Mini-teardown: Omicron B-WIC impedance test adapter

[precaud]

Your linear equation solving skills are fresh. Thanks for giving me a kick to brush up on mine 

If I go from the schematic in 1st post:
 
U1=Uref*Att (attenuation factor of the divider)
U2=Uref*2,35/(DUT+2,35)

OK

Uref=U1/Att
Uref=(DUT+2,35)*U2/2,35

Yup.

U1/Att=(DUT+2,35)*U2/2,35
U1*2,35/(U2*Att)=DUT+2,35

You're rockin'

DUT=(U1/U2)*(2,35/Att)-2,35
Att=47/(1000+47)

Isn't Att = 1 / (((50 + 1000) / 47) + 1)  , which = .0428...  ?

DUT=(U1/U2)*2,35/(47/1047)-2,35
DUT=(U1/U2)*52,35-2,35

Or DUT = (U1/U2 * .0428) -2.35   is fine for the computer

I'll try it today.

What are your results without calibration?

As I wrote in earlier post, without OSL, the results were accurate above an Ohm or so. This is consistent with the findings of others with this method using 50 Ohms Rref. It seems the Rref choice sets a "resolution baseline" for the measurement. Which makes sense, if you think about it.

If you had a wrong formula, and make a calibration, wouldn't the calibration fix your results to a certain degree(slopes, offset)? So it might work, till you run out of signal gain/precision?....

Exactly. And the further the DUT number is below the Rref, the worse the precision becomes. For the classic Rref=50 Ohms, it's not good at all. For Rref=2.35 Ohms, it's much better. If you lower Rref even more, then you need more preamp makeup gain, which adds its own problems (noise, imprecision, bandwidth limiting...). So all things considered, this seems like an intelligent choice.

[precaud]

In the formula, I replace the 50x2 Ohms with 2.35 Ohms.

Why did you that? What was the reasoning?

I assumed that the 50x2 was really 50 + 50, combining the source and terminating impedances.
As you noted, since the inputs are 1Meg, I chose to ignore the 50 Ohms source for now, and just use the 2.35 Rref.

And S21=U2/U1 - in linear scale, NOT dB!!

I know, that's why I had to convert it. No big deal - you work with what you are given... 

You can't get Anritsu to spit out separate data for each channel(you have only S21 available)?

Yes, but it takes separate sweeps to get each, and of course there's no phase data... only level.

[Pitrsek]

Yes, but it takes separate sweeps to get each, and of course there's no phase data... only level.

Actually this might not be a problem, as long as you are measuring passive RLCs, or any other minimum phase system, you can use Hilbert transform to calculate phase from magnitude. Depending on your math libraries, there might be some gotchas:
https://www.dsprelated.com/thread/2670/calculating-the-minimum-phase-of-a-given-magnitude-response

I can understand that with Hilbert transform  and two cal sweeps we are way past "nice test fixture that will be really useful, let me just connect it with 3 cables to ma VNA... " and two checkpoints in "not what I've bargained for" and "oh boy, why did I bought this  " territory.

[precaud]

Actually this might not be a problem, as long as you are measuring passive RLCs, or any other minimum phase system, you can use Hilbert transform to calculate phase from magnitude. Depending on your math libraries, there might be some gotchas:

Yes, I understand. I wrote a Hilbert routine decades ago to do that. And I stopped using it. Too many assumptions being made. Especially, assuming minimum-phase behavior is not a good idea when you are still sorting out the test system itself!

(Besides, why bother having a VNA if you're not going to look at phase?!?!)

I can understand that with Hilbert transform  and two cal sweeps we are way past "nice test fixture that will be really useful, let me just connect it with 3 cables to ma VNA... " and two checkpoints in "not what I've bargained for" and "oh boy, why did I bought this  " territory.

Yeah, that too. I think we can get to the bottom of this without resorting to such measures. But I like how you think.   

[precaud]

Ok, here's a worked example using the three methods. The DUT is a 0.1 Ohm resistor at 1kHz. The analyzer returns V1/V2 as 26.49dB, which = 21.11

For DUT=(U1/U2)*52,35-2,35 ( Pitrsek's version) :  21.11 * 52.35 - 2.35 = 1,102.76 (way off)
But if we use 1/21.11 instead, we get 0.1299 which is in the ballpark. (We'll call it Modified Pitrsek).

For DUT = (U1/U2 * .0428) -2.35 (my edit of ^) :  21.11 *.0428 - 2.35 = -1.4465  (impossible, of course)

For the Series-Thru method I first derived:  X=10^( (26.49 - 26.956) / 20.) = .94776. Then ( ( 1. -X) / X) * 2.35 = 0.1295 Ohms
It's nearly 30% error but that is without OSL. Very close to Modified Pitrsek.

