 Figure 5.4. (a) The phasor diagram when signal frequency is lower than carrier frequency. (b) The phasor diagram when signal frequency is higher than carrier frequency.

Figure 5.4. (a) The phasor diagram when signal frequency is lower than carrier frequency. (b) The phasor diagram when signal frequency is higher than carrier frequency.

Replacing R2 in Equation (5.2.7) by Z2 gives

It is evident that V1 and V2 are no longer at right angles to each other. The angle between them depends on the magnitude and sign of d. When d is positive, the angle between V1 and V2 is less than 90°, and when d is negative the angle is greater than 90° or vice versa. The phasor diagrams for positive and negative values of d are shown in Figure 5.4(a) and (b), respectively.

It is clear from these that the magnitudes of the input voltages V3 and V4 are unequal when d has any value other than zero. The characteristics of the Foster-Seeley discriminator are shown in Figure 5.5.

A variation on the Foster-Seeley discriminator which combines the functions of the amplitude limiter and frequency discriminator is called the ratio detector . Its performance however leaves much to be desired. Below resonance Above resonance Figure 5.5. The amplitude-frequency characteristics of the Foster-Seeley discriminator. Figure 5.6. The circuit diagram of the quadrature detector with an emitter follower to give a low impedance output.

5.2.7.2 Quadrature Detector. The basic circuit diagram of the quadrature detector is shown in Figure 5.6. All biasing circuit components have been omitted for clarity of its operation.

The circuit consists of a tuned amplifier Q1, with a very high Q factor collector load. The input to the circuit is the output from the amplitude limiter which is a frequency modulated square wave (i.e. a square wave of fixed frequency with relatively small deviations in its zero crossings). Due to the high Q factor of the tuned circuit, the output from the amplifier is a sinusoid at the fixed frequency. The same square wave is fed to the base of Q4 which is a constant current source for the differential pair Q2-Q3. Therefore current flows in the differential pair only when Q4 is switched on. The sinusoid applied to Q2 determines what proportion of the constant current in Q4 flows through Q2 as opposed to Q3. It can be seen from Figure 5.7(a) that, when the input signal is unmodulated, that is, when the phase difference between the sinusoid and the square wave is fixed, the circuit can be adjusted so that Q2 and Q3 conduct equal currents, giving a constant voltage across C3. The time-constant R3 C3 hold the base of Q5 at a dc value and the output remains constant.

When the input to the circuit is modulated, the sinusoid driving Q2 is no longer coincident with the square wave and Q3 now conducts for a period proportional to the "phase shift'' between the two signals. This can be seen in Figure 5.7(b). The voltage across C3 is a slowly varying direct current and the output is in fact the audio frequency which was used to frequency-modulate the radio-frequency.

It should be noted that: Current in Q3

Figure 5.7. (a) The phase difference between the sinusoid and the square wave when the carrier is unmodulated is such that currents of equal magnitude flow through Q2 and Q3 giving a dc output. (b) When the carrier is modulated the relative phase between the sinusoid and the square shifts and the currents in Q2 and Q3 are no longer equal; the dc changes its value - the changing dc is the audio-frequency signal.

Current in Q3

Figure 5.7. (a) The phase difference between the sinusoid and the square wave when the carrier is unmodulated is such that currents of equal magnitude flow through Q2 and Q3 giving a dc output. (b) When the carrier is modulated the relative phase between the sinusoid and the square shifts and the currents in Q2 and Q3 are no longer equal; the dc changes its value - the changing dc is the audio-frequency signal.

(1) the amplifier Q5 provides a low output impedance for the circuit,

(2) the structure of the circuit is suitable for realization in integrated circuit form,

(3) the time-constant R3 C3 is chosen to "follow'' the changes in the amplitude of the audio-frequency signal,

(4) when the two signals are 90° out of phase (in quadrature), Q2 and Q3 conduct equal currents and this condition may be used as a datum.

5.2.7.3 Phase-Locked Loop FM Detector. The phase-locked loop  FM detector is the most complex of FM detectors but it has the advantage that it can be realized in integrated circuit form where complexity is not necessarily a disadvantage. The basic system is as shown in Figure 5.8.

It consists of a phase detector that generates an output signal which is proportional to the difference between the phases of the two input signals ("error'' signal). The output signal is amplified and low-pass filtered and used to control a voltage-controlled oscillator (VCO) which usually operates at a higher frequency than the input signal. The output of the oscillator is divided by a suitable factor N to bring it to the same frequency as the input signal. This is the second input to the phase detector. Figure 5.8. The block diagram of the phase-locked loop FM detector. Note that the relatively slow-varying dc required to keep the loop in lock is the audio-frequency signal.

The error signal fed to the VCO causes it to change frequency so that f moves closer to fr. When the two frequencies are close to each other, the system locks, that is, the two frequencies become equal and their phase difference is zero. The control voltage from the low-pass filter is then dc. When the incoming signal changes its frequency, and hence phase, the control voltage will change its value to keep the system in lock. The excursions of the control voltage is, in fact, the required demodulated output.

The phase-locked loop FM detector has the advantage of having no LC tuned circuits. In its integrated-circuit form, it requires a number of external resistors and capacitors for its proper operation. This information is usually provided by the manufacturer. 