Transformer Measurements 1

[The Electrician]

I have some handheld LCR meters and a couple of bench models. For what I want to show in this thread, I'll be using the bench models. They are the Hioki IM3570 and the Keysight E4980A. The Hioki covers the range 4 Hz to 5 MHz, with a maximum stimulus voltage of 5 volts. The Keysight covers 20 Hz to 2 MHz, with a maximum stimulus voltage of 20 volts. Both meters can select the stimulus voltage with a resolution of millivolts, and the test frequency with 4 digit resolution. They both display the measured values with 7 digits; the basic accuracy of the meters (.05%) can't justify so many digits, but all those digits allow matching capacitors to much closer than .05% if that is wanted.

For my first post, I'm going to show something that is not earth shaking, but is well known, though not often shown as actual measurements. Tranformers that have iron cores such as OPTs for vacuum tube amplifiers exhibit winding self inductances that vary with measurement voltage. Here are the measured self inductances of the primary (secondary open) of a Softone output transformer: Softone RX-30-8 Push-Pull Audio Output Transformer with 4 different applied measurement voltages. The first 3 measurements are made with the Hioki, which shows 4 parameters at once; this is feature I like.

Here is the measured self inductance of the primary at 20 Hz, with a stimulus voltage of 1/10 volt:


Here is the self inductance with a stimulus voltage of 1 volt:


Here is the self inductance with a stimulus voltage of 5 volts:


Finally, the self inductance with a stimulus voltage of 20 volts. For this one I used the Keysight meter for its higher stimulus voltage capability:

It's late, but I'll have more to say tomorrow.

 

[ruffrecords]

That is well over 50 grands worth of measuring kit.

Cheers

Ian

 

[CJ]

Try both machines at say 5 vac and see if they give the same answer.

Put an iron core power xfmr on there and see if the inductance creeps up over time, an old one from storage if you got it,

 

[The Electrician]

That is well over 50 grands worth of measuring kit.

Cheers

Ian

Currently $25k for the Keysight and $11k for the Hioki, new today. Fortunately I inherited them.

 

[The Electrician]

A major building block in modern LCR meters is the signal generator that provides the sinewave of voltage as stimulus for the impedance being measured (the DUT). An aspect of that generator is that it has a nominal output impedance of 100 ohms. Its open circuit voltage is one of the settings in the meter, along with the test frequency. Most of the available handheld LCR meters have a fixed set voltage of .6 volts, chosen to hopefully avoid turning on semiconductor junctions. But what is often overlooked is that because of voltage drop in the 100 ohm output impedance, the DUT may not see the set voltage. The Hioki and Keysight display the actual voltage across the DUT.

Here's a measurement of the self inductance of the primary of the Softone OPT. The set voltage of 1 volt is circled in red, and the DUT voltage and current are circled in blue. The impedance of 35.6k is high enough that the actual applied voltage (vac) of .9996 volts is only a little less than the set voltage.


Here is a measurement of the secondary self inductance. The impedance is 97 ohms and this is low enough that the actual applied voltage is .5143 volts due to the loading of the 100 ohm output impedance of the meter.


Are these measured self inductances good for something? Let's calculate the turns ratio using the formula TR=sqrt(LP/LS) = sqrt(47.79/.1054) = 21.3

How does that compare with the turns ratio derived from the Softone's impedance spec, which is 8000:6 ohms. We use the analogous formula: TR = sqrt(ZP/ZS) = sqrt(8000/6) = 36.5

This is a very large error. The problem is that both self inductance measurements were made with essentially the same voltage applied to the windings. A voltage applied to the secondary, with its fewer turns, will generate more flux in the core than that same voltage applied to the primary, which means higher measured self inductance for the reason illustrated in the first post of this thread.

If two inductances for the transformer were wanted for use in simulation, for example, they must be measured with the core in the same state (same flux) for the two measurements. To do this, the applied voltages must be in the same ratio as the turns ratio. That is, we must apply the same volts per turn for each winding. We might apply .1 volt to the secondary and 3.65 volts to the primary. To do this with an LCR meter will require a meter that can vary the stimulus voltage over a wide range; a typical hand held LCR meter won't be able to do it.

It could be done indirectly with a variac, apply different voltages and measure the resulting currents, but this would confine the measurement frequency to be 60 Hz (in the U.S.)

