number result.s = self.s * npy.array(other).reshape(-1, self.nports, self.nports) return result def __add__(self, other:'Network') -> 'Network': """ Element-wise complex addition of s-matrix Returns ------- ntw : :class:`Network` """ result = self.copy() if isinstance(other, Network): self.__compatable_for_scalar_operation_test(other) result.s = self.s + other.s else: # other may be an array or a number result.s = self.s + npy.array(other).reshape(-1, self.nports, self.nports) return result def __radd__(self, other:'Network') -> 'Network': """ Element-wise complex addition of s-matrix Returns ------- ntw : :class:`Network` """ result = self.copy() if isinstance(other, Network): self.__compatable_for_scalar_operation_test(other) result.s = self.s + other.s else: # other may be an array or a number result.s = self.s + npy.array(other).reshape(-1, self.nports, self.nports) return result def __sub__(self, other:'Network') -> 'Network': """ Element-wise complex subtraction of s-matrix """ result = self.copy() if isinstance(other, Network): self.__compatable_for_scalar_operation_test(other) result.s = self.s - other.s else: # other may be an array or a number result.s = self.s - npy.array(other).reshape(-1, self.nports, self.nports) return result def __rsub__(self, other:'Network') -> 'Network': """ Element-wise complex subtraction of s-matrix Returns ------- ntw : :class:`Network` """ result = self.copy() if isinstance(other, Network): self.__compatable_for_scalar_operation_test(other) result.s = other.s - self.s else: # other may be an array or a number result.s = npy.array(other).reshape(-1, self.nports, self.nports) - self.s return result def __truediv__(self, other: 'Network') -> 'Network': return self.__div__(other) def __div__(self, other: 'Network') -> 'Network': """ Element-wise complex multiplication of s-matrix Returns ------- ntw : :class:`Network` """ result = self.copy() if isinstance(other, Network): self.__compatable_for_scalar_operation_test(other) result.s = self.s / other.s else: # other may be an array or a number result.s = self.s / npy.array(other).reshape(-1, self.nports, self.nports) return result def __eq__(self, other: object) -> bool: if not isinstance(other, self.__class__): return False if npy.all(npy.abs(self.s - other.s) < ZERO): return True else: return False def __ne__(self, other:object) -> bool: return (not self.__eq__(other)) def __getitem__(self, key:Union[str, int, slice, Sized]) -> 'Network': """ Slices a Network object based on an index, or human readable string Parameters ---------- key : str, or slice if slice; like [2-10] then it is interpreted as the index of the frequency. if str, then should be like '50.1-75.5ghz', or just '50'. If the frequency unit is omitted then self.frequency.unit is used. This will also accept a 2 or 3 dimensional index of the forms: port1, port2 key, port1, port2 where port1 and port2 are allowed to be string port names if the network has them defined (Network.port_names) If port1 and port2 are integers, will return the single-port network based on matrix notation (indices starts at 1 not 0) Returns ------- ntwk : skrf.Network interpolated in frequency if single dimension provided OR 1-port network if multi-dimensional index provided Examples -------- >>> from skrf.data import ring_slot >>> a = ring_slot['80-90ghz'] >>> a.plot_s_db() Multidimensional indexing: >>> import skrf as rf >>> b = rf.Network("sometouchstonefile.s2p") >>> c = b['80mhz', 'first_port_name', 'second_port_name'] >>> d = b['first_port_name', 'second_port_name'] Equivalently: >>> d = b[1,2] Equivalent to: >>> d = b.s12 """ a = self.z0 # HACK: to force getter for z0 to re-shape it (z0 getter has side effects...) # If user passes a multidimensional index, try to return that 1 port subnetwork if isinstance(key, tuple): if len(key) == 3: slice_like, p1_name, p2_name = key return self[slice_like][p1_name, p2_name] elif len(key) == 2: p1_name, p2_name = key if type(p1_name) == int and type(p2_name) == int: # allow integer indexing if desired if p1_name <= 0 or p2_name <= 0 or p1_name > self.nports or p2_name > self.nports: raise ValueError("Port index out of bounds") p1_index = p1_name - 1 p2_index = p2_name - 1 else: if self.port_names is None: raise ValueError("Can't index without named ports") try: p1_index = self.port_names.index(p1_name) except ValueError as e: raise KeyError("Unknown port {0}".format(p1_name)) try: p2_index = self.port_names.index(p2_name) except ValueError as e: raise KeyError("Unknown port {0}".format(p2_name)) ntwk = self.copy() ntwk.s = self.s[:, p1_index, p2_index] ntwk.z0 = self.z0[:, p1_index] ntwk.name = "{0}({1}, {2})".format(self.name, p1_name, p2_name) ntwk.port_names = None return ntwk else: raise ValueError("Don't understand index: {0}".format(key)) sliced_frequency = self.frequency[key] return self.interpolate(sliced_frequency) if isinstance(key, str): sliced_frequency = self.frequency[key] return self.interpolate(sliced_frequency) if isinstance(key, Frequency): return self.interpolate(key) # The following avoids interpolation when the slice is done directly with indices ntwk = self.copy_subset(key) return ntwk def __str__(self) -> str: """ """ f = self.frequency if self.name is None: name = '' else: name = self.name _z0 = self.z0 if _z0.ndim < 2: z0 = _z0 else: z0 = self.z0[0, :] output = '%i-Port Network: \'%s\', %s, z0=%s' % (self.number_of_ports, name, str(f), str(z0)) return output def __repr__(self) -> str: return self.__str__() def __len__(self) -> int: """ length of frequency axis """ return len(self.s) # INTERNAL CODE GENERATION METHODS def __compatable_for_scalar_operation_test(self, other:'Network') -> None: """ tests to make sure other network's s-matrix is of same shape """ if other.frequency != self.frequency: raise IndexError('Networks must have same frequency. See `Network.interpolate`') if other.s.shape != self.s.shape: raise IndexError('Networks must have same number of ports.') def __generate_secondary_properties(self) -> None: """ creates numerous `secondary properties` which are various different scalar projects of the primary properties. the primary properties are s,z, and y. """ for prop_name in PRIMARY_PROPERTIES: for func_name in COMPONENT_FUNC_DICT: func = COMPONENT_FUNC_DICT[func_name] if 'gd' in func_name: # scaling of gradient by frequency def fget(self: 'Network', f: Callable = func, p: str = prop_name) -> npy.ndarray: return f(getattr(self, p)) / (2 * npy.pi * self.frequency.step) else: def fget(self: 'Network', f: Callable = func, p: str = prop_name) -> npy.ndarray: return f(getattr(self, p)) doc = """ The %s component of the %s-matrix See Also -------- %s """ % (func_name, prop_name, prop_name) setattr(self.__class__, '%s_%s' % (prop_name, func_name), \ property(fget, doc=doc)) def __generate_subnetworks(self) -> None: """ generates all one-port sub-networks """ for m in range(self.number_of_ports): for n in range(self.number_of_ports): def fget(self: 'Network', m:int=m, n:int=n) -> 'Network': ntwk = self.copy() ntwk.s = self.s[:, m, n] ntwk.z0 = self.z0[:, m] return ntwk doc = """ one-port sub-network. """ setattr(self.__class__, 's%i%i' % (m + 1, n + 1), \ property(fget, doc=doc)) # PRIMARY PROPERTIES @property def s(self) -> npy.ndarray: """ Scattering parameter matrix. The s-matrix [#]_ is a 3-dimensional :class:`numpy.ndarray` which has shape `fxnxn`, where `f` is frequency axis and `n` is number of ports. Note that indexing starts at 0, so s11 can be accessed by taking the slice s[:,0,0]. Returns ------- s : complex :class:`numpy.ndarray` of shape `fxnxn` The scattering parameter matrix. See Also -------- s y z t a References ---------- .. [#] http://en.wikipedia.org/wiki/Scattering_parameters """ return self._s @s.setter def s(self, s: npy.ndarray) -> None: """ Scattering parameter matrix. Parameters ---------- s : :class:`numpy.ndarray` The input s-matrix should be of shape `fxnxn`, where f is frequency axis and n is number of ports. """ s_shape = npy.shape(s) if len(s_shape) < 3: if len(s_shape) == 2: # reshape to kx1x1, this simplifies indexing in function s = npy.reshape(s, (-1, s_shape[0], s_shape[0])) else: s = npy.reshape(s, (-1, 1, 1)) self._s = npy.array(s, dtype=complex) self.__generate_secondary_properties() self.__generate_subnetworks() @property def h(self) -> npy.ndarray: """ Hybrid parameter matrix. The h-matrix [#]_ is a 3-dimensional :class:`numpy.ndarray` which has shape `fxnxn`, where `f` is frequency axis and `n` is number of ports. Note that indexing starts at 0, so h11 can be accessed by taking the slice `h[:,0,0]`. Returns ------- h : complex :class:`numpy.ndarray` of shape `fxnxn` the hybrid parameter matrix. See Also -------- s y z t a h References ---------- .. [#] http://en.wikipedia.org/wiki/Two-port_network#Hybrid_parameters_(h-parameters) """ return s2h(self.s, self.z0) @h.setter def h(self, value: npy.ndarray) -> None: self._s = h2s(value, self.z0) @property def y(self) -> npy.ndarray: """ Admittance parameter matrix. The y-matrix [#]_ is a 3-dimensional :class:`numpy.ndarray` which has shape `fxnxn`, where `f` is frequency axis and `n` is number of ports. Note that indexing starts at 0, so y11 can be accessed by taking the slice `y[:,0,0]`. Returns ------- y : complex :class:`numpy.ndarray` of shape `fxnxn` the admittance parameter matrix. See Also -------- s y z t a References ---------- .. [#] http://en.wikipedia.org/wiki/Admittance_parameters """ return s2y(self._s, self.z0, s_def=self.s_def) @y.setter def y(self, value: npy.ndarray) -> None: self._s = y2s(value, self.z0, s_def=self.s_def) @property def z(self) -> npy.ndarray: """ Impedance parameter matrix. The z-matrix [#]_ is a 3-dimensional :class:`numpy.ndarray` which has shape `fxnxn`, where `f` is frequency axis and `n` is number of ports. Note that indexing starts at 0, so z11 can be accessed by taking the slice `z[:,0,0]`. Returns ------- z : complex :class:`numpy.ndarray` of shape `fxnxn` the Impedance parameter matrix. See Also -------- s y z t a References ---------- .. [#] http://en.wikipedia.org/wiki/impedance_parameters """ return s2z(self._s, self.z0, s_def=self.s_def) @z.setter def z(self, value: npy.ndarray) -> None: self._s = z2s(value, self.z0, s_def=self.s_def) @property def t(self) -> npy.ndarray: """ Scattering transfer parameters The t-matrix [#]_ is a 3-dimensional :class:`numpy.ndarray` which has shape `fx2x2`, where `f` is frequency axis. Note that indexing starts at 0, so t11 can be accessed by taking the slice `t[:,0,0]`. The t-matrix, also known as the wave cascading matrix, is only defined for a 2-port Network. Returns ------- t : complex numpy.ndarray of shape `fx2x2` t-parameters, aka scattering transfer parameters See Also -------- s y z t a References ----------- .. [#] http://en.wikipedia.org/wiki/Scattering_parameters#Scattering_transfer_parameters """ return s2t(self.s) @property def s_invert(self) -> npy.ndarray: """ Inverted scattering parameter matrix. Inverted scattering parameters are simply inverted s-parameters, defined as a = 1/s. Useful in analysis of active networks. The a-matrix is a 3-dimensional :class:`numpy.ndarray` which has shape `fxnxn`, where `f` is frequency axis and `n` is number of ports. Note that indexing starts at 0, so a11 can be accessed by taking the slice a[:,0,0]. Returns ------- s_inv : complex :class:`numpy.ndarray` of shape `fxnxn` the inverted scattering parameter matrix. See Also -------- s y z t a """ return 1 / self.s @s_invert.setter def s_invert(self, value: npy.ndarray) -> NoReturn: raise NotImplementedError @property def a(self) -> npy.ndarray: """ abcd parameter matrix. Used to cascade two-ports The abcd-matrix [#]_ is a 3-dimensional :class:`numpy.ndarray` which has shape `fxnxn`, where `f` is frequency axis and `n` is number of ports. Note that indexing starts at 0, so abcd11 can be accessed by taking the slice `abcd[:,0,0]`. Returns ------- abcd : complex :class:`numpy.ndarray` of shape `fxnxn` the Impedance parameter matrix. See Also -------- s y z t a abcd References ---------- .. [#] http://en.wikipedia.org/wiki/impedance_parameters """ return s2a(self.s, self.z0) @a.setter def a(self, value: npy.ndarray) -> None: self._s = a2s(value, self.z0) @property def z0(self) -> npy.ndarray: """ Characteristic impedance[s] of the network ports. This property stores the characteristic impedance of each port of the network. Because it is possible that each port has a different characteristic impedance each varying with frequency, `z0` is stored internally as a `fxn` array. However because `z0` is frequently simple (like 50ohm), it can be set with just number as well. Returns ------- z0 : :class:`numpy.ndarray` of shape fxn characteristic impedance for network """ # if we are unable to determine the s-matrix shape we return an scalar if not hasattr(self, '_s'): return self._z0 # _z0 is an scalar, so a npy.array with shape fxn is filled with _z0 if self._z0.ndim == 0: return npy.full(self._s.shape[:2], self._z0) elif self._z0.ndim == 1: # _z0 is a vector, either of length nports or frequency.npoints. # Create a npy.array with shape fxn and broadcast vector to array. z0 = npy.zeros(self._s.shape[:2], dtype=complex) if len(self._z0) == self.nports: z0[:] = self._z0[None, :] else: z0[:] = self._z0[:,None] return z0 elif self._z0.ndim == 2: # _z0 is a matrix of correct shape, so we can return directly return self._z0 @z0.setter def z0(self, z0: NumberLike) -> None: # cast any array like type (tuple, list) to a npy.array z0 = npy.array(z0, dtype=complex) # assign _z0 directly if z0 is a scalar if z0.ndim == 0: self._z0 = z0 return # if _z0 is a vector or matrix, we check if _s is already assigned. # If not, we cannot proof the correct dimensions and silently accept # any vector or fxn array if not hasattr(self, '_s'): if 1 <= z0.ndim <= 2: self._z0 = z0 return # if _z0 is a vector, we check if the dimension matches with either # nports or frequency.npoints. If yes, we accept the value. # Note that there can be an ambiguity in theory, if nports == npoints # # if _z0 is a matrix, we check if the shape matches with _s # In any other case raise an Exception if z0.ndim == 1: if len(z0) in (self.frequency.npoints, self.nports): self._z0 = z0 return elif z0.ndim == 2: if z0.shape == (self.frequency.npoints, self.nports): self._z0 = z0 return raise AttributeError('Unable to broadcast z0 to s shape') @property def frequency(self) -> Frequency: """ frequency information for the network. This property is a :class:`~skrf.frequency.Frequency` object. It holds the frequency vector, as well frequency unit, and provides other properties related to frequency information, such as start, stop, etc. Returns ------- frequency : :class:`~skrf.frequency.Frequency` object frequency information for the network. See Also -------- f : property holding frequency vector in Hz change_frequency : updates frequency property, and interpolates s-parameters if needed interpolate : interpolate function based on new frequency info """ try: return self._frequency except (AttributeError): self._frequency = Frequency(0, 0, 0) return self._frequency @frequency.setter def frequency(self, new_frequency: Union[Frequency, int, Sequence[float], npy.ndarray]) -> None: """ takes a Frequency object, see frequency.py """ if isinstance(new_frequency, Frequency): self._frequency = new_frequency.copy() else: try: self._frequency = Frequency.from_f(new_frequency) except (TypeError): raise TypeError('Could not convert argument to a frequency vector') @property def inv(self) -> 'Network': """ a :class:`Network` object with 'inverse' s-parameters. This is used for de-embedding. It is defined such that the inverse of the s-matrix cascaded with itself is a unity scattering transfer parameter (T) matrix. Returns ------- inv : a :class:`Network` object a :class:`Network` object with 'inverse' s-parameters. See Also -------- inv : function which implements the inverse s-matrix """ if self.number_of_ports < 2: raise (TypeError('One-Port Networks don\'t have inverses')) out = self.copy() out.s = inv(self.s) out.deembed = True return out @property def f(self) -> Frequency: """ the frequency vector for the network, in Hz. Returns ------- f : :class:`numpy.ndarray` frequency vector in Hz See Also -------- frequency : frequency property that holds all frequency information """ return self.frequency.f @f.setter def f(self, f: NumberLike) -> None: tmpUnit = self.frequency.unit self.frequency = Frequency.from_f(f, unit=tmpUnit) @property def noisy(self) -> bool: """ whether this network has noise """ try: return self.noise is not None and self.noise_freq is not None except: return False @property def n(self) -> npy.ndarray: """ the ABCD form of the noise correlation matrix for the network """ if not self.noisy: raise ValueError('network does not have noise') if self.noise_freq.f.size > 1 : noise_real = interp1d(self.noise_freq.f, self.noise.real, axis=0, kind=Network.noise_interp_kind) noise_imag = interp1d(self.noise_freq.f, self.noise.imag, axis=0, kind=Network.noise_interp_kind) return noise_real(self.frequency.f) + 1.0j * noise_imag(self.frequency.f) else : noise_real = self.noise.real noise_imag = self.noise.imag return noise_real + 1.0j * noise_imag @property def f_noise(self) -> Frequency: """ the frequency vector for the noise of the network, in Hz. """ if not self.noisy: raise ValueError('network does not have noise') return self.noise_freq @property def y_opt(self) -> npy.ndarray: """ the optimum source admittance to minimize noise """ noise = self.n return (npy.sqrt(noise[:,1,1]/noise[:,0,0] - npy.square(npy.imag(noise[:,0,1]/noise[:,0,0]))) + 1.j*npy.imag(noise[:,0,1]/noise[:,0,0])) @property def z_opt(self) -> npy.ndarray: """ the optimum source impedance to minimize noise """ return 1./self.y_opt @property def g_opt(self) -> npy.ndarray: """ the optimum source reflection coefficient to minimize noise """ return z2s(self.z_opt.reshape((self.f.shape[0], 1, 1)), self.z0[:,0])[:,0,0] @property def nfmin(self) -> npy.ndarray: """ the minimum noise figure for the network """ noise = self.n return npy.real(1. + (noise[:,0,1] + noise[:,0,0] * npy.conj(self.y_opt))/(2*K_BOLTZMANN*T0)) @property def nfmin_db(self) -> npy.ndarray: """ the minimum noise figure for the network in dB """ return mf.complex_2_db10(self.nfmin)
[docs] def nf(self, z: NumberLike) -> npy.ndarray: """ the noise figure for the network if the source impedance is z """ z0 = self.z0 y_opt = self.y_opt fmin = self.nfmin rn = self.rn ys = 1./z gs = npy.real(ys) return fmin + rn/gs * npy.square(npy.absolute(ys - y_opt))
[docs] def nfdb_gs(self, gs: NumberLike) -> npy.ndarray: """ return dB(NF) foreach gamma_source x noise_frequency """ g = self.copy().s11 nfreq = self.noise_freq.npoints if isinstance(gs, (int, float, complex)) : g.s[:,0,0] = gs nfdb = 10.*npy.log10(self.nf( g.z[:,0,0])) elif isinstance(gs, npy.ndarray) : npt = gs.shape[0] z = self.z0[0,0] * (1+gs)/(1-gs) zf = npy.broadcast_to(z[:,None], tuple((npt, nfreq))) nfdb = 10.*npy.log10(self.nf( zf)) else : g.s[:,0,0] = -1 nfdb = 10.*npy.log10(self.nf( g.z[:,0,0])) return nfdb
