"""
distributedCircuit (:mod:`skrf.media.distributedCircuit`)
============================================================
A transmission line mode defined in terms of distributed impedance and admittance values.
.. autosummary::
:toctree: generated/
DistributedCircuit
"""
from numpy import sqrt, real, imag
from .media import Media, DefinedGammaZ0
from ..constants import NumberLike
from typing import Union, TYPE_CHECKING
if TYPE_CHECKING:
from .. frequency import Frequency
[docs]class DistributedCircuit(Media):
r"""
A transmission line mode defined in terms of distributed impedance and admittance values.
Parameters
------------
frequency : :class:`~skrf.frequency.Frequency` object
frequency band of the media
z0 : number, array-like, or None
the port impedance for media. Only needed if its different
from the characteristic impedance of the transmission
line. if z0 is None then will default to Z0
C : number, or array-like
distributed capacitance, in F/m
L : number, or array-like
distributed inductance, in H/m
R : number, or array-like
distributed resistance, in Ohm/m
G : number, or array-like
distributed conductance, in S/m
Notes
-----
if C,I,R,G are vectors they should be the same length
:class:`DistributedCircuit` is `Media` object representing a
transmission line mode defined in terms of distributed impedance
and admittance values.
A `DistributedCircuit` may be defined in terms
of the following attributes:
================================ ================ ================
Quantity Symbol Property
================================ ================ ================
Distributed Capacitance :math:`C^{'}` :attr:`C`
Distributed Inductance :math:`L^{'}` :attr:`L`
Distributed Resistance :math:`R^{'}` :attr:`R`
Distributed Conductance :math:`G^{'}` :attr:`G`
================================ ================ ================
The following quantities may be calculated, which are functions of
angular frequency (:math:`\omega`):
=================================== ================================================== ==============================
Quantity Symbol Property
=================================== ================================================== ==============================
Distributed Impedance :math:`Z^{'} = R^{'} + j \omega L^{'}` :attr:`Z`
Distributed Admittance :math:`Y^{'} = G^{'} + j \omega C^{'}` :attr:`Y`
=================================== ================================================== ==============================
The properties which define their wave behavior:
=================================== ============================================ ==============================
Quantity Symbol Method
=================================== ============================================ ==============================
Characteristic Impedance :math:`Z_0 = \sqrt{ \frac{Z^{'}}{Y^{'}}}` :func:`Z0`
Propagation Constant :math:`\gamma = \sqrt{ Z^{'} Y^{'}}` :func:`gamma`
=================================== ============================================ ==============================
Given the following definitions, the components of propagation
constant are interpreted as follows:
.. math::
+\Re e\{\gamma\} = \text{attenuation}
-\Im m\{\gamma\} = \text{forward propagation}
See Also
--------
from_media
"""
[docs] def __init__(self, frequency: Union['Frequency', None] = None,
z0: Union[NumberLike, None] = None,
C: NumberLike = 90e-12, L: NumberLike = 280e-9,
R: NumberLike = 0, G: NumberLike = 0,
*args, **kwargs):
super().__init__(frequency=frequency,
z0=z0)
self.C, self.L, self.R, self.G = C,L,R,G
def __str__(self) -> str:
f=self.frequency
try:
output = \
'Distributed Circuit Media. %i-%i %s. %i points'%\
(f.f_scaled[0],f.f_scaled[-1],f.unit, f.npoints) + \
'\nL\'= %.2f, C\'= %.2f,R\'= %.2f, G\'= %.2f, '% \
(self.L, self.C,self.R, self.G)
except(TypeError):
output = \
'Distributed Circuit Media. %i-%i %s. %i points'%\
(f.f_scaled[0],f.f_scaled[-1],f.unit, f.npoints) + \
'\nL\'= %.2f.., C\'= %.2f..,R\'= %.2f.., G\'= %.2f.., '% \
(self.L[0], self.C[0],self.R[0], self.G[0])
return output
def __repr__(self) -> str:
return self.__str__()
[docs] @classmethod
def from_csv(self, *args, **kw):
"""
Create a `DistributedCircuit` from numerical values stored in a csv file.
The csv file format must be written by the function :func:`write_csv`,
or similar method which produces the following format::
f[$unit], Re(Z0), Im(Z0), Re(gamma), Im(gamma), Re(port Z0), Im(port Z0)
1, 1, 1, 1, 1, 1, 1
2, 1, 1, 1, 1, 1, 1
.....
See Also
--------
write_csv
"""
d = DefinedGammaZ0.from_csv(*args,**kw)
return self.from_media(d)
@property
def Z(self) -> NumberLike:
r"""
Distributed Impedance, :math:`Z^{'}`.
Defined as
.. math::
Z^{'} = R^{'} + j \omega L^{'}
Returns
-------
Z : npy.ndarray
Distributed impedance in units of ohm/m
"""
w = self.frequency.w
Z = self.R + 1j*w*self.L
# Avoid divide by zero.
# Needs to be imaginary to avoid all divide by zeros in the media class.
Z[Z.imag == 0] += 1j*1e-12
return Z
@property
def Y(self) -> NumberLike:
r"""
Distributed Admittance, :math:`Y^{'}`.
Defined as
.. math::
Y^{'} = G^{'} + j \omega C^{'}
Returns
-------
Y : npy.ndarray
Distributed Admittance in units of S/m
"""
w = self.frequency.w
Y = self.G + 1j*w*self.C
# Avoid divide by zero.
# Needs to be imaginary to avoid all divide by zeros in the media class.
Y[Y.imag == 0] += 1j*1e-12
return Y
@property
def Z0(self) -> NumberLike:
r"""
Characteristic Impedance, :math:`Z0`
.. math::
Z_0 = \sqrt{ \frac{Z^{'}}{Y^{'}}}
Returns
-------
Z0 : npy.ndarray
Characteristic Impedance in units of ohms
"""
return sqrt(self.Z/self.Y)
@property
def gamma(self) -> NumberLike:
r"""
Propagation Constant, :math:`\gamma`.
Defined as,
.. math::
\gamma = \sqrt{ Z^{'} Y^{'}}
Returns
-------
gamma : npy.ndarray
Propagation Constant,
Note
----
The components of propagation constant are interpreted as follows:
* positive real(gamma) = attenuation
* positive imag(gamma) = forward propagation
"""
return sqrt(self.Z*self.Y)