Making 2-port measurements without S-Params

[Andrew_K]

Hi,

I would like to make some 2-port measurements of a few circuits. However, S-params are fairly useless, since my circuits are not at Z0=50 ohm, and I'm not sure there is a characteristic impedance. So, a standard VNA is basically useless for my purposes.

Is there any standard test equipment that can measure, for example, Z params or ABCD params?


I do have access to an Impedance Analyzer, the 4990A. It is a 1-port device. Measuring Z11 and Z22 is trivial. However, Z12 and Z21 might not be possible.
Can multiple 1-port measurements be combined to create a 2-port model?

Otherwise, I suppose, I could use a signal generator and 4-probe oscilloscope with active/differential probes.
Make a shunt, measure voltage across the shunt, measure voltage across port 1, then measure voltage across port 2. That should give me Z11 and Z21.
A sweep would be rather annoying, though, but I guess I could automate measurement with pyvisa...
I've found that a scope's phase measurements aren't the most useful, either. Can't do expanded phase like a VNA or impedance analyzer might have.


Has anyone done anything like this before?

[Terry Bites]

Use a matching transformer?

[mag_therm]

What type of circuits, are they linear?
 If not possible to get inside, there are 3 ways to measure:
Open circuit impedance parameters
Short circuit admittance parameters (does involve s/c on output though)
Hybrid parameters

Usually only one of those 3 test will give the 4 parameters.

If non linear, parameters might become dependent on internal current or voltages. (partial derivatives are used)
For example the small signal hybrid pi for bjt is only an approximation over certain input signal levels.

A text book might be needed.
I think it could be said that S params are a more recent  subset of network  measurement to make it easy for the 50 Ohm users. (swr etc)

[TheUnnamedNewbie]

Hi,

I would like to make some 2-port measurements of a few circuits. However, S-params are fairly useless, since my circuits are not at Z0=50 ohm, and I'm not sure there is a characteristic impedance. So, a standard VNA is basically useless for my purposes.

Is there any standard test equipment that can measure, for example, Z params or ABCD params?


I do have access to an Impedance Analyzer, the 4990A. It is a 1-port device. Measuring Z11 and Z22 is trivial. However, Z12 and Z21 might not be possible.
Can multiple 1-port measurements be combined to create a 2-port model?

Otherwise, I suppose, I could use a signal generator and 4-probe oscilloscope with active/differential probes.
Make a shunt, measure voltage across the shunt, measure voltage across port 1, then measure voltage across port 2. That should give me Z11 and Z21.
A sweep would be rather annoying, though, but I guess I could automate measurement with pyvisa...
I've found that a scope's phase measurements aren't the most useful, either. Can't do expanded phase like a VNA or impedance analyzer might have.


Has anyone done anything like this before?

If it is a passive circuit (or sometimes even an active circuit very far from any non-linearities, but don't quote me on that one), measuring s-parameters will still work. We do this all the time in simulations where we export s-parameter files based on 50 ohm impedances, even though they are (for example) complex matching networks matching something like say 16-56j ohm to 12-43j ohm.

The only issues are that if your impedances are very far from 50 ohm, you get into problems with measurement uncertainty.

After getting the s-parameters, you can just hook them up to ports with whatever impedance you want in a simulator, or even analyze thigs like gmax etc...

And there is always an impedance - it is just how voltage and current are related at your ports.

You cannot really combine one-port measurements to give two-port parameters. Just think of the following: Imagine two circuits, both black boxes, where each port is just connected to a 50 ohm resistor. However, in the second box, an idea amplifier is connected and amplifies the voltage over the resistor at port one and puts it at port 2. Both of these have the exact same S/Z11 and S/Z22, yet clearly very differnt 21 and 12 parameters.

[The Electrician]

Hi,

I would like to make some 2-port measurements of a few circuits.

Over what frequency range do you need to make measurements?  Do you need only a few discrete frequencies, or a complete parameterization over a band?  Is you circuit passive or active?

[Andrew_K]

Use a matching transformer?

Perhaps. Few concerns: Frequency range is rather large. 5Hz to ~1MHz. Impedance changes dramatically throughout that range.

Over what frequency range do you need to make measurements?  Do you need only a few discrete frequencies, or a complete parameterization over a band?  Is you circuit passive or active?

I'm looking for complete parameterization over a sweep, ideally.

The part I'm looking to characterize is passive. This signal path feeds into an amplifier, but since those parameters are known, I'm looking to get the characterization of the passive circuit.
I have schematics of everything that can be taken apart or separated into discrete elements.

There are a few elements that don't have a nice lumped element model. One is a high impedance cable. It functions like a transmission line, but I'm having trouble getting parameters from it with an impedance analyzer.