@property def rn(self) -> npy.ndarray: """ the equivalent noise resistance for the network """ return npy.real(self.n[:,0,0]/(4.*K_BOLTZMANN*T0)) # SECONDARY PROPERTIES @property def number_of_ports(self) -> int: """ the number of ports the network has. Returns ------- number_of_ports : number the number of ports the network has. """ try: return self.s.shape[1] except (AttributeError): return 0 @property def nports(self) -> int: """ the number of ports the network has. Returns ------- number_of_ports : number the number of ports the network has. """ return self.number_of_ports @property def port_tuples(self) -> List[Tuple[int, int]]: """ Returns a list of tuples, for each port index pair A convenience function for the common task for iterating over all s-parameters index pairs This just calls:: [(y,x) for x in range(self.nports) for y in range(self.nports)] Returns ------- ports_ind : list of tuples list of all port index tuples. Examples -------- >>> ntwk = skrf.data.ring_slot >>> for (idx_i, idx_j) in ntwk.port_tuples: print(idx_i, idx_j) """ return [(y, x) for x in range(self.nports) for y in range(self.nports)] @property def passivity(self) -> ndarray: """ passivity metric for a multi-port network. This returns a matrix who's diagonals are equal to the total power received at all ports, normalized to the power at a single excitement port. mathematically, this is a test for unitary-ness of the s-parameter matrix [#]_. for two port this is .. math:: ( |S_{11}|^2 + |S_{21}|^2 \, , \, |S_{22}|^2+|S_{12}|^2) in general it is .. math:: S^H \\cdot S where :math:`H` is conjugate transpose of S, and :math:`\\cdot` is dot product. Returns ------- passivity : :class:`numpy.ndarray` of shape fxnxn References ---------- .. [#] http://en.wikipedia.org/wiki/Scattering_parameters#Lossless_networks """ return passivity(self.s) @property def reciprocity(self) -> npy.ndarray: """ reciprocity metric for a multi-port network. This returns the difference between the s-parameter matrix and its transpose. for two port this is .. math:: S - S^T where :math:`T` is transpose of S Returns ------- reciprocity : :class:`numpy.ndarray` of shape `fxnxn` """ return reciprocity(self.s) @property def reciprocity2(self) -> npy.ndarray: """ Reciprocity metric #2 .. math:: abs(1 - S/S^T ) for the two port case, this evaluates to the distance of the determinant of the wave-cascading matrix from unity. Returns ------- reciprocity : :class:`numpy.ndarray` of shape `fxnxn` """ return abs(1 - self.s / self.s.swapaxes(1, 2)) @property def stability(self) -> npy.ndarray: """ Stability factor .. math:: K = ( 1 - |S_{11}|^2 - |S_{22}|^2 + |D|^2 ) / (2 * |S_{12}| * |S_{21}|) with D = S_{11} S_{22} - S_{12} S_{21} Returns ------- K : :class:`numpy.ndarray` of shape `f` """ assert self.nports == 2, "Stability factor K is only defined for two ports" D = self.s[:, 0, 0] * self.s[:, 1, 1] - self.s[:, 0, 1] * self.s[:, 1, 0] K = (1 - npy.abs(self.s[:, 0, 0]) ** 2 - npy.abs(self.s[:, 1, 1]) ** 2 + npy.abs(D) ** 2) / ( 2 * npy.abs(self.s[:, 0, 1]) * npy.abs(self.s[:, 1, 0])) return K @property def group_delay(self) -> npy.ndarray: """ The group delay Usually used as a measure of dispersion (or distortion). Defined as the derivative of the unwrapped s-parameter phase (in rad) with respect to the frequency:: -d(self.s_rad_unwrap)/d(self.frequency.w) Returns ------- gd : :class:`numpy.ndarray` of shape `xnxn` References ---------- https://en.wikipedia.org/wiki/Group_delay_and_phase_delay """ gd = self.s * 0 # quick way to make a new array of correct shape phi = self.s_rad_unwrap dw = self.frequency.dw for m, n in self.port_tuples: dphi = gradient(phi[:, m, n]) gd[:, m, n] = -dphi / dw return gd ## NETWORK CLASSIFIERs
[docs] def is_reciprocal(self, tol: float = mf.ALMOST_ZERO) -> bool: """ Test for reciprocity Parameters ---------- tol : float, optional Numerical tolerance. The default is :data:`skrf.mathFunctions.ALMOST_ZERO`. Returns ------- bool : boolean See Also -------- reciprocity """ return npy.allclose(reciprocity(self.s), npy.zeros_like(self.s), atol=tol)
[docs] def is_symmetric(self, n: int = 1, port_order: Dict[int, int] = {}, tol: float = mf.ALMOST_ZERO) -> bool: """ Returns whether the 2N-port network has n-th order reflection symmetry by checking :math:`S_{i,i} == S_{j,j}` for appropriate pair(s) of :math:`i` and :math:`j`. Parameters ---------- n : int Order of line symmetry to test for port_order : dict[int, int] Renumbering of zero-indexed ports before testing tol : float Tolerance in numeric comparisons. Default is :data:`skrf.mathFunctions.ALMOST_ZERO`. Returns ------- bool : boolean Raises ------ ValueError (1) If the network has an odd number of ports (2) If n is not in the range 1 to N (3) If n does not evenly divide 2N (4) If port_order is not a valid reindexing of ports e.g. specifying x->y but not y->z, specifying x->y twice, or using an index outside the range 0 to 2N-1 References ---------- https://en.wikipedia.org/wiki/Two-port_network#Scattering_parameters_(S-parameters) """ nfreqs, ny, nx = self.s.shape # nfreqs is number of frequencies, and nx, ny both are number of ports (2N) if nx % 2 != 0 or nx != ny: raise ValueError('Using is_symmetric() is only valid for a 2N-port network (N=2,4,6,8,...)') n_ports = nx // 2 if n <= 0 or n > n_ports: raise ValueError('specified order n = ' + str(n) + ' must be ' + 'between 1 and N = ' + str(n_ports) + ', inclusive') if nx % n != 0: raise ValueError('specified order n = ' + str(n) + ' must evenly divide ' + 'N = ' + str(n_ports)) from_ports = list(map(lambda key: int(key), port_order.keys())) to_ports = list(map(lambda val: int(val), port_order.values())) test_network = self.copy() # TODO: consider defining renumbered() if len(from_ports) > 0 and len(to_ports) > 0: test_network.renumber(from_ports, to_ports) offs = npy.array(range(0, n_ports)) # port index offsets from each mirror line for k in range(0, n_ports, n_ports // n): # iterate through n mirror lines mirror = k * npy.ones_like(offs) i = mirror - 1 - offs j = mirror + offs if not npy.allclose(test_network.s[:, i, i], test_network.s[:, j, j], atol=tol): return False return True
[docs] def is_passive(self, tol: float = mf.ALMOST_ZERO) -> bool: """ Test for passivity Parameters ---------- tol : float, optional Numerical tolerance. The default is :data:`skrf.mathFunctions.ALMOST_ZERO` Returns ------- bool : boolean """ try: M = npy.square(self.passivity) except ValueError: return False I = npy.identity(M.shape[-1]) for f_idx in range(len(M)): D = I - M[f_idx, :, :] # dissipation matrix if not mf.is_positive_definite(D) \ and not mf.is_positive_semidefinite(mat=D, tol=tol): return False return True
[docs] def is_lossless(self, tol: float = mf.ALMOST_ZERO) -> bool: """ Test for losslessness [S] is lossless if [S] is unitary, i.e. if :math:`([S][S]^* = [1])` Parameters ---------- tol : float, optional Numerical tolerance. The default is :data:`skrf.mathFunctions.ALMOST_ZERO` Returns ------- bool : boolean See Also -------- is_passive, is_symmetric, is_reciprocal References ---------- https://en.wikipedia.org/wiki/Unitary_matrix """ for f_idx in range(len(self.s)): mat = npy.matrix(self.s[f_idx, :, :]) if not mf.is_unitary(mat, tol=tol): return False return True
## CLASS METHODS
[docs] def copy(self) -> 'Network': """ Returns a copy of this Network Needed to allow pass-by-value for a Network instead of pass-by-reference Returns ------- ntwk : :class:`Network` Copy of the Network """ ntwk = Network(s=self.s, frequency=self.frequency.copy(), z0=self.z0, s_def=self.s_def ) ntwk.name = self.name if self.noise is not None and self.noise_freq is not None: if False : ntwk.noise = npy.copy(self.noise) ntwk.noise_freq = npy.copy(self.noise_freq) ntwk.noise = self.noise.copy() ntwk.noise_freq = self.noise_freq.copy() try: ntwk.port_names = copy(self.port_names) except(AttributeError): ntwk.port_names = None return ntwk
[docs] def copy_from(self, other: 'Network') -> None: """ Copies the contents of another Network into self Uses copy, so that the data is passed-by-value, not reference Parameters ---------- other : Network the network to copy the contents of Examples -------- >>> a = rf.N() >>> b = rf.N('my_file.s2p') >>> a.copy_from (b) """ for attr in ['_s', 'frequency', '_z0', 'name']: self.__setattr__(attr, copy(other.__getattribute__(attr)))
[docs] def copy_subset(self, key: npy.ndarray) -> 'Network': """ Returns a copy of a frequency subset of this Network Needed to allow pass-by-value for a subset Network instead of pass-by-reference Parameters ----------- key : numpy array the array indices of the frequencies to take Returns ------- ntwk : :class:`Network` Copy of the frequency subset of the Network """ ntwk = Network(s=self.s[key,:], frequency=self.frequency[key].copy(), z0=self.z0[key,:], ) if isinstance(self.name, str): ntwk.name = self.name + '_subset' else: ntwk.name = self.name if self.noise is not None and self.noise_freq is not None: ntwk.noise = npy.copy(self.noise[key,:]) ntwk.noise_freq = npy.copy(self.noise_freq[key]) try: ntwk.port_names = copy(self.port_names) except(AttributeError): ntwk.port_names = None return ntwk
[docs] def set_noise_a(self, noise_freq: Frequency = None, nfmin_db: float = 0, gamma_opt: float = 0, rn: NumberLike = 1 ) -> None: """ sets the "A" (ie cascade) representation of the correlation matrix, based on the noise frequency and input parameters. """ sh_fr = noise_freq.f.shape nfmin_db = npy.broadcast_to(npy.atleast_1d(nfmin_db), sh_fr) gamma_opt = npy.broadcast_to(npy.atleast_1d(gamma_opt), sh_fr) rn = npy.broadcast_to(npy.atleast_1d(rn), sh_fr) nf_min = npy.power(10., nfmin_db/10.) # TODO maybe interpolate z0 as above y_opt = 1./(self.z0[0, 0] * (1. + gamma_opt)/(1. - gamma_opt)) noise = 4.*K_BOLTZMANN*T0*npy.array( [[rn, (nf_min-1.)/2. - rn*npy.conj(y_opt)], [(nf_min-1.)/2. - rn*y_opt, npy.square(npy.absolute(y_opt)) * rn]] ) self.noise = noise.swapaxes(0, 2).swapaxes(1, 2) self.noise_freq = noise_freq
# touchstone file IO
[docs] def read_touchstone(self, filename: str) -> None: """ loads values from a touchstone file. The work of this function is done through the :class:`~skrf.io.touchstone` class. Parameters ---------- filename : str or file-object touchstone file name. Note ---- Only the scattering parameters format is supported at the moment """ from .io import touchstone touchstoneFile = touchstone.Touchstone(filename) if touchstoneFile.get_format().split()[1] != 's': raise NotImplementedError('only s-parameters supported for now.') self.comments = touchstoneFile.get_comments() try: self.variables = touchstoneFile.get_comment_variables() except: pass self.port_names = touchstoneFile.port_names # set z0 before s so that y and z can be computed if touchstoneFile.is_from_hfss(): self.gamma, self.z0 = touchstoneFile.get_gamma_z0() else: self.z0 = complex(touchstoneFile.resistance) f, self.s = touchstoneFile.get_sparameter_arrays() # note: freq in Hz self.frequency = Frequency.from_f(f, unit='hz') self.frequency.unit = touchstoneFile.frequency_unit if touchstoneFile.noise is not None: noise_freq = touchstoneFile.noise[:, 0] * touchstoneFile.frequency_mult nfmin_db = touchstoneFile.noise[:, 1] gamma_opt_mag = touchstoneFile.noise[:, 2] gamma_opt_angle = npy.deg2rad(touchstoneFile.noise[:, 3]) # TODO maybe properly interpolate z0? # it probably never actually changes if touchstoneFile.version == '1.0': rn = touchstoneFile.noise[:, 4] * self.z0[0, 0] else: rn = touchstoneFile.noise[:, 4] gamma_opt = gamma_opt_mag * npy.exp(1j * gamma_opt_angle) nf_min = npy.power(10., nfmin_db/10.) # TODO maybe interpolate z0 as above y_opt = 1./(self.z0[0, 0] * (1. + gamma_opt)/(1. - gamma_opt)) # use the voltage/current correlation matrix; this works nicely with # cascading networks self.noise_freq = Frequency.from_f(noise_freq, unit='hz') self.noise_freq.unit = touchstoneFile.frequency_unit self.set_noise_a(self.noise_freq, nfmin_db, gamma_opt, rn ) if self.name is None: try: self.name = os.path.basename(os.path.splitext(filename)[0]) # this may not work if filename is a file object except(AttributeError, TypeError): # in case they pass a file-object instead of file name, # get the name from the touchstone file try: self.name = os.path.basename(os.path.splitext(touchstoneFile.filename)[0]) except(): print('warning: couldn\'t inspect network name') self.name = '' pass
[docs] @classmethod def zipped_touchstone(cls, filename: str, archive: zipfile.ZipFile) -> 'Network': """ read a Network from a Touchstone file in a ziparchive Parameters ---------- filename : str the full path filename of the touchstone file archive : zipfile.ZipFile the opened zip archive Returns ------- ntwk : :class:`Network` Network from the Touchstone file """ with archive.open(filename) as touchstone_file: ntwk = cls() ntwk.read_touchstone(touchstone_file) return ntwk
[docs] def write_touchstone(self, filename: str = None, dir: str = None, write_z0: bool = False, skrf_comment: bool = True, return_string: bool = False, to_archive: bool = None, form: str = 'ri', format_spec_A: str = '{}', format_spec_B: str = '{}', format_spec_freq : str = '{}') -> Optional[str]: """ Write a contents of the :class:`Network` to a touchstone file. Parameters ---------- filename : a string, optional touchstone filename, without extension. if 'None', then will use the network's :attr:`name`. dir : string, optional the directory to save the file in. write_z0 : boolean write impedance information into touchstone as comments, like Ansoft HFSS does skrf_comment : bool, optional write `created by skrf` comment return_string : bool, optional return the file_string rather than write to a file to_archive : zipfile.Zipfile opened ZipFile object to place touchstone file in form : string format to write data: 'db': db, deg. 'ma': mag, deg. 'ri': real, imag. format_spec_A : string, optional Any valid format specifying string as given by https://docs.python.org/3/library/string.html#format-string-syntax This specifies the formatting in the resulting touchstone file for the A part of the S parameter, (e.g. the dB magnitude for 'db' format, the linear magnitude for 'ma' format, or the real part for 'ri' format) format_spec_B : string, optional Any valid format specifying string as given by https://docs.python.org/3/library/string.html#format-string-syntax This specifies the formatting in the resulting touchstone file for the B part of the S parameter, (e.g. the angle in degrees for 'db' format, the angle in degrees for 'ma' format, or the imaginary part for 'ri' format) format_spec_freq : string, optional Any valid format specifying string as given by https://docs.python.org/3/library/string.html#format-string-syntax This specifies the formatting in the resulting touchstone file for the frequency. Note ---- Format supported at the moment are [Hz/kHz/MHz/GHz] S [DB/MA/RI] Frequency unit can be changed by setting Network.frequency.unit property Note ---- The functionality of this function should take place in the :class:`~skrf.io.touchstone.Touchstone` class. """ # according to Touchstone 2.0 spec # [no tab, max. 4 coeffs per line, etc.] if filename is None: if self.name is not None: filename = self.name else: raise ValueError('No filename given. Network must have a name, or you must provide a filename') if get_extn(filename) is None: filename = filename + '.s%ip' % self.number_of_ports if dir is not None: filename = os.path.join(dir, filename) # set internal variables according to form form = form.upper() if form == "RI": formatDic = {"labelA": "Re", "labelB": "Im"} funcA = npy.real funcB = npy.imag elif form == "DB": formatDic = {"labelA": "dB", "labelB": "ang"} funcA = mf.complex_2_db funcB = mf.complex_2_degree elif form == "MA": formatDic = {"labelA": "mag", "labelB": "ang"} funcA = mf.complex_2_magnitude funcB = mf.complex_2_degree else: raise ValueError('`form` must be either `db`,`ma`,`ri`') # add formatting to funcA and funcB so we don't have to write it out many many times. def c2str_A(c: NumberLike) -> str: """Function which takes a complex number for the A part of param and returns an appropriately formatted string""" return format_spec_A.format(funcA(c)) def c2str_B(c: NumberLike) -> str: """Function which takes a complex number for B part of param and returns an appropriately formatted string""" return format_spec_B.format(funcB(c)) def get_buffer() -> StringIO: if return_string is True or type(to_archive) is zipfile.ZipFile: from .io.general import StringBuffer # avoid circular import buf = StringBuffer() else: buf = open(filename, "w") return buf with get_buffer() as output: # Add '!' Touchstone comment delimiters to the start of every line in self.comments commented_header = '' try: if self.comments: for comment_line in self.comments.split('\n'): commented_header += '!{}\n'.format(comment_line) except AttributeError: pass if skrf_comment: commented_header += '!Created with skrf (http://scikit-rf.org).\n' output.write(commented_header) # write header file. # the '#' line is NOT a comment it is essential and it must be # exactly this format, to work # [HZ/KHZ/MHZ/GHZ] [S/Y/Z/G/H] [MA/DB/RI] [R n] output.write('# {} S {} R {} \n'.format(self.frequency.unit, form, str(abs(self.z0[0, 0])))) # write ports try: if self.port_names and len(self.port_names) == self.number_of_ports: ports = '' for port_idx, port_name in enumerate(self.port_names): ports += '! Port[{}] = {}\n'.format(port_idx+1, port_name) output.write(ports) except AttributeError: pass scaled_freq = self.frequency.f_scaled if self.number_of_ports == 1: # write comment line for users (optional) output.write('!freq {labelA}S11 {labelB}S11\n'.format(**formatDic)) # write out data for f in range(len(self.f)): output.write(format_spec_freq.format(scaled_freq[f]) + ' ' \ + c2str_A(self.s[f, 0, 0]) + ' ' \ + c2str_B(self.s[f, 0, 0]) + '\n') # write out the z0 following hfss's convention if desired if write_z0: output.write('! Port Impedance ') for n in range(self.number_of_ports): output.write('%.14f %.14f ' % (self.z0[f, n].real, self.z0[f, n].imag)) output.write('\n') elif self.number_of_ports == 2: # 2-port is a special case with # - single line, and # - S21,S12 in reverse order: legacy ? # write comment line for users (optional) output.write( '!freq {labelA}S11 {labelB}S11 {labelA}S21 {labelB}S21 {labelA}S12 {labelB}S12 {labelA}S22 {labelB}S22\n'.format( **formatDic)) # write out data for f in range(len(self.f)): output.write(format_spec_freq.format(scaled_freq[f]) + ' ' \ + c2str_A(self.s[f, 0, 0]) + ' ' \ + c2str_B(self.s[f, 0, 0]) + ' ' \ + c2str_A(self.s[f, 1, 0]) + ' ' \ + c2str_B(self.s[f, 1, 0]) + ' ' \ + c2str_A(self.s[f, 0, 1]) + ' ' \ + c2str_B(self.s[f, 0, 1]) + ' ' \ + c2str_A(self.s[f, 1, 1]) + ' ' \ + c2str_B(self.s[f, 1, 1]) + '\n') # write out the z0 following hfss's convention if desired if write_z0: output.write('! Port Impedance') for n in range(2): output.write(' %.14f %.14f' % (self.z0[f, n].real, self.z0[f, n].imag)) output.write('\n') elif self.number_of_ports == 3: # 3-port is written over 3 lines / matrix order # write comment line for users (optional) output.write('!freq') for m in range(1, 4): for n in range(1, 4): output.write(" {labelA}S{m}{n} {labelB}S{m}{n}".format(m=m, n=n, **formatDic)) output.write('\n!') output.write('\n') # write out data for f in range(len(self.f)): output.write(format_spec_freq.format(scaled_freq[f])) for m in range(3): for n in range(3): output.write(' ' + c2str_A(self.s[f, m, n]) + ' ' \ + c2str_B(self.s[f, m, n])) output.write('\n') # write out the z0 following hfss's convention if desired if write_z0: output.write('! Port Impedance') for n in range(3): output.write(' %.14f %.14f' % (self.z0[f, n].real, self.z0[f, n].imag)) output.write('\n') elif self.number_of_ports >= 4: # general n-port # - matrix is written line by line # - 4 complex numbers / 8 real numbers max. for a single line # - continuation lines (anything except first) go with indent # this is not part of the spec, but many tools handle it this way # -> allows to parse without knowledge of number of ports # write comment line for users (optional) output.write('!freq') for m in range(1, 1 + self.number_of_ports): for n in range(1, 1 + self.number_of_ports): if (n > 0 and (n % 4) == 0): output.write('\n!') output.write(" {labelA}S{m}{n} {labelB}S{m}{n}".format(m=m, n=n, **formatDic)) output.write('\n!') output.write('\n') # write out data for f in range(len(self.f)): output.write(format_spec_freq.format(scaled_freq[f])) for m in range(self.number_of_ports): for n in range(self.number_of_ports): if (n > 0 and (n % 4) == 0): output.write('\n') output.write(' ' + c2str_A(self.s[f, m, n]) + ' ' \ + c2str_B(self.s[f, m, n])) output.write('\n') # write out the z0 following hfss's convention if desired if write_z0: output.write('! Port Impedance') for n in range(self.number_of_ports): output.write(' %.14f %.14f' % (self.z0[f, n].real, self.z0[f, n].imag)) output.write('\n') if type(to_archive) is zipfile.ZipFile: to_archive.writestr(filename, output.getvalue()) elif return_string is True: return output.getvalue()