I'll show another useful series of measurements that can be done with a meter having a wide range of stimulus voltage capability.

 

[The Electrician]

Try both machines at say 5 vac and see if they give the same answer.

Put an iron core power xfmr on there and see if the inductance creeps up over time, an old one from storage if you got it,

I saw your post: https://groupdiy.com/threads/measuring-transformer-inductance.82950/page-2#post-1077158

I noticed years ago that when you measure a transformer with an iron core, the measurement can drift for a long time. An iron core inductance that has been excited can be left with the core in a partially magnetized state if the excitation is removed in an uncontrolled manner. If a power transformer is energized with AC, and the AC is turned off at some time in the sine waveform other than one particular magic time, the core will be left with remanent non-zero flux. Any old transformer that has been used will likely be slightly magnetized unless it has been fully degaussed.

The small AC voltage applied to a winding by an LCR meter will slowly over time degauss a core that is partially magnetized at the beginning of the measurement. This causes the measured inductance to slowly drift, and it can take several hours for the measurement to finally stabilize.

Also, the very sudden application of an AC sine wave to a winding causes a transient dying exponential pulse with DC content unless the AC is applied with one particular phase which doesn't cause that transient.

If I measure a winding of a transformer with the LCR meter and wait for a few hours (literally) for the reading to stabilize, note the reading and disconnect the LCR meter, then reconnect the meter, the reading will be slightly different and will then drift for a long time again. The very act of disconnecting the LCR meter happened at an uncontrolled phase of the measurement voltage sine wave, leaving the core slightly magnetized. This is a very small effect, but it can be seen when the LCR meter being used is one with lots of digits in the display.

CJ, here are measurements of the primary of the Softone OPT taken with both the Hioki and the Keysight. I only waited for about a half hour and the readings weren't fully stablized.

There's no such thing as precision measurements when an iron core is involved.

 

[cyrano]

I've always been told that some capacitors' value also changes with the applied voltage. It's a small discrepancy, so I don't pay attention to it. IIRC, it's mainly with bigger electrolytes.

 

[The Electrician]

Toward the end of post #6, I pointed out that if a pair of inductances of an audio transformer are wanted that can be used for simulation, they must be measured with the same core flux for each winding. I will call such a pair of inductances "core compatible", or just "compatible".

We were able to get a value for the turns ratio of the Softone OPT of 36.5 that we hope is reasonably correct. To get the compatible pair of inductance values it's necessary to use two stimulus voltages for the measurements that are in the same ratio as the turns ratio. Two such voltages would be .1 volt for the secondary measurement, and 3.65 volts for the primary measurement. We know these because we know the turns ratio.

What if we wanted to get compatible inductances for an OPT for which we don't know the turns ratio? There is an iterative procedure which I'll show in this post. It has the disadvantage of requiring the use of an LCR meter with a wide range of selectable stimulus voltage. But the procedure should also work with the variac method of inductance measurement.

First set the LCR meter a low value such as .1 volt and measure the secondary winding. Notice that the .1 volt must be the actual applied voltage, the vac in the display:


Next, using the same stimulus voltage, measure the primary:


Make a test calculation of the turns ratio using the formula TR = sqrt(Lp/Ls). For these two measurements we get TR = sqrt(32.054/.1871) = 13.09

The stimulus voltage of .1 volt needs to be multiplied by the test value of the TR. So, make another measurement of the primary, but with a stimulus voltage of 1.309 volts:


Calculate another test value of the turns ratio: TR = sqrt(154.45/.1871) = 28.73. Increase the stimulus voltage to .1*28.73 = 2.873 volts and again measure the primary:


Once more calculate the test value of the TR: TR = sqrt(219.57/.1871) = 34.26. Finally increase the stimulus voltage again to 3.426 volts and measure the primary:


Calculate the TR using this inductance: TR = sqrt(235.42/.1871) = 35.47. This compares very favorably with the value of 36.5 we got from the Softone impedance spec of 8000:6 ohms. We could go even one more step for maximum obsessiveness, which I didn't do.

This gives a pair of compatible inductances, and also the TR for the transformer.

Next I'll show a method to get compatible inductances without so much trouble.

 

[The Electrician]

I've always been told that some capacitors' value also changes with the applied voltage. It's a small discrepancy, so I don't pay attention to it. IIRC, it's mainly with bigger electrolytes.