If not possible to get inside, there are 3 ways to measure:
Open circuit impedance parameters
Short circuit admittance parameters (does involve s/c on output though)
Hybrid parameters

That's a really good point about hybrid parameters!
I do already have the open impedance(h22), short admittance(h11), and high impedance voltage transfer function (h12).

And I see on wikipedia that h12 = -h21 for reciprocal networks (which mine happens to be)!

A text book might be needed.
I think it could be said that S params are a more recent  subset of network  measurement to make it easy for the 50 Ohm users. (swr etc)

I have been reading every appnote and book I can find. I would love recommendations on more books to read and study, though.

Definitely lot of shortcuts from S-parameters being dedicated to 50 ohm. Has made my analysis more challenging/interesting, seeing as most app notes and literature is based on S.

[virtualparticles]

You may be able to extract a model of your circuit using chain parameter analysis. See the attached article written by yours truly. As noted earlier, impedances far from 50 ohms will add uncertainty to the measurement.

[The Electrician]

Over what frequency range do you need to make measurements?  Do you need only a few discrete frequencies, or a complete parameterization over a band?  Is you circuit passive or active?

I'm looking for complete parameterization over a sweep, ideally.

The part I'm looking to characterize is passive. This signal path feeds into an amplifier, but since those parameters are known, I'm looking to get the characterization of the passive circuit.
I have schematics of everything that can be taken apart or separated into discrete elements.

There are a few elements that don't have a nice lumped element model. One is a high impedance cable. It functions like a transmission line, but I'm having trouble getting parameters from it with an impedance analyzer.

I ask again: "Over what frequency range do you need to make measurements?"

[TheUnnamedNewbie]

Definitely lot of shortcuts from S-parameters being dedicated to 50 ohm. Has made my analysis more challenging/interesting, seeing as most app notes and literature is based on S.

As I said earlier, there is no reason for s-parameters to be limited to 50 ohm,and for passive networks, even if you use a 50 ohm VNA to measure the s-parameters, you can still measure a network with non-50 ohm impedances. S-parameters completly define a network, just like ABCD or Y or Z or whatever parameters. There is math to transition between them. 

[mag_therm]

Frequency range already given  post #5

[The Electrician]

Frequency range already given  post #5

How embarassing! 

I missed it because I went directly to the part of his post where he was responding to my questions and the frequency range was not there; it was in response to a question about a matching transformer.

My next question to Andrew_K is how much budget money do you have? Is this a company project, or are you a student?

The instrument you need is the Hioki IM3570 impedance analyzer: https://www.hioki.com/us-en/products/lcr-meters/3-ghz/id_5772

It covers the range 4 Hz to 5 MHz, and it only costs about $10000. It is available to rent.  I've used one to determine the ABCD parameters of small audio transformers.

[Andrew_K]

As I said earlier, there is no reason for s-parameters to be limited to 50 ohm,and for passive networks, even if you use a 50 ohm VNA to measure the s-parameters, you can still measure a network with non-50 ohm impedances. S-parameters completly define a network, just like ABCD or Y or Z or whatever parameters. There is math to transition between them. 

This is true, however, I was running into significant errors given the mismatch.

The instrument you need is the Hioki IM3570 impedance analyzer: https://www.hioki.com/us-en/products/lcr-meters/3-ghz/id_5772

It covers the range 4 Hz to 5 MHz, and it only costs about $10000. It is available to rent.  I've used one to determine the ABCD parameters of small audio transformers.

I mentioned that I have access to an Impedance Analyzer, the 4990A.

I used the impedance analyzer to get H11 and H22, then used a gain-phase analyzer (high impedance probes) to determine H12. I then determined H21 (H21 = -H12 by reciprocal network).


So I now have h parameters across the frequency range I wanted. But, I may be a complete idiot.

I had read that LT Spice could handle S parameters, and I assumed it could handle other network parameters, or, at the least, I could use behavioral sources and frequency tables to simulate:



The S-parameter model seems to have issues. Because again, I'm not at 50 ohms. The mismatch seems too significant, even if it should be equivalent mathematically.

Unfortunately, the behavioral R is largely undocumented and completely unstable. https://ltwiki.org/?title=B_sources_%28complete_reference%29

Is there any sensible way to simulate 2-port networks with circuit elements together?

[The Electrician]

Is there any sensible way to simulate 2-port networks with circuit elements together?

Could you explain what you mean by this in some detail?  How about a block diagram or schematic of what's in your two-port?  Is the high impedance cable from another thread part of the signal path of this two port?

[Andrew_K]

Could you explain what you mean by this in some detail?  How about a block diagram or schematic of what's in your two-port? 

Sure, let me explain what I am trying / want to do.

