Measurements of a small transformer

Hello Forum, I just read Trafo Bestimmung by  Gerhard Bischof.

Gerhard's post shows the analysis of a large power transformer with several hundred watts of capacity. His post inspired me to share some measurements of a small wall transformer, that I made a few months ago to get a better appreciation of it's operating parameters.

My measurements focus on input currents, transformer dissipation and loading on the 23V secondary.

A few basic transformer characteristics are:

Primary small signal inductance with 10VAC60Hz is 11.5H.

Primary resistance is 217 Ohms

Secondary small signal inductance with 1.96VAC60Hz is 440mH. The secondary resonates with 16uF at 60Hz.

Secondary resistance is 9.5 Ohms.

Overall dimensions are around 4cm/1.5inches.

This is the little transformer, which also came from the control board of a dead microwave oven.

The measurements revealed several practical aspects of transformer operation regarding core saturation, power factor and reactive secondary loading. For example, if you want to use two back-to-back filament transformers to make a small isolated vacuum tube power supply, you should add a power factor correction capacitor in parallel with the two common low voltage windings, which usually supply low voltage for the heaters. A back-to-back isolated transformer connection connection can be made with a first transformer that is powered off the wall with 120V(or 220V) and puts out 12.6V, which then drives an identical transformer in reverse, with the two 12.6V windings tied together, plus the power factor correction capacitor to reduce loading by the second transformer. This setup provides isolated 12.6VAC, and 120VAC secondaries.

This first photo shows the overall setup without any loading on the transformer, which is barely visible under the words "secondary resistance" to the left of the yellow Fluke meter.

The various instruments include:

1-TEK 475 scope showing transformer votlages or currents. The peaky  waveform is the primary current, and the sinewave is the secondary voltage.

2-On top of the scope is a true VAC RMS Fluke bench meter, showing secondary voltage 23.2VACrms

3-Further up, on the aluminum shelf, there is an HP428 current probe meter showing an analog face in the +/-300mA scale. The gray current probe for the HP428 is visible in front of the yellow cased Fluke 87 meter at the front.

4-Another True RMS voltmeter sits to the left of this HP428 current probe meter and is driven by the normalized +/-1VFS output of the HP428. It reads 200mV/1V*300mA=60mArms of primary current.

5-directly below the analog HP428 there is a small red panel meter that monitors the normalized DC +/-1V normalized output. This photo shows a residual 18mV offset.

6-Finally, the yellow cased Fluke 87 portable multimeter monitors the output of the power meter that is seen covered with the white outtlet plate. This true RMS power meter puts out 100uV/W for the Fluke 87. The power reading is 1.8W, and the transformer under test is unloaded. You can see details for this power meter's circuit in the thumbnail to the right of the photo, with right-click and view or save.

The following photo shows how adding a 33uF unpoloarized capacitor to the secondary, reduced the primary current to 24.4mArms. This value of capacitance produces the smallest amount of input current, but the overal power dissipation increasese slightly, to 1.9V because of the ohmic losses in the secondary that drives the 33uF capacitor. The calculated capacitance value to resonate with the secondary is 16uF, but this value was calculated from a small signal inductance measurement of 440mH. Core saturation reduces the average inductance, so the 33uF value was found empirically to produce a minimum input current.

Still with the 33uF load, the secondary current of 308mArms is measured and shown on the scope. The scondary voltage is 23.57VRMS and is also on the scope.

Now, for a bit of magic, the following shot shows a significant reduction of total power dissipation in the transformer, from 1.8W to 1.5W, when the load capacitor is optimized at 20uF. The primary current at 33mA is not as low as the 24.4mA rms seen in with the 33uF load. The reasons for the net reduction in power dissipation are that the primary ohmic losses were reduced, along with the core losses. Secondary current can cancel some of the field of at the core and reduce saturation. But this current must be of the proper phase, in this case, capacitive.

Show primary current on a 10mA/div on the scope with the 20uF minimum power 1.5W dissipation.

Another non-obvious result, is the slight reduction of input current from 60mA unloaded to only 56.4mA, when a light 1kOhm load is presented to the secondary.

The actual current flowing through the 1kOhm secondary load.

This shot shows a step in experimental procedure to check processing delay of the current sensed by the gray current probe at the front of the photo, as it passes through the HP428B on the aluminum shelf and is fed to the scope. One scope trace is the secondary votlage on the 1kOhm resistor and the slightly delayed curve is the current.

Another non-obvious result. The primary current increased only slightly, from 60mArms-unloaded to 66mArms when a heavy 72_Ohm rehostat load was applied to the secondary. The total dissipation increased from 1.8W to 7.3W, but the input current hardly changed.

The secondary load current and voltage are shown on the scope and they measures 245mA and 18.22V, respectively.

Verify original 60mA unloaded current before proceeding to next experiment.

Now, for the worst possible kind of load for this small transformer, I chose a 380mH inductive load of a much larger transformer, that is large enough to stay out of saturation. The loading inductor is one of the transformers in the pair. The primary current increased to 79.5mA, but the power dissipation, which is nearly exclusivelly in the small transformer under test shot up from 1.8W to 4.8W. This example shows the trouble with the back-to-back isolated transformer pair. But most of this current could have been resonated away, with a properly sized capacitor at the secondary. A first estimate for this capacitor could be taken as the capacitance that resonates with the two parallel secondary and load inductances at the 60Hz line frequency, then some experimentation with a smaller value could give the lowest possible dissipation. This is how I went from 33uF to 22uF in the examples above.

Compare how this 300mA load from a 55 Ohm resistor in this photo affects transformer losses, as compared to the the same 300mA load from a 33uF capacitor in the last photo. A 5.1W/300mA load increases transformer losses from 1.8W to 3.3W.

Now the same 300mA (290mA on the meter) only increase transformer dissipation by 100mW.

This series of experiments illustrates how much can be learned from a power transformer. More experiments and measurements could be done, like measuring input primary current as a function of primary voltage. It seems that most comercial transformers are designed to operate at the edge of saturation, even large ones, such as the transformer that Gerhard Bischof analyzed in his Trafo Bestimmung.

Comments and other transformer experiences invited,

Regards,

-Joe

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Fello Radiophiles,

Our Prof Dietmar Rudolph has posted another of his very informative posts.This time the topic explores in great detail, measurements of primary transformer current as a function primary voltage.  I read the German language article with the Google translator.

This topic is of particular importance to antique radios that may have been designed to operate at a slightly lower, perhaps 5-10% lower, voltage than current voltages available at the mains.

The problem is more significant for AC sets with a power transformer that may have been designed to operate just below saturation. Some of the measured curves in Prof Rudolph's article show disproportinate increases in current from only 5-10% increases in mains voltage.

Best Regards,

-Joe

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Fellow Radiophiles,

Metalic conductors offer a handy way to estimate their temperature rise because their resistance is approximately directly proportional to absolute (Kelvin) temperature. The temperature estimate comes from comparing the room temperature resistance ~27°C (~300°K absolute) and the resistance shortly after the conductor is disconnected from service, before the conductor has had a chance to cool down.

The winding resistance of the primary offers a very convenient resistance to measure before and after warmup. This resistance is easy to measure because it ranges from a few tens of Ω to a few hundred Ω. The primary winding may also be the hottest winding in the transformer.

The approximate temperatue coefficient for copper Resistance is +0.0039/°C.

For example, a primary winding with a 100Ω at 27°C that reads 117Ω when disconnected after a long period of warm up, will have an approximate temperature of 71°C. 

Best Regards,

-Joe Sousa

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