Let's try a 1 Ohm DUT. The analyzer returns V1/V2 as 23.63dB .
X=10^( (23.63 - 26.956) / 20.) = .68187. Then ( ( 1. -X) / X) * 2.35 = 1.096 Ohms  Which is better at about 10% error.
Modified Pitrsek = 1/15.188  * 52.35 - 2.35 = 1.097  VERY close again.

And now let's see what a 10 Ohm DUT looks like (10.03 actually). The analyzer returns V1/V2 as 14.58dB .
X=10^( (14.58 - 26.956) / 20.) = .24055. Then ( ( 1. -X) / X) * 2.35 = 7.420 Ohms  Which is total stink.
Modified Pitrsek = 1/5.358  * 52.35 - 2.35 = 7.420  Same stink, and same as Series-thru again.

And just to see where the trend goes, let's look at 100 Ohm DUT (99.98 actual). The analyzer returns V1/V2 as -4.03dB .
X=10^( (-4.03 - 26.956) / 20.) = .02823. Then ( ( 1. -X) / X) * 2.35 = 80.89 Ohms.
Modified Pitrsek = 1 / .6288  * 52.35 - 2.35 = 80.91 .

It appears we haven't found the correct formula yet. Or it totally relies on OSL to pull it into line.

I just got the Omicron short/load card in the mail. It won't change these results, because we're not using OSL...

[r0d3z1]

It appears we haven't found the correct formula yet. Or it totally relies on OSL to pull it into line.

But we are moving near to the right result .
I have checked Pitrsek calc, and they look right. However we are still missing something.

[r0d3z1]

hoping this will be useful, here is a brief explanation of ApInstruments about impedance measurement

http://www.apinstruments.com/techImpedance.html

[precaud]

Yes, that is the "Series-R, shunt DUT" method. Pitrsek's first equation gives right answers for that method. But for "Series-DUT, shunt-R" we have to change it to:
52.35 / (V1/V2) - 2.35

I agree, we're heading in the right direction; both approaches are giving identical answers. But we're still missing something in the analysis.

The main problem I see with this Series-DUT method is in the computational model. For a perfect short, neither V1 or V2 approach zero; in particular, V2 is the reference R (2.35) divided by the output R of the generator (47.5 here), or about .0495 . That is the smallest number the divisor can be. That is the main reason why all the papers on Series-DUT method says it is not useful at low impedances. It runs out of numerical accuracy. And that is why OSL (especially for Short) is absolutely necessary. The results have to be re-mapped to the real-world. Without OSL, the lowest this method can go is about 125mOhm. So that becomes zero.

Here's another good paper that compares Series-Thru to other methods.
http://electronics.etfbl.net/journal/Vol18No1/xPaper_05.pdf

It appears to have very careful analysis of the parasitics. The math for Series-thru with parasitics is on bottom of p.3, with a general case on p.4. It is the same formula that the Keysight paper gave. Like all previous analysis, it assumes 50 Ohms Rsource and Rref. But maybe we can get some clues from it. (My son is better at this math than I am, I can ask him when he returns tomorrow).

(One problem I see with their measurement is the ground connection between their type-N connectors, it has significant inductance not accounted for in their model...)

[r0d3z1]

I'

Here's another good paper that compares Series-Thru to other methods.
http://electronics.etfbl.net/journal/Vol18No1/xPaper_05.pdf

I am also reading it, at the end of page 9 in section "ANALYSIS OF THE MEASUREMENT RESULTS AND MEASUREMENT ERRORS", they said that shunt-through measurement report a big error when you try to measure DUT with impedance quite high. So in quite normal that the measurement of 100ohm report some strange result but it doesn't means that the equation is wrong for low impedance DUT.

There is another importanr concept that i have understand from this AN
http://literature.cdn.keysight.com/litweb/pdf/5989-5935EN.pdf
If I am right, the source of measurement error is the ratio between Transmitted/Reflected wave. So, if the impedance is too low, the Reflected wave is small and difficult to measure.

[precaud]

I'

Here's another good paper that compares Series-Thru to other methods.
http://electronics.etfbl.net/journal/Vol18No1/xPaper_05.pdf

I am also reading it, at the end of page 9 in section "ANALYSIS OF THE MEASUREMENT RESULTS AND MEASUREMENT ERRORS", they said that shunt-through measurement report a big error when you try to measure DUT with impedance quite high. So in quite normal that the measurement of 100ohm report some strange result but it doesn't means that the equation is wrong for low impedance DUT.