I have a few subcircuits that do not seem to play nice with lumped element analysis, or are complete black boxes to me. But, they are in the signal path and cannot be changed.

Some of the "signal of interest" that my circuit measures is actually being "distorted" by the circuit response. If the transfer function is known, I can reasonably compensate the signal in a later (independent / buffered) stage by boosting. Much like Oscilloscope Probe compensation. https://www.electronics-notes.com/articles/test-methods/oscilloscope/scope-probe-compensation.php
 
I wanted to model the circuit to find the zeros/poles of the entire circuit. More importantly though, I want to determine how the input impedance or other changes will affect the response / zeros & poles.

A simple H(s) transfer function is not sufficient for determining impact of input impedance or loading. And the transfer function of each piece individually does not correlate to the entire H(s).
My understanding is that a proper 2-port network should encapsulate all of the necessary information.

Is the high impedance cable from another thread part of the signal path of this two port?

Yes, the high impedance cable is one of the circuits in the signal path. The LTRA model in spice does NOT play nice with high R.


I would like to combine 2-port networks with circuit elements in the same simulation, so I can combine the "known" circuits with the "black box" circuits.

Perhaps it would be better to convert the "known" circuits to 2-port networks, then use purely 2-port analysis?

[mag_therm]

Sounds interesting.
I use qucs and have not tried specifically, but it has VCIS and ICVS etc , presumably LT does too.
As you are owner of the 2 port models , they don't have to follow the standard hybrid model.
You can for example put lumped components inside yours .
A classical example I think is to look at the way Giacoletto morphed the standard hybrid 2 port model of common emitter bjt  into the hybrid pi.

It is similar to Design of Experiment (DOE) where a model is created not so much  based on physics of the real system,  but on forcing the model to approximate your real system tests  subject to limits on input variable range etc.

[Andrew_K]

Sounds interesting.
I use qucs and have not tried specifically, but it has VCIS and ICVS etc , presumably LT does too.
As you are owner of the 2 port models , they don't have to follow the standard hybrid model.
You can for example put lumped components inside yours .
A classical example I think is to look at the way Giacoletto morphed the standard hybrid 2 port model of common emitter bjt  into the hybrid pi.

It is similar to Design of Experiment (DOE) where a model is created not so much  based on physics of the real system,  but on forcing the model to approximate your real system tests  subject to limits on input variable range etc.

VCIS and ICVS do work reasonably well in LT spice for frequency analysis. Instead of doing an arbitrary impedance, I needed to use the VCIS and ICVS.


So I'm able to measure the h parameters. h11 and h22 with an impedance analyzer, h12 by using a gain-phase analyzer.
However, I'm noticing the model of the network isn't passive. For some reason, when hooked up to a voltage source, the output of the model goes above 0dB.
This is strange, since the device is 100% passive.

There must be error somewhere in my measurements. My hunch is the h22 open-circuit admittance isn't being measured well. I think the open-impedance is too high for my impedance analyzer.
That, or, there is too much variation when switching between devices...

Is there any alternate way to derive or measure h22? If the network is symmetrical, the determinant = 1. However, not all components are symmetrical.
Could I, for example, use a known load to measure and solve for the open admittance?
Could I take other measurements to derive or convert to the open admittance?


Alternately, could I use a transformer, or cascaded transformers, to take proper S measurements to reduce the mis-match for a standard VNA?
The DC R = 30k, 60k, for my components.
I know some transformers are 50 ohm characteristic, but I'm not really sure what that means for a transformer.

[mag_therm]

If there are reactive terms +/- j  in the parameters, then it is possible the voltage (not power)  can "ring up" above 0dB
But that would need both L and C  ( + and - j terms)

[The Electrician]

Andrew_K, you say:

"I have a few subcircuits that do not seem to play nice with lumped element analysis, or are complete black boxes to me. But, they are in the signal path and cannot be changed."

How do you simulate your subcircuits?  Do you have a parameterization of each one?  Are their two-port parameters known?  Which parameters are used to describe them?  Can you show your signal chain as a cascade of two-ports; perhaps a block diagram of the signal chain?

You said you've made measurements of several parameters such as z11, z12, h11, h12, h22, but you didn't say at what frequency you made those measurements.

There is a lot of detail you're not telling us.

It is not too hard to obtain the ABCD parameters of a passive network from measurement of the impedances at both ports.  Using ABCD (chain) parameters for each block of a signal chain allows you to get the overall chain parameters for the signal chain by multiplying the parameters of each subcircuit or block in the chain.  I'm sure you know this, but to help you, we need more details of your circuitry.

[Andrew_K]

How do you simulate your subcircuits? 

I mean, I really can't/don't without models. That is why I am attempting to pursue 2-port analysis.

