Transformer Inductance

Hi all,

I received an audio transformer for a project from my prof and went ahead and started to characterize it before using it.

CT-side DC resistance: 46R
Non-CT-side DC resistance: 2R
Voltage gain ratio: 1:13

The part is an audio transformer (1.2K primary, 8R secondary) 60-282-0

While doing LC tank measurements to figure out the inductance, I determined the resonant frequencies with different parallel capacitor values (1nF, 1.5nF, and 10nF) and both the primary and secondary windings had roughly the same inductance 10-12 uH.

Maybe I'm just double-guessing myself but shouldn't the ratio of inductance be roughly the turns ratio and not one?

For each measurement, I left the other winding open and unconnected.

Thank you,
JP
I found a similar transformer in my junk box. It is an old transistor radio output transformer. It's dimensions are almost identical to yours, but the DC resistance measurements are a little different. The primary is a 1k ohm winding with a DC resistance of 65.3 ohms. The secondary is an 8 ohm winding with a DC resistance of .61 ohms.

Your method of determining the inductance of the windings is not going to work because you end up measuring at a much too high frequency.

I made some measurements on my transformer with an impedance analyzer. This analyzer can measure over a wide frequency range and can display several parameters such as impedance magnitude, impedance angle, inductance, capacitance, Q, etc.

Here are two plots of impedance magnitude and angle over a frequency range of 10 Hz to 1 MHz. The plots show impedance in green and angle in yellow. The scale is shown on the plot; there are two makers labeled A and B. The A marker is at the left end of the plot--at 10 Hz; the B marker is at 1 kHz.

The vertical scale of the impedance plot is logarithmic with the grid shown and the angle plot is linear with 100° at the top and -100° at the bottom with a linear grid not shown.

The first plot shows the impedance and its angle for the high impedance winding (the 1k ohm winding) with the impedance scale ranging from 100k ohms at the top, to 100 ohms at the bottom; the other winding (the 8 ohm winding) is left open for this measurement.

The impedance is not purely inductive. You can see this because the angle (yellow) is not a horizontal line at +90° (that would be nearly at the top of the display). One could calculate the inductance at any particular frequency by using the imaginary part of the impedance (the reactance). Divide the reactance by (2 Pi f) and you have the inductance. The impedance also has a real part which represents loss in the inductance.



The second plot shows the impedance of the 8 ohm winding with the other winding left open:



Note that in both plots, the impedance (green) reaches a maximum just past 10kHz. The high impedance winding consists of many turns of very fine wire, and that winding has a self resonance which is responsible for the impedance maximum.

The 8 ohm winding also has its own self resonance which is at a much higher frequency and doesn't show up in these plots.

The impedance peak in the second plot above, which is of the 8 ohm winding, has an impedance peak because the self resonance of the 1k winding is reflected into the 8 ohm winding by the coupling between the two windings; it is not due to the self resonance of the 8 ohm winding itself.

We also see a sharp dip in the impedance of the 8 ohm winding at about 108 kHz. This is due to the resonance between the leakage inductance of the 8 ohm winding and the reflected impedance of the 1k ohm winding, which is a capacitance at this frequency (since this frequency is above the self resonance of the 1k ohm winding).

This transformer is designed to be used at audio frequencies and you can't characterize it by connecting capacitors which cause resonances at frequencies as high as 500 kHz

Look at the impedance curve for the 1k ohm winding. It varies from about 164 ohms at 10 Hz to about 20k ohms at 10 kHz. But, it's supposed to be a constant 1k ohms at all frequencies, isn't it? Its impedance is steadily increasing from 10 Hz to 10 kHz; what's going on? I'll explain in the next post.
 

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Here is a plot of the impedance of the 1k ohm winding with the other winding connected to a resistor of 8 ohms:



We see that the impedance shows a region from about 800 Hz to about 20 kHz where the impedance is relatively flat at about 1k ohms. Now the resonance peak appears to have moved to about 100 kHz; higher than the approximately 10 kHz when the other winding was unloaded.

Here is a plot of the 8 ohm winding with the other winding connected to a 1k ohm resistor:



Here the impedance is about 9 ohms from around 800 Hz to about 30 or 40 kHz, a somewhat wider band than the 1k ohm winding.

Now we see that the rated impedance of either winding depends on the other winding being loaded in its rated impedance. Look at the phase angle of the impedance (yellow curve) over the useable frequency range; it's near the center of the plot (zero degrees) and is a nearly horizontal line there. That means that the impedance is not only about 1k ohms, but it's also nearly pure resistance. This is the behavior we would want from our transformer. Outside of this range, the angle of the impedance is not approximately zero degrees.