[docs] def write(self, file: str = None, *args, **kwargs) -> None: """ Write the Network to disk using the :mod:`pickle` module. The resultant file can be read either by using the Networks constructor, :func:`__init__` , the read method :func:`read`, or the general read function :func:`skrf.io.general.read` Parameters ---------- file : str or file-object filename or a file-object. If left as None then the filename will be set to Network.name, if its not None. If both are None, ValueError is raised. \*args, \*\*kwargs : passed through to :func:`~skrf.io.general.write` Note ---- If the self.name is not None and file is can left as None and the resultant file will have the `.ntwk` extension appended to the filename. Examples -------- >>> n = rf.N(f=[1,2,3],s=[1,1,1],z0=50, name = 'open') >>> n.write() >>> n2 = rf.read('open.ntwk') See Also -------- skrf.io.general.write : write any skrf object skrf.io.general.read : read any skrf object """ # this import is delayed until here because of a circular dependency from .io.general import write if file is None: if self.name is None: raise (ValueError('No filename given. You must provide a filename, or set the name attribute')) file = self.name write(file, self, *args, **kwargs)
[docs] def read(self, *args, **kwargs) -> None: """ Read a Network from a 'ntwk' file A ntwk file is written with :func:`write`. It is just a pickled file. Parameters ---------- \*args, \*\*kwargs : args and kwargs passed to :func:`skrf.io.general.read` Note ---- This function calls :func:`skrf.io.general.read`. Examples -------- >>> rf.read('myfile.ntwk') >>> rf.read('myfile.p') See Also -------- skrf.io.general.read write skrf.io.general.write """ from .io.general import read self.copy_from(read(*args, **kwargs))
[docs] def write_spreadsheet(self, *args, **kwargs) -> None: """ Write contents of network to a spreadsheet, for your boss to use. See Also -------- skrf.io.general.network_2_spreadsheet """ from .io.general import network_2_spreadsheet network_2_spreadsheet(self, *args, **kwargs)
[docs] def to_dataframe(self, *args, **kwargs) -> 'pd.DataFrame': """ Convert attributes of a Network to a pandas DataFrame Use the same parameters than :func:`skrf.io.general.network_2_dataframe` Parameters ---------- attrs : list of string Network attributes to convert, like ['s_db','s_deg'] ports : list of tuples list of port pairs to write. defaults to ntwk.port_tuples (like [[0,0]]) Returns ------- df : `pandas.DataFrame` See Also --------- skrf.io.general.network_2_dataframe """ from .io.general import network_2_dataframe return network_2_dataframe(self, *args, **kwargs)
[docs] def write_to_json_string(self) -> str: """ Serialize and convert network to a JSON string. This is ~3x faster than writing to and reading back from touchstone for a 4port 20,000 point device. Returns ------- jsonstr : string JSON string See Also -------- skrf.io.general.to_json_string """ from .io.general import to_json_string return to_json_string(self)
# interpolation
[docs] def interpolate(self, freq_or_n: Union[Frequency, NumberLike], basis: str = 's', coords: str = 'cart', f_kwargs: dict = {}, return_array: bool = False, **kwargs) -> Union['Network', npy.ndarray]: """ Interpolate a Network along frequency axis The input 'freq_or_n` can be either a new :class:`~skrf.frequency.Frequency` or an `int`, or a new frequency vector (in hz). This interpolates a given `basis`, ie s, z, y, etc, in the coordinate system defined by `coord` like polar or cartesian. Different interpolation types ('linear', 'quadratic') can be used by passing appropriate `\*\*kwargs`. This function returns an interpolated Network. Alternatively :func:`~Network.interpolate_self` will interpolate self. Parameters ---------- freq_or_n : :class:`~skrf.frequency.Frequency` or int or list-like The new frequency over which to interpolate. this arg may be one of the following: * a new :class:`~skrf.frequency.Frequency` object * an int: the current frequency span is resampled linearly. * a list-like: create a new frequency using :meth:`~skrf.frequency.Frequency.from_f` basis : ['s','z','y','a'], etc The network parameter to interpolate coords : string Coordinate system to use for interpolation: 'cart' or 'polar': 'cart' is cartesian is Re/Im. 'polar' is unwrapped phase/mag return_array: bool return the interpolated array instead of re-assigning it to a given attribute **kwargs : keyword arguments passed to :func:`scipy.interpolate.interp1d` initializer. `kind` controls interpolation type. `kind` = `rational` uses interpolation by rational polynomials. `d` kwarg controls the degree of rational polynomials when `kind`=`rational`. Defaults to 4. Returns ------- result : :class:`Network` an interpolated Network, or array Note ---- The interpolation coordinate system (`coords`) makes a big difference for large amounts of interpolation. polar works well for duts with slowly changing magnitude. try them all. See :func:`scipy.interpolate.interpolate.interp1d` for useful kwargs. For example: kind : string or int Specifies the kind of interpolation as a string ('linear', 'nearest', 'zero', 'slinear', 'quadratic, 'cubic') or as an integer specifying the order of the spline interpolator to use. See Also -------- resample interpolate_self interpolate_from_f Examples -------- .. ipython:: @suppress In [21]: import skrf as rf In [21]: n = rf.data.ring_slot In [21]: n In [21]: new_freq = rf.Frequency(75,110,501,'ghz') In [21]: n.interpolate(new_freq, kind = 'cubic') """ # make new network and fill with interpolated values result = self.copy() if kwargs.get('kind', None) == 'rational': f_interp = mf.rational_interp #Not supported by rational_interp del kwargs['kind'] else: f_interp = interp1d # interpret input if isinstance(freq_or_n, Frequency): # input is a frequency object new_frequency = freq_or_n else: dim = len(shape(freq_or_n)) if dim == 0: # input is a number n = int(freq_or_n) new_frequency = self.frequency.copy() new_frequency.npoints = n elif dim == 1: # input is a array, or list new_frequency = Frequency.from_f(freq_or_n, **f_kwargs) # set new frequency and pull some variables result.frequency = new_frequency f = self.frequency.f f_new = new_frequency.f # interpolate z0 ( this must happen first, because its needed # to compute the basis transform below (like y2s), if basis!='s') interp_z0_re = f_interp(f, self.z0.real, axis=0, **kwargs) interp_z0_im = f_interp(f, self.z0.imag, axis=0, **kwargs) result.z0 = interp_z0_re(f_new) + 1j * interp_z0_im(f_new) # interpolate parameter for a given basis x = self.__getattribute__(basis) if coords == 'cart': interp_re = f_interp(f, x.real, axis=0, **kwargs) interp_im = f_interp(f, x.imag, axis=0, **kwargs) x_new = interp_re(f_new) + 1j * interp_im(f_new) elif coords == 'polar': rad = npy.unwrap(npy.angle(x), axis=0) mag = npy.abs(x) interp_rad = f_interp(f, rad, axis=0, **kwargs) interp_mag = f_interp(f, mag, axis=0, **kwargs) x_new = interp_mag(f_new) * npy.exp(1j * interp_rad(f_new)) # interpolate noise data too if self.noisy: f_noise = self.noise_freq.f f_noise_new = new_frequency.f interp_noise_re = f_interp(f_noise, self.noise.real, axis=0, **kwargs) interp_noise_im = f_interp(f_noise, self.noise.imag, axis=0, **kwargs) noise_new = interp_noise_re(f_noise_new) + 1j * interp_noise_im(f_noise_new) if return_array: return x_new else: result.__setattr__(basis, x_new) if self.noisy: result.noise = noise_new result.noise_freq = new_frequency return result
[docs] def interpolate_self_npoints(self, npoints: int, **kwargs) -> None: """ Interpolate network based on a new number of frequency points Note ---- The function :func:`~Network.resample` is an alias for :func:`~Network.interpolate_self_npoints`. Parameters ---------- npoints : int number of frequency points **kwargs : keyword arguments passed to :func:`scipy.interpolate.interp1d` initializer. See Also -------- interpolate_self : same functionality but takes a Frequency object interpolate : same functionality but takes a Frequency object and returns a new Network, instead of updating itself. Examples -------- .. ipython:: @suppress In [21]: import skrf as rf In [21]: n = rf.data.ring_slot In [21]: n In [21]: n.resample(501) # resample is an alias In [21]: n """ warnings.warn('Use interpolate_self', DeprecationWarning) new_frequency = self.frequency.copy() new_frequency.npoints = npoints self.interpolate_self(new_frequency, **kwargs)
[docs] def interpolate_self(self, freq_or_n: Union[Frequency, NumberLike], **kwargs) -> None: """ Interpolates s-parameters given a new :class:'~skrf.frequency.Frequency' object. See :func:`~Network.interpolate` for more information. Parameters ---------- new_frequency : :class:`~skrf.frequency.Frequency` frequency information to interpolate at **kwargs : keyword arguments passed to :func:`scipy.interpolate.interp1d` initializer. See Also -------- resample interpolate interpolate_from_f """ ntwk = self.interpolate(freq_or_n, **kwargs) self.frequency, self.s, self.z0 = ntwk.frequency, ntwk.s, ntwk.z0 if self.noisy: self.noise, self.noise_freq = ntwk.noise, ntwk.noise_freq
##convenience resample = interpolate_self
[docs] def interpolate_from_f(self, f: Frequency, interp_kwargs: dict = {}, **kwargs) -> 'Network': """ Interpolates s-parameters from a frequency vector. Given a frequency vector, and optionally a `unit` (see \*\*kwargs) , interpolate the networks s-parameters linearly in real and imaginary components. See :func:`~Network.interpolate` for more information. Note ---- This creates a new :class:`~skrf.frequency.Frequency`, object using the method :func:`~skrf.frequency.Frequency.from_f`, and then calls :func:`~Network.interpolate_self`. Parameters ---------- new_frequency : :class:`~skrf.frequency.Frequency` frequency information to interpolate at interp_kwargs : dictionary of kwargs to be passed through to :func:`scipy.interpolate.interpolate.interp1d` \*\*kwargs : passed to :func:`scipy.interpolate.interp1d` initializer. See Also -------- resample interpolate interpolate_self """ warnings.warn('Use interpolate', DeprecationWarning) return self.interpolate(freq_or_n=f, f_kwargs=kwargs, **interp_kwargs)
# freq = Frequency.from_f(f,**kwargs) # self.interpolate_self(freq, **interp_kwargs)
[docs] def extrapolate_to_dc(self, points: int = None, dc_sparam: NumberLike = None, kind: str = 'rational', coords: str = 'cart', **kwargs) -> 'Network': """ Extrapolate S-parameters down to 0 Hz and interpolate to uniform spacing. If frequency vector needs to be interpolated aliasing will occur in time-domain. For the best results first frequency point should be a multiple of the frequency step so that points from DC to the first measured point can be added without interpolating rest of the frequency points. Parameters ---------- points : int or None Number of frequency points to be used in interpolation. If None number of points is calculated based on the frequency step size and spacing between 0 Hz and first measured frequency point. dc_sparam : class:`numpy.ndarray` or None NxN S-parameters matrix at 0 Hz. If None S-parameters at 0 Hz are determined by linear extrapolation. kind : str or int Specifies the kind of interpolation as a string ('linear', 'nearest', 'zero', 'slinear', 'quadratic, 'cubic') or as an integer specifying the order of the spline interpolator to use for `scipy.interp1d`. `kind` = 'rational' uses interpolation by rational polynomials. `d` kwarg controls the degree of rational polynomials when `kind` is 'rational'. Defaults to 4. coords : str Coordinate system to use for interpolation: 'cart' or 'polar'. 'cart' is cartesian is Re/Im, 'polar' is unwrapped phase/mag. Passed to :func:`Network.interpolate` Returns ------- result : :class:`Network` Extrapolated Network See Also -------- interpolate impulse_response step_response """ result = self.copy() if self.frequency.f[0] == 0: return result if points == None: fstep = self.frequency.f[1] - self.frequency.f[0] points = len(self) + int(round(self.frequency.f[0]/fstep)) if dc_sparam == None: #Interpolate DC point alone first using linear interpolation, because #interp1d can't extrapolate with other methods. #TODO: Option to enforce passivity x = result.s[:2] f = result.frequency.f[:2] rad = npy.unwrap(npy.angle(x), axis=0) mag = npy.abs(x) interp_rad = interp1d(f, rad, axis=0, fill_value='extrapolate') interp_mag = interp1d(f, mag, axis=0, fill_value='extrapolate') dc_sparam = interp_mag(0) * npy.exp(1j * interp_rad(0)) else: #Make numpy array if argument was list dc_sparam = npy.array(dc_sparam) result.s = npy.insert(result.s, 0, dc_sparam, axis=0) result.frequency.f = npy.insert(result.frequency.f, 0, 0) result.z0 = npy.insert(result.z0, 0, result.z0[0], axis=0) if result.noisy: result.noise = npy.insert(result.noise, 0, 0, axis=0) result.noise_freq.f = npy.insert(result.noise_freq.f, 0, 0) new_f = Frequency(0, result.frequency.f_scaled[-1], points, unit=result.frequency.unit) #None of the default interpolation methods are too good #and cause aliasing in the time domain. #Best results are obtained when no interpolation is needed, #e.g. first frequency point is a multiple of frequency step. result.interpolate_self(new_f, kind=kind, coords=coords, **kwargs) #DC value must have zero imaginary part result.s[0,:,:] = result.s[0,:,:].real return result
[docs] def subnetwork(self, ports: Sequence[int], offby: int = 1) -> 'Network': """ Returns a subnetwork of a the Network from a list of port numbers. A subnetwork is Network which S-parameters corresponds to selected ports, with all non-selected ports considered matched. The resulting subNetwork is given a new Network.name property from the initial name and adding the kept ports indices (ex: 'device' -> 'device13'). Such name should make easier the use of functions such as n_twoports_2_nport. Parameters ---------- ports : list of int List of ports to keep in the resultant Network. Indices are the Python indices (starts at 0) offby : int starting value for s-parameters indexes in the sub-Network name parameter. A value of `1`, assumes that a s21 = ntwk.s[:,1,0]. Default is 1. Returns ------- subntw : :class:`Network` object Resulting subnetwork of the Network from the given ports See also -------- subnetwork, n_twoports_2_nport """ return subnetwork(self, ports, offby)
[docs] def crop(self, f_start: float, f_stop: float, unit: str = None) -> None: """ Crop Network based on start and stop frequencies. No interpolation is done. Parameters ---------- f_start : number start frequency of crop range, in units of self.frequency.unit. If `f_start` is lower than the lowest frequency, no change to the network is made by the lower bound. f_stop : number stop frequency of crop range, in units of self.frequency.unit If `f_stop` is higher than the highest frequency, no change to the network is made by the higher bound. unit : string Units that `f_start` and `f_stop` are described in. This must be a string recognized by the Frequency class, e.g. 'Hz','MHz', etc. A value of `None` assumes units are same as `self` See Also -------- cropped """ if f_start == None: f_start = -npy.inf if f_stop == None: f_stop = npy.inf if f_stop<f_start: raise ValueError("`f_stop` was {}, which was smaller than `f_start`, which was {}".format(f_stop,f_start)) if unit is not None: # if `unit` is specified, we must retranslate the frequency units scaleFactor = Frequency.multiplier_dict[unit.lower()]/self.frequency.multiplier# make a multiplier to put f_start and f_stop in the right units, e.g. 'GHz' -> 'MHz' f_start *=scaleFactor f_stop *=scaleFactor if f_start > self.frequency.f_scaled.max(): raise ValueError("`f_start` was {}, which was larger than the largest frequency in this Network object, which was {}".format(f_start,self.frequency.f_scaled.max())) if f_stop < self.frequency.f_scaled.min(): raise ValueError("`f_stop` was {}, which was smaller than the smallest frequency in this Network object, which was {}".format(f_stop,self.frequency.f_scaled.min())) start_idx,stop_idx = 0,self.frequency.npoints-1 # start with entire frequency range selected if f_start > self.frequency.f_scaled.min(): start_idx = find_nearest_index(self.frequency.f_scaled, f_start) if f_start > self.frequency.f_scaled[start_idx]: # we do not want the start index to be at a frequency lower than `f_start` start_idx += 1 if f_stop < self.frequency.f_scaled.max(): stop_idx = find_nearest_index(self.frequency.f_scaled, f_stop) if f_stop < self.frequency.f_scaled[stop_idx]: # we don't want the stop index to be at a frequency higher than `f_stop` stop_idx -=1 if stop_idx < start_idx : raise ValueError("Stop index/frequency lower than start: stop_idx: {}, start_idx: {}, self.frequency.f[stop_idx]: {}, self.frequency.f[start_idx]: {}"\ .format(stop_idx,start_idx,self.frequency.f[stop_idx],self.frequency.f[start_idx] )) ntwk = self[start_idx:stop_idx + 1] self.frequency, self.s, self.z0 = ntwk.frequency, ntwk.s, ntwk.z0