Yes, but this is not "Shunt-thru" we are using, it is "Series-thru".

There is another important concept that i have understand from this AN
http://literature.cdn.keysight.com/litweb/pdf/5989-5935EN.pdf
If I am right, the source of measurement error is the ratio between Transmitted/Reflected wave. So, if the impedance is too low, the Reflected wave is small and difficult to measure.

Yes, it is true. That is a good paper also, but it only looks at Shunt-thru method... it is not what this fixture uses.

[rx8pilot]

There is another importanr concept that i have understand from this AN
http://literature.cdn.keysight.com/litweb/pdf/5989-5935EN.pdf

This is a good one. Thanks!

[precaud]

This graphic was culled from the paper I referenced a few posts earlier. The authors lay out the 50 Ohm source and load series-thru measurement in quite some detail, along with cable and connector (fixture) parasitics. The complete formula is in the upper right corner. The circuit diagram shows which specific item in the physical layout relate to which parasitics. And in the lower-left corner, they show the familiar Series-thru formula (if parasitics are ignored) as also was given in the Agilent app notes.

It seems to me our case lies somewhere between these extremes. Some of the parasitcs can be ignored - they will be picked up by the OSL compensation. (But maybe some need to be included in this form?). And some need to be modified to reflect the conditions of the B-WIC. For instance, the resistance Rp1 can represent the total resistance of the 1k/47 divider. And of course the 50 Ohm R at VNA port 2 will be replaced by the 2.35 Ohm Rref in the B-WIC.

I don't have any results yet, I'm just sharing this as my next possible approach to find an improved formula.

[precaud]

A couple days ago I shared my math with the boys at Omicron and kindly asked if they would review it and correct any errors.
They respectfully declined. Not surprisingly, they don't want to give away the company jewels.

So I decided first to satisfy myself that, if everything were measured correctly, then is the technique I'm pursuing capable of giving the right answers?
I wrote a simple program to calculate the impedances and voltages at each node, and then run them through the math to see if the answers are correct.

First attachment is the circuit diagram with the important nodes and components labeled. Voltage points are in orange, resistances in red.
Constant values:
Rs=50.          ! Generator source resistance
Rref=2.35      ! B-WIC Reference Resistor
Vs=1.           ! Assume a 1 volt source at some low freq so the parasitics can be ignored
Vdiv = 1000 / 47     ! Voltage divider in the Ref channel output
Rdiv = 1047           ! Total shunt resistance of the divider

Some key variables:
V1 = the voltage present at the source end of the DUT
Vt =           "          "         "       load    "      "       "
Rdut =  the resistance value of the Device Under Test.

For each DUT, calculate:
V1 as:
X = 1 / (1 / Rdiv + (1 / (Rdut+2.35))      ! actual shunt impedance at the V1 node, including the divider
then V1 = X / (Rs + X)                         ! voltage presented to DUT, including generator output resistance

Vref = V1 / Vdiv                                  ! the value presented to VNA Ch1 or R channel. Later, multiply it by Vdiv to restore the correct value

then Vt as:
Vt = V1 * (Rref / (Rdut + Rref))             ! voltage at DUT, already corrected for Rs and Rdiv, goes through Rdut / Rref divider

and then S21 ( or Vt / V1):
S21 = Vt / (Vref * Vdiv)                         ! Corrected output of the VNA, from which the Z is calculated

and then the impedance, using the equation we started with :
Zv = 2.35 * ((1 - S21) / S21)

The second attachment is a chart showing each element calculated for each DUT value. It's interesting to see which ones change very little. The voltage at the T channel changes very little. Most of the movement is on the source side of the DUT.

The impedances at each node are shown for interest's sake.

So, as you can see, yes, it can be done. If the voltages are calculated correctly, and all factors accounted for, then this equation [ Zmag = 2.35 * ((1 - S21) / S21) ] gives the correct results. To solve for DUT from the measurements, the effects of the source resistance and the R channel divider have to be precisely removed from V1 and Vt for the result to be correct. That is what we haven't done yet, and what we have to figure out.

The boys at Omicron are indeed very clever.

The question now is: Can Rs and Rdiv effects be accurately removed from the numbers that the VNA put out (Vt/V1)? Or do we need access to V1 and Vt separately?

Time for a hot tub.

[precaud]

So we know the equation works for Real numbers, i.e. resistances.
So why, when I measured a 1,000uF capacitor, was the impedance and phase way low below a few hundred Hz?

