TRABEM wrote in message ...
Is the value of a capacitor placed in series with the secondary of a
transformer multiplied (as viewed from the primary) by the turns ratio
or the square of the turns ratio?

Thanks,

T

Since I just started playing with the LMS impedance bridge featured in this
months QST (and the current QEX), I thought it would be interesting to try
to answer this one by experiment.

I have an old audio matching transformer labeled to transform 20 ohms to 8
ohms, a 2.5 ratio. I took a 10 uF capacitor and measured it at 9 uF, with Z
of 14.43/_ -85 degrees at a measurement frequency of 1225 Hz. Hooked it to
the low resistance side of the transformer and the meter to the high side.
The reading obtained was 1.99 uF or Z = 74.4/_ -62 degrees.

So I got a transformation ratio of 4.5 or 5 in terms of capacitance or
impedance, instead of the expected 2.5.

Now, how far is the transformer from ideal? Measuring its high side
inductance with the low side open, I get 10.1 mH. This is the magnetizing
inductance of the transformer, which appears in parallel with the
transformed capacitive reactance. In a transformer that approaches ideal,
the inductance is large enough to have a very large reactance compared to
the transformed load from the secondary. In this case it's only sort of
negligible. The transformed capacitance of 9/2.5 uF = 3.6 uF has a
reactance of -j36.1 ohms. The reactance of the transformer's magnetizing
inductance is j77.7 ohms. Combining the two in parallel gives a resultant
capacitive reactance of -j67.11. And this is equivalent to 1.94 uF at my
measurement frequency. Not too far from the measured value of 1.99 uF. I
did neglect leakage inductance, assuming that it would be pretty small for
this type of transformer.

Another interesting point to note is that the unadorned capacitor had a
phase angle of 85 degrees, but the transformed version showed 62 degrees.
The equivalent loss resistance of the transformer decreased the quality a
fair amount, as one would expect I guess.

So I guess the answer to your question is yes, it will be transformed just
like a resistive load would be, providing the transformed capacitive
reactance is fairly small with respect to the magnetizing reactance of the
transformer.

73--Nick, WA5BDU