The output voltage of an ideal transformer is independent of frequency. However. in a real transformer. we must consider how the inductive components affect the output when frequency changes. because the reactances of those components increase with frequency. Furthermore, every transformer has capacitance between the turns of its wind.ugs, and capacitive reactance is also affected by frequency. Recall that capacitance exists whenever two conductors are separated by an insulator. which is precisely the situation when the insulated conductors of a transformer winding arc wrapped around the core. The capacitances of both windings arc distributed throughout the windings, but it is convenient to lump their effect into equivalent capacitors in parallel with each winding. The primary and secondary

capacitance. C, and C” are shunt capacitances, because they divert current that would otherwise now in the windings. Figure 11-3S(a) shows the equivalent circuit of a transformer. including the lumped capacitance and the lumped inductance we discussed earlier. Also shown is the internal resistance. of the voltage source connected to the primary winding. because this resistance also affects frequency respouse.

To understand how frequency affects the response of the circuit in we can study the effects of low frequencies and high frequencies scpa rately, Let us first suppose that the frequency of e.; is quite low. In that case, the capacitive reactances of C and CI, arc quite large (I XI’I = I/UlC). Since the capacitances arc in parallel with the input and output. their large reactances can be neglected at a sufficiently low frequency. Furthermore. the reactances of the leakage inductances, XI.”I and XI become very small in comparison to R” and R” since inductive reactance decreases with frequency. Figure 11-38(h) shows the low frequency equivalent circuit when the shunt capacitances and the leakage inductances are neglected (capacitances replaced by open circuits and inductances replaced by short circuits). It is clear that the inductive reactance of L/’III and the total series resistance (Rilll + R,o) form a voltage divider across the primary winding. This voltage divider is, in fact, a high-pass filter. The lower the frequency, the smaller the voltage drop across X” Consequently, as frequency decreases, the voltage appearing at the primary decreases, and the output of the transformer decreases. In the limiting case, where f == 0 Hz (de), Xl,pm = 0 n, and there is zero voltage across the primary. This confirms our previous discussion of the fact that a transformer does not respond to de.

Let us now consider the other frequency extreme. that is, the situation when the frequency of (‘ill becomes very large. In that case, the reactances of the shunt capacitances become very small and can’ no longer he neglected. Referring again to Figure ll-3X(a), notice that Rilll and C” form a low-pass RC filter. As we know, the voltage across the output capacitor in a low-pass filter decreases as frequency increases. Furthermore. the reactance of L,o/ increases with frequency, so a greater portion of the input voltage is dropped across it. The combined effects of the shunt capacitance and the series inductance cause the voltage at the primary to decrease rapidly as frequency increases. Similarly, R” and C, form a low-pass RC filter on the secondarv side of the transformer. The effect ofthis filter, and the series reactance 01 L\I’ further educt rh0; voltage V,. appearing at the lood. The reduction in output voltage due to all these effects is responsible for a frequency response that falls rapidly at nigh (I cqucncies,

**IMG**

a typical frequency response for a transformer used in audio circuits (an audio transformer). Note that the frequencies are about Ion Hz and 5 kHz. which means that the passband is a relatively small portion of the audio range (20 Ilz to 20 kHz). In modern high-fidelity systems, audio transformers are avoided whenever possible, because of their bulk and their limited frequency response.