DIY Transformer for use with Bode Plots.

[joeqsmith]

...
Of course the intrinsic transformer doesn't have a basic 10Hz 3dB corner, just look at the primary inductance measurements of ~8mH which implies an impedance of 1/2 ohm at 10Hz!!! This is not to say the core transformer low end isn't important for Close Loop Injection use, the transformer must inject a signal into the DUT and this injection level falls off at the high and low frequency end due to transformer and source characteristics, as well as other effects.
...
In the Closed Loop Bode measurement the loop gain of the DUT comes into play, and usually the loop gain has a general low pass type charteristic.
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Please spend some time studying the mentioned video (and other related papers on Bode Plots and Close Loop Measurement Techniques), this is an excellent resource for getting an understanding of Closed Loop Bode measurements, and even illustrates how this method can be utilized to measure the very complex non-linear nature of SMPS even tho Bode is a linear type function. 
...

Your point about the impedance at such low frequency is certainly valid.  In the video you link, he tests his transformer manually with a 10 ohm load, 50 ohm source and from 300kHz to 4Hz.   I suspect he has higher inductance.  He drops the drive to 100mVp to avoid saturation at 4Hz then seems he stays with that drive level.   

While the video was talking about SMPS and it sounds like that is also your area of use.  I don't see why it couldn't be used for testing other control systems stability.   

If I attempt to look at the last core I made  using his technique,  probes set to 1X, 200mVp-p drive. Shown is the difference from 10kHz to 4Hz.  I understand your comment about the DUTs loop response.

[joeqsmith]

Well really Joe why did you even dig out that old storm in a teacup ? 

Because OP asked for the data.

[joeqsmith]

If I run a similar test with the other transformer (much higher inductance)  we can see that the lower frequency coupling is much better.  Phase isn't great.   Again, what we expect.  For testing SMPSs, again I agree that it may not be useful to have such a transformer.

Should mention this was taken with 10X probes rather than 1X.   Same drive levels. 

[mawyatt]

Your point about the impedance at such low frequency is certainly valid.  In the video you link, he tests his transformer manually with a 10 ohm load, 50 ohm source and from 300kHz to 4Hz.   I suspect he has higher inductance.  He drops the drive to 100mVp to avoid saturation at 4Hz then seems he stays with that drive level.   

While the video was talking about SMPS and it sounds like that is also your area of use.  I don't see why it couldn't be used for testing other control systems stability.   

If I attempt to look at the last core I made  using his technique,  probes set to 1X, 200mVp-p drive. Shown is the difference from 10kHz to 4Hz.  I understand your comment about the DUTs loop response.

We just used the magnet type wire that came with the CM Filter and twisted the 2 wires together and wound this back onto the core. If we had more wire then we could have increased the primary inductance with more turns, but didn't, so used what we had. Need to find some old Cat 5 cable to strip!!

In the video, he uses more wire and turns, thus greater primary inductance. This is why we were asking about the various core types, especially the large core shown by TopQuark but have no idea how to order from Taobao!! Wanted to use a larger core with more windings to create a larger primary inductance. Your core looks to have more windings and should yield a higher primary inductance than the ones we made.

Actually our use is more inline with op-amp type circuits as well as SMPS, both are difficult but the op-amp types usually have lots of loop gain which creates problems with accurately sensing small signals and the reason for the low frequency somewhat randomness in the plots, and keeping the signal low so the core doesn't saturate is important for good results. This is the type of area where synchronous sampling pays big dividends, but that's another complex topic best served in a separate thread.

Edit: This method is certainly valid for testing all sorts of feedback control systems, from op-amps, SMPS circuits, optically coupled systems, electromechanical systems and so on. Very powerful technique and why we were amazed this is essentially a scope built-in feature, and with the excellent front end with low noise, high dynamic range, and accurate scaling factors, can cover quite a range of uses. By far the best value electronic instrument we have

Anyway, hope this helps.

Best,

[joeqsmith]

In the video, he uses more wire and turns, thus greater primary inductance. This is why we were asking about the various core types, especially the large core shown by TopQuark but have no idea how to order from Taobao!! Wanted to use a larger core with more windings to create a larger primary inductance. Your core looks to have more windings and should yield a higher primary inductance than the ones we made.