[docs] def cropped(self, f_start: float, f_stop: float, unit: str = None) -> 'Network': """ Returns a cropped network, leaves self alone. Parameters ---------- f_start : number start frequency of crop range, in units of self.frequency.unit. If `f_start` is lower than the lowest frequency, no change to the network is made by the lower bound. f_stop : number stop frequency of crop range, in units of self.frequency.unit If `f_stop` is higher than the highest frequency, no change to the network is made by the higher bound. unit : string Units that `f_start` and `f_stop` are described in. This must be a string recognized by the Frequency class, e.g. 'Hz','MHz', etc. A value of `None` assumes units are same as `self` Returns ------- ntwk : :class:`Network` object Resulting cropped network See Also -------- crop """ out = self.copy() out.crop(f_start=f_start, f_stop=f_stop,unit=unit) return out
[docs] def flip(self) -> None: """ Swaps the ports of a 2n-port Network (inplace). In case the network is 2n-port and n > 1, 'second' numbering scheme is assumed to be consistent with the ** cascade operator:: +--------+ +--------+ 0-|0 n|-n 0-|n 0|-n 1-|1 n+1|-n+1 flip 1-|n+1 1|-n+1 ... ... => ... ... n-1-|n-1 2n-1|-2n-1 n-1-|2n-1 n-1|-2n-1 +--------+ +--------+ See Also -------- flipped renumber renumbered """ if self.number_of_ports % 2 == 0: n = int(self.number_of_ports / 2) old = list(range(0, 2*n)) new = list(range(n, 2*n)) + list(range(0, n)) self.renumber(old, new) else: raise ValueError('you can only flip two-port Networks')
[docs] def flipped(self) -> 'Network': """ Returns a flipped network, leaves self alone. Returns ------- ntwk : :class:`Network` object Resulting flipped Network See Also -------- flip renumber renumbered """ out = self.copy() out.flip() return out
[docs] def renormalize(self, z_new: NumberLike, s_def: str = S_DEF_DEFAULT) -> None: """ Renormalize s-parameter matrix given a new port impedances. Parameters ---------- z_new : complex array of shape FxN, F, N or a scalar new port impedances s_def : str -> s_def : can be: 'power', 'pseudo' or 'traveling' Scattering parameter definition : 'power' for power-waves definition, 'pseudo' for pseudo-waves definition. 'traveling' corresponds to the initial implementation. Default is 'power'. NB: results are the same for real-valued characteristic impedances. See Also -------- renormalize_s fix_z0_shape """ self.s = renormalize_s(self.s, self.z0, z_new, s_def) self.z0 = fix_z0_shape(z_new, self.frequency.npoints, self.nports)
[docs] def renumber(self, from_ports: Sequence[int], to_ports: Sequence[int]) -> None: """ Renumbers ports of a Network (inplace). Parameters ---------- from_ports : list-like List of port indices to change. Size between 1 and N_ports. to_ports : list-like List of desired port indices. Size between 1 and N_ports. NB : from_ports and to_ports must have same size. Returns ------- None The reorganization of the Network's port is performed inplace. Examples -------- In the following example, the ports of a 3-ports Network are reorganized. Dummy reference impedances are set only to follow more easily the renumbering. >>> f = rf.Frequency(1, 1, 1) >>> s = np.ones((1, 3, 3)) >>> z0 = [10, 20, 30] >>> ntw = rf.Network(frequency=f, s=s, z0=z0) # our OEM Network In picture, we have:: Order in Original Order skrf.Network ┌───────────────────┐ │ OEM │ │ │ 0 ────────┤ A (10 Ω) │ │ │ │ │ 1 ────────┤ B (20 Ω) │ │ │ │ │ 2 ────────┤ C (30 Ω) │ │ │ └───────────────────┘ While after renumbering >>> ntw.renumber([0,1,2], [1, 2, 0]) we now have:: Order in Original Order skrf.Network ┌───────────────────┐ │ OEM │ │ │ 1 ────────┤ A (10 Ω) │ │ │ │ │ 2 ────────┤ B (20 Ω) │ │ │ │ │ 0 ────────┤ C (30 Ω) │ │ │ └───────────────────┘ **Other examples:** To flip the ports of a 2-port network 'foo': >>> foo.renumber( [0,1], [1,0] ) To rotate the ports of a 3-port network 'bar' so that port 0 becomes port 1: >>> bar.renumber( [0,1,2], [1,2,0] ) To swap the first and last ports of a N-port (N>=2) Network 'duck': >>> duck.renumber( [0,-1], [-1,0] ) See Also -------- renumbered flip flipped """ from_ports = npy.array(from_ports) to_ports = npy.array(to_ports) if len(npy.unique(from_ports)) != len(from_ports): raise ValueError('an index can appear at most once in from_ports or to_ports') if any(npy.unique(from_ports) != npy.unique(to_ports)): raise ValueError('from_ports and to_ports must have the same set of indices') self.s[:, to_ports, :] = self.s[:, from_ports, :] # renumber rows self.s[:, :, to_ports] = self.s[:, :, from_ports] # renumber columns self.z0[:, to_ports] = self.z0[:, from_ports]
[docs] def renumbered(self, from_ports: Sequence[int], to_ports: Sequence[int]) -> 'Network': """ Returns a renumbered Network, leave self alone. Parameters ---------- from_ports : list-like List of port indices to change. Size between 1 and N_ports. to_ports : list-like List of desired port indices. Size between 1 and N_ports. NB: from_ports and to_ports must have same size. Returns ------- ntwk : :class:`Network` object Resulting renumbered Network See Also -------- renumber flip flipped """ out = self.copy() out.renumber(from_ports, to_ports) return out
[docs] def rotate(self, theta: NumberLike, unit: str = 'deg') -> None: """ Rotate S-parameters """ if unit == 'deg': theta = mf.degree_2_radian(theta ) self.s = self.s * npy.exp(-1j*theta)
[docs] def delay(self, d: float, unit: str = 'deg', port: int = 0, media: Any = None, **kw) -> 'Network': """ Add phase delay to a given port. This will cascade a matched line of length `d/2` from a given `media` in front of `port`. If `media==None`, then freespace is used. Parameters ---------- d : number the length of transmission line (see unit argument) unit : ['deg','rad','m','cm','um','in','mil','s','us','ns','ps'] the units of d. See :func:`Media.to_meters`, for details port : int port to add delay to. media: skrf.media.Media media object to use for generating delay. If None, this will default to freespace. Returns ------- ntwk : :class:`Network` object Resulting delayed Network """ if d ==0: return self d=d/2. if media is None: from .media import Freespace media = Freespace(frequency=self.frequency,z0=self.z0[:,port]) l =media.line(d=d, unit=unit,**kw) return connect(self, port, l, 0)
[docs] def windowed(self, window: Union[str, float, Tuple[str, float]]=('kaiser', 6), normalize: bool = True, center_to_dc: bool = None) -> 'Network': """ Return a windowed version of s-matrix. Used in time-domain analysis. When using time domain through :attr:`s_time_db`, or similar properties, the spectrum is usually windowed, before the IFFT is taken. This is done to compensate for the band-pass nature of a spectrum [#]_ . This function calls :func:`scipy.signal.get_window` which gives more details about the windowing. Parameters ---------- window : string, float, or tuple The type of window to create. See :func:`scipy.signal.get_window` for details. normalize : bool Normalize the window to preserve power. ie sum(ntwk.s,axis=0) == sum(ntwk.windowed().s,axis=0) center_to_dc : bool or None If True only the positive half of the window is applied to the signal. This should be used if frequency vector begins from DC or from "close enough" to DC. If False full window is used which also attenuates low frequencies. If None then value is determined automatically based on if frequency vector begins from 0. Returns ------- ntwk : :class:`Network` object Resulting windowed Network Examples -------- >>> ntwk = rf.Network('myfile.s2p') >>> ntwk_w = ntwk.windowed() >>> ntwk_w.plot_s_time_db() References ---------- .. [#] Agilent Time Domain Analysis Using a Network Analyzer Application Note 1287-12 """ if center_to_dc == None: center_to_dc = self.frequency.f[0] == 0 if center_to_dc: window = signal.get_window(window, 2*len(self))[len(self):] else: window = signal.get_window(window, len(self)) window = window.reshape(-1, 1, 1) * npy.ones((len(self), self.nports, self.nports)) windowed = self * window if normalize: # normalize the s-parameters to account for power lost in windowing windowed.s = windowed.s * npy.sum(self.s_mag, axis=0) / \ npy.sum(windowed.s_mag, axis=0) return windowed
[docs] def time_gate(self, *args, **kw) -> 'Network': """ Time gate this Network Returns ------- ntwk : :class:`Network` object Resulting time-gated Network see `skrf.time_domain.time_gate` """ return time_gate(self, *args, **kw)
# noise
[docs] def add_noise_polar(self, mag_dev: float, phase_dev: float, **kwargs) -> None: """ adds a complex zero-mean gaussian white-noise. adds a complex zero-mean gaussian white-noise of a given standard deviation for magnitude and phase Parameters ---------- mag_dev : number standard deviation of magnitude phase_dev : number standard deviation of phase [in degrees] """ phase_rv = stats.norm(loc=0, scale=phase_dev).rvs(size=self.s.shape) mag_rv = stats.norm(loc=0, scale=mag_dev).rvs(size=self.s.shape) phase = (self.s_deg + phase_rv) mag = self.s_mag + mag_rv self.s = mag * npy.exp(1j * npy.pi / 180. * phase)
[docs] def add_noise_polar_flatband(self, mag_dev: float, phase_dev: float, **kwargs) -> None: """ adds a flatband complex zero-mean gaussian white-noise signal of given standard deviations for magnitude and phase Parameters ---------- mag_dev : number standard deviation of magnitude phase_dev : number standard deviation of phase [in degrees] """ phase_rv = stats.norm(loc=0, scale=phase_dev).rvs(size=self.s[0].shape) mag_rv = stats.norm(loc=0, scale=mag_dev).rvs(size=self.s[0].shape) phase = (self.s_deg + phase_rv) mag = self.s_mag + mag_rv self.s = mag * npy.exp(1j * npy.pi / 180. * phase)
[docs] def multiply_noise(self, mag_dev: float, phase_dev: float, **kwargs) -> None: """ multiplies a complex bivariate gaussian white-noise signal of given standard deviations for magnitude and phase. magnitude mean is 1, phase mean is 0 Parameters ---------- mag_dev: float standard deviation of magnitude phase_dev: float standard deviation of phase [in degrees] """ phase_rv = stats.norm(loc=0, scale=phase_dev).rvs( \ size=self.s.shape) mag_rv = stats.norm(loc=1, scale=mag_dev).rvs( \ size=self.s.shape) self.s = mag_rv * npy.exp(1j * npy.pi / 180. * phase_rv) * self.s
[docs] def nudge(self, amount: float = 1e-12) -> 'Network': """ Perturb s-parameters by small amount. This is useful to work-around numerical bugs. Parameters ---------- amount : float amount to add to s parameters Returns ------- ntwk : :class:`Network` object Resulting renumbered Network Note ---- This function is:: self.s = self.s + amount """ self.s = self.s + amount
# other
[docs] def func_on_parameter(self, func: Callable, attr: str = 's', *args, **kwargs) -> 'Network': """ Applies a function parameter matrix, one frequency slice at a time This is useful for functions that can only operate on 2d arrays, like numpy.linalg.inv. This loops over f and calls `func(ntwkA.s[f,:,:], \*args, \*\*kwargs)` Parameters ---------- func : func function to apply to s-parameters, on a single-frequency slice. (ie `func(ntwkA.s[0,:,:], \*args, \*\*kwargs)` attr: string Name of the parameter to operate on. Ex: 's', 'z', etc. Default is 's'. \*args, \*\*kwargs : passed to the func Returns ------- ntwk : :class:`Network` object Resulting renumbered Network Examples -------- >>> from numpy.linalg import inv >>> ntwk.func_on_parameter(inv) """ ntwkB = self.copy() p = self.__getattribute__(attr) ntwkB.s = npy.r_[[func(p[k, :, :], *args, **kwargs) \ for k in range(len(p))]] return ntwkB
[docs] def nonreciprocity(self, m: int, n: int, normalize: bool = False) -> 'Network': """ Normalized non-reciprocity metric. This is a port-by-port measure of how non-reciprocal a n-port network is. It is defined by, .. math:: (S_{mn} - S_{nm}) / \\sqrt ( S_{mn} S_{nm} ) Parameters ---------- m : int m index n : int n index normalize : bool Normalize the result. Default is False. Returns ------- ntwk : :class:`Network` object Resulting renumbered Network """ forward = self.__getattribute__('s%i%i' % (m, n)) reverse = self.__getattribute__('s%i%i' % (n, m)) if normalize: denom = forward * reverse denom.s = npy.sqrt(denom.s) return (forward - reverse) / denom else: return (forward - reverse)
# generalized mixed mode transformations # XXX: experimental implementation of gmm s parameters # TODO: automated test cases
[docs] def se2gmm(self, p: int, z0_mm: npy.ndarray = None) -> None: """ Transform network from single ended parameters to generalized mixed mode parameters [#]_ .. warning:: This is not fully tested, and should be considered as experimental Parameters ---------- p : int number of differential ports z0_mm : Numpy array `f x n x n` matrix of mixed mode impedances, optional if input is None, 2 * z_o Ohms differential and z_0 / 2 Ohms common mode reference impedance is used Note Odd Number of Ports In the case where there are an odd number of ports (such as a 3-port network with ports 0, 1, and 2), se2gmm() assumes that the last port (port 2) remains single-ended and ports 0 and 1 are converted to differential mode and common mode, respectively. For networks in which the port ordering is not suitable, port renumbering can be used. Examples -------- For example, a 3-port single-ended network is converted to mixed-mode parameters:: | Port 0 (single-ended, 50 ohms) --> Port 0 (single-ended, 50 ohms) | Port 1 (single-ended, 50 ohms) --> Port 1 (differential mode, 100 ohms) | Port 2 (single-ended, 50 ohms) --> Port 2 (common mode, 25 ohms) >>> ntwk.renumber([0,1,2], [2,1,0]) >>> ntwk.se2gmm(p=1) >>> ntwk.renumber([2,1,0], [0,1,2]) In the resulting network, port 0 is single-ended, port 1 is differential mode, and port 2 is common mode. References ---------- .. [#] Ferrero and Pirola; Generalized Mixed-Mode S-Parameters; IEEE Transactions on Microwave Theory and Techniques; Vol. 54; No. 1; Jan 2006 See Also -------- gmm2se """ # XXX: assumes 'proper' order (first differential ports, then single ended ports) if z0_mm is None: z0_mm = self.z0.copy() z0_mm[:, 0:p] *= 2 # differential mode impedance z0_mm[:, p:2 * p] /= 2 # common mode impedance Xi_tilde_11, Xi_tilde_12, Xi_tilde_21, Xi_tilde_22 = self._Xi_tilde(p, self.z0, z0_mm) A = Xi_tilde_21 + npy.einsum('...ij,...jk->...ik', Xi_tilde_22, self.s) B = Xi_tilde_11 + npy.einsum('...ij,...jk->...ik', Xi_tilde_12, self.s) self.s = npy.transpose(npy.linalg.solve(npy.transpose(B, (0, 2, 1)).conj(), npy.transpose(A, (0, 2, 1)).conj()), (0, 2, 1)).conj() # (34) self.z0 = z0_mm
[docs] def gmm2se(self, p: int, z0_se: NumberLike = None) -> None: """ Transform network from generalized mixed mode parameters [#]_ to single ended parameters .. warning:: This is not fully tested, and should be considered as experimental Parameters ---------- p : int number of differential ports z0_mm: Numpy array `f x n x n` matrix of single ended impedances, optional if input is None, extract the reference impedance from the differential network References ---------- .. [#] Ferrero and Pirola; Generalized Mixed-Mode S-Parameters; IEEE Transactions on Microwave Theory and Techniques; Vol. 54; No. 1; Jan 2006 See Also -------- se2gmm """ # TODO: testing of reverse transformation # XXX: assumes 'proper' order (differential ports, single ended ports) if z0_se is None: z0_se = self.z0.copy() z0_se[:, 0:p] /= 2 # differential mode impedance z0_se[:, p:2 * p] *= 2 # common mode impedance Xi_tilde_11, Xi_tilde_12, Xi_tilde_21, Xi_tilde_22 = self._Xi_tilde(p, z0_se, self.z0) A = Xi_tilde_22 - npy.einsum('...ij,...jk->...ik', self.s, Xi_tilde_12) B = Xi_tilde_21 - npy.einsum('...ij,...jk->...ik', self.s, Xi_tilde_11) self.s = npy.linalg.solve(A, B) # (35) self.z0 = z0_se
# generalized mixed mode supplement functions _T = npy.array([[1, 0, -1, 0], [0, 0.5, 0, -0.5], [0.5, 0, 0.5, 0], [0, 1, 0, 1]]) # (5) def _m(self, z0: npy.ndarray) -> npy.ndarray: scaling = npy.sqrt(z0.real) / (2 * npy.abs(z0)) Z = npy.ones((z0.shape[0], 2, 2), dtype=npy.complex128) Z[:, 0, 1] = z0 Z[:, 1, 1] = -z0 return scaling[:, npy.newaxis, npy.newaxis] * Z def _M(self, j: int, k: int, z0_se: npy.ndarray) -> npy.ndarray: # (14) M = npy.zeros((self.f.shape[0], 4, 4), dtype=npy.complex128) M[:, :2, :2] = self._m(z0_se[:, j]) M[:, 2:, 2:] = self._m(z0_se[:, k]) return M def _M_circle(self, l: int, p: int, z0_mm: npy.ndarray) -> npy.ndarray: # (12) M = npy.zeros((self.f.shape[0], 4, 4), dtype=npy.complex128) M[:, :2, :2] = self._m(z0_mm[:, l]) # differential mode impedance of port pair M[:, 2:, 2:] = self._m(z0_mm[:, p + l]) # common mode impedance of port pair return M def _X(self, j: int, k: int , l: int, p: int, z0_se: npy.ndarray, z0_mm: npy.ndarray) -> npy.ndarray: # (15) return npy.einsum('...ij,...jk->...ik', self._M_circle(l, p, z0_mm).dot(self._T), npy.linalg.inv(self._M(j, k, z0_se))) # matrix multiplication elementwise for each frequency def _P(self, p: int) -> npy.ndarray: # (27) (28) n = self.nports Pda = npy.zeros((p, 2 * n), dtype=npy.bool) Pdb = npy.zeros((p, 2 * n), dtype=npy.bool) Pca = npy.zeros((p, 2 * n), dtype=npy.bool) Pcb = npy.zeros((p, 2 * n), dtype=npy.bool) Pa = npy.zeros((n - 2 * p, 2 * n), dtype=npy.bool) Pb = npy.zeros((n - 2 * p, 2 * n), dtype=npy.bool) for l in npy.arange(p): Pda[l, 4 * (l + 1) - 3 - 1] = True Pca[l, 4 * (l + 1) - 1 - 1] = True Pdb[l, 4 * (l + 1) - 2 - 1] = True Pcb[l, 4 * (l + 1) - 1] = True if Pa.shape[0] != 0: Pa[l, 4 * p + 2 * (l + 1) - 1 - 1] = True Pb[l, 4 * p + 2 * (l + 1) - 1] = True return npy.concatenate((Pda, Pca, Pa, Pdb, Pcb, Pb)) def _Q(self) -> npy.ndarray: # (29) error corrected n = self.nports Qa = npy.zeros((n, 2 * n), dtype=npy.bool) Qb = npy.zeros((n, 2 * n), dtype=npy.bool) for l in npy.arange(n): Qa[l, 2 * (l + 1) - 1 - 1] = True Qb[l, 2 * (l + 1) - 1] = True return npy.concatenate((Qa, Qb)) def _Xi(self, p: int, z0_se: npy.ndarray, z0_mm: npy.ndarray) -> npy.ndarray: # (24) n = self.nports Xi = npy.ones(self.f.shape[0])[:, npy.newaxis, npy.newaxis] * npy.eye(2 * n, dtype=npy.complex128) for l in npy.arange(p): Xi[:, 4 * l:4 * l + 4, 4 * l:4 * l + 4] = self._X(l * 2, l * 2 + 1, l, p, z0_se, z0_mm) return Xi def _Xi_tilde(self, p: int, z0_se: npy.ndarray, z0_mm: npy.ndarray) -> npy.ndarray: # (31) n = self.nports P = npy.ones(self.f.shape[0])[:, npy.newaxis, npy.newaxis] * self._P(p) QT = npy.ones(self.f.shape[0])[:, npy.newaxis, npy.newaxis] * self._Q().T Xi = self._Xi(p, z0_se, z0_mm) Xi_tilde = npy.einsum('...ij,...jk->...ik', npy.einsum('...ij,...jk->...ik', P, Xi), QT) return Xi_tilde[:, :n, :n], Xi_tilde[:, :n, n:], Xi_tilde[:, n:, :n], Xi_tilde[:, n:, n:]
[docs] def impulse_response(self, window: str = 'hamming', n: int = None, pad: int = 1000, bandpass: bool = None) -> Tuple[npy.ndarray, npy.ndarray]: """Calculates time-domain impulse response of one-port. First frequency must be 0 Hz for the transformation to be accurate and the frequency step must be uniform. Positions of the reflections are accurate even if the frequency doesn't begin from 0, but shapes will be distorted. Real measurements should be extrapolated to DC and interpolated to uniform frequency spacing. Y-axis is the reflection coefficient. Parameters ---------- window : string FFT windowing function. n : int Length of impulse response output. If n is not specified, 2 * (m - 1) points are used, where m = len(self) + pad pad : int Number of zeros to add as padding for FFT. Adding more zeros improves accuracy of peaks. bandpass : bool or None If False window function is center on 0 Hz. If True full window is used and low frequencies are attenuated. If None value is determined automatically based on if the frequency vector begins from 0. Returns ------- t : class:`numpy.ndarray` Time vector y : class:`numpy.ndarray` Impulse response See Also -------- step_response extrapolate_to_dc """ if self.nports != 1: raise ValueError('Only one-ports are supported') if n is None: # Use zero-padding specification. Note that this does not allow n odd. n = 2 * (self.frequency.npoints + pad - 1) fstep = self.frequency.step if n % 2 == 0: t = npy.fft.ifftshift(npy.fft.fftfreq(n, fstep)) else: t = npy.fft.ifftshift(npy.fft.fftfreq(n+1, fstep))[1:] if bandpass in (True, False): center_to_dc = not bandpass else: center_to_dc = None if window != None: w = self.windowed(window=window, normalize=False, center_to_dc=center_to_dc) else: w = self return t, mf.irfft(w.s, n=n).ravel()
