TDR or Impedance mismatch analysis

[lowpon]

Hi all,
First I'd like to thank M. Liebig for this amazing tool and M. Jagos for its FreeCAD to openEMS very helpful macro.
I started few weeks ago with openEMS and got recently my first results.
Based on tutorials, as shown below, it was easy to plot s-parameters in the frequency domain or voltage in the time domain, but how could I plot the impedance in the time domain now ?
This would be a TDR analysis, showing impedance mismatch along the transmission line.
Thanks for your help

[LubomirJagos]

Hi, thanks for using my addon, what do you mean plot impedance in time domain? Impedance is not changing over time, there are voltage and current captured in time domain and impedance is always calculated as U/I

[thliebig]

It's not about time. Its about location. The idea is to send a signal and from the reflections determine how the impedance changes a long the length of the e.g. transmission line. Most importantly to e.g. find damages on a TL.

See here.

I'm not aware that anybody has done this with openEMS thus far and I'm not familiar with the details of TDR.
I only know that the FDTD method can be used for it.
But I fear that you have to implement the necessary processing yourself.

[thliebig]

But on reading your description again I would agree that calling it "Impedance in Time-Domain" is not really accurate and can indeed be a bit misleading...

[lowpon]

You're right, I have modified the title.
I'll come back soon with first results following a step excitation, but I'm not sure to be able to define the risetime corresponding to my signal speed. For sure, Ohm's law will be convenient.

[VolkerMuehlhaus]

@lowpon Just in case someone wants to post example code: Do you use openEMS with Python or Matlab?

I have done TDR analysis using other EM tools (appnote) and can provide some basic hints:
My preferred excitation for line discontinuity analysis is a simple step transition: voltage off a short period of time, then jump to voltage on and hold that voltage.
Simulation timesteps are used here to limit the FDTD simulation time: we only need to capture a short period of time after the initial pulse, it is not necessary to run further until energy threshold is reached.
For evaluation I look at reflected voltage, step down means the impedance at that point reached by the pulse is too low (or capacitive) and step up means impdance is too high (or inductive).
To get started, I recommend to build some simple test structures line a line with known discontinuities, to get familar with the resulting patterns in reflected signal in time domain.

What I described above is based on reflected voltage for a single step, and things get complicated when you reach a time where multiple reflections between multiple discontinuities show up. But as you can see from the TDR appnote that I linked above, it is already quite useful.

Getting true impedance over time (or distance) without that multi-reflection issue is more complicated. One solution that I use at work is the TDR testbench in Keysight ADS, which removes these multi-reflection artefacts. I don't know how to perform that task in openEMS.

[lowpon]

Thank you @VolkerMuehlhaus
Here are the last results following your reply.
I still don't know why impedance seems to be referenced to 100ohm and voltage levels different from yours

Below, an extract but the complete code is available here
https://github.com/lowpon/openEMS-TDR/blob/76ad73a71ddd2fb86f5d6afb3dc4f3e16e1b27fb/PCB_TDR

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% POST-PROCESSING AND TIME DOMAIN PLOT GENERATION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

freq = linspace( fstart, fstop, numfreq );
port{1} = calcPort( port{1}, Sim_Path, freq, 'RefImpedance', Z0);
port{2} = calcPort( port{2}, Sim_Path, freq, 'RefImpedance', Z0);

% port.ut.tot total voltage (time-domain)
% port.it.tot total current (time-domain)
% port.ut.time voltage time vector
% port.it.time current time vector (same as voltage)

U1 = port{1}.ut.tot;
U2 = port{2}.ut.tot;
I1 = port{1}.it.tot;
I2 = port{2}.it.tot;
t = port{1}.ut.time;

U1_inc = 0.5 * (U1 + I1.* Z0);
U1_ref = U1 - U1_inc;
U2_inc = 0.5 * (U2 + I2.* Z0);
U2_ref = U2 - U2_inc;

figure
plot( t, U1./ U1_inc, 'k-', 'Linewidth', 2 );
hold on;
plot( t, U2./ U1_inc, 'r--', 'Linewidth', 2 );
hold on;
plot( t, U1_ref./ U1_inc, 'b--', 'Linewidth', 2 );
%ylim([0 2]);
xlim([0 6e-10]);
grid on;
grid minor on;
legend( 'U1', 'U2', 'U1 ref' );
ylabel('Port voltages (normalized to incident)');
xlabel('Time (s)');
savefig('voltages.png');

%% estimate impedance magnitude
r = U1_ref./ U1_inc;
Z = Z0 * (1+r)./(1-r);

figure
plot( t, Z, 'b-', 'Linewidth', 2 );
ylim([60 120]);
xlim([0 6e-10]);

grid on;
grid minor on;

title( 'Impedance vs Time' );
xlabel( 'Time (s)' );
ylabel( 'Impedance (ohm)' );
legend( 'Z' );

[VolkerMuehlhaus]

We can't reproduce your issue because you didn't share the model, only the plotting part. You should check if port impedances are consistent between model code and plotting code.