This is true, but, as you say, the effect is very small.

Using an LCR meter with what, for ordinary measurements, is an excessive number of digits in the result measurement, I notice that a much larger effect is the result of holding the capacitor between my fingers thereby warming it up before inserting it into the meter fixture. It can take 5 or 10 minutes to cool back down to room temperature. The difference in temperature coefficient between a mylar capacitor and a polystyrene capacitor is readily apparent just due to the finger warm up effect.

I don't see this happen when I use one of the handheld LCR meters I use for everyday measurements.

 

[cyrano]

That's news to me, but it sounds logical. The heat will push the electrodes closer, resulting in a higher capacity.

I bet the transformer differences are because of magnetism? How about a transformer without iron? Does such a beast even exist?

 

[CJ]

Air core inductors are used in rf, I am sure there are air core transformers used in rf also.

If a big core transformer has been sitting in the same position for a long time, I bet that the earths magnetic field could conceivably magnetize the core ever so slightly, I know ships have thus problem with their compass,


Does that inductance meter have the ability to apply a DC bias to the transformer under test?

Stevie Ray Vaughan used to hammer on his output transformers to demagnetize them, DC imbalance no doubt,

 

[The Electrician]

I want to talk about what can be done to measure winding self inductance of an OPT when a fancy bench LCR meter isn't available.

First it's good to be aware that the stand-alone word "impedance" can be ambiguous. Strictly speaking "impedance" alone refers to the complex number used in AC circuit analysis. The letter "Z" is used to denote it, and we have Z = Rs + jX, where Rs is the resistive (real) part and X is the reactive part; note well that this "complex impedance" has two parts.

There is another use for the single word "impedance" which should really be called "impedance magnitude". This is a single number which is calculated from the two-valued complex impedance. It is denoted by the symbol |Z| and calculated as: |Z| = sqrt{Rs^2 + X^2). It's quite common for the single word "impedance" to be used for the impedance magnitude; I do it and so does everyone else!
Usually the context will tell you what definition of "impedance" is being used, but if it matters, one can say "complex impedance" or "impedance magnitude" to be perfectly clear.

Note that the images from the Hioki LCR meter I've been posting show just the letter "Z" when in fact what is being displayed is impedance magnitude.

One common way to measure self inductance of an OPT primary is to apply an AC voltage of some particular frequency to the winding and measure the resulting current, divide the applied voltage by the current, assume that value is the reactance, and divide by 2*pi*f giving the inductance.

The problem with that method is that the result of dividing the applied voltage by the resulting current gives a number which is not just the reactance. It would be just reactance if the winding were an ideal inductance with no loss--no DCR in the winding, no hysteresis and eddy current loss in the core. The actual impedance being measured has the form Z = Rs + X; there is more than just the reactance X affecting the resulting current. To get a good value for the inductance, we need to get rid of the effect of the resistive part Rs.

I have an OPT I bought from eBay. It was described as a universal replacement OPT. There were no impedance specs and no power rating. l bought it to use as example of a not so good OPT to illustrate how to measure an OPT. It has a primary DCR of 195 ohms. Here are 3 measurements with a different parameter for the 4th item among the three. Note well that the value of Rs is not equal to the DCR of the winding. The winding DCR is 195 ohms, but the resistive part of the impedance, Rs, is 787 ohms.


So, to get a good value for the inductance, we need to eliminate the Rs part of the complex impedance, leaving the reactance X behind. This can be done with a little math if the impedance magnitude and Rs are known.
We do this calculation: X = sqrt( |X|^2 - Rs^2 ); then L = X/(2*pi*f)

There was a long thread in 2016 about this topic: https://groupdiy.com/threads/inductance-measurement-problem.61436/post-778141 In that thread CJ posted a chart showing a bunch of measurements. Column "G" in that chart is titled "XL-Corrected", and just below the title it says "(subtract DCR from Z)". That had me going for a minute because in line 5, when I subtracted DCR which was 107, from 457, I got 350 rather that 444.57. Further study revealed that rather than just subtracting, the proper calculation was used, to wit: XL = sqrt( Z^2 - DCR^2 )

But even that correction for DCR is not `what should be done. What should be done is to correct for Rs because Rs is the resistive part of the value we got when the applied voltage was divided by the resulting current. We can see this in the images of the Hioki measurements of the OPT just above. The value of Rs is like the ESR of a capacitor. It is the equivalent series resistance of the winding; that word "equivalent" is key. Rs includes the effect of not only DCR, but also hysteresis loss and eddy current loss.