[docs] def step_response(self, window: str = 'hamming', n: int = None, pad: int = 1000) -> Tuple[npy.ndarray, npy.ndarray]: """Calculates time-domain step response of one-port. First frequency must be 0 Hz for the transformation to be accurate and the frequency step must be uniform. Real measurements should be extrapolated to DC and interpolated to uniform frequency spacing. Y-axis is the reflection coefficient. Parameters ---------- window : string FFT windowing function. n : int Length of step response output. If n is not specified, 2 * (m - 1) points are used, where m = len(self) + pad pad : int Number of zeros to add as padding for FFT. Adding more zeros improves accuracy of peaks. Returns ------- t : class:`numpy.ndarray` Time vector y : class:`numpy.ndarray` Step response Raises ------ ValueError If used with an Network with more than one port NotImplementedError If used with non equidistant sampled frequency vector See Also -------- impulse_response extrapolate_to_dc """ if self.frequency.sweep_type != 'lin': raise NotImplementedError( 'Unable to transform non equidistant sampled points to time domain') if self.frequency.f[0] != 0: warnings.warn( "Frequency doesn't begin from 0. Step response will not be correct.", RuntimeWarning ) t, y = self.impulse_response(window=window, n=n, pad=pad, bandpass=False) return t, npy.cumsum(y)
# Network Active s/z/y/vswr parameters
[docs] def s_active(self, a: npy.ndarray) -> npy.ndarray: """ Returns the active s-parameters of the network for a defined wave excitation a. The active s-parameter at a port is the reflection coefficients when other ports are excited. It is an important quantity for active phased array antennas. Active s-parameters are defined by [#]_: .. math:: \mathrm{active(s)}_{m} = \sum_{i=1}^N s_{mi}\\frac{a_i}{a_m} where :math:`s` are the scattering parameters and :math:`N` the number of ports Parameters ---------- a : complex array of shape (n_ports) forward wave complex amplitude (pseudowave formulation [#]_) Returns ------- s_act : complex array of shape (n_freqs, n_ports) active S-parameters for the excitation a See Also -------- z_active : active Z-parameters y_active : active Y-parameters vswr_active : active VSWR References ---------- .. [#] D. M. Pozar, IEEE Trans. Antennas Propag. 42, 1176 (1994). .. [#] D. Williams, IEEE Microw. Mag. 14, 38 (2013). """ return s2s_active(self.s, a)
[docs] def z_active(self, a: npy.ndarray) -> npy.ndarray: """ Returns the active Z-parameters of the network for a defined wave excitation a. The active Z-parameters are defined by: .. math:: \mathrm{active}(z)_{m} = z_{0,m} \\frac{1 + \mathrm{active}(s)_m}{1 - \mathrm{active}(s)_m} where :math:`z_{0,m}` is the characteristic impedance and :math:`\mathrm{active}(s)_m` the active S-parameter of port :math:`m`. Parameters ---------- a : complex array of shape (n_ports) forward wave complex amplitude Returns ------- z_act : complex array of shape (nfreqs, nports) active Z-parameters for the excitation a See Also -------- s_active : active S-parameters y_active : active Y-parameters vswr_active : active VSWR """ return s2z_active(self.s, self.z0, a)
[docs] def y_active(self, a: npy.ndarray) -> npy.ndarray: """ Returns the active Y-parameters of the network for a defined wave excitation a. The active Y-parameters are defined by: .. math:: \mathrm{active}(y)_{m} = y_{0,m} \\frac{1 - \mathrm{active}(s)_m}{1 + \mathrm{active}(s)_m} where :math:`y_{0,m}` is the characteristic admittance and :math:`\mathrm{active}(s)_m` the active S-parameter of port :math:`m`. Parameters ---------- a : complex array of shape (n_ports) forward wave complex amplitude Returns ------- y_act : complex array of shape (nfreqs, nports) active Y-parameters for the excitation a See Also -------- s_active : active S-parameters z_active : active Z-parameters vswr_active : active VSWR """ return s2y_active(self.s, self.z0, a)
[docs] def vswr_active(self, a: npy.ndarray) -> npy.ndarray: """ Returns the active VSWR of the network for a defined wave excitation a. The active VSWR is defined by : .. math:: \mathrm{active}(vswr)_{m} = \\frac{1 + |\mathrm{active}(s)_m|}{1 - |\mathrm{active}(s)_m|} where :math:`\mathrm{active}(s)_m` the active S-parameter of port :math:`m`. Parameters ---------- a : complex array of shape (n_ports) forward wave complex amplitude Returns ------- vswr_act : complex array of shape (nfreqs, nports) active VSWR for the excitation a See Also -------- s_active : active S-parameters z_active : active Z-parameters y_active : active Y-parameters """ return s2vswr_active(self.s, a)
COMPONENT_FUNC_DICT = Network.COMPONENT_FUNC_DICT PRIMARY_PROPERTIES = Network.PRIMARY_PROPERTIES Y_LABEL_DICT = Network.Y_LABEL_DICT ## Functions operating on Network[s]
[docs]def connect(ntwkA: Network, k: int, ntwkB: Network, l: int, num: int = 1) -> Network: """ Connect two n-port networks together. Connect ports `k` thru `k+num-1` on `ntwkA` to ports `l` thru `l+num-1` on `ntwkB`. The resultant network has (ntwkA.nports+ntwkB.nports-2*num) ports. The port indices ('k','l') start from 0. Port impedances **are** taken into account. When the two networks have overlapping frequencies, the resulting network will contain only the overlapping frequencies. Note ---- The effect of mis-matched port impedances is handled by inserting a 2-port 'mismatch' network between the two connected ports. This mismatch Network is calculated with the :func:`impedance_mismatch` function. Parameters ---------- ntwkA : :class:`Network` network 'A' k : int starting port index on `ntwkA` ( port indices start from 0 ) ntwkB : :class:`Network` network 'B' l : int starting port index on `ntwkB` num : int number of consecutive ports to connect (default 1) Returns ------- ntwkC : :class:`Network` new network of rank (ntwkA.nports + ntwkB.nports - 2*num) See Also -------- connect_s : actual S-parameter connection algorithm. innerconnect_s : actual S-parameter connection algorithm. Examples -------- To implement a *cascade* of two networks >>> ntwkA = rf.Network('ntwkA.s2p') >>> ntwkB = rf.Network('ntwkB.s2p') >>> ntwkC = rf.connect(ntwkA, 1, ntwkB,0) """ # some checking try: check_frequency_equal(ntwkA, ntwkB) except IndexError as e: common_freq = npy.intersect1d(ntwkA.frequency.f, ntwkB.frequency.f, return_indices=True) if common_freq[0].size == 0: raise e else: ntwkA = ntwkA[common_freq[1]] ntwkB = ntwkB[common_freq[2]] warnings.warn("Using a frequency subset:\n" + str(ntwkA.frequency)) if (k + num - 1 > ntwkA.nports - 1): raise IndexError('Port `k` out of range') if (l + num - 1 > ntwkB.nports - 1): raise IndexError('Port `l` out of range') # create output Network, from copy of input ntwkC = ntwkA.copy() # if networks' z0's are not identical, then connect a impedance # mismatch, which takes into account the effect of differing port # impedances. # import pdb;pdb.set_trace() if assert_z0_at_ports_equal(ntwkA, k, ntwkB, l) == False: ntwkC.s = connect_s( ntwkA.s, k, impedance_mismatch(ntwkA.z0[:, k], ntwkB.z0[:, l]), 0) # the connect_s() put the mismatch's output port at the end of # ntwkC's ports. Fix the new port's impedance, then insert it # at position k where it belongs. ntwkC.z0[:, k:] = npy.hstack((ntwkC.z0[:, k + 1:], ntwkB.z0[:, [l]])) ntwkC.renumber(from_ports=[ntwkC.nports - 1] + list(range(k, ntwkC.nports - 1)), to_ports=list(range(k, ntwkC.nports))) # call s-matrix connection function ntwkC.s = connect_s(ntwkC.s, k, ntwkB.s, l) # combine z0 arrays and remove ports which were `connected` ntwkC.z0 = npy.hstack( (npy.delete(ntwkA.z0, range(k, k + 1), 1), npy.delete(ntwkB.z0, range(l, l + 1), 1))) # if we're connecting more than one port, call innerconnect recursively # until all connections are made to finish the job if num > 1: ntwkC = innerconnect(ntwkC, k, ntwkA.nports - 1 + l, num - 1) # if ntwkB is a 2port, then keep port indices where you expect. if ntwkB.nports == 2 and ntwkA.nports > 2 and num == 1: from_ports = list(range(ntwkC.nports)) to_ports = list(range(ntwkC.nports)) to_ports.pop(k); to_ports.append(k) ntwkC.renumber(from_ports=from_ports, to_ports=to_ports) # if ntwkA and ntwkB are both 2port, and either one has noise, calculate ntwkC's noise either_are_noisy = False try: either_are_noisy = ntwkA.noisy or ntwkB.noisy except: pass if num == 1 and ntwkA.nports == 2 and ntwkB.nports == 2 and either_are_noisy: if ntwkA.noise_freq is not None and ntwkB.noise_freq is not None and ntwkA.noise_freq != ntwkB.noise_freq: raise IndexError('Networks must have same noise frequency. See `Network.interpolate`') cA = ntwkA.noise cB = ntwkB.noise noise_freq = ntwkA.noise_freq if noise_freq is None: noise_freq = ntwkB.noise_freq if cA is None: cA = npy.broadcast_arrays(npy.array([[0., 0.], [0., 0.]]), ntwkB.noise)[0] if cB is None: cB = npy.broadcast_arrays(npy.array([[0., 0.], [0., 0.]]), ntwkA.noise)[0] if k == 0: # if we're connecting to the "input" port of ntwkA, recalculate the equivalent noise of ntwkA, # since we're modeling the noise as a pair of sources at the "input" port # TODO raise (NotImplementedError) if l == 1: # if we're connecting to the "output" port of ntwkB, recalculate the equivalent noise, # since we're modeling the noise as a pair of sources at the "input" port # TODO raise (NotImplementedError) # interpolate abcd into the set of noise frequencies if ntwkA.deembed : if ntwkA.frequency.f.size > 1 : a_real = interp1d(ntwkA.frequency.f, ntwkA.inv.a.real, axis=0, kind=Network.noise_interp_kind) a_imag = interp1d(ntwkA.frequency.f, ntwkA.inv.a.imag, axis=0, kind=Network.noise_interp_kind) a = a_real(noise_freq.f) + 1.j * a_imag(noise_freq.f) else : a_real = ntwkA.inv.a.real a_imag = ntwkA.inv.a.imag a = a_real + 1.j * a_imag a = npy_inv(a) a_H = npy.conj(a.transpose(0, 2, 1)) cC = npy.matmul(a, npy.matmul(cB -cA, a_H)) else : if ntwkA.frequency.f.size > 1 : a_real = interp1d(ntwkA.frequency.f, ntwkA.a.real, axis=0, kind=Network.noise_interp_kind) a_imag = interp1d(ntwkA.frequency.f, ntwkA.a.imag, axis=0, kind=Network.noise_interp_kind) a = a_real(noise_freq.f) + 1.j * a_imag(noise_freq.f) else : a_real = ntwkA.a.real a_imag = ntwkA.a.imag a = a_real + 1.j * a_imag a_H = npy.conj(a.transpose(0, 2, 1)) cC = npy.matmul(a, npy.matmul(cB, a_H)) + cA ntwkC.noise = cC ntwkC.noise_freq = noise_freq return ntwkC
def connect_fast(ntwkA: Network, k: int, ntwkB: Network, l: int) -> Network: """ Connect two n-port networks together (using C-implementation) Specifically, connect ports `k` on `ntwkA` to ports `l` thru on `ntwkB`. The resultant network has `(ntwkA.nports + ntwkB.nports - 2)` ports. The port indices ('k','l') start from 0. Port impedances **are** taken into account. Parameters ---------- ntwkA : :class:`Network` network 'A' k : int starting port index on `ntwkA` ( port indices start from 0 ) ntwkB : :class:`Network` network 'B' l : int starting port index on `ntwkB` Returns ------- ntwkC : :class:`Network` new network of rank `(ntwkA.nports + ntwkB.nports - 2)` Note ---- The effect of mis-matched port impedances is handled by inserting a 2-port 'mismatch' network between the two connected ports. This mismatch Network is calculated with the :func:`impedance_mismatch` function. Examples -------- To implement a *cascade* of two networks >>> ntwkA = rf.Network('ntwkA.s2p') >>> ntwkB = rf.Network('ntwkB.s2p') >>> ntwkC = rf.connect(ntwkA, 1, ntwkB,0) """ num = 1 from .src import connect_s_fast # some checking check_frequency_equal(ntwkA, ntwkB) # create output Network, from copy of input ntwkC = ntwkA.copy() # if networks' z0's are not identical, then connect a impedance # mismatch, which takes into account the effect of differing port # impedances. if assert_z0_at_ports_equal(ntwkA, k, ntwkB, l) == False: ntwkC.s = connect_s( ntwkA.s, k, impedance_mismatch(ntwkA.z0[:, k], ntwkB.z0[:, l]), 0) # the connect_s() put the mismatch's output port at the end of # ntwkC's ports. Fix the new port's impedance, then insert it # at position k where it belongs. ntwkC.z0[:, k:] = npy.hstack((ntwkC.z0[:, k + 1:], ntwkB.z0[:, [l]])) ntwkC.renumber(from_ports=[ntwkC.nports - 1] + range(k, ntwkC.nports - 1), to_ports=range(k, ntwkC.nports)) # call s-matrix connection function ntwkC.s = connect_s_fast(ntwkC.s, k, ntwkB.s, l) # combine z0 arrays and remove ports which were `connected` ntwkC.z0 = npy.hstack( (npy.delete(ntwkA.z0, range(k, k + num), 1), npy.delete(ntwkB.z0, range(l, l + num), 1))) return ntwkC
[docs]def innerconnect(ntwkA: Network, k: int, l: int, num: int = 1) -> Network: """ connect ports of a single n-port network. this results in a (n-2)-port network. remember port indices start from 0. Note ---- A 2-port 'mismatch' network is inserted between the connected ports if their impedances are not equal. Parameters ---------- ntwkA : :class:`Network` network 'A' k,l : int starting port indices on ntwkA ( port indices start from 0 ) num : int number of consecutive ports to connect Returns ------- ntwkC : :class:`Network` new network of rank (ntwkA.nports - 2*num) See Also -------- connect_s : actual S-parameter connection algorithm. innerconnect_s : actual S-parameter connection algorithm. Examples -------- To connect ports '0' and port '1' on ntwkA >>> ntwkA = rf.Network('ntwkA.s3p') >>> ntwkC = rf.innerconnect(ntwkA, 0,1) """ if (k + num - 1 > ntwkA.nports - 1): raise IndexError('Port `k` out of range') if (l + num - 1 > ntwkA.nports - 1): raise IndexError('Port `l` out of range') # create output Network, from copy of input ntwkC = ntwkA.copy() if not (ntwkA.z0[:, k] == ntwkA.z0[:, l]).all(): # connect a impedance mismatch, which will takes into account the # effect of differing port impedances mismatch = impedance_mismatch(ntwkA.z0[:, k], ntwkA.z0[:, l]) ntwkC.s = connect_s(ntwkA.s, k, mismatch, 0) # print 'mismatch %i-%i'%(k,l) # the connect_s() put the mismatch's output port at the end of # ntwkC's ports. Fix the new port's impedance, then insert it # at position k where it belongs. ntwkC.z0[:, k:] = npy.hstack((ntwkC.z0[:, k + 1:], ntwkC.z0[:, [l]])) ntwkC.renumber(from_ports=[ntwkC.nports - 1] + list(range(k, ntwkC.nports - 1)), to_ports=list(range(k, ntwkC.nports))) # call s-matrix connection function ntwkC.s = innerconnect_s(ntwkC.s, k, l) # update the characteristic impedance matrix ntwkC.z0 = npy.delete(ntwkC.z0, list(range(k, k + 1)) + list(range(l, l + 1)), 1) # recur if we're connecting more than one port if num > 1: ntwkC = innerconnect(ntwkC, k, l - 1, num - 1) return ntwkC
[docs]def cascade(ntwkA: Network, ntwkB: Network) -> Network: """ Cascade two 2, 2N-ports Networks together. Connects ports N through 2N-1 on `ntwkA` to ports 0 through N of `ntwkB`. This calls `connect()`, which is a more general function. Use `Network.renumber` to change port order if needed. Note ---- connection diagram:: A B +---------+ +---------+ -|0 N |---|0 N |- -|1 N+1|---|1 N+1|- ... ... ... ... -|N-2 2N-2|---|N-2 2N-2|- -|N-1 2N-1|---|N-1 2N-1|- +---------+ +---------+ Parameters ---------- ntwkA : :class:`Network` network `ntwkA` ntwkB : :class:`Network` network `ntwkB` Returns ------- C : :class:`Network` the resultant network of ntwkA cascaded with ntwkB See Also -------- connect : connects two Networks together at arbitrary ports. Network.renumber : changes the port order of a network """ if ntwkA.nports<2: raise ValueError('nports must be >1') N = int(ntwkA.nports/2 ) if ntwkB.nports == 1: # we are terminating a N-port with a 1-port. # which port on self to use is ambiguous. choose N return connect(ntwkA, N, ntwkB, 0) elif ntwkA.nports % 2 == 0 and ntwkA.nports == ntwkB.nports: # we have two 2N-port balanced networks return connect(ntwkA, N, ntwkB, 0, num=N) elif ntwkA.nports % 2 == 0 and ntwkA.nports == 2 * ntwkB.nports: # we have a 2N-port balanced network terminated by a N-port network return connect(ntwkA, N, ntwkB, 0, num=N) else: raise ValueError('I dont know what to do, check port shapes of Networks')
[docs]def cascade_list(l: Sequence[Network]) -> Network: """ cascade a list of 2N-port networks all networks must have same frequency Parameters ---------- l : list-like (ordered) list of networks Returns ------- out : 2-port Network the results of cascading all networks in the list `l` """ return reduce(cascade, l)
[docs]def de_embed(ntwkA: Network, ntwkB: Network) -> Network: """ De-embed `ntwkA` from `ntwkB`. This calls `ntwkA.inv ** ntwkB`. The syntax of cascading an inverse is more explicit, it is recommended that it be used instead of this function. Parameters ---------- ntwkA : :class:`Network` network `ntwkA` ntwkB : :class:`Network` network `ntwkB` Returns ------- C : Network the resultant network of ntwkB de-embedded from ntwkA See Also -------- connect : connects two Networks together at arbitrary ports. """ return ntwkA.inv ** ntwkB
[docs]def stitch(ntwkA: Network, ntwkB: Network, **kwargs) -> Network: """ Stitches ntwkA and ntwkB together. Concatenates two networks' data. Given two networks that cover different frequency bands this can be used to combine their data into a single network. Parameters ---------- ntwkA, ntwkB : :class:`Network` objects Networks to stitch together \*\*kwargs : keyword args passed to :class:`Network` constructor, for output network Returns ------- ntwkC : :class:`Network` result of stitching the networks `ntwkA` and `ntwkB` together Examples -------- >>> from skrf.data import wr2p2_line, wr1p5_line >>> rf.stitch(wr2p2_line, wr1p5_line) 2-Port Network: 'wr2p2,line', 330-750 GHz, 402 pts, z0=[ 50.+0.j 50.+0.j] """ A, B = ntwkA, ntwkB C = Network( frequency=Frequency.from_f(npy.r_[A.f[:], B.f[:]], unit='hz'), s=npy.r_[A.s, B.s], z0=npy.r_[A.z0, B.z0], name=A.name, **kwargs ) C.frequency.unit = A.frequency.unit return C
[docs]def overlap(ntwkA: Network, ntwkB: Network) -> Tuple[Network, Network]: """ Returns the overlapping parts of two Networks, interpolating if needed. If frequency vectors for each ntwk don't perfectly overlap, then ntwkB is interpolated so that the resultant networks have identical frequencies. Parameters ---------- ntwkA : :class:`Network` a ntwk which overlaps `ntwkB`. (the `dominant` network) ntwkB : :class:`Network` a ntwk which overlaps `ntwkA`. Returns ------- ntwkA_new : :class:`Network` part of `ntwkA` that overlapped `ntwkB` ntwkB_new : :class:`Network` part of `ntwkB` that overlapped `ntwkA`, possibly interpolated See Also -------- :func:`skrf.frequency.overlap_freq` """ new_freq = ntwkA.frequency.overlap(ntwkB.frequency) return ntwkA.interpolate(new_freq), ntwkB.interpolate(new_freq)
