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Difficulty using Q(Tg) for NISM on DC-DC POL's where impedance peak is <~30mOhm

Hello, I'm currently working on an assessment of the NISM method in my lab where I am measuring the phase margin of a POL using both NISM and Bode plot methods to see how similar the results are. I'm running into some trouble trying to make the measurement on some of my buck converter POL's. Some of these converters measure very low impedances at low frequencies (<10mOhm). When looking for the impedance peak (where the DC-DC converter stops being able to keep the impedance low and the MLCC's take over) I will typically find that the peak can be 30mOhms or less.

Looking at the Q(Tg) plot, I find that whenever the impedance is less than about 30mOhms, it becomes incredibly noisy. I have tried increasing signal power, increasing number of points, reducing receiver BW and none of these allow me to get a clean Q(Tg) plot. I find that there are peaks that show up, but as I lower the receiver BW, increase number of points, or increase signal power in an attempt to increase the fidelity of Q(Tg), I get multiple large peaks concentrated near the same frequency. Below is an image I took of a POL. My setup is a Bode 100 with the P2102A 2-port probe, a J2113A differential amplifier on the receiver port, and a P2130A DC block on the input to the J2113A. I know from performing transient step loads and looking at the response to assess the damping ratio, that the actual phase margin can't be only 5.8 degrees. Besides this one example below, I have measured other DC-DC's where the impedance peak is even lower than this plot, and I can't obtain any meaningful Q(Tg) plot.

Overall, how do I overcome this issue of a noisy Q(Tg) when the impedance peak near the crossover frequency of the POL ends up being at a low impedance below 30mOhms? I also have a J2112A that I have experimented performing a 3-port impedance analysis with as well, but I run into the exact same issue, and I have not been able to determine a method to properly calibrate the VNA when using the J2112A since voltage is needed for calibration. Any advice/tips/pointers would be very helpful as so far I am having trouble overcoming this limitation.

3 comments

3 Comments

nicholas.kuntzler

Jun 29, 2022

Thanks for the feedback, so I guess I have some follow-up questions.

So from my understanding, the Q(Tg) plot is essentially related to the S21 magnitude by some derivative. This means that the tiny, but sharp, blips in the impedance are responsible for the massive Q(Tg) spikes. In general, I noticed that as I increased the number of points in my measurement, the more definition these blips got, the sharper they would get as well, resulting in increasingly large Q(Tg) peaks. I also notice that these blips shift around from measurement-to-measurement, my main suspicion is that they might be caused by changes in the load of the POL adding noise to my measurement, or causing small shifts in the loop gain of the converter (since the bode plot I've measured isn't constant over load). It seems to me that these blips can be generally ignored, but one area where I could see a problem coming up is where I have a less well-behaved DC-DC converter. If I increase the number of points of my measurement, I think I might be worried about these sharp "fake" peaks blowing out the true, lesser peak. Could there maybe be an issue where I might want to set an upper limit on the number of samples I take to reduce the impact of the small blips?

Picotest

Jun 30, 2022

Replying to

Precisely! One tip I often give is for cleaner plots, use fewer datapoints. I think I mentioned this in my online classes too. This does trade-off definition, but you’ll lose some definition in the peaks (that you didn’t want) and also fewer datapoints mean more interpolation, which includes smoothing. Q(Tg) is related to the phase slope, so the higher the Q the steeper the slope, or the steeper the slope the higher the Q.

Often these noise blips are due to external noise – for example maybe the noise from LED lighting or fluorescent lights, noise from other circuits in the system, etc. In rare cases, they are because the system is oscillating. Even poor phase margin does not create such a narrow “spur” but an oscillation can. Most of these noise blips are external, they may also be there when the power is OFF, confirming you can ignore it. In any case, store the OFF measurement in memory and then look at the ON measurement. You are interested in where the two curves converge, and in the case of poor stability, the ON impedance will be greater than the OFF impedance. It IS possible for these blips to be stability related, so I am NOT telling you to ignore them, but to be cautious and look for additional signs that it isn’t just passive noise. If it IS stability-related it generally looks smoother and broader, not like this.

You can also create the Bode plot from these two traces, since BODE=1-OFF/ON. This is from small signal theory closed loop=open loop/(1-T) and solving for T, where closed loop is ON and open loop is OFF. I have a few papers on this, but see attached.

We do have one customer that insists on 1600 datapoints, so there isn’t really a guide, but for mine I usually like to see 20points/decade UNLESS I am looking at a sharp peak. For example, xtal is very high Q, so needs a lot of datapoints for good definition. The series resonance of a ceramic cap also might require more points to accurately produce the sharp impedance dip.

One more tip is to use LOG magnitude for the Qtg curve (and the impedance curve) and it won't get as “blown out.”

Steve

Picotest

Jun 27, 2022

Thanks for this question, it is a good one, and probably of general interest. I looked at your settings, and you did all the right things to manage noise. Which is great. There are few things to be aware of here. First, the best method for this impedance measurement, voltage permitting is the 2-port shunt through. That is the lowest noise and is optimum for measuring very low impedance.

NISM uses Qtg, which is a derivative, making it very susceptible to noise, but this is generally overcome by good noise management technique, which you have applied well here.

This is not about the magnitude of the impedance, but about the Q.

The measurement itself is very low Q, so we don’t actually expect to see a peak, and the NISM would generally report >71 degrees. Pat yourself on the back, this is a keeper. It is also generally recommended that you measure with power both OFF and ON, again making the 2-port shunt through measurement ideal. This will clearly show where the ON impedance is greater than the OFF impedance, and that is the peak we want to measure.
You do have a very sharp peak at around 10kHz. This could be noise from your board, noise from external sources (we have seen LED lamps, monitors, etc. create such noise) and it can also be control loop related. Measuring with power OFF and ON would help determine that.
You could use the traditional 3dB cursors (Bode 100 offers these) to determine the Q, which looks to be below 0.5. This is a very stable loop, and that is why you are having trouble finding the peak – there isn’t one!!

If you see this situation generally, congratulations, you are doing well. If you perform a step load on this VRM you will also note that there is no ringing, since this is overdamped. Well done!

Steve