He talked about 7 meters of wire in the video you linked.  He backs that up with his comment about his DC resistance.   Yours appeared closer to 25 turns so yes, I wasn't too surprised.   Again, I started out with 30 turns on tape as it seemed it had not been considered. 

Primary inductance was 109.4mH
Leakage inductance was 4.1uH
Coupling capacitance was 119.8pF
Resistance 4-wire was 0.589 ohms

Maybe "tape" was glossed over or the assumption was my inductance was off by a decimal point (typo).   Anyway, just something to keep in mind.   
 
https://www.magneticmetals.com/products-materials/tape-wound-toroidal-cores

Also,  for the wire I am using Teflon insulated single strand silver coated.   I used the hand drill to for the tight twisted pairs.   Just an FYI.   Good luck with your project and thanks for the all the additional information.

[mawyatt]

Yes our smaller core has 25 turns, and noted in the video the long ~7M wire, ours was only ~2 meters. Did note your larger inductance and assumed you had a much higher permeability core, so a metal tape core seems reasonable. Have no idea about the core we used since it was part of the CM Filter. One could do tests and figure out some core parameters, but no time budget for that at the moment.

Best,

[Jay_Diddy_B]

Hi,

I am late to the party. I missed the start of this thread. Do you have any questions for me?

Jay_Diddy_B

[mawyatt]

We used the PicoScope Frequency Response Analysis tool with a PicoScope 4262 (16 Bit ADC) to see if we could improve the Bode Plot results with the Closed Loop measurements with a OP-07 in a non-inverting 11X Gain configuration. Using the Noise Reject Mode with a Sample Rate of 500KHz and Noise Rejection Bandwidth of 1Hz (64X oversampling) we attempted to improve the Close Loop Bode Plot results hoping the PicoScope 16bit ADC and the FRA DSP Noise Reduction effects would pull out Ch1 signal and smooth out the randomness below 100Hz. As you can see that was not the case.

Conclusion is that the Isolation transformer needs to have a much higher Primary inductance to keep the low frequency signal level reasonable for the scope to capture accurately since the high gain feedback loop is effectively nulling the scope Ch1 Vin signal, so we'll be getting a larger core and winding another transformer with larger primary inductance for these low frequency Closed Loop Bode measurements with high gain Op-amps like the OP-07.

Others with larger primary inductance Isolation transformers might want to give this Close Loop Bode Plot a try, very interesting and useful technique.

Best,

[Jay_Diddy_B]

Hi,

Let me use LTspice to illustrate some of the features of the measuring the open loop gain of an op-amp. I have used the universal op-amp in LTspice so that I have a known answer. I have configured the op-amp to have an open loop gain of 1E6 and and a GBW product of 500K.

AC domain Model




In SPICE I can have a floating source so I do not need to include the transformer. The open loop gain is obtained by plotting V(a)/V(b).
The results show that I have an amplifier with a single pole slope, a gain of 1E6 and a GBW of 500kHz. This is the correct answer for the universal op-amp used in the model.
The gain is 94dB at 10Hz.

Time Domain Model



Switching to the time domain, transient analysis, and using a 10Hz 2V p-p signal the signals at nodes A and B can be examined.
The voltage between nodes A and B is 2V p-p, as defined by the source. The voltage from A to ground is 2V p-p. The voltage on node B with respect to ground is only 40uV p-p. This is the inject signal divided by the loop gain at the injection frequency.

The signal on Node B is very small. It is -94dB, 50000 times smaller than the injection signal.

Coupling Transformer LF bandwidth



The coupling transformer LF -3dB point is given by:

F = (Rsource // Rload) / 2 x Pi x Lmag

I have chosen Lmag = 68mH

This gives a LF (-3dB) point at 58.5 Hz


Adding the Transformer to the open loop measurement




Adding the transformer with a -3dB point of 60Hz does not impact the open loop response at all as shown in this model. It does reduce the signal amplitude at 10Hz by 16dB.

It is the signal to noise ratio and the noise floor of the FRA that impacts the measurement, not the bandwidth of the isolation transformer directly.