[docs]def concat_ports(ntwk_list: Sequence[Network], port_order: str = 'second', *args, **kw) -> Network: """ Concatenate networks along the port axis Note ---- The `port_order` ='first', means front-to-back, while `port_order`='second' means left-to-right. So, for example, when concatenating two 2-networks, `A` and `B`, the ports are ordered as follows: 'first' a0 o---o a1 -> 0 o---o 1 b0 o---o b1 -> 2 o---o 3 'second' a0 o---o a1 -> 0 o---o 2 b0 o---o b1 -> 1 o---o 3 use `Network.renumber` to change port ordering. Parameters ---------- ntwk_list : list of skrf.Networks ntwks to concatenate port_order : ['first', 'second'] Examples -------- >>>concat([ntwkA,ntwkB]) >>>concat([ntwkA,ntwkB,ntwkC,ntwkD], port_order='second') To put for lines in parallel >>> from skrf import air >>> l1 = air.line(100, z0=[0,1]) >>> l2 = air.line(300, z0=[2,3]) >>> l3 = air.line(400, z0=[4,5]) >>> l4 = air.line(400, z0=[6,7]) >>> concat_ports([l1,l2,l3,l4], port_order='second') See Also -------- stitch : concatenate two networks along the frequency axis renumber : renumber ports """ # if ntwk list is longer than 2, recursively call myself # until we are done if len(ntwk_list) > 2: f = lambda x, y: concat_ports([x, y], port_order='first') out = reduce(f, ntwk_list) # if we want to renumber ports, we have to wait # until after the recursive calls if port_order == 'second': N = out.nports old_order = list(range(N)) new_order = list(range(0, N, 2)) + list(range(1, N, 2)) out.renumber(new_order, old_order) return out ntwkA, ntwkB = ntwk_list if ntwkA.frequency != ntwkB.frequency: raise ValueError('ntwks don\'t have matching frequencies') A = ntwkA.s B = ntwkB.s nf = A.shape[0] # num frequency points nA = A.shape[1] # num ports on A nB = B.shape[1] # num ports on B nC = nA + nB # num ports on C # create composite matrix, appending each sub-matrix diagonally C = npy.zeros((nf, nC, nC), dtype='complex') C[:, :nA, :nA] = A.copy() C[:, nA:, nA:] = B.copy() ntwkC = ntwkA.copy() ntwkC.s = C ntwkC.z0 = npy.hstack([ntwkA.z0, ntwkB.z0]) if port_order == 'second': old_order = list(range(nC)) new_order = list(range(0, nC, 2)) + list(range(1, nC, 2)) ntwkC.renumber(old_order, new_order) return ntwkC
[docs]def average(list_of_networks: Sequence[Network], polar: bool = False) -> Network: """ Calculates the average network from a list of Networks. This is complex average of the s-parameters for a list of Networks. Parameters ---------- list_of_networks : list of :class:`Network` objects the list of networks to average polar : boolean, optional Average the mag/phase components individually. Default is False. Returns ------- ntwk : :class:`Network` the resultant averaged Network Note ---- This same function can be accomplished with properties of a :class:`~skrf.networkset.NetworkSet` class. Examples -------- >>> ntwk_list = [rf.Network('myntwk.s1p'), rf.Network('myntwk2.s1p')] >>> mean_ntwk = rf.average(ntwk_list) """ out_ntwk = list_of_networks[0].copy() if polar: # average the mag/phase components individually raise NotImplementedError else: # average the re/im components individually for a_ntwk in list_of_networks[1:]: out_ntwk += a_ntwk out_ntwk.s = out_ntwk.s / (len(list_of_networks)) return out_ntwk
def stdev(list_of_networks: Sequence[Network], attr: str = 's') -> npy.ndarray: """ Calculates the standard deviation of a network attribute from a list of Networks. This is the standard deviation for complex values of the s-parameters and other related attributes for a list of Networks. Parameters ---------- list_of_networks : list of :class:`Network` objects the list of networks to average attr : str, optional name of attribute to average Returns ------- stdev_array : ndarray An array of standard deviation values computed after combining the s-parameter values of the given networks. Examples -------- >>> ntwk_list = [rf.Network('myntwk.s1p'), rf.Network('myntwk2.s1p')] >>> ntwk_stdev = rf.stdev(ntwk_list) """ return npy.array([getattr(network, attr) for network in list_of_networks]).std(axis=0)
[docs]def one_port_2_two_port(ntwk: Network) -> Network: """ Calculates the 2-port network given a symmetric, reciprocal and lossless 1-port network. Parameters ---------- ntwk : :class:`Network` a symmetric, reciprocal and lossless one-port network. Returns ------- ntwk : :class:`Network` the resultant two-port Network """ result = ntwk.copy() result.s = npy.zeros((result.frequency.npoints, 2, 2), dtype=complex) s11 = ntwk.s[:, 0, 0] result.s[:, 0, 0] = s11 result.s[:, 1, 1] = s11 ## HACK: TODO: verify this mathematically result.s[:, 0, 1] = npy.sqrt(1 - npy.abs(s11) ** 2) * \ npy.exp(1j * ( npy.angle(s11) + npy.pi / 2. * (npy.angle(s11) < 0) - npy.pi / 2 * (npy.angle(s11) > 0))) result.s[:, 1, 0] = result.s[:, 0, 1] result.z0 = npy.hstack([ntwk.z0,ntwk.z0]) return result
[docs]def chopinhalf(ntwk: Network, *args, **kwargs) -> Network: """ Chops a sandwich of identical, reciprocal 2-ports in half. Given two identical, reciprocal 2-ports measured in series, this returns one. Note ---- In other words, given .. math:: B = A\\cdot A Return A, where A port2 is connected to A port1. The result may be found through signal flow graph analysis and is, .. math:: a_{11} = \\frac{b_{11}}{1+b_{12}} a_{22} = \\frac{b_{22}}{1+b_{12}} a_{12}^2 = b_{21}(1-\\frac{b_{11}b_{22}}{(1+b_{12})^2} Parameters ---------- ntwk : :class:`Network` a 2-port that is equal to two identical two-ports in cascade """ if ntwk.nports != 2: raise ValueError('Only valid on 2ports') b11, b22, b12 = ntwk.s11, ntwk.s22, ntwk.s12 kwargs['name'] = kwargs.get('name', ntwk.name) a11 = b11 / (1 + b12) a22 = b22 / (1 + b12) a21 = b12 * (1 - b11 * b22 / (1 + b12) ** 2) # this is a21^2 here a21.s = mf.sqrt_phase_unwrap(a21.s) A = n_oneports_2_nport([a11, a21, a21, a22], *args, **kwargs) return A
def evenodd2delta(n: Network, z0: NumberLike = 50, renormalize: bool = True, doublehalf: bool = True) -> Network: """ Convert ntwk's s-matrix from even/odd mode into a delta (normal) s-matrix This assumes even/odd ports are ordered [1e,1o,2e,2o] This is useful for handling coupler sims. Only 4-ports supported for now. Parameters ---------- n : skrf.Network Network with an even/odd mode s-matrix z0: number, list of numbers the characteristic impedance to set output networks port impedance to , and used to renormalize s-matrix before conversio if `renormalize`=True. renormalize : Bool if impedances are in even/odd then they must be renormalized to get correct transformation doublehalf: Bool convert even/odd impedances to double/half their values. this is required if data comes from hfss waveports . Returns ------- out: skrf.Network same network as `n` but with s-matrix in normal delta basis See Also -------- Network.se2gmm, Network.gmm2se """ # move even and odd ports, so we have even and odd # s-matrices contiguous n_eo = n.copy() n_eo.renumber([0,1,2,3],[0,2,1,3]) if doublehalf: n_eo.z0 = n_eo.z0*[2,2,.5,.5] # if the n_eo s-matrix is given with e/o z0's we need # to renormalize into 50 if renormalize: n_eo.renormalize(z0) even = n_eo.s[:,0:2,0:2] odd = n_eo.s[:,2:4,2:4] # compute sub-networks for symmetric 4port s_a = .5*(even+odd) s_b = .5*(even-odd) # create output network n_delta = n_eo.copy() n_delta.s[:,0:2,0:2] = n_delta.s[:,2:4,2:4] = s_a n_delta.s[:,2:4,0:2] = n_delta.s[:,0:2,2:4] = s_b n_delta.z0=z0 return n_delta
[docs]def subnetwork(ntwk: Network, ports: int, offby:int = 1) -> Network: """ Returns a subnetwork of a given Network from a list of port numbers. A subnetwork is Network which S-parameters corresponds to selected ports, with all non-selected ports considered matched. The resulting subNetwork is given a new Network.name property from the initial name and adding the kept ports indices (ex: 'device' -> 'device13'). Such name should make easier the use of functions such as n_twoports_2_nport. Parameters ---------- ntwk : :class:`Network` object Network to split into a subnetwork ports : list of int List of ports to keep in the resultant Network. Indices are the Python indices (starts at 0) offby : int starting value for s-parameters indexes in the sub-Network name parameter. A value of `1`, assumes that a s21 = ntwk.s[:,1,0]. Default is 1. Returns ------- subntwk : :class:`Network` object Resulting subnetwork from the given ports See also -------- Network.subnetwork, n_twoports_2_nport Examples -------- >>> tee = rf.data.tee # 3 port Network >>> tee12 = rf.subnetwork(tee, [0, 1]) # 2 port Network from ports 1 & 2, port 3 matched >>> tee23 = rf.subnetwork(tee, [1, 2]) # 2 port Network from ports 2 & 3, port 1 matched >>> tee13 = rf.subnetwork(tee, [0, 2]) # 2 port Network from ports 1 & 3, port 2 matched """ # forging subnetwork name subntwk_name = (ntwk.name or 'p') + ''.join([str(index+offby) for index in ports]) # create a dummy Network with same frequency and z0 from the original subntwk = Network(frequency=ntwk.frequency, z0=ntwk.z0[:,ports], name=subntwk_name) # keep requested rows and columns of the s-matrix. ports can be not contiguous subntwk.s = ntwk.s[npy.ix_(npy.arange(ntwk.s.shape[0]), ports, ports)] return subntwk
## Building composit networks from sub-networks
[docs]def n_oneports_2_nport(ntwk_list: Sequence[Network], *args, **kwargs) -> Network: """ Builds a N-port Network from list of N one-ports Parameters ---------- ntwk_list : list of :class:`Network` objects must follow left-right, top-bottom order, ie, s11,s12,s21,s22 \*args, \*\*kwargs : passed to :func:`Network.__init__` for the N-port Returns ------- nport : n-port :class:`Network` result """ nports = int(npy.sqrt(len(ntwk_list))) s_out = npy.concatenate( [npy.concatenate( [ntwk_list[(k + (l * nports))].s for k in range(nports)], 2) \ for l in range(nports)], 1) z0 = npy.concatenate( [ntwk_list[k].z0 for k in range(0, nports ** 2, nports + 1)], 1) frequency = ntwk_list[0].frequency return Network(s=s_out, z0=z0, frequency=frequency, *args, **kwargs)
[docs]def n_twoports_2_nport(ntwk_list: Sequence[Network], nports: int, offby:int = 1, **kwargs) -> Network: """ Builds a N-port Network from list of two-ports This method was made to reconstruct a n-port network from 2-port subnetworks as measured by a 2-port VNA. So, for example, given a 3-port DUT, you might measure the set p12.s2p, p23.s2p, p13.s2p. From these measurements, you can construct p.s3p. By default all entries of result.s are filled with 0's, in case you dont fully specify the entire s-matrix of the resultant ntwk. Parameters ---------- ntwk_list : list of :class:`Network` objects the names must contain the port index, ie 'p12' or 'p43', ie. define the Network.name property of the :class:`Network` object. offby : int starting value for s-parameters indices. ie a value of `1`, assumes that a s21 = ntwk.s[:,1,0] \*args, \*\*kwargs : passed to :func:`Network.__init__` for the N-port Returns ------- nport : n-port :class:`Network` result See Also -------- concat_ports : concatenate ntwks along their ports """ frequency = ntwk_list[0].frequency nport = Network(frequency=frequency, s=npy.zeros(shape=(frequency.npoints, nports, nports)), **kwargs) for subntwk in ntwk_list: for m, n in nport.port_tuples: if m != n and m > n: if '%i%i' % (m + offby, n + offby) in subntwk.name: pass elif '%i%i' % (n + offby, m + offby) in subntwk.name: subntwk = subntwk.flipped() else: continue for mn, jk in zip(product((m, n), repeat=2), product((0, 1), repeat=2)): m, n, j, k = mn[0], mn[1], jk[0], jk[1] nport.s[:, m, n] = subntwk.s[:, j, k] nport.z0[:, m] = subntwk.z0[:, j] return nport
[docs]def four_oneports_2_twoport(s11: Network, s12: Network, s21: Network, s22: Network, *args, **kwargs) -> Network: """ Builds a 2-port Network from list of four 1-ports Parameters ---------- s11 : one-port :class:`Network` s11 s12 : one-port :class:`Network` s12 s21 : one-port :class:`Network` s21 s22 : one-port :class:`Network` s22 \*args, \*\*kwargs : passed to :func:`Network.__init__` for the twoport Returns ------- twoport : two-port :class:`Network` result See Also -------- n_oneports_2_nport three_twoports_2_threeport """ return n_oneports_2_nport([s11, s12, s21, s22], *args, **kwargs)
[docs]def three_twoports_2_threeport(ntwk_triplet: Sequence[Network], auto_order:bool = True, *args, **kwargs) -> Network: """ Creates 3-port from three 2-port Networks This function provides a convenient way to build a 3-port Network from a set of 2-port measurements. Which may occur when measuring a three port device on a 2-port VNA. Note ---- if `auto_order` is False, ntwk_triplet must be of port orderings: [p12, p13, p23] else if `auto_order`is True, then the 3 Networks in ntwk_triplet must contain port identification in their names. For example, their names may be like `me12`, `me13`, `me23` Parameters ---------- ntwk_triplet : list of 2-port Network objects list of three 2-ports. see notes about order. auto_order : bool if True attempt to inspect port orderings from Network names. Names must be like 'p12', 'p23', etc contains : str only files containing this string will be loaded. \*args,\*\*kwargs : passed to :func:`Network.__init__` for resultant network Returns ------- threeport : 3-port Network See Also -------- n_oneports_2_nport Examples -------- >>> rf.three_twoports_2_threeport(rf.read_all('.').values()) """ raise DeprecationWarning('Use n_twoports_2_nport instead') if auto_order: p12, p13, p23 = None, None, None s11, s12, s13, s21, s22, s23, s31, s32, s33 = None, None, None, None, None, None, None, None, None for k in ntwk_triplet: if '12' in k.name: p12 = k elif '13' in k.name: p13 = k elif '23' in k.name: p23 = k elif '21' in k.name: p12 = k.flipped() elif '31' in k.name: p31 = k.flipped() elif '32' in k.name: p23 = k.flipped() else: p12, p13, p23 = ntwk_triplet p21 = p12.flipped() p31 = p13.flipped() p32 = p23.flipped() if p12 != None: s11 = p12.s11 s12 = p12.s12 s21 = p12.s21 s22 = p12.s22 if p13 != None: s11 = p13.s11 s13 = p13.s12 s31 = p13.s21 s33 = p13.s22 if p23 != None: s22 = p23.s11 s23 = p23.s12 s32 = p23.s21 s33 = p23.s22 ntwk_list = [s11, s12, s13, s21, s22, s23, s31, s32, s33] for k in range(len(ntwk_list)): if ntwk_list[k] == None: frequency = ntwk_triplet[0].frequency s = npy.zeros((len(ntwk_triplet[0]), 1, 1)) ntwk_list[k] = Network(s=s, frequency=frequency) threeport = n_oneports_2_nport(ntwk_list, *args, **kwargs) return threeport
## Functions operating on s-parameter matrices
[docs]def connect_s(A: npy.ndarray, k: int, B: npy.ndarray, l: int) -> npy.ndarray: """ Connect two n-port networks' s-matrices together. Specifically, connect port `k` on network `A` to port `l` on network `B`. The resultant network has nports = (A.rank + B.rank-2). This function operates on, and returns s-matrices. The function :func:`connect` operates on :class:`Network` types. Parameters ---------- A : :class:`numpy.ndarray` S-parameter matrix of `A`, shape is fxnxn k : int port index on `A` (port indices start from 0) B : :class:`numpy.ndarray` S-parameter matrix of `B`, shape is fxnxn l : int port index on `B` Returns ------- C : :class:`numpy.ndarray` new S-parameter matrix Note ---- Internally, this function creates a larger composite network and calls the :func:`innerconnect_s` function. see that function for more details about the implementation See Also -------- connect : operates on :class:`Network` types innerconnect_s : function which implements the connection algorithm """ if k > A.shape[-1] - 1 or l > B.shape[-1] - 1: raise (ValueError('port indices are out of range')) nf = A.shape[0] # num frequency points nA = A.shape[1] # num ports on A nB = B.shape[1] # num ports on B nC = nA + nB # num ports on C # create composite matrix, appending each sub-matrix diagonally C = npy.zeros((nf, nC, nC), dtype='complex') C[:, :nA, :nA] = A.copy() C[:, nA:, nA:] = B.copy() # call innerconnect_s() on composit matrix C return innerconnect_s(C, k, nA + l)
[docs]def innerconnect_s(A: npy.ndarray, k: int, l: int) -> npy.ndarray: """ connect two ports of a single n-port network's s-matrix. Specifically, connect port `k` to port `l` on `A`. This results in a (n-2)-port network. This function operates on, and returns s-matrices. The function :func:`innerconnect` operates on :class:`Network` types. Note ---- The algorithm used to calculate the resultant network is called a 'sub-network growth', can be found in [#]_. The original paper describing the algorithm is given in [#]_. Parameters ---------- A : :class:`numpy.ndarray` S-parameter matrix of `A`, shape is fxnxn k : int port index on `A` (port indices start from 0) l : int port index on `A` Returns ------- C : :class:`numpy.ndarray` new S-parameter matrix References ---------- .. [#] Compton, R.C.; , "Perspectives in microwave circuit analysis," Circuits and Systems, 1989., Proceedings of the 32nd Midwest Symposium on , vol., no., pp.716-718 vol.2, 14-16 Aug 1989. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=101955&isnumber=3167 .. [#] Filipsson, Gunnar; , "A New General Computer Algorithm for S-Matrix Calculation of Interconnected Multiports," Microwave Conference, 1981. 11th European , vol., no., pp.700-704, 7-11 Sept. 1981. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4131699&isnumber=4131585 """ if k > A.shape[-1] - 1 or l > A.shape[-1] - 1: raise (ValueError('port indices are out of range')) nA = A.shape[1] # num of ports on input s-matrix # create an empty s-matrix, to store the result C = npy.zeros(shape=A.shape, dtype='complex') # loop through ports and calculates resultant s-parameters for i in range(nA): for j in range(nA): C[:, i, j] = \ A[:, i, j] + \ (A[:, k, j] * A[:, i, l] * (1 - A[:, l, k]) + \ A[:, l, j] * A[:, i, k] * (1 - A[:, k, l]) + \ A[:, k, j] * A[:, l, l] * A[:, i, k] + \ A[:, l, j] * A[:, k, k] * A[:, i, l]) / \ ((1 - A[:, k, l]) * (1 - A[:, l, k]) - A[:, k, k] * A[:, l, l]) # remove ports that were `connected` C = npy.delete(C, (k, l), 1) C = npy.delete(C, (k, l), 2) return C
