Strange impedance measurement results

[BrainInVat]

I have created a setup for taking impedance measurements.  I have been doing some simple tests to make sure that the setup is working correctly.  When the impedance is low I get approximately what I expect, but as I increase the impedance my results get weirder.  For example when I measure the impedance of a 1 KOhm resistor at 10 Hz the resistance is 971 Ohm and the reactance is less than an Ohm, but when I increase the frequency the resistance decreases and the reactance increases such that at around 90 KHz the resistance is 888 Ohms and the reactance is 5 Ohms.  My expectation is that the resistance should increase slightly due to the skin effect and that reactance would stay at near 0.  For larger resistors the problem gets much worse.  For example with a 100 KOhm resistor I measure a resistance of 96 KOhm and a reactance of 2 Ohms for a frequency of 10 Hz, but for a frequency of 90 KHz I measure a resistance of 2.7 KOhm and a reactance of 600 Ohms.  That does not seem right at all.  In both cases the phase increases linearly with frequency.  What is going on?

About my setup:
I have a Tektronix MDO3012 oscilloscope and Keithley 6221 current source.  I have written a python script to control the two instruments.  I use the KI6221 to create a sine wave of known frequency and current amplitude.  The oscilloscope records the voltages across a reference resistor on one channel and the voltages across the device under study on another.  The reference resistor and device under study are in series.   I have written a C++ program to calculate the impedance from the data.  I have debugged and tested that program and I do not think it is at fault, especially since I can actually see the voltage readings on the oscilloscope drop when the frequency is increased.  For each impedance measurement I record approximately 5000 cycles and 100 points per cycle. Increasing these parameters does not change the results.  The results are reproducible.  The script automatically sweeps through a range of frequencies.

[VK5RC]

I can't quite visualise your set up,  I would hazard a guess you are getting into stray capacitance of your leads,  also a standing wave due to impedance mismatch between the source and load,  try moving the voltage and current sensors for the same settings of frequency and amplitude,  if these vary you have your answer.  Transmission line theory may be relevant.
Regards Rob

[T3sl4co1l]

Yeah, doesn't sound like a properly balanced bridge.  Work on that first -- and verify its balance at all frequencies -- before trying to take measurements of real components.  Especially near-ideal components like 1k resistors.  To do otherwise is simply absolute nonsense.

For example, your series equivalent for 1k at 90kHz is 8.8uH, which is ludicrous, even for poor construction.  A parallel equivalent wouldn't make sense, unless it were a capacitor, but you said the reactance was positive, so this is meaningless.

Tim

[uncle_bob]

Hi

What you really have (I think) is:

Current source + capacitance to ground

driving junction of upper resistor and first scope probe (more capacitance to ground).

resistor is connected to junction of DUT and second scope probe (more capacitance to ground).

The DUT is grounded.

If so, the caps are what is throwing you off.

Bob

[BrainInVat]

Thank you for your quick responses.  I did not know about impedance matching, transmission line theory, or balancing bridges, so I thought I should study those things before replying.  I still need to study those things a lot more.  I am not sure what bridge balancing has to do with what I am trying to do.  I think that the bulk of the problem comes from the capacitance of the current source.  I read in the user manual of the KI6221 that the command "OUTPut:ISHield GUARd", reduces the capacitance of the instrument, so I used that command and obtained very different results.  For the 100 KOhm resistor I find that the resistance increases to 195 KOhm at 8 KHz, and then rapidly decreases to 4 KOhms at 90 KHz.  I know that the skin effect should increase resistance with frequency, but should it double it at 8 KHz?  For the 1 KOhm the resistance increases from 980 Ohms at 10 Hz to 1013 Ohms at 45 KHz and then decreases to 976 Ohms at 90 KHz.  Should the skin effect be about the same for the 100 KOhm resistor and 1 KOhm resistor?  The reactances have remained low for the resistors, and have sometimes decreased and sometimes increased.  For example now the reactance for the 100 KOhm resistor at 90 KHz is 950 Ohms, whereas before it was 600 Ohms.  I have also tested a 1 uF capacitor, and a 0.1 uF capacitor in parallel with 1 KOhm resistor and obtained results close to what I expect.  I still need to test inductors.

I have attached a couple of crude drawings.  The first drawing is my current setup.  I measure the voltage across Zunknown by taking the difference between CH2 and CH1.  The second drawing is what I am considering changing my setup to based on the replies to my post and my research on impedance matching.  When testing the 1 KOhm resistor and capacitors my Zknown is a 1 KOhm resistor.  When testing the 100 KOhm resistor my Zknown is a 100 KOhm resistor. 

In my original post I meant to write "resistance of 2.7 KOhm and a reactance of 600 Ohms" not  "reactance of 2.7 KOhm and a reactance of 600 Ohms".  I think people understood what I meant.