[lowpon]

The Freecad model, XML, STL, model code, plotting code and configuration file for @LubomirJagos plugin are now available here
https://github.com/lowpon/openEMS-TDR/blob/0a2b433749edc7274c32ee651730e4f142264606/PCB.FCStd

[VolkerMuehlhaus]

Looking at your port 2 voltage above, that also looks unexpected. I guess the issue is more than just port impedances.

Your XML isn't easy to debug, because it links the STL files in your file system locations. I give up here, this turns out to be very time consuming with your workflow. Hopefully Lubomir can help you, he is more familiar with the workflow that you used.

Best regards
Volker

[lowpon]

Thanks for your time Volker
Cross fingers with @LubomirJagos
Regards

[biergaizi]

Based on tutorials, as shown below, it was easy to plot s-parameters in the frequency domain or voltage in the time domain, but how could I plot the impedance in the time domain now ?

TL;DR: You can calculate TDR responses from S-parameters using the powerful Python software library scikit-rf with 1 line of code. I've used it with both measured data and openEMS simulation results and it works perfectly (of course, within the limitation of calculating Inverse Fourier Transform from S-parameters). Read the documentation of scikit-rf for more information.

Using S-parameters for time-domain simulations like these is supported by almost all commercial and even some free RF circuit simulators. This is the main reason why I think using custom time-domain excitation within openEMS is usually unnecessary. I'd like to think of openEMS as a virtual network analyzer, once you've obtained the frequency-domain S-parameters, one can do nearly every kind of further analysis imaginable using standard RF circuit tools at its downstream (but do beware causality and passivity). Of course, trying to just openEMS as "just" a VNA can be inefficient - you're simulating in time domain and converting it to frequency domain before converting it to time domain again (with an appropriate simulation setup, one can avoid the extra work), but the advantage is that one can use tools one is already familiar with.

---

By taking an Inverse Fourier Transform, it's possible to convert S11 measurements from a VNA to its equivalent time-domain response as measured by a TDR. Previously, this capability is often exclusive in expensive simulation packages or in the firmware of expensive VNAs. Now, with the power of scikit-rf, a free and open source Python software library for RF/microwave modeling and analysis, it's accessible to everyone with basic programming knowledge.

Here's a demo from my recent experiment (this is only meant to be a quick example, the measurement is not fully calibrated and the parameters used for the calculations are not optimized, so please don't complain too much about the data).

To evaluate the impedance discontinuity and signal integrity impact caused by a 1206 resistor footprint, I fabricated a test fixture shown in the picture below.

It's a 4-layer circuit board with three solid ground planes. Two through-hole SMA connectors are located on both ends, with a 50-ohm microstrip in between. At the center is the Device Under Test, a 0-ohm, 1206 resistor. Also, to compensate for the excess capacitance caused by the large resistor pads, the ground plane under the resistor body is partially removed.

After I've received the board, I measured its S11 from 10 MHz to 4 GHz using a Vector Network Analyzer. It shows the return loss is good up to 1.2 GHz. But is it the full picture?

Using the scikit-rf software library and the following Python code, we can transform the data from frequency domain to time domain.

import sys
import skrf
import matplotlib.pyplot as plt
skrf.stylely()

network = skrf.Network(sys.argv[1])
network_dc = network.extrapolate_to_dc(kind='linear')

plt.figure()
plt.title("Time Domain Reflectometry")
network_dc.s11.plot_z_time_step(window='hamming', label="impedance")
plt.xlim((-0.5, 1.5))

plt.tight_layout()
plt.show()

This calculated TDR plot immediately reveals that the test fixture was poorly designed with non-ideal SMA-to-microstrip transitions. When the signal hits the first SMA connector, the instantaneous impedance drops to 45 ohms due to a capacitive discontinuity, then it hits the 50-ohm trace, hits the device-under-test, hits the 50-ohm trace again, and finally hits the second connector.

In fact, after de-embedding, it turned out that the resistor footprint only has 20 dB return loss at 800 MHz, not 1.2 GHz. The bad SMA connector footprints and the resistor footprint actually compensated each other. It would be difficult to spot this problem using the Smith Chart, on the other hand, it's obvious from the computed TDR response.

You can find more information from scikit-rf's documentation, Time domain reflectometry, measurement vs simulation. scikit-rf also supports time-gating, it's possible to use time-gating as a simple way to de-embed the connectors from the DUT by deleting the reflections from the time domain, see Time Domain and Gating.

It's also worth pointing out that in principle, all calibration and de-embedding techniques developed for VNA measurements can also be applied to simulation data, such as SOLT, TRL, or IEEE P370 - all of these are implemented in scikit-rf, just pass the S-parameters to scikit-rf and call the APIs, and you get calibrated results. In my opinion, these are especially useful as VNA calibration is a solved problem with mature solutions, so one can use pre-existing tools to do that. For example, if the signal launch at the port is imperfect, one can create a virtual SOLT test fixture in openEMS and run those simulations as "control", then those mismatches can be removed in later analysis.

[VolkerMuehlhaus]

This is very useful, thank you!

[lowpon]

Even if I'd rather work with the native time domain data, I really appreciate your scikit-rf proposal where I discover your huge and inspiring contribution. Thanks @biergaizi