## network parameter conversion
[docs]def s2z(s: npy.ndarray, z0: NumberLike = 50, s_def: str = S_DEF_DEFAULT) -> npy.ndarray: """ Convert scattering parameters [#]_ to impedance parameters [#]_ For power-waves, Eq.(19) from [#Kurokawa]_: .. math:: Z = F^{-1} (1 - S)^{-1} (S G + G^*) F where :math:`G = diag([Z_0])` and :math:`F = diag([1/2\\sqrt{|Re(Z_0)|}])` For pseudo-waves, Eq.(74) from [#Marks]_: .. math:: Z = (1 - U^{-1} S U)^{-1} (1 + U^{-1} S U) G where :math:`U = \\sqrt{Re(Z_0)}/|Z_0|` Parameters ---------- s : complex array-like scattering parameters z0 : complex array-like or number port impedances. s_def : str -> s_def : can be: 'power', 'pseudo' or 'traveling' Scattering parameter definition : 'power' for power-waves definition [#Kurokawa]_, 'pseudo' for pseudo-waves definition [#Marks]_. 'traveling' corresponds to the initial implementation. Default is 'power'. Returns ------- z : complex array-like impedance parameters References ---------- .. [#] http://en.wikipedia.org/wiki/S-parameters .. [#] http://en.wikipedia.org/wiki/impedance_parameters .. [#Kurokawa] Kurokawa, Kaneyuki "Power waves and the scattering matrix", IEEE Transactions on Microwave Theory and Techniques, vol.13, iss.2, pp. 194–202, March 1965. .. [#Marks] Marks, R. B. and Williams, D. F. "A general waveguide circuit theory", Journal of Research of National Institute of Standard and Technology, vol.97, iss.5, pp. 533–562, 1992. """ nfreqs, nports, nports = s.shape z0 = fix_z0_shape(z0, nfreqs, nports) # Add a small real part in case of pure imaginary char impedance # to prevent numerical errors for both pseudo and power waves definitions z0 = z0.astype(dtype=npy.complex) z0[z0.real == 0] += ZERO s = s.copy() # to prevent the original array from being altered s[s == -1.] = -1. + 1e-12 # solve numerical singularity s[s == 1.] = 1. + 1e-12 # solve numerical singularity # The following is a vectorized version of a for loop for all frequencies. # # Creating Identity matrices of shape (nports,nports) for each nfreqs Id = npy.zeros_like(s) # (nfreqs, nports, nports) npy.einsum('ijj->ij', Id)[...] = 1.0 if s_def == 'power': # Power-waves. Eq.(19) from [Kurokawa et al.] # Creating diagonal matrices of shape (nports,nports) for each nfreqs F, G = npy.zeros_like(s), npy.zeros_like(s) npy.einsum('ijj->ij', F)[...] = 1.0/npy.sqrt(z0.real)*0.5 npy.einsum('ijj->ij', G)[...] = z0 # z = npy.linalg.inv(F) @ npy.linalg.inv(Id - s) @ (s @ G + npy.conjugate(G)) @ F # Python > 3.5 z = npy.matmul(npy.linalg.inv(F), npy.matmul(npy.linalg.inv(Id - s), npy.matmul(npy.matmul(s, G) + npy.conjugate(G), F))) elif s_def == 'pseudo': # Pseudo-waves. Eq.(74) from [Marks et al.] # Creating diagonal matrices of shape (nports,nports) for each nfreqs ZR, U = npy.zeros_like(s), npy.zeros_like(s) npy.einsum('ijj->ij', U)[...] = npy.sqrt(z0.real)/npy.abs(z0) npy.einsum('ijj->ij', ZR)[...] = z0 # USU = npy.linalg.inv(U) @ s @ U # z = npy.linalg.inv(Id - USU) @ (Id + USU) @ ZR USU = npy.matmul(npy.linalg.inv(U), npy.matmul(s , U)) z = npy.matmul(npy.linalg.inv(Id - USU), npy.matmul((Id + USU), ZR)) elif s_def == 'traveling': # Traveling-waves definition. Cf.Wikipedia "Impedance parameters" page. # Creating diagonal matrices of shape (nports, nports) for each nfreqs sqrtz0 = npy.zeros_like(s) # (nfreqs, nports, nports) npy.einsum('ijj->ij', sqrtz0)[...] = npy.sqrt(z0) # s -> z z = npy.zeros_like(s) # z = sqrtz0 @ npy.linalg.inv(Id - s) @ (Id + s) @ sqrtz0 # Python>3.5 z = npy.matmul(npy.matmul(npy.matmul(sqrtz0, npy.linalg.inv(Id - s)), (Id + s)), sqrtz0) return z
[docs]def s2y(s: npy.ndarray, z0:NumberLike = 50, s_def: str = S_DEF_DEFAULT) -> npy.ndarray: """ convert scattering parameters [#]_ to admittance parameters [#]_ Equations are the inverse of :func:`s2z`. Parameters ---------- s : complex array-like scattering parameters z0 : complex array-like or number port impedances s_def : str -> s_def : can be: 'power', 'pseudo' or 'traveling' Scattering parameter definition : 'power' for power-waves definition [#]_, 'pseudo' for pseudo-waves definition [#]_. 'traveling' corresponds to the initial implementation. Default is 'power'. Returns ------- y : complex array-like admittance parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/S-parameters .. [#] http://en.wikipedia.org/wiki/Admittance_parameters .. [#] Kurokawa, Kaneyuki "Power waves and the scattering matrix", IEEE Transactions on Microwave Theory and Techniques, vol.13, iss.2, pp. 194–202, March 1965. .. [#] Marks, R. B. and Williams, D. F. "A general waveguide circuit theory", Journal of Research of National Institute of Standard and Technology, vol.97, iss.5, pp. 533–562, 1992. """ nfreqs, nports, nports = s.shape z0 = fix_z0_shape(z0, nfreqs, nports) # Add a small real part in case of pure imaginary char impedance # to prevent numerical errors for both pseudo and power waves definitions z0 = z0.astype(dtype=npy.complex) z0[z0.real == 0] += ZERO s = s.copy() # to prevent the original array from being altered s[s == -1.] = -1. + 1e-12 # solve numerical singularity s[s == 1.] = 1. + 1e-12 # solve numerical singularity # The following is a vectorized version of a for loop for all frequencies. # Creating Identity matrices of shape (nports,nports) for each nfreqs Id = npy.zeros_like(s) # (nfreqs, nports, nports) npy.einsum('ijj->ij', Id)[...] = 1.0 if s_def == 'power': # Power-waves. Inverse of Eq.(19) from [Kurokawa et al.] # Creating diagonal matrices of shape (nports,nports) for each nfreqs F, G = npy.zeros_like(s), npy.zeros_like(s) npy.einsum('ijj->ij', F)[...] = 1.0/npy.sqrt(z0.real)*0.5 npy.einsum('ijj->ij', G)[...] = z0 # y = npy.linalg.inv(F) @ npy.linalg.inv((s @ G + npy.conjugate(G))) @ (Id - s) @ F # Python > 3.5 y = npy.matmul(npy.linalg.inv(F), npy.matmul(npy.linalg.inv(npy.matmul(s, G) + npy.conjugate(G)), npy.matmul((Id - s), F))) elif s_def == 'pseudo': # pseudo-waves. Inverse of Eq.(74) from [Marks et al.] YR, U = npy.zeros_like(s), npy.zeros_like(s) npy.einsum('ijj->ij', U)[...] = npy.sqrt(z0.real)/npy.abs(z0) npy.einsum('ijj->ij', YR)[...] = 1/z0 # USU = npy.linalg.inv(U) @ s @ U # y = YR @ npy.linalg.inv(Id + USU) @ (Id - USU) USU = npy.matmul(npy.linalg.inv(U), npy.matmul(s, U)) y = npy.matmul(YR, npy.matmul(npy.linalg.inv(Id + USU), (Id - USU))) elif s_def == 'traveling': # Traveling-waves definition. Cf.Wikipedia "Impedance parameters" page. # Creating diagonal matrices of shape (nports, nports) for each nfreqs sqrty0 = npy.zeros_like(s) # (nfreqs, nports, nports) npy.einsum('ijj->ij', sqrty0)[...] = npy.sqrt(1.0/z0) # s -> y y = npy.zeros_like(s) # y = sqrty0 @ (Id - s) @ npy.linalg.inv(Id + s) @ sqrty0 # Python>3.5 y = npy.matmul(npy.matmul(npy.matmul(sqrty0, (Id - s)), npy.linalg.inv(Id + s)), sqrty0) return y
[docs]def s2t(s: npy.ndarray) -> npy.ndarray: """ Converts scattering parameters [#]_ to scattering transfer parameters [#]_ . transfer parameters are also referred to as 'wave cascading matrix' [#]_, this function only operates on 2N-ports networks with same number of input and output ports, also known as 'balanced networks'. Parameters ---------- s : :class:`numpy.ndarray` (shape fx2nx2n) scattering parameter matrix Returns ------- t : numpy.ndarray scattering transfer parameters (aka wave cascading matrix) See Also -------- inv : calculates inverse s-parameters s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/S-parameters .. [#] http://en.wikipedia.org/wiki/Scattering_transfer_parameters#Scattering_transfer_parameters .. [#] Janusz A. Dobrowolski, "Scattering Parameter in RF and Microwave Circuit Analysis and Design", Artech House, 2016, pp. 65-68 """ z, y, x = s.shape # test here for even number of ports. # s-parameter networks are square matrix, so x and y are equal. if(x % 2 != 0): raise IndexError('Network don\'t have an even number of ports') t = npy.zeros((z, y, x), dtype=complex) yh = int(y/2) xh = int(x/2) # S_II,I^-1 sinv = npy.linalg.inv(s[:, yh:y, 0:xh]) # np.linalg.inv test for singularity (matrix not invertible) for k in range(len(s)): # T_I,I = S_I,II - S_I,I . S_II,I^-1 . S_II,II t[k, 0:yh, 0:xh] = s[k, 0:yh, xh:x] - s[k, 0:yh, 0:xh].dot(sinv[k].dot(s[k, yh:y, xh:x])) # T_I,II = S_I,I . S_II,I^-1 t[k, 0:yh, xh:x] = s[k, 0:yh, 0:xh].dot(sinv[k]) # T_II,I = -S_II,I^-1 . S_II,II t[k, yh:y, 0:xh] = -sinv[k].dot(s[k, yh:y, xh:x]) # T_II,II = S_II,I^-1 t[k, yh:y, xh:x] = sinv[k] return t
[docs]def z2s(z: NumberLike, z0:NumberLike = 50, s_def: str = S_DEF_DEFAULT) -> npy.ndarray: """ convert impedance parameters [#]_ to scattering parameters [#]_ For power-waves, Eq.(18) from [#Kurokawa]_: .. math:: S = F (Z – G^*) (Z + G)^{-1} F^{-1} where :math:`G = diag([Z_0])` and :math:`F = diag([1/2\\sqrt{|Re(Z_0)|}])` For pseudo-waves, Eq.(73) from [#Marks]_: .. math:: S = U (Z - G) (Z + G)^{-1} U^{-1} where :math:`U = \\sqrt{Re(Z_0)}/|Z_0|` Parameters ---------- z : complex array-like impedance parameters z0 : complex array-like or number port impedances s_def : str -> s_def : can be: 'power', 'pseudo' or 'traveling' Scattering parameter definition : 'power' for power-waves definition [#Kurokawa]_, 'pseudo' for pseudo-waves definition [#Marks]_. 'traveling' corresponds to the initial implementation. Default is 'power'. Returns ------- s : complex array-like scattering parameters References ---------- .. [#] http://en.wikipedia.org/wiki/impedance_parameters .. [#] http://en.wikipedia.org/wiki/S-parameters .. [#Kurokawa] Kurokawa, Kaneyuki "Power waves and the scattering matrix", IEEE Transactions on Microwave Theory and Techniques, vol.13, iss.2, pp. 194–202, March 1965. .. [#Marks] Marks, R. B. and Williams, D. F. "A general waveguide circuit theory", Journal of Research of National Institute of Standard and Technology, vol.97, iss.5, pp. 533–562, 1992. """ nfreqs, nports, nports = z.shape z0 = fix_z0_shape(z0, nfreqs, nports) # Add a small real part in case of pure imaginary char impedance # to prevent numerical errors for both pseudo and power waves definitions z0 = z0.astype(dtype=npy.complex) z0[z0.real == 0] += ZERO if s_def == 'power': # Power-waves. Eq.(18) from [Kurokawa et al.3] # Creating diagonal matrices of shape (nports,nports) for each nfreqs F, G = npy.zeros_like(z), npy.zeros_like(z) npy.einsum('ijj->ij', F)[...] = 1.0/npy.sqrt(z0.real)*0.5 npy.einsum('ijj->ij', G)[...] = z0 # s = F @ (z - npy.conjugate(G)) @ npy.linalg.inv(z + G) @ npy.linalg.inv(F) # Python > 3.5 s = npy.matmul(F, npy.matmul((z - npy.conjugate(G)), npy.matmul(npy.linalg.inv(z + G), npy.linalg.inv(F)))) elif s_def == 'pseudo': # Pseudo-waves. Eq.(73) from [Marks et al.] # Creating diagonal matrices of shape (nports,nports) for each nfreqs ZR, U = npy.zeros_like(z), npy.zeros_like(z) npy.einsum('ijj->ij', U)[...] = npy.sqrt(z0.real)/npy.abs(z0) npy.einsum('ijj->ij', ZR)[...] = z0 # s = U @ (z - ZR) @ npy.linalg.inv(z + ZR) @ npy.linalg.inv(U) # Python > 3.5 s = npy.matmul(U, npy.matmul((z - ZR), npy.matmul(npy.linalg.inv(z + ZR), npy.linalg.inv(U)))) elif s_def == 'traveling': # Traveling-waves definition. Cf.Wikipedia "Impedance parameters" page. # Creating Identity matrices of shape (nports,nports) for each nfreqs Id = npy.zeros_like(z) # (nfreqs, nports, nports) npy.einsum('ijj->ij', Id)[...] = 1.0 # Creating diagonal matrices of shape (nports, nports) for each nfreqs sqrty0 = npy.zeros_like(z) # (nfreqs, nports, nports) npy.einsum('ijj->ij', sqrty0)[...] = npy.sqrt(1.0/z0) # z -> s s = npy.zeros_like(z) # s = (sqrty0 @ z @ sqrty0 - Id) @ npy.linalg.inv(sqrty0 @ z @ sqrty0 + Id) # Python>3.5 s = npy.matmul((npy.matmul(npy.matmul(sqrty0, z), sqrty0) - Id), npy.linalg.inv(npy.matmul(npy.matmul(sqrty0, z), sqrty0) + Id)) return s
[docs]def z2y(z: npy.ndarray) -> npy.ndarray: """ convert impedance parameters [#]_ to admittance parameters [#]_ .. math:: y = z^{-1} Parameters ---------- z : complex array-like impedance parameters Returns ------- y : complex array-like admittance parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/impedance_parameters .. [#] http://en.wikipedia.org/wiki/Admittance_parameters """ return npy.array([npy.mat(z[f, :, :]) ** -1 for f in range(z.shape[0])])
[docs]def z2t(z: npy.ndarray) -> NoReturn: """ Not Implemented yet convert impedance parameters [#]_ to scattering transfer parameters [#]_ Parameters ---------- z : complex array-like or number impedance parameters Returns ------- s : complex array-like or number scattering parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/impedance_parameters .. [#] http://en.wikipedia.org/wiki/Scattering_transfer_parameters#Scattering_transfer_parameters """ raise (NotImplementedError)
def a2s(a: npy.ndarray, z0: NumberLike = 50) -> npy.ndarray: """ convert abcd parameters to s parameters Parameters ---------- a : complex array-like abcd parameters z0 : complex array-like or number port impedances Returns ------- s : complex array-like abcd parameters """ nfreqs, nports, nports = a.shape if nports != 2: raise IndexError('abcd parameters are defined for 2-ports networks only') z0 = fix_z0_shape(z0, nfreqs, nports) z01 = z0[:,0] z02 = z0[:,1] A = a[:,0,0] B = a[:,0,1] C = a[:,1,0] D = a[:,1,1] denom = A*z02 + B + C*z01*z02 + D*z01 s = npy.array([ [ (A*z02 + B - C*z01.conj()*z02 - D*z01.conj() ) / denom, (2*npy.sqrt(z01.real * z02.real)) / denom, ], [ (2*(A*D - B*C)*npy.sqrt(z01.real * z02.real)) / denom, (-A*z02.conj() + B - C*z01*z02.conj() + D*z01) / denom, ], ]).transpose() return s #return z2s(a2z(a), z0) def a2z(a: npy.ndarray) -> npy.ndarray: """ Converts abcd parameters to z parameters [#]_ . Parameters ---------- a : :class:`numpy.ndarray` (shape fx2x2) abcd parameter matrix Returns ------- z : numpy.ndarray impedance parameters See Also -------- inv : calculates inverse s-parameters s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ----------- .. [#] https://en.wikipedia.org/wiki/Two-port_network """ return z2a(a)
[docs]def z2a(z: npy.ndarray) -> npy.ndarray: """ Converts impedance parameters to abcd parameters [#]_ . Parameters ---------- z : :class:`numpy.ndarray` (shape fx2x2) impedance parameter matrix Returns ------- abcd : numpy.ndarray scattering transfer parameters (aka wave cascading matrix) See Also -------- inv : calculates inverse s-parameters s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] https://en.wikipedia.org/wiki/Two-port_network """ abcd = npy.array([ [z[:, 0, 0] / z[:, 1, 0], 1. / z[:, 1, 0]], [(z[:, 0, 0] * z[:, 1, 1] - z[:, 1, 0] * z[:, 0, 1]) / z[:, 1, 0], z[:, 1, 1] / z[:, 1, 0]], ]).transpose() return abcd
[docs]def s2a(s: npy.ndarray, z0: NumberLike = 50) -> npy.ndarray: """ Converts scattering parameters to abcd parameters [#]_ . Parameters ---------- s : :class:`numpy.ndarray` (shape `fx2x2`) impedance parameter matrix z0: number or, :class:`numpy.ndarray` (shape `fx2`) port impedance Returns ------- abcd : numpy.ndarray scattering transfer parameters (aka wave cascading matrix) References ---------- .. [#] https://en.wikipedia.org/wiki/Two-port_network """ nfreqs, nports, nports = s.shape if nports != 2: raise IndexError('abcd parameters are defined for 2-ports networks only') z0 = fix_z0_shape(z0, nfreqs, nports) z01 = z0[:,0] z02 = z0[:,1] denom = (2*s[:,1,0]*npy.sqrt(z01.real * z02.real)) a = npy.array([ [ ((z01.conj() + s[:,0,0]*z01)*(1 - s[:,1,1]) + s[:,0,1]*s[:,1,0]*z01) / denom, ((1 - s[:,0,0])*(1 - s[:,1,1]) - s[:,0,1]*s[:,1,0]) / denom, ], [ ((z01.conj() + s[:,0,0]*z01)*(z02.conj() + s[:,1,1]*z02) - s[:,0,1]*s[:,1,0]*z01*z02) / denom, ((1 - s[:,0,0])*(z02.conj() + s[:,1,1]*z02) + s[:,0,1]*s[:,1,0]*z02) / denom, ], ]).transpose() return a
[docs]def y2s(y: npy.ndarray, z0:NumberLike = 50, s_def: str = S_DEF_DEFAULT) -> Network: """ convert admittance parameters [#]_ to scattering parameters [#]_ For power-waves, from [#Kurokawa]_: .. math:: S = F (1 – G Y) (1 + G Y)^{-1} F^{-1} where :math:`G = diag([Z_0])` and :math:`F = diag([1/2\\sqrt{|Re(Z_0)|}])` For pseudo-waves, Eq.(73) from [#Marks]_: .. math:: S = U (Y^{-1} - G) (Y^{-1} + G)^{-1} U^{-1} where :math:`U = \\sqrt{Re(Z_0)}/|Z_0|` Parameters ---------- y : complex array-like admittance parameters z0 : complex array-like or number port impedances s_def : str -> s_def : can be: 'power', 'pseudo' or 'traveling' Scattering parameter definition : 'power' for power-waves definition [#Kurokawa]_, 'pseudo' for pseudo-waves definition [#Marks]_. 'traveling' corresponds to the initial implementation. Default is 'power'. Returns ------- s : complex array-like or number scattering parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/Admittance_parameters .. [#] http://en.wikipedia.org/wiki/S-parameters .. [#Kurokawa] Kurokawa, Kaneyuki "Power waves and the scattering matrix", IEEE Transactions on Microwave Theory and Techniques, vol.13, iss.2, pp. 194–202, March 1965. .. [#Marks] Marks, R. B. and Williams, D. F. "A general waveguide circuit theory", Journal of Research of National Institute of Standard and Technology, vol.97, iss.5, pp. 533–562, 1992. """ nfreqs, nports, nports = y.shape z0 = fix_z0_shape(z0, nfreqs, nports) # Add a small real part in case of pure imaginary char impedance # to prevent numerical errors for both pseudo and power waves definitions z0 = z0.astype(dtype=npy.complex) z0[z0.real == 0] += ZERO # The following is a vectorized version of a for loop for all frequencies. # Creating Identity matrices of shape (nports,nports) for each nfreqs Id = npy.zeros_like(y) # (nfreqs, nports, nports) npy.einsum('ijj->ij', Id)[...] = 1.0 if s_def == 'power': # Creating diagonal matrices of shape (nports,nports) for each nfreqs F, G = npy.zeros_like(y), npy.zeros_like(y) npy.einsum('ijj->ij', F)[...] = 1.0/npy.sqrt(z0.real)*0.5 npy.einsum('ijj->ij', G)[...] = z0 # s = F @ (Id - npy.conjugate(G) @ y) @ npy.linalg.inv(Id + G @ y) @ npy.linalg.inv(F) # Python > 3.5 s = npy.matmul(F, npy.matmul((Id - npy.matmul(npy.conjugate(G), y)), npy.matmul(npy.linalg.inv(Id + npy.matmul(G, y)), npy.linalg.inv(F)))) elif s_def == 'pseudo': # Pseudo-waves # Creating diagonal matrices of shape (nports,nports) for each nfreqs ZR, U = npy.zeros_like(y), npy.zeros_like(y) npy.einsum('ijj->ij', U)[...] = npy.sqrt(z0.real)/npy.abs(z0) npy.einsum('ijj->ij', ZR)[...] = z0 # s = U @ (npy.linalg.inv(y) - ZR) @ npy.linalg.inv(npy.linalg.inv(y) + ZR) @ npy.linalg.inv(U) # Python > 3.5 s = npy.matmul(U, npy.matmul((npy.linalg.inv(y) - ZR), npy.matmul(npy.linalg.inv(npy.linalg.inv(y) + ZR), npy.linalg.inv(U)))) elif s_def == 'traveling': # Traveling-waves definition. Cf.Wikipedia "Impedance parameters" page. # Creating diagonal matrices of shape (nports, nports) for each nfreqs sqrtz0 = npy.zeros_like(y) # (nfreqs, nports, nports) npy.einsum('ijj->ij', sqrtz0)[...] = npy.sqrt(z0) # y -> s s = npy.zeros_like(y) # s = (Id - sqrtz0 @ y @ sqrtz0) @ npy.linalg.inv(Id + sqrtz0 @ y @ sqrtz0) # Python>3.5 s = npy.matmul( Id - npy.matmul(npy.matmul(sqrtz0, y), sqrtz0), npy.linalg.inv(Id + npy.matmul(npy.matmul(sqrtz0, y), sqrtz0))) return s
[docs]def y2z(y: npy.ndarray) -> npy.ndarray: """ convert admittance parameters [#]_ to impedance parameters [#]_ .. math:: z = y^{-1} Parameters ---------- y : complex array-like admittance parameters Returns ------- z : complex array-like impedance parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/Admittance_parameters .. [#] http://en.wikipedia.org/wiki/impedance_parameters """ return npy.array([npy.mat(y[f, :, :]) ** -1 for f in range(y.shape[0])])
[docs]def y2t(y: npy.ndarray) -> NoReturn: """ Not Implemented Yet convert admittance parameters [#]_ to scattering-transfer parameters [#]_ Parameters ---------- y : complex array-like or number impedance parameters Returns ------- t : complex array-like or number scattering parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/Admittance_parameters .. [#] http://en.wikipedia.org/wiki/Scattering_transfer_parameters#Scattering_transfer_parameters """ raise (NotImplementedError)