[uncle_bob]

Hi

Ok, so you have 100K ohms. At 10 KHz a capacitance of about 180 pf is 100K ohms. At 100 KHz, 18 pf is 100K. From your diagram, you have a scope probe at two locations in the circuit. Rather than measuring just a resistance, you are looking at a resistance plus a capacitance. The capacitance is significant in relation to your resistance, so it throws off your data. Depending on your wiring (cables etc) it must be > 18 pf and it might be much more.

People have been measuring this stuff for a couple hundred years now. There has been a *lot* of research on how to do it right and what the issues all are. The "balanced bridge" approach dates back into the 1800's and is still a very good way to do things. Your approach is more like a network analyzer approach. In this case, both your source and termination impedances need to be carefully controlled. That's hard enough at 50 ohms. It can be quite difficult at higher impedance. This of course assumes that frequencies are fairly high.

A second possibility is that your code or data collection process has a bug in it. That's not a knock, only a comment from somebody who has chased down a lot of bugs in their own code over many decades.

Bottom line:

Your resistor is not going from 100K to 1K over the 5K to 45K frequency range. It's likely going from 10x.xx K to 10x.yy K over that range. The x's and y's will be as much from un-avoidable measurement error as anything  else. A reasonable model for a resistor is a resistance in parallel with a capacitance. The C is modeled independent of the R. Except in the special case of carbon comp resistors (which are weird in this respect) that model holds pretty well into the "many MHz range" for normal resistors. The other exception is (of course) wire wound resistors. They are not something that most people run into these days. For most normal resistors the C in the model is in the < 1 pf range.

Bob

[BrainInVat]

After a little bit of research I understand why the bridge method is better than what I was trying to do.  I still have a question about it though.  I need to measure the voltage difference between two points in the bridge.  I recently learned that I can only measure the voltage between ground and some point in the circuit using an oscilloscope.  So I would still need two channels, with the voltages measured between ground and two points in the circuit.  In that case I would still be providing new pathways for the current to go to the ground which would effect the results.  How can I get around that?

In the very beginning  of my impedance measurement attempts I performed my data analysis using the value of the reference resistor, but not the amplitude of the current.  After awhile I decided that it would be more accurate to use the amplitude of the current, since I know that to a high precision, but only know the resistance of the reference resistor to about 2%.  However, now it seems that I get more accurate results using the value of reference resistor rather than the value of the current amplitude.  This does not seem like a very satisfactory solution  to me.

I have been coding for many years and have learned to be humble.  I make many mistakes, and admit that there could be mistakes in my current code.  However, I have looked at the oscilloscope while it is taking data.  When I am measuring the impedance of the 100 KOhms resistor using a 10 uA current source at 10 Hz, I see that the amplitude is roughly 1 V, and that when the frequency is 90 KHz the amplitude is less than 10 mV.  So something is definitely going wrong other than my code.  I have also plotted the voltages and the fit that my program obtains.  They match very well with R^2>0.999.  I have also calculated impedance using an Excel spreadsheet, and obtained the same results as my program.  So I don't think that there are major problems with my analysis.

[VK5RC]

Hi BIV, if I understand your set up, at low frequency the voltage drop across your reference resistor relates to the current from the source and the resistor's known DC value, but when you increase the frequency the voltage measured across it drops dramatically, is that correct?
IF so I would wonder whether the source is supplying the AC frequency but due to impedance mismatch the AC signal is primarily reflected and not transmitted through the resistor. Some current sources can also be quite good sinks and 'reabsorb' the reflected AC signal. What sort of resistor is it? Do you know its stray inductance / capacitance ? A wire wound resistor makes quite a good inductor.
Please don't imagine I am an expert in this area!! One of the best explanations re transmission lines is a lovely old video, you may have seen it

[uncle_bob]

Hi

In any measurement, there is a level of care that must be taken. In general DC is easier to measure than AC. That's because most of the time there are no pesky inductances and capacitances to worry about. Upper frequency limitations on signal sources and measuring gear are not an issue at DC. A basic DC bridge can be checked with a ballistic galvanometer and you get a cool spot moving on the wall as a bonus. (Very entertaining if you have a pet). Isolating everything at DC may be as easy as finding a good rubber mat.

As soon as you do any AC measurement, you no longer have a simple situation. You always must worry about R, L, C and F limits. There are two paths you can take. One path is to use conventional setups and conventional techniques. That way somebody else has worked through (some of) the messy details. The guy may have gotten a nice title from Queen Victoria as a result. The other path is to dig into learning circuit analysis and understand the possible parasitics. You then measure them and include them in your model.

If you go with the second path and the setup you have, the first step is to look at your data. If the current source and scope are both doing what you expect (you can verify that), then you have a capacitance or inductance of some ammount involved. If it's a series inductance it's massive. If it's a shunt capacitance it can be pretty small. A bit of research into the dimensions of multi henry coils will rule the inductance out pretty fast. That leaves capacitance. Grab a device that will measure C and check what you have. If the numbers work out ...there's your answer. If they don't work out, you may have some of each. That's a bit more complex to analyze. The approach is the same. As you go up in frequency (and precision) it is not uncommon to spend months calibrating and modeling a test setup. Been there / done that many times. You loop through the process a *lot*.

