One Port Tiered Calibration

Intro

A one-port network analyzer can be used to measure a two-port device, provided that the device is reciprocal. This is accomplished by performing two calibrations, which is why its called a tiered calibration.

First, the VNA is calibrated at the test-port like normal. This is called the first tier. Next, the device is connected to the test-port, and a calibration is performed at the far end of the device, the second tier. A diagram is shown below,

In [1]:
from IPython.display import SVG
SVG('oneport_tiered_calibration/images/boxDiagram.svg')
Out[1]:
../../_images/examples_metrology_One_Port_Tiered_Calibration_3_0.svg

This notebook will demonstrate how to use skrf to do a two-tiered one-port calibration. We’ll use data that was taken to characterize a waveguide-to-CPW probe. So, for this specific example the diagram above looks like:

In [2]:
SVG('oneport_tiered_calibration/images/probe.svg')
Out[2]:
../../_images/examples_metrology_One_Port_Tiered_Calibration_5_0.svg

Some Data

The data available is the folders 'tier1/' and 'tier2/'.

In [3]:
ls oneport_tiered_calibration/
images/  probe.s2p  tier1/  tier2/

(if you dont have the git repo for these examples, the data for this notebook can be found here)

In each folder you will find the two sub-folders, called 'ideals/' and 'measured/'. These contain touchstone files of the calibration standards ideal and measured responses, respectively.

In [4]:
ls oneport_tiered_calibration/tier1/
ideals/  measured/

The first tier is at waveguide interface, and consisted of the following set of standards

  • short
  • delay short
  • load
  • radiating open (literally an open waveguide)
In [5]:
ls oneport_tiered_calibration/tier1/measured/
ds.s1p  load.s1p  ro.s1p  short.s1p

Creating Calibrations

Tier 1

First defining the calibration for Tier 1

In [6]:
from skrf.calibration import OnePort
import skrf as rf
%matplotlib inline
from pylab import *
rf.stylely()


tier1_ideals = rf.read_all_networks('oneport_tiered_calibration/tier1/ideals/')
tier1_measured = rf.read_all_networks('oneport_tiered_calibration/tier1/measured/')


tier1 = OnePort(measured = tier1_measured,
                ideals = tier1_ideals,
                name = 'tier1',
                sloppy_input=True)
tier1
Out[6]:
OnePort Calibration: 'tier1', 500.0-750.0 GHz, 401 pts, 4-standards

Because we saved corresponding ideal and measured standards with identical names, the Calibration will automatically align our standards upon initialization. (More info on creating Calibration objects this can be found in the docs.)

Similarly for the second tier 2,

Tier 2

In [7]:
tier2_ideals = rf.read_all_networks('oneport_tiered_calibration/tier2/ideals/')
tier2_measured = rf.read_all_networks('oneport_tiered_calibration/tier2/measured/')


tier2 = OnePort(measured = tier2_measured,
                ideals = tier2_ideals,
                name = 'tier2',
                sloppy_input=True)
tier2
Out[7]:
OnePort Calibration: 'tier2', 500.0-750.0 GHz, 401 pts, 5-standards

Error Networks

Each one-port Calibration contains a two-port error network, that is determined from the calculated error coefficients. The error network for tier1 models the VNA, while the error network for tier2 represents the VNA and the DUT. These can be visualized through the parameter 'error_ntwk'.

For tier 1,

In [8]:
tier1.error_ntwk.plot_s_db()
title('Tier 1 Error Network')
/home/docs/checkouts/readthedocs.org/user_builds/scikit-rf/conda/stable/lib/python3.5/site-packages/scikit_rf-0.14.9-py3.5.egg/skrf/calibration/calibration.py:1051: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.
To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.
  abcTmp, residualsTmp = npy.linalg.lstsq(Q,m)[0:2]
Out[8]:
Text(0.5,1,'Tier 1 Error Network')
../../_images/examples_metrology_One_Port_Tiered_Calibration_22_2.png

Similarly for tier 2,

In [9]:
tier2.error_ntwk.plot_s_db()
title('Tier 2 Error Network')
/home/docs/checkouts/readthedocs.org/user_builds/scikit-rf/conda/stable/lib/python3.5/site-packages/scikit_rf-0.14.9-py3.5.egg/skrf/calibration/calibration.py:1051: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.
To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.
  abcTmp, residualsTmp = npy.linalg.lstsq(Q,m)[0:2]
Out[9]:
Text(0.5,1,'Tier 2 Error Network')
../../_images/examples_metrology_One_Port_Tiered_Calibration_24_2.png

De-embedding the DUT

As previously stated, the error network for tier1 models the VNA, and the error network for tier2 represents the VNA+DUT. So to deterine the DUT’s response, we cascade the inverse S-parameters of the VNA with the VNA+DUT.

\[DUT = VNA^{-1}\cdot (VNA \cdot DUT)\]

In skrf, this is done as follows

In [10]:
dut = tier1.error_ntwk.inv ** tier2.error_ntwk
dut.name = 'probe'
dut.plot_s_db()
title('Probe S-parameters')
ylim(-60,10)
Out[10]:
(-60, 10)
../../_images/examples_metrology_One_Port_Tiered_Calibration_27_1.png

You may want to save this to disk, for future use,

dut.write_touchstone()
In [11]:
ls probe*
probe.s2p