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5 THE FREQUENCY MODULATED RADIO RECEIVER 5.1 INTRODUCTION In amplitude modulation, the frequency of the carrier is kept constant while its amplitude is changed in accordance with the amplitude of the modulating signal. In frequency modulation, the amplitude of the carrier is kept constant and its frequency is changed in accordance with the amplitude of the modulating signal. It is evident that, if a circuit could be found which will convert changes in frequency to changes in amplitude, the techniques used for detecting AM can be used for FM as well. In Section 4.3.3.4, three frequency-to-amplitude conversion circuits were discussed and their performance in terms of linearity and dynamic range were examined. It therefore follows that the FM receiver must have the same basic form as the AM receiver. The structure of the FM receiver is as shown in Figure 5.1. The superheterodyne technique is used in FM for the same reasons it is used in AM; it translates all incoming frequencies to a fixed intermediate frequency at which the filtering process can be carried out effectively. The antenna is responsible for capturing part of the electromagnetic energy propagated by the transmitter. The basic rules of antenna design apply but, because in commercial FM radio the frequency of the electromagnetic energy is between 88 and 108 MHz, it is practical to have antennas whose physical dimensions are within tolerable limits. The radio-frequency amplifier raises the power level to a point where it can be used in a mixer or frequency changer to change the center frequency to a lower frequency – the intermediate frequency (IF). The mixer in conjunction with the local oscillator translate the incoming radio frequency to an intermediate frequency of 10.7 MHz. There is nothing special about an intermediate frequency of 10.7 MHz except that it is a relatively low frequency at which the required values of Ls and Cs are large enough to reduce the effects of circuit strays. It is at this fixed frequency that filtering to remove the unwanted products of the mixing process and other 143 Telecommunication Circuit Design, Second Edition. Patrick D. van der Puije Copyright # 2002 John Wiley & Sons, Inc. ISBNs: 0-471-41542-1 (Hardback); 0-471-22153-8 (Electronic) Figure 5.1. The block diagram of the domestic FM receiver showing frequency ranges and bandwidths. 144 interfering signals and noise takes place. The filtered signal then proceeds to the amplitude limiter. The need for the limiter becomes evident when one recalls that the FM signal is usually converted into an AM signal in the discriminator before it is detected. This means that any variation in the amplitude of the FM signal will be superimposed on the proper signal from the discriminator and hence will cause distortion. The amplitude limiter very severely clips the signal to a constant amplitude and also filters out the unwanted harmonics that are produced by the limiter. The signal then proceeds to the frequency discriminator (frequency-to- amplitude convertor) and onto the envelope detector. The audio-frequency amplifier raises the output of the envelope detector to a level suitable for driving a loudspeaker. Although the structures of AM and FM receivers are similar, there are very important differences which require different design and construction approaches. These are the following: 1. The higher carrier frequencies (88–108 MHz) used in FM requires small values of both L and C in the tuned circuits used. This means that stray inductances and capacitances will constitute a larger percentage of the designed value and hence have a much greater effect on all tuned circuits. Although measures can be taken to incorporate the effects of fixed circuit strays in the design, there are other changes in element values, due to such factors as temperature and vibration, which can cause sufficient drift to necessitate retuning of the receiver during a program. The local oscillator is most vulnerable to stray elements, especially because it has to operate at a frequency 10.7 MHz above the carrier frequency. To ensure the stability of the oscillator, high circuit Q factors, negative temperature-coefficient capacitors and automatic frequency control (AFC) are used. Some radio-frequency amplifiers for FM front-ends use distributed parameter circuit components such as coaxial and transmission lines. 2. With the intermediate frequency set at 10.7 MHz, the band from which image interference can originate is from 109.4 to 129.4 MHz. This frequency band is reserved for aeronautical radionavigation systems. It follows that one FM station cannot cause image interference for another but the aeronautical radionavigation systems can. As in AM, image interference can be reduced by differentially amplifying the desired signal relative to the image signal. A high Q factor tuned radio-frequency amplifier is used for this purpose. 