In this case, I got the proper value of Rs by using an LCR meter. How would I get Rs if I didn't have the fancy LCR meter? We may not need to try to compensate for Rs to get a useful measurement of L.

 

[The Electrician]

Suppose we are able to make a measurement with an LCR meter of the complex impedance of the primary of our OPT. This means that we have the values of Rs and X where Z = Rs + jX. Then it's easy to get the inductance--it's just L = X/(2*pi*f)

The LCR meter has done the work of separating out the reactance X from the impedance magnitude; impedance magnitude |Z| is what we get if we do the manual measurement of applying an AC voltage to the winding and measuring the resulting current, dividing the voltage by the current.

How much error do we get if we do the apply voltage, measure current technique, divide voltage by current, which gives us |Z|, and calculate |Z|/(2*pi*f) from that value, calling that result the inductance?

To determine the error is just a calculation with a complex number. For example, suppose at a frequency of 100 Hz the value of Rs is 1000 ohms, and X is 2000 ohms. In other words, X is twice as large as Rs. In that case |Z| is sqrt( 1000^2+2000^2) which is 2236 ohms. If we calculate the inductance from that we get 2236/(2*pi*100) = 3.5587 H; this value is too high. If we had made the calculation with the value of X instead of the value of |Z|, we would get 2000/(2*pi*100) = 3.1831 H. for an error of 11.8%. When making measurements of windings on iron cores, I consider a 12% error not bad!

If the ratio of X to Rs is larger than 2:1, the error will be less, of course. If the ratio is 3:1, the error in using |Z| to calculate L instead of using X, the error will be 5.4%; and so forth.

Looking at the first image in post #12, we see that ratio of X to Rs is 9.163; that ratio is just the measured Q of the winding. If we calculated the inductance using |Z| instead of X the error would be .6%; the measurements themselves aren't that good!

The upshot of this is that you can make a measurement using a handheld LCR meter at 100 Hz with a typical applied set voltage of .6 volts. Most of those meters can display the Q of the DUT; if that value is greater than 4, you're golden. Then you can use a manual method of applying a much higher voltage than .6 volts, measuring the resulting current and calculating the inductance from that value of |Z|. A consideration in this is that the ratio X/Rs might not be the same at a higher applied voltage or different frequency, but I've checked a number of windings on iron cores with various voltages and frequencies, and I found that if the ratio X/Rs (Q) is >4 on a handheld LCR meter, it is almost always >2 for all applied voltages and frequencies. It would be good if others could check this out. It's a good place to start, anyway.

To make a calculation where the presence of Rs doesn't cause an error, we need to extract the value of X from our measurement of |Z|. To do this we need to know the relative phase of the resultant current with respect to the applied voltage. In the absence of a phase meter , we will have to use an oscilloscope to measure the phase. That's what an LCR meter does for you. It applies an AC voltage, measures the amplitude and phase of the resulting current, and calculates various parameters.

I'll report measurements made with signal generator and scope next.

 

[The Electrician]

I did some measurements using a signal generator and scope. I wanted to be able to compare to the result from the Hioki. I connected the primary of the low cost eBay OPT referenced earlier in series with a 100 ohm resistor. This series combination was driven from a 100 Hz source and the amplitude was adjusted to give .6 volts across the combination. I wanted to have .6 volts across only the primary, but I had already made the measurements when I realized that the voltage drop across the 100 ohm resistor is subtracted from the total of .6 volts leaving .591 across the primary. This is only about 1% less than the desired .6 volts, so I didn't put everything back on the bench and rerun the experiment.


Here's the setup I used. The voltage across the series combination is connected to channel 1 (yellow) of the scope, and the voltage across the resistor is connected to channel 2 (green). It would be ideal if channel 1 would only see the voltage across the primary, but as is it's only about a 1% error, it's good enough for measurements of a winding on an iron core.