Regards,
Jay_Diddy_B

[Jay_Diddy_B]

Hi,

Here is a very simple test to circuit to determine if your FRA is capable of making the measurement:




It is a 100dB attenuator.

Jay_Diddy_B

[RoGeorge]

Conclusion is that the Isolation transformer needs to have a much higher Primary inductance to keep the low frequency signal level reasonable for the scope to capture accurately since the high gain feedback loop is effectively nulling the scope Ch1 Vin signal, so we'll be getting a larger core and winding another transformer with larger primary inductance for these low frequency Closed Loop Bode measurements with high gain Op-amps like the OP-07.

About achieving less than 100Hz lower frequencies, are they really needed?

Asking that because (in my understanding) the instability of a feedback loop is expected to happen at the frequency where the amplitude of the feedback loop bode plot crosses the open loop amplifier's bode plot.  Usually this intersection of the two plots happens at a frequency in the kHz range, at least, so why bother testing at 10Hz?

A feedback network designed to work up to only 10Hz will have a bode plot that will not intersect the amplifier's open loop bode plot at all (thinking here the casual opamps with gain bandwidth ~1MHz).

Is the sub 100Hz injection useful for "just in case", is it for something else than testing loop stability, or am I missing/misunderstanding something else entirely?

[2N3055]

Conclusion is that the Isolation transformer needs to have a much higher Primary inductance to keep the low frequency signal level reasonable for the scope to capture accurately since the high gain feedback loop is effectively nulling the scope Ch1 Vin signal, so we'll be getting a larger core and winding another transformer with larger primary inductance for these low frequency Closed Loop Bode measurements with high gain Op-amps like the OP-07.

About achieving less than 100Hz lower frequencies, are they really needed?

Asking that because (in my understanding) the instability of a feedback loop is expected to happen at the frequency where the amplitude of the feedback loop bode plot crosses the open loop amplifier's bode plot.  Usually this intersection of the two plots happens at a frequency in the kHz range, at least, so why bother testing at 10Hz?

A feedback network designed to work up to only 10Hz will have a bode plot that will not intersect the amplifier's open loop bode plot at all (thinking here the casual opamps with gain bandwidth ~1MHz).

Is the sub 100Hz injection useful for "just in case", is it for something else than testing loop stability, or am I missing/misunderstanding something else entirely?

One area I know that needs it are PFC controllers... sometimes you need to look at frequencies even less than 5-10 Hz...


EDIT: My bad I misunderstood the question.... In context of measuring open loop gain of opamp very low frequencies are not very interesting..

[Jay_Diddy_B]

Hi,
Measuring a control loop is different than measuring the open loop bandwidth of an op-amp. When measuring a control loop the main frequency of interest, as pointed out by RoGeorge, is when the gain is 0dB. By definition the amplitudes of the signals at nodes A and B are equal in amplitude and there is no concern about the signal to noise ratio.

When measuring an op-amp open loop gain, the low frequency gain is very high, 1E6 typical, 120dB. The signal on Node B is 1 million times smaller the signal on Node A.

Low crossover frequency

I have created a model of an amplifier with a dc gain of 10,000 and a Gain Bandwidth of 5Hz. This is G1 and E1 in the model.




In the AC analysis the 0db point is 5Hz as designed. The gain at 1Hz is 14dB.

In the time domain, at 1 Hz, the signal at node B is only 5x smaller, -14dB, with respect to the signal at node A.



With the relatively large signals, there are no SNR challenges.

At the 0dB frequency

For completeness, at the 0dB frequency, the signals at Nodes A and B are equal in amplitude, and phase shifted by 90 degrees.



Jay_Diddy_B

[mawyatt]

Lots of interesting discussions

Accessing gain and phase margin in op-amp based circuits generally are not a problem for the DSO because the signal levels are sufficient to resolve. However trying to determine overall loop gain and phase at lower frequencies becomes increasingly difficult as the frequency decreases because the signal amplitude decreases due the negative feedback and the isolation transformer lower frequency response. Increasing the signal level available at lower frequencies from the isolation tansformer may help and why we're looking into a higher primary inductance transformer.