[docs]def t2s(t: npy.ndarray) -> npy.ndarray: """ converts scattering transfer parameters [#]_ to scattering parameters [#]_ transfer parameters are also referred to as 'wave cascading matrix', this function only operates on 2N-ports networks with same number of input and output ports, also known as 'balanced networks'. Parameters ---------- t : :class:`numpy.ndarray` (shape fx2nx2n) scattering transfer parameters Returns ------- s : :class:`numpy.ndarray` scattering parameter matrix. See Also -------- inv : calculates inverse s-parameters s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ----------- .. [#] http://en.wikipedia.org/wiki/Scattering_transfer_parameters#Scattering_transfer_parameters .. [#] http://en.wikipedia.org/wiki/S-parameters .. [#] Janusz A. Dobrowolski, "Scattering Parameter in RF and Microwave Circuit Analysis and Design", Artech House, 2016, pp. 65-68 """ z, y, x = t.shape # test here for even number of ports. # t-parameter networks are square matrix, so x and y are equal. if(x % 2 != 0): raise IndexError('Network don\'t have an even number of ports') s = npy.zeros((z, y, x), dtype=complex) yh = int(y/2) xh = int(x/2) # T_II,II^-1 tinv = npy.linalg.inv(t[:, yh:y, xh:x]) # np.linalg.inv test for singularity (matrix not invertible) for k in range(len(s)): # S_I,I = T_I,II . T_II,II^-1 s[k, 0:yh, 0:xh] = t[k, 0:yh, xh:x].dot(tinv[k]) # S_I,II = T_I,I - T_I,I,II . T_II,II^-1 . T_II,I s[k, 0:yh, xh:x] = t[k, 0:yh, 0:xh]-t[k, 0:yh, xh:x].dot(tinv[k].dot(t[k, yh:y, 0:xh])) # S_II,I = T_II,II^-1 s[k, yh:y, 0:xh] = tinv[k] # S_II,II = -T_II,II^-1 . T_II,I s[k, yh:y, xh:x] = -tinv[k].dot(t[k, yh:y, 0:xh]) return s
[docs]def t2z(t: npy.ndarray) -> NoReturn: """ Not Implemented Yet Convert scattering transfer parameters [#]_ to impedance parameters [#]_ Parameters ---------- t : complex array-like or number impedance parameters Returns ------- z : complex array-like or number scattering parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/Scattering_transfer_parameters#Scattering_transfer_parameters .. [#] http://en.wikipedia.org/wiki/impedance_parameters """ raise (NotImplementedError)
[docs]def t2y(t: npy.ndarray) -> NoReturn: """ Not Implemented Yet Convert scattering transfer parameters to admittance parameters [#]_ Parameters ---------- t : complex array-like or number t-parameters Returns ------- y : complex array-like or number admittance parameters See Also -------- s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ---------- .. [#] http://en.wikipedia.org/wiki/Scattering_transfer_parameters#Scattering_transfer_parameters """ raise (NotImplementedError)
[docs]def h2z(h: npy.ndarray) -> npy.ndarray: """ Converts hybrid parameters to z parameters [#]_ . Parameters ---------- h : :class:`numpy.ndarray` (shape fx2x2) hybrid parameter matrix Returns ------- z : numpy.ndarray impedance parameters See Also -------- inv : calculates inverse s-parameters s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ----------- .. [#] https://en.wikipedia.org/wiki/Two-port_network """ return z2h(h)
[docs]def h2s(h: npy.ndarray, z0: NumberLike = 50) -> npy.ndarray: """ convert hybrid parameters to s parameters Parameters ---------- h : complex array-like hybrid parameters z0 : complex array-like or number port impedances Returns ------- s : complex array-like scattering parameters """ return z2s(h2z(h), z0)
[docs]def s2h(s: npy.ndarray, z0: NumberLike = 50) -> npy.ndarray: """ Convert scattering parameters [#]_ to hybrid parameters [#]_ Parameters ---------- s : complex array-like scattering parameters z0 : complex array-like or number port impedances. Returns ------- h : complex array-like hybrid parameters References ---------- .. [#] http://en.wikipedia.org/wiki/S-parameters .. [#] http://en.wikipedia.org/wiki/Two-port_network#Hybrid_parameters_(h-parameters) """ return z2h(s2z(s, z0))
def z2h(z: npy.ndarray) -> npy.ndarray: """ Converts impedance parameters to hybrid parameters [#]_ . Parameters ---------- z : :class:`numpy.ndarray` (shape fx2x2) impedance parameter matrix Returns ------- h : numpy.ndarray hybrid parameters See Also -------- inv : calculates inverse s-parameters s2z s2y s2t z2s z2y z2t y2s y2z y2z t2s t2z t2y Network.s Network.y Network.z Network.t References ----------- .. [#] https://en.wikipedia.org/wiki/Two-port_network """ h = npy.array([ [(z[:, 0, 0] * z[:, 1, 1] - z[:, 1, 0] * z[:, 0, 1]) / z[:, 1, 1], -z[:, 1, 0] / z[:, 1, 1]], [z[:, 0, 1] / z[:, 1, 1], 1. / z[:, 1, 1]], ]).transpose() return h ## these methods are used in the secondary properties
[docs]def passivity(s: npy.ndarray) -> npy.ndarray: """ Passivity metric for a multi-port network. A metric which is proportional to the amount of power lost in a multiport network, depending on the excitation port. Specifically, this returns a matrix who's diagonals are equal to the total power received at all ports, normalized to the power at a single excitement port. mathematically, this is a test for unitary-ness of the s-parameter matrix [#]_. for two port this is .. math:: \sqrt( |S_{11}|^2 + |S_{21}|^2 \, , \, |S_{22}|^2+|S_{12}|^2) in general it is .. math:: \\sqrt( S^H \\cdot S) where :math:`H` is conjugate transpose of S, and :math:`\\cdot` is dot product. Note ---- The total amount of power dissipated in a network depends on the port matches. For example, given a matched attenuator, this metric will yield the attenuation value. However, if the attenuator is cascaded with a mismatch, the power dissipated will not be equivalent to the attenuator value, nor equal for each excitation port. Returns ------- passivity : :class:`numpy.ndarray` of shape fxnxn References ------------ .. [#] http://en.wikipedia.org/wiki/Scattering_parameters#Lossless_networks """ if s.shape[-1] == 1: raise (ValueError('Doesn\'t exist for one ports')) pas_mat = s.copy() for f in range(len(s)): pas_mat[f, :, :] = npy.sqrt(npy.dot(s[f, :, :].conj().T, s[f, :, :])) return pas_mat
[docs]def reciprocity(s: npy.ndarray) -> npy.ndarray: """ Reciprocity metric for a multi-port network. This returns the magnitude of the difference between the s-parameter matrix and its transpose. for two port this is .. math:: | S - S^T | where :math:`T` is transpose of S Parameters ---------- s : :class:`numpy.ndarray` of shape `fxnxn` s-parameter matrix Returns ------- reciprocity : :class:`numpy.ndarray` of shape `fxnxn` """ if s.shape[-1] == 1: raise (ValueError('Doesn\'t exist for one ports')) rec_mat = s.copy() for f in range(len(s)): rec_mat[f, :, :] = abs(s[f, :, :] - s[f, :, :].T) return rec_mat
## renormalize
[docs]def renormalize_s(s: npy.ndarray, z_old: NumberLike, z_new: NumberLike, s_def:str = S_DEF_DEFAULT) -> npy.ndarray: """ Renormalize a s-parameter matrix given old and new port impedances Note ---- This re-normalization assumes power-wave formulation per default. To use the pseudo-wave formulation, use s_def='pseudo'. However, results should be the same for real-valued characteristic impedances. See the [#Marks]_ and [#Anritsu]_ for more details. Note ---- This just calls :: z2s(s2z(s, z0=z_old), z0=z_new, s_def=s_def) Parameters ---------- s : complex array of shape `fxnxn` s-parameter matrix z_old : complex array of shape `fxnxn` or a scalar old (original) port impedances z_new : complex array of shape `fxnxn` or a scalar new port impedances s_def : str -> s_def : can be: 'power', 'pseudo' or 'traveling' Scattering parameter definition : 'power' for power-waves definition, 'pseudo' for pseudo-waves definition. 'traveling' corresponds to the initial implementation. Default is 'power'. NB: results are the same for real-valued characteristic impedances. Returns ------- :class:`numpy.ndarray` renormalized s-parameter matrix (shape `fxnxn`) See Also -------- Network.renormalize : method of Network to renormalize s fix_z0_shape s2z z2s References ---------- .. [#Marks] R. B. Marks and D. F. Williams, "A general waveguide circuit theory," Journal of Research of the National Institute of Standards and Technology, vol. 97, no. 5, pp. 533-561, 1992. .. [#Anritsu] Anritsu Application Note: Arbitrary Impedance, https://web.archive.org/web/20200111134414/https://archive.eetasia.com/www.eetasia.com/ARTICLES/2002MAY/2002MAY02_AMD_ID_NTES_AN.PDF?SOURCES=DOWNLOAD Examples -------- >>> s = zeros(shape=(101,2,2)) >>> renormalize_s(s, 50,25) """ if s_def not in S_DEFINITIONS: raise ValueError('s_def parameter should be either:', S_DEFINITIONS) # thats a heck of a one-liner! return z2s(s2z(s, z0=z_old, s_def=s_def), z0=z_new, s_def=s_def)
[docs]def fix_z0_shape(z0: NumberLike, nfreqs: int, nports: int) -> npy.ndarray: """ Make a port impedance of correct shape for a given network's matrix This attempts to broadcast z0 to satisfy npy.shape(z0) == (nfreqs,nports) Parameters ---------- z0 : number, array-like z0 can be: * a number (same at all ports and frequencies) * an array-like of length == number ports. * an array-like of length == number frequency points. * the correct shape ==(nfreqs,nports) nfreqs : int number of frequency points nports : int number of ports Returns ------- z0 : array of shape ==(nfreqs,nports) z0 with the right shape for a nport Network Examples -------- For a two-port network with 201 frequency points, possible uses may be >>> z0 = rf.fix_z0_shape(50 , 201,2) >>> z0 = rf.fix_z0_shape([50,25] , 201,2) >>> z0 = rf.fix_z0_shape(range(201) , 201,2) """ if npy.shape(z0) == (nfreqs, nports): # z0 is of correct shape. super duper.return it quick. return z0.copy() elif npy.isscalar(z0): # z0 is a single number return npy.array(nfreqs * [nports * [z0]]) elif len(z0) == nports: # assume z0 is a list of impedances for each port, # but constant with frequency return npy.array(nfreqs * [z0]) elif len(z0) == nfreqs: # assume z0 is a list of impedances for each frequency, # but constant with respect to ports return npy.array(nports * [z0]).T else: raise IndexError('z0 is not an acceptable shape')
## cascading assistance functions
[docs]def inv(s: npy.ndarray) -> npy.ndarray: """ Calculates 'inverse' s-parameter matrix, used for de-embedding This is not literally the inverse of the s-parameter matrix. Instead, it is defined such that the inverse of the s-matrix cascaded with itself is a unity scattering transfer parameter (T) matrix. .. math:: inv(s) = t2s({s2t(s)}^{-1}) where :math:`x^{-1}` is the matrix inverse. In words, this is the inverse of the scattering transfer parameters matrix transformed into a scattering parameters matrix. Parameters ---------- s : :class:`numpy.ndarray` (shape fx2nx2n) scattering parameter matrix. Returns ------- s' : :class:`numpy.ndarray` inverse scattering parameter matrix. See Also -------- t2s : converts scattering transfer parameters to scattering parameters s2t : converts scattering parameters to scattering transfer parameters """ # this idea is from lihan t = s2t(s) tinv = npy.linalg.inv(t) sinv = t2s(tinv) #for f in range(len(i)): # i[f, :, :] = npy.linalg.inv(i[f, :, :]) # could also be written as # # npy.mat(i[f,:,:])**-1 -- Trey return sinv
[docs]def flip(a: npy.ndarray) -> npy.ndarray: """ Invert the ports of a networks s-matrix, 'flipping' it over left and right. in case the network is 2n-port and n > 1, 'second' numbering scheme is assumed to be consistent with the ** cascade operator:: +--------+ +--------+ 0-|0 n|-n 0-|n 0|-n 1-|1 n+1|-n+1 flip 1-|n+1 1|-n+1 ... ... => ... ... n-1-|n-1 2n-1|-2n-1 n-1-|2n-1 n-1|-2n-1 +--------+ +--------+ Parameters ---------- a : :class:`numpy.ndarray` scattering parameter matrix. shape should be should be `2nx2n`, or `fx2nx2n` Returns ------- c : :class:`numpy.ndarray` flipped scattering parameter matrix See Also -------- renumber """ c = a.copy() n2 = a.shape[-1] m2 = a.shape[-2] n = int(n2/2) if (n2 == m2) and (n2 % 2 == 0): old = list(range(0,2*n)) new = list(range(n,2*n)) + list(range(0,n)) if(len(a.shape) == 2): c[new, :] = c[old, :] # renumber rows c[:, new] = c[:, old] # renumber columns else: c[:, new, :] = c[:, old, :] # renumber rows c[:, :, new] = c[:, :, old] # renumber columns else: raise IndexError('matrices should be 2nx2n, or kx2nx2n') return c
## COMMON CHECKS (raise exceptions) def check_frequency_equal(ntwkA: Network, ntwkB: Network) -> None: """ checks if two Networks have same frequency """ if assert_frequency_equal(ntwkA, ntwkB) == False: raise IndexError('Networks don\'t have matching frequency. See `Network.interpolate`') def check_z0_equal(ntwkA: Network, ntwkB: Network) -> None: """ checks if two Networks have same port impedances """ # note you should check frequency equal before you call this if assert_z0_equal(ntwkA, ntwkB) == False: raise ValueError('Networks don\'t have matching z0.') def check_nports_equal(ntwkA: Network, ntwkB: Network) -> None: """ checks if two Networks have same number of ports """ if assert_nports_equal(ntwkA, ntwkB) == False: raise ValueError('Networks don\'t have matching number of ports.') ## TESTs (return [usually boolean] values) def assert_frequency_equal(ntwkA: Network, ntwkB: Network) -> bool: """ """ return (ntwkA.frequency == ntwkB.frequency) def assert_z0_equal(ntwkA: Network, ntwkB: Network) -> bool: """ """ return (ntwkA.z0 == ntwkB.z0).all() def assert_z0_at_ports_equal(ntwkA: Network, k: int, ntwkB: Network, l: int) -> bool: """ """ return (ntwkA.z0[:, k] == ntwkB.z0[:, l]).all() def assert_nports_equal(ntwkA: Network, ntwkB: Network) -> bool: """ """ return (ntwkA.number_of_ports == ntwkB.number_of_ports) ## Other # don't belong here, but i needed them quickly # this is needed for port impedance mismatches def impedance_mismatch(z1: NumberLike, z2: NumberLike) -> npy.ndarray: """ creates a two-port s-matrix for a impedance mis-match Parameters ---------- z1 : number or array-like complex impedance of port 1 z2 : number or array-like complex impedance of port 2 Returns ------- s' : 2-port s-matrix for the impedance mis-match """ from .tlineFunctions import zl_2_Gamma0 gamma = zl_2_Gamma0(z1, z2) result = npy.zeros(shape=(len(gamma), 2, 2), dtype='complex') result[:, 0, 0] = gamma result[:, 1, 1] = -gamma result[:, 1, 0] = (1 + gamma) * npy.sqrt(1.0 * z1 / z2) result[:, 0, 1] = (1 - gamma) * npy.sqrt(1.0 * z2 / z1) return result
[docs]def two_port_reflect(ntwk1: Network, ntwk2: Network = None) -> Network: """ Generates a two-port reflective two-port, from two one-ports. Parameters ---------- ntwk1 : one-port Network object network seen from port 1 ntwk2 : one-port Network object, or None network seen from port 2. if None then will use ntwk1. Returns ------- result : Network object two-port reflective network Note ---- The resultant Network is copied from `ntwk1`, so its various properties(name, frequency, etc) are inherited from that Network. Examples -------- >>> short,open = rf.Network('short.s1p', rf.Network('open.s1p') >>> rf.two_port_reflect(short,open) """ result = ntwk1.copy() if ntwk2 is None: ntwk2 = ntwk1 s11 = ntwk1.s[:, 0, 0] s22 = ntwk2.s[:, 0, 0] s21 = npy.zeros(ntwk1.frequency.npoints, dtype=complex) result.s = npy.array( \ [[s11, s21], \ [s21, s22]]). \ transpose().reshape(-1, 2, 2) result.z0 = npy.hstack([ntwk1.z0, ntwk2.z0]) try: result.name = ntwk1.name + '-' + ntwk2.name except(TypeError): pass return result
def s2s_active(s: npy.ndarray, a:npy.ndarray) -> npy.ndarray: """ Returns active s-parameters for a defined wave excitation a. The active s-parameter at a port is the reflection coefficients when other ports are excited. It is an important quantity for active phased array antennas. Active s-parameters are defined by [#]_: .. math:: \mathrm{active}(s)_{m} = \sum_{i=1}^N\left( s_{mi} a_i \right) / a_m where :math:`s` are the scattering parameters and :math:`N` the number of ports Parameters ---------- s : complex array scattering parameters (nfreqs, nports, nports) a : complex array of shape (n_ports) forward wave complex amplitude (pseudowave formulation [#]_) Returns ------- s_act : complex array of shape (n_freqs, n_ports) active S-parameters for the excitation a See Also -------- s2z_active : active Z-parameters s2y_active : active Y-parameters s2vswr_active : active VSWR References ---------- .. [#] D. M. Pozar, IEEE Trans. Antennas Propag. 42, 1176 (1994). .. [#] D. Williams, IEEE Microw. Mag. 14, 38 (2013). """ # TODO : vectorize the for loop nfreqs, nports, nports = s.shape s_act = npy.zeros((nfreqs, nports), dtype='complex') s[ s == 0 ] = 1e-12 # solve numerical singularity for fidx in range(s.shape[0]): s_act[fidx] = npy.matmul(s[fidx], a) / a return s_act # shape : (n_freqs, n_ports) def s2z_active(s: npy.ndarray, z0: NumberLike, a: npy.ndarray) -> npy.ndarray: """ Returns the active Z-parameters for a defined wave excitation a. The active Z-parameters are defined by: .. math:: \mathrm{active}(z)_{m} = z_{0,m} \frac{1 + \mathrm{active}(s)_m}{1 - \mathrm{active}(s)_m} where :math:`z_{0,m}` is the characteristic impedance and :math:`\mathrm{active}(s)_m` the active S-parameter of port :math:`m`. Parameters ---------- s : complex array scattering parameters (nfreqs, nports, nports) z0 : complex array-like or number port impedances. a : complex array of shape (n_ports) forward wave complex amplitude Returns ------- z_act : complex array of shape (nfreqs, nports) active Z-parameters for the excitation a See Also -------- s2s_active : active S-parameters s2y_active : active Y-parameters s2vswr_active : active VSWR """ # TODO : vectorize the for loop nfreqs, nports, nports = s.shape z0 = fix_z0_shape(z0, nfreqs, nports) z_act = npy.zeros((nfreqs, nports), dtype='complex') s_act = s2s_active(s, a) for fidx in range(s.shape[0]): z_act[fidx] = z0[fidx] * (1 + s_act[fidx])/(1 - s_act[fidx]) return z_act def s2y_active(s: npy.ndarray, z0: NumberLike, a: npy.ndarray) -> npy.ndarray: """ Returns the active Y-parameters for a defined wave excitation a. The active Y-parameters are defined by: .. math:: \mathrm{active}(y)_{m} = y_{0,m} \frac{1 - \mathrm{active}(s)_m}{1 + \mathrm{active}(s)_m} where :math:`y_{0,m}` is the characteristic admittance and :math:`\mathrm{active}(s)_m` the active S-parameter of port :math:`m`. Parameters ---------- s : complex array scattering parameters (nfreqs, nports, nports) z0 : complex array-like or number port impedances. a : complex array of shape (n_ports) forward wave complex amplitude Returns ------- y_act : complex array of shape (nfreqs, nports) active Y-parameters for the excitation a See Also -------- s2s_active : active S-parameters s2z_active : active Z-parameters s2vswr_active : active VSWR """ nfreqs, nports, nports = s.shape z0 = fix_z0_shape(z0, nfreqs, nports) y_act = npy.zeros((nfreqs, nports), dtype='complex') s_act = s2s_active(s, a) for fidx in range(s.shape[0]): y_act[fidx] = 1/z0[fidx] * (1 - s_act[fidx])/(1 + s_act[fidx]) return y_act def s2vswr_active(s: npy.ndarray, a: npy.ndarray) -> npy.ndarray: """ Returns the active VSWR for a defined wave excitation a.. The active VSWR is defined by : .. math:: \mathrm{active}(vswr)_{m} = \frac{1 + |\mathrm{active}(s)_m|}{1 - |\mathrm{active}(s)_m|} where :math:`\mathrm{active}(s)_m` the active S-parameter of port :math:`m`. Parameters ---------- s : complex array scattering parameters (nfreqs, nports, nports) a : complex array of shape (n_ports) forward wave complex amplitude Returns ------- vswr_act : complex array of shape (nfreqs, nports) active VSWR for the excitation a See Also -------- s2s_active : active S-parameters s2z_active : active Z-parameters s2y_active : active Y-parameters """ nfreqs, nports, nports = s.shape vswr_act = npy.zeros((nfreqs, nports), dtype='complex') s_act = s2s_active(s, a) for fidx in range(s.shape[0]): vswr_act[fidx] = (1 + npy.abs(s_act[fidx]))/(1 - npy.abs(s_act[fidx])) return vswr_act