The point of this is to get a number for the phase shift between the applied voltage and the resulting current, and from that, the value of the reactance. We get a value for the impedance magnitude by dividing the voltage across the primary (.6V) by the current. The current is the voltage across the resistor divided by its resistance. The voltage across the primary has two parts; the part due to the AC resistance of the primary Rs, and the part due to the reactance X. We would like to know how much of the .6 volts across the primary is due to X, and we get that by multiplying the .6 volts by the sine of the phase angle. This "reactance voltage" is then divided by (2*pi*f), and we have the inductance. Here is the scope capture:


The phase angle is 82 degrees, and sine(82) = .99 so the voltage due to the reactance is .6*.99 = .594 Now divide the voltage across the resistor by the value of the resistor, giving the current through the resistor and the primary; we get .00856/100 = 85.6 uA. Divide .594 volts by 85.6 uA and get the reactance X = .594/.0000856 = 6.939k ohms. To get the inductance we calculate 6939/(2*pi*100) = 11.04 henries.
If we hadn't bothered to use the phase to eliminate the Rs effect, we could have calculated the inductance using the full .6 volts, and the result would have been 11.16 henries. It was hardly worth the trouble, but that is only because the ratio X/Rs (the Q) is rather high for this transformer.

I also made measurements with the Hioki for the same conditions: .6 volts applied and a frequency of 100 Hz. The values in the Hioki images compare very favorably with the manual measurement results.


The manual setup can be used with other applied voltages and frequencies as desired. It does require an oscilloscope to get the phase which is needed to eliminate the effect of Rs. Here's where a handheld LCR meter is useful. Measuring with such a meter, If the ratio X/Rs at 100 Hz, which is just the measured Q, is high enough (greater than 4 is probably enough), or if the measured angle theta is greater than 75 degrees, then not eliminating Rs results in negligible error, and you don't need a scope.

 

[Wavelength]

Doesn't all of this require the DC voltage and current running through it before any of the calculations can be made? We did a bunch of single ended designs using parallel feed. That is where the tube is loaded with a large choke and the output can be smaller and is basically cap coupled. DIY guys complained that when they measured the choke with a LCR meter that they got poor results. The designer said you can't do that unless you are pulling current through the choke as the inductance was calculated and the air gap determined that way. Less so in PP output as the current I think washes for the + and - side of the output.

 

[The Electrician]

Both the Softone OPT and the cheap eBay OPT are designed for push-pull use. I didn't show the center tap in the setup video of post #14, but it's there.

So far, all the measurements I've shown have been made on windings where there is no unbalanced DC in use.

CJ asked me in post #11 if the inductance meter has the ability to apply a DC bias to the transformer under test. The Keysight meter has that ability, and I'll show some measurements soon. It's surprising just how little DC in an OPT primary greatly reduces the inductance.

 

[The Electrician]

Does that inductance meter have the ability to apply a DC bias to the transformer under test?

Section 5 of the Softone spec: http://softone.a.la9.jp/english/RX30-8/RX-30-8.htm
shows the effect of small amounts of DC bias, up to 5 mA

Here is a measurement of the self inductance of the Softone's primary with zero DC:


Now with 10 mA of DC bias:


And with 30 mA of DC bias:

 

[Wavelength]

If you want everything to really go south, just unbalance the DC. Peerless use to spec that usually less than 3ma. One of the reasons why matching is so critical.

 

[The Electrician]

Here are 4 measurements of the Softone OPT primary self inductance vs. increasing frequency. This shows another property of iron cored windings that is often mentioned on the forum--inductance decreases with increasing frequency.

Here is an image illustrating a feature of the Hioki I haven't used yet. Besides being an LCR meter, it's also an impedance analyzer. This is a sweep from 20 Hz to 20 kHz of the self inductance of the Softone OPT primary. We see a steady decrease of inductance as frequency increases until resonance is reached a little over 1 kHz above which the primary impedance becomes capacitive.

 

[Wavelength]

Remember the L is only required for the low end, so diminishing L as it goes up in frequency is not going to have effect on the output.
Going up in frequency is only hampered by the capacity of the windings. Just like all good engineering there are diminishing returns on everything you do inside a transformer. Increased windings = more L, more C and more Rdc, iron usage, air gap etc...
A big rule of thumb is Rdc * Idc < 20V, same for inductors/chokes. Every transformer designer I ever talked to would say that. Of course the rest of it could be crap and still hold that rule true. But there's a start.