We also see that the useable frequency range of the transformer is rather limited; it doesn't even cover the full modern hi-fi range of 20Hz to 20kHz.
 

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Here's a plot showing the measured inductance of the 1k ohm winding with the other winding open:



Notice that the measured inductance varies considerably over the frequency range 10 Hz to 10 kHz. This is in large part because of the presence of the self resonance at 10 kHz. After the measurement frequency passes 10 kHz, the apparent inductance becomes negative (capacitive, in other words).

Your model will have to include a capacitor across the 1k ohm winding to cause a resonance at 10 kHz (or at whatever frequency your own transformer has a self resonance).

Here is the same plot, but with the 8 ohm winding shorted (note the scale change for inductance). Now we are measuring the leakage inductance. Note that the apparent leakage inductance rises at low frequencies; this is due to the resistance of the windings. I would use the 1 kHz value of 2.3 mH. You can calculate the coupling coefficient (k) to use in your model from this.



If you use the various parameters I have measured for my transformer, you will would have a good start for modeling your own transformer.

I see that you are in Canada. If you mail me one of your transfomers (I see they cost $1.92), I'll measure it for you! :D
 

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Tesla23

Joined May 10, 2009
542
An impressively accurate box! How do you think it does a measurement at 1kHz in 1.5ms - only 1.5 cycles? Is it using sinusoidal excitation (which you would think would give it transient problems as the frequency is changed) or some sort of noise excitation followed by some FFT technique to make multiple measurements at once?

Your plots reminded me of the HP4195A I used to have access to, which made it easy to design LC filters that worked. It was one of my favourite instruments.
 
An impressively accurate box! How do you think it does a measurement at 1kHz in 1.5ms - only 1.5 cycles? Is it using sinusoidal excitation (which you would think would give it transient problems as the frequency is changed) or some sort of noise excitation followed by some FFT technique to make multiple measurements at once?
I don't know right off hand. I almost never use it in "meter" mode, making a measurement at a single frequency (I think that's the mode the timing applies to). But, now that you ask, I'll set it up to do that and look at the excitation across a capacitor with a scope!

Now, for your further amusement, consider this product:

http://www.hioki.com/product/im3533/index.html

Check out the frequency range: 1mHz to 200 kHz! That's "one millihertz to 200 kilohertz"! And, they say the measurement time is 2 ms at 1 kHz; they don't say anything about measurement time at 1 mHz! Surely it must be at least 1000 seconds.
 

Tesla23

Joined May 10, 2009
542
I don't know right off hand. I almost never use it in "meter" mode, making a measurement at a single frequency (I think that's the mode the timing applies to). But, now that you ask, I'll set it up to do that and look at the excitation across a capacitor with a scope!
I would have thought the fast measurements were when it was sweeping - that's when you make many measurements in a hurry. I was wondering if it was applying a sine wave at each frequency point, or using linearity to apply a sum of sine waves (noise like waveform) to essentially make many measurements at once. I've seen it done in audio network analysis where you apply a wideband PRBS type excitation, measure the response then FFT both the excitation and response and work out the transfer function (or whatever) frequency by frequency.

It would be impressive to measure phase to a tenth of a degree or so in around one cycle.
 
I put the analyzer in LCR meter mode at 1kHz, and with a .1 uF film cap in the fixture, I looked at the voltage across the cap with a scope. I see a continuous 1kHz sine wave when the meter is in auto trigger mode. Then I switched to manual trigger mode, and the 1kHz sine is still there continuously. Upon pressing the trigger button, it takes a reading very quickly.

Consider that the value of the typical capacitor is often specified at 1kHz. In production of capacitors that are 100% tested, one would want an instrument that could perform a basic test at 1kHz very quickly. So if one is testing a reel of caps, the mechanics will have to make a connection to a cap and then trigger the instrument to take a reading. The sine is applied as soon as the connection to the cap is made and the transient is dying out before a reading is taken.

In sweep mode, I can see that it's stepping the applied frequency. It spends about 5 ms at each frequency in the fastest mode as it approaches the high frequency limit. At the low frequency end, I can't tell what it's doing (how long the steps last) because the steps are small frequency changes, but they definitely take longer at low frequencies, as one would expect. No FFT techniques are used, it would seem.
 
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