In a way we are asking a general purpose DSO to perform as a dedicated high input impedance & sensitivity network analyzer and it does a nice job within reason. However, dealing with high loop gain such as op-amp circuits, the available signal level becomes so low at lower frequencies the DSO can't resolve such and the results show. Here's where a dedicated instrument shines, and likely using techniques such as synchronous sampling to help "pull out" the signal from the noise and produce accurate and repeatable results.

Most of the time the lower frequency performance can be easily estimated and the lack of performance here isn't a problem, however there are certain case where one needs this lower frequency performance. We ran into one such case a number of years ago when developing a closed loop piezo electric nanometer positioner utilizing "Flexures" as bearings, the control loop for this device was quite complex even at lower frequencies.

Anyway, quite pleased that a general purpose DSO can actually perform these type of measurements and produce respectable results within a reasonable range of operating parameters.

Now to see if a larger transformer can slightly expand that operating range 

Best,

[TopQuark]

I have been down this path of building wide BW transformers before as well.

Could you change the vertical scale to 0.2dB/div and repost?

Apologies for the delayed response, I've attached the results as per requested. Love your videos btw, keep up the good work.

I have received questions regarding the core I used and its availability. I got mine from Taobao which is not very accessible to the rest of the world. If purchasing from Aliexpress is an option to you, you can find cores similar to mine by searching for "nanocrystalline core" at the site.
https://www.aliexpress.com/item/4000447631159.html <- This core looks to be the same as the one I have used, although I didn't purchase mine from them. The seller also offer similar cores with other sizes.

Conclusion is that the Isolation transformer needs to have a much higher Primary inductance to keep the low frequency signal level reasonable for the scope to capture accurately since the high gain feedback loop is effectively nulling the scope Ch1 Vin signal, so we'll be getting a larger core and winding another transformer with larger primary inductance for these low frequency Closed Loop Bode measurements with high gain Op-amps like the OP-07.

About achieving less than 100Hz lower frequencies, are they really needed?

Asking that because (in my understanding) the instability of a feedback loop is expected to happen at the frequency where the amplitude of the feedback loop bode plot crosses the open loop amplifier's bode plot.  Usually this intersection of the two plots happens at a frequency in the kHz range, at least, so why bother testing at 10Hz?

A feedback network designed to work up to only 10Hz will have a bode plot that will not intersect the amplifier's open loop bode plot at all (thinking here the casual opamps with gain bandwidth ~1MHz).

Is the sub 100Hz injection useful for "just in case", is it for something else than testing loop stability, or am I missing/misunderstanding something else entirely?

I echo the same thoughts, usually I only look at crossover frequency, gain slope at crossover, gain and phase margin for SMPS control loops. I don't deal with PFC much, so if crossover is <100Hz, I probably don't need to run a FRA

I also agree the bode plot performance issues <100Hz has more to do with the instrument than the transformer. Looking at the videos showing the Bode 100 at work, it is obvious that whatever hardware/software they are using is way faster, has high dynamic range and noise rejection capabilities than the Siglent scope even at <100Hz, using transformers with similar sizes compared to ours.

Looking at the whole picture, I think what the industry can really benefit from is something with Bode 100 speed and accuracy, Cleverscope style isolated DAC/DDS (so no isolation transformer needed), NanoVNA design philosophy and price. Although that's just me daydreaming. 

[mawyatt]

Here's an example from 2019 where we could have used these Closed Loop techniques. Please read through the entire thread to get an idea of what's involved, one of the more complex analog feedback systems we've encountered in our career.

https://www.photomacrography.net/forum/viewtopic.php?f=25&t=40510&hilit=PIezo+Electric

Note the positioning graph with 200nm (0.2um) total range in 8~10nm (yes nanometers!!) steps 

The technique developed to make these nanometer measurements is another interesting topic 

Having this Closed Loop capability back when developing this project would have certainly helped, we knew about the technique and had used such as early as <1990 but with dedicated HP equipment, and didn't consider a mid-level MSO for this in 2019.