Look at the diagram of the fixture in the previous post. Let's say the DUT is a 1,000uF capacitor with 20 milliOhms ESR. Some calculations are attached below.
In mag/phase terms, 1000uF @ 20 mOhm at 100Hz equates to 1.5917 Ohms at -89.28 deg phase.
In resistance/reactance terms (real/imag), it is .02 Real Ohms and -1.5915 Imag Ohms, or (.02,-1.5915). Almost all reactance.

Now we're going to try to measure it in the fixture. The "reference resistor" is 2.35 Ohms (larger than the DUT). In real/imag, that is (2.35, 0) .

And you know what happens when you put a resistance in series with a reactance. They add. (.02,-1.5915) + (2.35, 0) = (2.37,-1.5915). Which in mag/phase is 2.84 Ohms @ -33.9 deg phase. What happened?
From the V1 point of view (which connects to the Reference input of the VNA), the DUT looks like a sh!tty 1,000uF capacitor with 2.37 Ohms of ESR. Ooops.

This is stinky stuff. It leads me to think that, when using its fixtures, it is quite possible that the Bode 100 isn't actually measuring phase. Perhaps it converts the measurement immediately to magnitude and, as Pitrsek suggested, it calculates and plots a Hilbert transform of the magnitude for the phase. Either that, or else it is not measuring in "Series-thru" configuration. It has the ability to sample the source signal before the 50 Ohm resistor, so it could be some sort of hybrid technique.

I need another hot tub. Wish I had one...

[precaud]

Perserverence furthers. By golly, it works! The ruminations of the last day or two helped identify three errors I was making.

One of the main problems was errors caused by the mixing of real and complex math operations in my code. The equations themselves were fine; but a couple were being executed wrongly. Some operations, like correcting for the R channel L-pad, need to be done on the magnitude vector, in polar. But others, like (especially) scaling the data to the 2.35 Ohm reference R, must be done as a complex number in rectangular coords, which leaves the imaginary term intact, or else the phase gets demolished, and rectances measure wrong.

Another issue is the fixture's sensitivity to the BNC cables' shield resistance. One of my big beefs with BNC cables is that they don't solder the ground braid to the connector shell. So with some of 'em you get variable ground impedance with each cable. Just move it a tad and it changes. Well this fixture needs short cables with as-low-as-possible shield impedance.

And lastly, when using Open-Short-Load compensation, doing a Thru sweep on the analyzer is unnecessary and will cause major errors. It turns out, the channel imbalances which the Thru quantifies are taken care of by the OSL routines.

Having corrected these things, I'm getting good results, all the way up to 10MHZ and down to about 20-ish milliOhms. Including large capacitors. See the attached plot. Three current sense R's; a 1 Ohm Caddock radial-lead, a 100mOhm axial, and a 25mOhm axial. And a 1,000uF lytic which measures 44mOhm ESR on the Wayne Kerr meter.

As you can see, the traces start getting noisy at say 50mOhm and below. This isn't caused by a measurement dynamic range problem, per se; there was plenty of dynamic range to spare on both channels, and very little difference between sweeps with a 30Hz IF and 10Hz IF. it's a numeric precision issue with the Anritsu analyzer. It rounds and stores its magnitude data with 0.01dB precision. Normally, that would be plenty good. But with this measurement, at low impedances, .01dB in the raw measurement converts to linear voltage ratio and then impedance at 2-4 milliOhms per hundredth of a dB! The lower the impedance value, the coarser the conversion, hence what looks like "noise". That coarseness is also transferred into the OSL routines. So an analyzer which stores its data with more precision will give much smoother traces (and better data) with this method.

Anyway, I'm a happy camper. Being able to measure the impedance of thru-hole parts up into the MHZ region was one of my major goals. Once I get the noise issue solved (I have a couple ideas), I can live with a 20mOhm lower limit over a 10Hz - 10MHz range.

I also have Omicron's B-SMC fixture, which uses the same network inside. So it should be plug-and-play and give the same results with SMD parts.
 
BTW, for anyone making their own fixture, this approach is worth considering. If anyone wants details on the corrected math routines, let me know.

[Pitrsek]

Nice job 

[precaud]

Nice job 

Thanks Pitrsek, I couldn't have done it without your help!   

[Pitrsek]

Glad to help

[precaud]

There is no question that the B-WIC fixture is well-conceived and executed, and easy to use. It's limitations are more a consequence of the Series-Thru method. Above about 1/2 an Ohm or so, it is quite reliable and gives good results. But it still has problems at lower impedances, even with the clever modified topology Omicron came up with. These problems can be clearly seen in the graph a few posts up, and in Pitrsek's measurement of two low-ESR 'lytics posted on p.1 of this thread. (I am concentrating on the low-impedance performance because that's where I'll use them the most.)