Using 2-port models, I can use LT Spice and VCIS/ICVS and frequency response tables to do a frequency analysis.
I can also use Python and basic network analysis to calculate frequency response.

Do you have a parameterization of each one?  Are their two-port parameters known?  Which parameters are used to describe them? 

If the two-port parameters were actually "known", I wouldn't be asking on the best way to measure them.

The parameters to describe them are arbitrary, since any parameter network can be converted to another.
My equipment only allows 1-port impedance measurements and thru 2-port measurements, which is what hybrid parameters are, hence why I chose hybrid.

I don't know how to measure Z12 or Z21, since they are current/voltage measurements on both ports of the DUT.

Can you show your signal chain as a cascade of two-ports; perhaps a block diagram of the signal chain?

It's like 3-4 cascaded blocks, series connection. I'm not sure if drawing it out would really help here. I'll draw it out if you really think it would help.

You said you've made measurements of several parameters such as z11, z12, h11, h12, h22, but you didn't say at what frequency you made those measurements.

There is a lot of detail you're not telling us.

I've mentioned before.
20Hz to ~1MHz. My equipment goes that low. I really don't care about anything above 1MHz.

What other detail is needed? I'm asking advice on how to measure these parameters.

It is not too hard to obtain the ABCD parameters of a passive network from measurement of the impedances at both ports.  Using ABCD (chain) parameters for each block of a signal chain allows you to get the overall chain parameters for the signal chain by multiplying the parameters of each subcircuit or block in the chain.  I'm sure you know this, but to help you, we need more details of your circuitry.

Given what I can physically measure, I only have A and D. Obviously B and C can be calculated, but I have no way to actually measure these at frequency.

Simulation isn't my problem here, my issue is measurement.

[Andrew_K]

If there are reactive terms +/- j  in the parameters, then it is possible the voltage (not power)  can "ring up" above 0dB
But that would need both L and C  ( + and - j terms)

Interesting, so would that indicate resonance in the circuit?

[mag_therm]

For your post #18, In case you don't know it, I mention how  a nanovna can be used to measure tuned circuit, filter etc even if HiZ.
I have done this on HF radio tuned circuit/filters with and without coupling transformers.
First connect a 20dB or 10 dB attenuator to CH0.

Now connect that attenuator to a low Z part of the network input (make one with a tapped capacitor or tapped inductor if necessary)
 Connect CH1 to the network output.

Now run a sweep using both LogMag and Smith (*)

The LogMag response will ( always be below 0dB) and  obtained by adding the attenuator value back to the sweep values.

For your post #19, Yes the voltage can "ring up" even if the ciricuit did not actually get to resonance in the sweep.

Correction: run Smith without the attenuator. Run LogMag with the attenuator

[The Electrician]

It's like 3-4 cascaded blocks, series connection.

Using this page for reference: https://en.wikipedia.org/wiki/Two-port_network

A little over halfway down the page under the heading "Combinations of two-port networks" are several figures.

My question to you is: are your two-ports connected in cascade as in Figure 16, or are they series connected as in Figure 10.  Those are different things.

[Andrew_K]

It's like 3-4 cascaded blocks, series connection.

Using this page for reference: https://en.wikipedia.org/wiki/Two-port_network

A little over halfway down the page under the heading "Combinations of two-port networks" are several figures.

My question to you is: are your two-ports connected in cascade as in Figure 16, or are they series connected as in Figure 10.  Those are different things.

It is cascaded, like figure 16.

[The Electrician]

So why must you determine the parameters of each individual block?  Why not just determine the parameters for the whole chain as a single two port?

[virtualparticles]

For your post #18, In case you don't know it, I mention how  a nanovna can be used to measure tuned circuit, filter etc even if HiZ.
I have done this on HF radio tuned circuit/filters with and without coupling transformers.
First connect a 20dB or 10 dB attenuator to CH0.

Now connect that attenuator to a low Z part of the network input (make one with a tapped capacitor or tapped inductor if necessary)
 Connect CH1 to the network output.

Now run a sweep using both LogMag and Smith (*)

The LogMag response will ( always be below 0dB) and  obtained by adding the attenuator value back to the sweep values.

For your post #19, Yes the voltage can "ring up" even if the ciricuit did not actually get to resonance in the sweep.

Correction: run Smith without the attenuator. Run LogMag with the attenuator

This is interesting. I'm not sure where you're going with this. Are you suggesting the low impedance tap in order to measure the resonance without loading it with the 50 ohm source of the VNA? How is the attenuator helpful other than improving the awful source match of the Nano? If the circuit is measured in the Smith Chart mode, measuring S21, impedances will only be accurate from about 20 ohms to 200 ohms for about 5% accuracy.

Thanks