Best,

[bicycleguy]

@mawyatt
Very interesting posts.  Slightly off topic as far as the bode response but you might find this pdf about the actuators that align the mirrors on the Jame Webb Space telescope interesting.  Quoting from the first page:
 'This linear actuator is capable of 10 nanometer position resolution over a range of 20 mm and can operate under cryogenic conditions'

[mawyatt]

@mawyatt
Very interesting posts.  Slightly off topic as far as the bode response but you might find this pdf about the actuators that align the mirrors on the Jame Webb Space telescope interesting.  Quoting from the first page:
 'This linear actuator is capable of 10 nanometer position resolution over a range of 20 mm and can operate under cryogenic conditions'

Thanks, that's a very interesting article and quite an amazing device. Figures 12 & 14 show very good linearity and amazing repeatability.

Our efforts pale in comparison, but in defense we did this at home and within a few $K out of pocket.

We've been asked at other places how one measures sub-micron position, and since we're the OP guess it's Ok to go a little "off topic".

The technique utilized to measure position levels down to the nanometer region (and at home) employs optical alignment of a target. The target is a simple piece of quality print paper laser printed with a medium grey patch. Detailed observation of the paper under high magnification revels a totally random pattern of carbon black "dots" of laser powder (which is low temperature plastic impregneted carbon) and fused to the white paper under thermal and pressure, which give a medium grey appearance from afar.

The paper is cut and glued to a glass microscope slide and the slide placed on the piezo electric positioned almost normal to the optical axis to be viewed. A rigid fixed custom lens/camera fixture is arranged to view the slide and focused with a high quality (Mitutoyo 20X) stable lens & assembly on the slide center. Because the slide is almost normal optical axis the area above and below the center will be out of focus and a band of in focus will show with the DoF of the lens assembly (usually a few microns, a little trig will show how wide the band will be). The piezo element is commanded over the measurement range and at each position an image is captured with the hi res camera (Nikon D850). This small movement causes the DoF band to move across the image as the target moves under the piezo electric actuator.

After the images are captured, they are feed into a software stacking routine like Zerene. This is setup to attempt to align each image in-focus band to the first image in-focus band. The software uses high contrast areas like the white paper and random carbon black dots to use as alignment guides, and uses algorithms to define in-focus areas. These tiny random carbon black deposits fused onto the paper actually work better as alignment points than the usual alignment guides, and there's plenty of them!!

The amount of movement the image requires to realign with the first image is the movement the target imposed and is recorded. This recorded data shows the relative image shift required by each image in the stacking routine and used to evaluate the piezo electric positioning when compared to the total range involved. All this is done at the image pixel level and this is then converted to actual physical movement by the pixel dimensions.

This is a relatively complex task and takes time, but in the end can resolve target position movements in the nanometer region as shown......and it doesn't require an expensive lab, or complex expensive setup

Anyway, hope some folks find this interesting.

Best,

[mawyatt]

Just for fun we just did an open loop gain/phase measurement with the popular TL-431 shunt regulator. The setup was with the SDS2104X+ and a DIY Isolation transformer, with the primary driven by a AWG and unterminated. The secondary was placed between the Cathode and Reference in the feedback loop. The TO-92 package was plugged into a Photo-Board with jumpers, so lots of parasitic capacitance and contact resistance.

Also did an output impedance plot by driving the TL-431 Cathode with a signal thru a 1K resistor and plotting the response across the 1K resistor. The results are shown in dB K Ohms, so 0dB is 1000, -20 is 100, -40 is 10, -60 is 1 and -80dB is 0.1 ohms.

#19 is the Bode Plot of the TL-431 Open Loop Response with bias at 10ma, with Data Sheet from UMW (actual device OEM).

#17 is with TL-431 Output Impedance biased at 10ma, with Data Sheet plot from TI (UMW doesn't have a 10ma plot)

#18 TL-431 Output Impedance biased at 100ma, with Data Sheet plot from UMW.

Edit: Added another plot (#23) showing a TL-431 with a shunt 101.4nF ESR 1.72 ohm cheap ceramic load capacitor. This is in the "Forbidden Zone" as shown in the data sheet graph and the Open Loop Bode plots shows the Phase Margin as ~8 degrees at ~310KHz, or just on the verge of oscillations, and somewhat confirms the Data Sheet zone!!

Best,




Best,