There are basically two problems:
1. Raggedness in the measurement in the 1MHz-10MHz range, due to impedance discontinuities in the input stage of the VNA. My Anritsu has it. The Bode 100 has it too. An AP 102B is much better. And an HP 3577A is excellent and has no sign of it.
2. Numeric precision limitations that come into play from about 50mOhm and below. Both magnitude and phase are significantly impacted by it.

And so I wondered, how does the B-WIC compare at low impedances to my homemade Series-R fixture?

The attached plot uses Series-R method with 10 Ohm series R, and the same OSL (Open-Short-Load) compensation math used for the B-WIC. For consistency, I used a 100 Ohm load reference just like the B-WIC. The parts measured are the same ones I've been using.

As you can see, the Series-R method is much more accurate and usable at low impedances. With greater numeric precision data to work with, the OSL routines do a better job of removing the discontinuities above 1MHz, and are way better below 100mOhms.

I also compared the results using these two fixtures, to the same parts measured in several dedicated 4-wire impedance meters (only up to 300kHz) from HP and Wayne Kerr. The Series-R results are more accurate.

As a result, I am seriously considering removing the B-WIC's resistor network and converting it to Series-R topology.

[precaud]

Before converting the B-WIC to Series-R, I decided to try a different VNA with it, one that does not have the .01dB resolution limit that causes the "noise" at low impedances (as shown in the post and plot in Reply #39 above). I have an AP Instruments 102B VNA that I've been wanting to interface with my program and this gave me the reason to do it. It also flung me into unknown territory; the only way to gain access to its measurement data is via Windows DDE, or Direct Data Exchange, the method Windows has provided (since inception) for applications to share data. It's fast and actually more straightforward than GPIB programming, IF your language of choice has a good DDE interface driver. The one HTBasic provides (with all versions) works but has a bug. It has a maximum size limit of 256 bytes per transfer. Which is useless when you want to fetch say 200 points of Magnitude and Phase each with full 48-bit Real precision. It wasn't until yesterday that they sent me a workaround that actually works.

Anyway, enough grumbling, on to the measurements. I first wanted to see what an uncompensated Short looked like, since that's the problem area for this Series-Thru method, and it basically sets the usable low-impedance limit. It's the blue trace in the first plot below, labelled "Direct". The curve is indeed smoother than it was with the Anritsu, confirming that its .01dB resolution limit was the cause of the rough traces. But now we see the infamous "braid error" rear its ugly head. (Braid error is a fancy term for a ground loop between the fixture and the analyzer.) Like most VNA's, the shell of the 102B's input and output connectors are all referenced to its chassis and circuit ground, hence the ground loop. (I have been spoiled by the Anritsu's isolated inputs, which I have come to really appreciate...)

Having seen that the reference divider and reference resistor in the fixture connect right at the B-WIC's R channel output, I reasoned that would be the most important ground reference to maintain. So I inserted a wideband isolation transformer (North Hills 0017 CC) to isolate the source. See the yellow trace labelled "xfmr". Ground loop gone.

So now we can see the low-impedance limit of the Series-Thru technique with a VNA that has good numeric precision, but grounded inputs. Without OSL compensation, zero ohms measures at about 23 milliOhms (before the expected inductive rise). (The Anritsu measures this at around 2 or 3 mOhms, nearly 10X better.) This high Short impedance impacts the accuracy below 100mOhms, as we'll see.

I did the same series of measurements using OSL, using the same parts as in post #39. Traces are much smoother with the better numeric precision, but less accurate below 100mOhms due to the high Short impedance. The 25mOhm R measures closer to 20mOhm. The ESR of the capacitor measures closer to 33mOhms than its actual of 38. At around 100mOhms and up its fine.

So changing VNA's solved one problem and created another. Tradeoffs.

I've seen three ways to deal with the ground loop problem. 1. A large common mode choke on the T channel output. (not very practical in this case) 2. Keysight lifts shell of the Source and T channel connectors off ground by 30 Ohms (not an option here). 3. Source isolation transformer, as I've done here.

I'm not sure what the next move is. Cogitate a bit. Any feedback is welcomed.

[Pitrsek]

Or you can go for differential pre-amps for inputs. And toss in some gain, while you're at it.

[precaud]

Or you can go for differential pre-amps for inputs. And toss in some gain, while you're at it.

Well I agree, in the sense that isolated or diff inputs is the way to go, better than isolating the output...

With isolated-ground inputs, you can forget about braid error, ground loops, etc. which impact all low-level measurements, not just impedance...