Mutual inductance is a measure of the ability of one winding to induce a voltage in a second winding. Contrast this concept with that of self-inductance, which is a measure of the ability of a winding to induce a voltage in itself. Of course, in both cases, a voltage is induced only when current is changing with time. In a transformer, a change of current in the primary winding induces a voltage in the secondary winding, and ice versa. Thus, mutual inductance M relates rate of change of current in each winding to voltage induced in the other winding:
Like self-inductance. the units of mutual inductance arc henries (II). Mutual inductance is a parameter used most frequently in connection with loosely coupled air-core transformers. because thc turns ratio in those types of transformers is of little value in predicting output voltages. As might be expected. the value of mutual inductance depends on the coefficient of coupling k between the windings. as well as upon the self-inductance of each winding:
The coupling coefficient between the primary and secondary windings of an aircore transformer is n.os. The self-inductances of the primary and secondary windings are and 12 mH, respectively. Find the voltage induced in the secondary winding when the current in the primary winding is changing at the rate of 600 A/s.
The loosely coupled transformer in the amplifier circuit shown in Figure 11:””40(a) ‘I SPICE has primary inductance 100 p.H, secondary inductance I mH, and a coupling coefficient of 0.1. The primary winding resistance is 0.5 n and the secondary winding resistance is I n. Note that the secondary winding is in a parallel-resonant (lank) circuit with tuning capacitance C, = 2533 pF. The amplifier is operated at the resonant frequency of the tank circuit. Assuming default parameters for the transistor, use SPICE as an aid in finding.
1. the magnitude of the voltage gain of the transistor:
2. the magnitude of the voltage gain of the amplifier;
3. the power gain of the amplifier;
4. the ac power losses in the primary and secondary windings.
Solution Te SPICE circuit and input file. Notice that the winding resistances are lumped and shown as separate resistors connected in series with the windings. Since the secondary winding resistance is small,’ the resonant frequency is, to a close approximation, given by
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Gain Relations in Multistage Amplifiers
11-1. The in-circat ‘ullage gains of the stages in a multistage amplifier are . Find
a. the overall voltage gain, V.,/Vin; and
b. the voltage gain that would be necessary in a fifth stage, which, if added to the cascade would make the overall voltage gain 100 dB.
11-2. The in-circuit voltage gains of the stages in a multistage amplifier. (The gain of the first stage does not include loading by the signal source and that of the fourth stage does not include loading . by a load resistor.) The input resistance.
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