3. The use of a high Q factor tuned amplifier in the radio-frequency stage requires a very stable local oscillator frequency which will accurately track the incoming radio frequency and produce a minimum variation from the selected intermediate frequency. The local oscillator by itself is not capable of this but, used in conjunction with the AFC and other stabilizing measures, it can perform satisfactorily. 4. The ideal intermediate-frequency filter should have a bandpass characteristic which is flat with infinitely steep sides. The flat top is required to avoid any 5.1 INTRODUCTION 145 frequency dependent amplitude variation, the steep sides to eliminate inter- ference from the unwanted products of the mixing process and from adjacent channels. Two techniques, both involving a number of successive stages of tuned circuits, are used to obtain an approximation to the ideal filter characteristics. In the first, all the tuned circuits have the same resonant frequency. This is known as synchronous tuning. In the second the resonant frequencies are placed at different points in the passband. This is known as stagger tuning. The above qualitative as well as quantitative changes from the AM system discussed in Chapter 3 make a separate consideration necessary. 5.2 COMPONENT DESIGN 5.2.1 Antenna An important point to remember is that an antenna is a reciprocal device, that is, it can be used both for transmitting signals as well as for receiving them. An antenna structure that produces a good ground wave radiation pattern will have a good response to the same ground wave radiation when used in the receiving mode. Commercial FM receivers commonly use two types of antennas: the vertical whip antenna, most commonly used with automobile radios, and the dipole and folded dipole antennas used with other types of portable and non-portable FM radios. Assuming that the vertical whip antenna approximates a vertical grounded antenna, a half-wavelength antenna for the middle of the FM band will be about 1.5 m long. Such an antenna can be conveniently mounted on a vehicle. The field patterns of vertical grounded antennas are given in Figure 2.54. It can be seen that when the height h is less than l=2, the response is limited to the ground wave. Commercial FM stations are designed to operate within a local area and therefore have antennas which ensure that most of the radiated power goes into the ground wave. An FM receiver with an antenna whose height is equal to or less than l=2 will have a good response. The dipole and its variation, the folded dipole, are commonly used with non- portable FM receivers. They can be used in conjunction with directors and=or reflectors to increase the gain of the antenna. Such an arrangement is called a Yagi– Uda antenna. Antenna design is beyond the scope of this text. However the interested reader is encouraged to refer to any standard text on antennas. 5.2.2 Radio-Frequency Amplifier The purpose of the radio-frequency amplifier is to boost the power of the incoming signal relative to all the other signals picked up by the antenna to a level which can be used in the frequency changer. A second function of the radio-frequency amplifier 146 THE FREQUENCY MODULATED RADIO RECEIVER is to act as a matched load to the antenna so that the antenna signal is not reflected at the interface leading to the loss of efficiency. The bandwidth of an FM signal in commercial radio was calculated to be approximately 240 kHz in Section 4.3.3.1. With a carrier frequency of about 100 MHz, the required Q factor is therefore about 400. Such a high value of Q factor cannot normally be achieved in a simple tunable radio-frequency amplifier and the practical approach is to use a lower Q circuit and to correct for this in the intermediate-frequency stage that follows. An alternate technique uses a number of stages in cascade separated by buffer amplifiers. For the superheterodyne system to work, the local oscillator frequency must be set equal to the radio frequency plus the intermediate frequency; for the commercial FM band, the standard intermediate frequency is 10.7 MHz. The frequency of the local oscillator must be variable from 98.7 to 118.7 MHz. This is normally not a problem since the ratio of the high frequency to the low frequency is only 1.2 : 1. The more important point is that the center frequency of the radio-frequency amplifier and the frequency of the local oscillator must maintain the difference of 10.7 MHz throughout the FM frequency band. In the case of AM, the frequencies were low and some drift could be tolerated without serious deterioration of the signal. In the FM system, the frequencies are much higher and small percentage changes in one or both radio frequency and local oscillator frequency can cause large changes in the intermediate frequency. To overcome this problem, a system for automatic control of the frequency (AFC) of the local oscillator is used. The basic operation is similar to that described in Section 4.3.2. 