Lots of Fun

Bob

[BrainInVat]

Thank you for the interesting and informative video, VK5RC.  I calculated my SWR at 20 KHz for the 100 KOhm resistor.  I found that my swr=1.09.  I believe this to be an overestimate as noise makes the maximum amplitude higher and the minimum amplitude smaller.  My percentage reflected then is about 0.2 %.  That and the fact that my measured resistance sometimes increases with frequency would suggest that reflected waves resulting from impedance mismatch is not the problem.  I will investigate this possibility further however.  When I first posted my problem the resistance always decreased with frequency, but I changed one of the settings on the current source and now the resistance first increases and then decreases. 

Yes, VK5RC, you are correct that the problem is that the voltage drops across the resistors drops dramatically with frequency, though they go up initially.  The resistor is just an ordinary resistor.  I do not believe it to be a wire wound resistor, though I could be wrong.  I do not know the stray capacitance or inductance of my resistor.  I am not even sure how to find that without measuring the impedance.

[uncle_bob]

Hi

Unless you have at least 1/10th wavelength of transmission line, it's not going to matter (in terms of transmission line equations / modeling). At 20 KHz one wavelength (in air) is just under 48.4 Km. One tenth wavelength would be 4.8 Km. That's a lot of wire. In addition, to calculate the SWR you need to know the characteristic impedance of the line. Due to various things (like the skin depth you keep mentioning) a line that is 50 ohms at 100 MHz may be a very different impedance at 20 KHz.

Bottom line:

At the frequencies you are looking at, don't worry about transmission line effects. It is a very cool video though ....

Bob

[BrainInVat]

I did not calculate SWR correctly at all.  I want to make sure I know how to calculate wavelength.  v=f*lamda where v is velocity, f is frequency and lamda is wavelength.  So lamda=v/f.  I am guessing that v is the speed of light c in this case.  The electric field travels at the speed of light, but the electrons travel much slower.  So at 30 KHz lamda=3*10^8/(3*10^4)=10^4 m=10 km, so the distance between the trough and crest is 5 km.  My cables are obviously much shorter than that.  So I guess that would mean that uncle_bob is right that a reflecting wave due to an impedance mismatch is not the problem.  I added an extra wire of about 2 m and measured the impedance at various points along it.  I did not find that the differences were statistically significant, but I can't rule out that there is variation due to reflected waves.

I do want to use conventional techniques.  I came up with this setup on my own, but I also searched on google how to measure impedance and the first few results had the same setup as mine.  As a result of the helpful replies on this thread I have found more sophisticated methods, but I don't understand how to implement these methods fully.  For one thing what is the best method to measure the voltage across the bridge using an oscilloscope?  I also don't have variable capacitors.  I want to automate this so I would want a variable resistor, whose resistance I can set with a computer, as well as a variable capacitor whose capacitance I can set with a computer.  I don't have either of those things, right now, but I plan on getting them.  One of the sources I have looked at is http://www.allaboutcircuits.com/textbook/alternating-current/chpt-12/ac-bridge-circuits/.  It states that the problem with stray capacitance is made worse if one side of the AC current supply is grounded, which is what I have, but it doesn't seem to have a solution for this case.  The web page also shows how to measure impedance with a Wagner Earth, but how do I determine the capacitance and resistance to use in the Wagner Earth?  Maybe I should just do more research.  Sorry.

I will try the bridge method tomorrow.

[uncle_bob]

Hi

The people who came up with these techniques spent years working out the details and chasing down all of the issues. Physics still applies today just as it applied back then. If you intend to invent an entirely new way to do a measurement, you will have to do the grunt work to find and fix the nasty details. Measurement is *always* about the details. Having somebody else chase down the details is great, the bottom line then is that they are the inventors (they did the work).

A lot of people said "how about a powered gizmo that we could fly around in". Lots of great theories got tossed back and forth, some of them quite workable. The guys who we consider the inventors of the airplane are the ones who actually figured out all the nasty details and demonstrated it would work.

Dig into the circuit theory, dig into the modeling. That is what will let you analyze the setup you have in front of you. Your setup will always have strays. You need to be able to evaluate that part of it *before* you invest more money in gear for this. A box that by it's design is limited to < 10 KHz may not be useful to you. The fact that it has that limitation is likely to be buried deep in the specs on the device.

One simple example of this is a transformer used to isolate an AC source from ground. There are tons of them out there. They have been used this way for over 100 years. Some are intended for AC power, others are intended for audio output stages. Some are designed for RF transmitters. Typically if they work over a couple of decades of frequency (at the 3db points) that's doing ok. The same 3db data that indicates they work from 1MHz to 100MHz often does not indicate they have good isolation or balance over that range. If your application requires balance, then the 3db numbers that are up in bold print at the top are of little value.

There are lots of details like this ....

Bob