# Computing stuff tied to the physical world

## Component Tester revisited

In Hardware on Apr 27, 2012 at 00:01

In January, I described the concept of a Component Tester, and how it can help understand what various types of components are doing.

In theory, you can just hook up a small transformer to generate the signal needed for the CT, i.e. a 50 Hz ±10V sine wave. Here is the circuit again, which is delightfully simple as you can see:

That secondary voltage is a bit high, though. Here’s what I get with two 6.3 VAC in series, i.e. 12.6 VAC:

Half that would be fine. But it’s not really a sine wave, as you can see from the many harmonics in an FFT:

And it shows – here’s what you get when placing a 1 µF electrolytic capacitor under test:

Yikes, what a mess! With a (clean) sine wave, that would have been a (clean) oval!

I don’t think it makes sense to build a CT this way. Not with this particular small transformer anyway…

1. which rises the question: what makes a good quality transformer?

• I don’t know. Note that it might also be the incoming non-sinusoidial shape. I haven’t checked that yet.

2. If you start with a perfect sine wave and use that as input to a power supply that has a full bridge rectifier charging up a capacitor, and the capacitor is mostly charged up, the bridge only conducts at the peaks of the sine wave, causing a “flat top” effect on the AC input- similar to your scope trace.

• Understood – but there is no rectifier in this case.

3. Small power transformers designers are driven by cost/size. The result is usually insufficient iron in the core – this takes the operating point well towards the saturation region of the driving amp.turns versus magnetic flux curve. The effect is to compress the tops of the input waveform – add this to the “straightening” effect the transfer curve gives to the sides of the waveform; the output shape gets ugly.

Map this to the frequency domain and you will see a rich array of odd harmonics of the input frequency. Designers of larger transformers have more scope to scale the copper/iron better and generally create less distortion.

Is an ideal transformer even possible?

Yes indeed – throw away the iron! The flux will still link in air or even vacuum. Unfortunately, at low frequencies, the coupling becomes too inefficient to be practical.

Next best is to use better-quality core laminations, then operate in the lower, more linear part of the transfer curve. Some of the best audio microphone matching transformers are built this way and boast low distortion over a wide frequency range.

Of course, as jbeale points out – the many nonlinear loads on the input waveform cause similar flat topping and a standard transformer can’t correct input errors.

• Again, understood – but I don’t understand why this happens even in an unloaded (or very lightly loaded) transformer.

4. Many years ago, I was asked almost exactly this question at a job interview. The answer is that the unloaded transformer is the worst case, not the best case.

At constant frequency, the magnetic flux in a transformer core is proportional to the peak voltage applied. Any current flowing in the primary winding drops a voltage across the winding resistance, which is ‘wasted’ and so does not add to the peak flux. So when the transformer is fully loaded, the flux is lower and the iron core remins in its linear, non-saturated regime. When it is unloaded, there is no voltage drop and the iron starts to saturate.

A transformer is designed to work at a rated load, without getting too hot. At least for small cheap, transformers, this means a relatively high winding resistance (since copper is expensive) which means the difference in peak flux between no-load and full load is relatively large, so the iron is well into saturation at no load. This actually increases the power lost in the iron above the full-load condition, though the copper losses are still lower at no load. High-power transformers have to be designed with a lower peak flux in the no-load condition, because the primary winding resistance is so much less. The parameter that describes this effect is called the ‘regulation’ of the transformer (the lower the better). Small transformers have worse regulation, because it makes them cheaper, and because the manufacturer can get away with it!

Try adding a load resistor across the transformer secondary, to draw about 1/3 of the transformer’s rated load. That should clean the waveform up a bit.

5. Ah – practical transformers! What they don’t explain in the textbooks, but Max has described well above. Lightly loading the secondary gets the primary working quite hard generating enough back EMF to balance the applied primary feed voltage.

Simply regard the unloaded secondary as a many-turn probe of the magnetic circuit – then you are really sampling the wave shape of the magnetic flux passing through the core. The primary takes just enough current to generate just enough flux to induce the right back emf to reach the lowest energy balance point. Nature solving the differential equations faster than a Cray.

With little and/or cheap iron, the amp.turns required already drive the core far enough around the B/H curve that the non-linearity shows up as gross distortion of the waveform. Theory tells us odd harmonics only in the frequency domain. But some even harmonics are clearly there also?

Another “undocumented” feature. With the input feed connected, the magnetic flux sweeps from one direction to the opposite at 50/60 times a second, passing through zero – essentially resetting the core. Switch off at some arbitrary time not synchronised with the incoming feed then a certain level of flux gets “trapped” in the magnetic memory (or remnance) of the core.

Next time the power feed is applied, the remnance reinforces one polarity/apposes the opposite. This introduces an asymmetry around the zero level. FFT theory comes into play – it takes even harmonics to create this asymmetry.

Big deal, just an academic point? For designers of highly stressed switching supplies, this memory effect is an issue. Having the storage inductor locked up in the “easy” direction can destroy the switching element on first re-application of power.

6. Out of curiosity, I hooked up the scope w/ FFT to this same 12.6V @ 200 mA transformer again, and loaded it with 10 kΩ, 1 kΩ, and 100 Ω. The only effect was that the voltage dropped a bit when loaded with 100 Ω, as expected (and my resistor started smoking, as it was only 1/2 W). The harmonics are mostly odd, with a few even peaks – same as above. The 3rd and 5th harmonic at 150 and 250 Hz resp. are 30 dB down.

This isn’t good enough for a CT, I think I’m going to have to look for a simple sine-wave generator instead.

7. I learned a lot about transformers when I worked for QUAD (the interview question was asked by the late, great PJ Walker himself!) The audio transformers in the ESL63’s were a work of art: step up 30 Vrms to 3.5 kV, over a 20Hz – 20kHz bandwidth, with overall distortion less than 0.1%.

For those in the know, the secondary leakage inductance was used as the first stage inductor in an L-C delay line, which drove the speaker electrodes. That removed its effect on the frequency response, which would otherwise have been calamitous – I think the actual leakage inductance was around 2H.

8. Its marvelous watching you gladiators gnaw on the electronic bones of nature.