The transformer, as used in a TVC, consists of a primary winding, (the input) and the secondary winding (the output). Each winding consists of a coil with certain number of turns of wire. These coils are wound around a core made of iron or other high-grade alloy steel.
If we let Nin be the number of turns in the input coil, and Nout be the number of turns in the output coil, the voltage applied at the input Vin, and the voltage obtained at the output, Vout, have the following relationship:
Vin Nin
------ = ------
Vout Nout
Nin/Nout is also called the turns ratio of the transformer.
The currents on the other hand have an inverse relationship with the turns ratio:
Iin Nout
------ = ------
Iout Nin
So, the following relationships can be derived:
Vin*Iin = Vout*Iout
and
Vin/Iin = (Nin/Nout)^2 * Vout/Iout
Zin = (Nin/Nout)^2 * Zout
So, in an ideal transformer:
1. If the output voltage reduces, there is a corresponding increase in the output current Iout.
2. An impedance connected at the output appears on the input side transformed by the square of the turns ratio of the transformer.
When used as a TVC, the transformer will have the source (CD player for example) connected at the input. The amplifier with an impedance of Zamp is connected at the output.
With no attenuation of the input signal, Nout = Nin. And so, the amplifier impedance Zamp is presented to the source.
As the input signal gets attenuated, Nout becomes smaller than Nin. Nin/Nout is greater than 1, and so is the square of Nin/Nout.
Therefore, the impedance presented to the source is greater than Zamp. It is Zamp multiplied by the square of the turns ratio of the transformer.
A rule of thumb in matching an output stage with an input stage is that the input impedance presented by the input stage be at least 10 times the output impedance of the output stage.
With the TVC, if at no attenuation, you know that Zamp > 10*Zsource, you are guaranteed that Zamp will be greater than 10*Zsource at other levels of attenuation also.
Further, at lower volumes (higher attenuation), there will be more current Iout to drive the amplifier.
It is important to note that the analysis above assumes an ideal transformer - no resistive losses of any sort, and winding inductances are zero. In real life, there will be losses in the core of the transformer and in the transformer coils. These can be made small with proper choice of material and construction techniques. There will also be a finite inductance in the transformer windings. The equivalent impedance presented by the winding inductance is directly proportional to the frequency of the input signal.
An autotransformer is a variation of the transformer. While the transformer has two terminals for the input and two for the output, the autotransformer is a three-terminal device. The electrical isolation between the input and output that is available in a transformer with separate windings is not present in an autotransformer. But an auto will give you a higher power handling capacity.
Gurus out there: please point out any errors in my discussion.
Ashok