5.2.3 Local Oscillator The local oscillator can take any of the usual oscillator forms with a bipolar transistor as the active element. It must produce enough power to drive the mixer. The values of the inductors and capacitors have to be chosen to minimize the effects of circuit strays. As mentioned earlier, the local oscillator incorporates an AFC circuit for stable tracking with the (tunable) radio-frequency amplifier. 5.2.4 Frequency Changer The basic frequency changer was discussed in Section 3.4.3. For this application the dual-gate FET mixer has the advantage of low leakage of the local oscillator signal to the antenna via the radio-frequency amplifier. Such a leakage and its subsequent radiation can cause interference with other communication and radionavigation equipment. 5.2.5 Intermediate-Frequency Stage The intermediate frequency for commercial FM radio is 10.7 MHz. The required bandwidth of the filter is about 240 kHz centered at 10.7 MHz, giving a Q factor of 5.2 COMPONENT DESIGN 147 about 45. It is usual to realize the filter in two or more stagger-tuned stages with suitable buffer amplifiers between them. 5.2.6 Amplitude Limiter The radio-frequency amplifier, the mixer, and the intermediate-frequency amplifier, in theory, should have a flat amplitude response in their pass bands. In practice, this is not so. The result is that the signal emerging from the intermediate-frequency amplifier has some variation of amplitude with respect to frequency. This is a form of AM and it must be removed if distortion is to be avoided. The amplitude limiter was discussed in Sections 4.3.3.1 and 4.3.3.2. It is worth noting that sometimes the amplitude limiter is preceded by an automatic gain control. This reduces the severity of the clipping action and hence the required signal power and the spurious harmonics produced. 5.2.7 Frequency Discriminator The purpose of the frequency discriminator is to convert relatively small changes of frequency (in a very high-frequency signal) to relatively large changes in amplitude with respect to time. The signal can then be demodulated using a simple envelope detector which was discussed in Section 3.4.6. Two basic frequency discriminators were discussed in Section 4.3.3.4 and these serve to illustrate the concepts. In practice, a number of more sophisticated discriminators are used. Some of these will now be discussed. 5.2.7.1 Foster–Seeley Discriminator. The Foster–Seeley discriminator [1,2] is similar to the balanced slope discriminator shown in Figure 4.11. The major difference is that it has two tuned circuits instead of three and both are tuned to the same frequency. This is a major advantage when the receiver is being aligned. A secondary advantage is that it has a larger linear range of operation than the slope discriminator. The basic circuit of the Foster–Seeley discriminator is shown in Figure 5.2. Connected to the collector of the transistor, L 1 and C 1 are tuned to resonate at the frequency f o (the intermediate frequency of the receiver). The inductance L 1 is mutually coupled to a center-tapped inductor L 2 . The center tap is connected by a coupling capacitor C c to the collector of the transistor. The inductor L 2 and C 2 are tuned to resonate at the frequency f o . Two identical circuits consisting of a diode in series with a parallel combination of a resistance and a capacitance (D 3 –R 3 –C 3 and D 4 –R 4 –C 4 ) are connected across L 2 to form a symmetrical circuit. A radio-frequency choke (RFC – a high-valued inductance which can be considered to be an open- circuit at high frequency but a short-circuit at low frequency) connects the center tap to the ‘‘neutral’’ node of the D 3 –R 3 –C 3 and D 4 –R 4 –C 4 circuits. The circuit can be divided up into two parts by the line connecting X –X 0 . The parts of the circuit to the left of X –X 0 operate at a high frequency f o with a relatively small deviation ÆDf . The circuit to the right of X –X 0 are two envelope detectors, as 148 THE FREQUENCY MODULATED RADIO RECEIVER Figure 5.2. The Foster–Seeley discriminator. The line X –X 0 divides the circuit into high (radio) and low (audio) frequency. 149 discussed in Section 3.2. The high-frequency input voltages to the envelope detectors are rectified by the diodes D 3 and D 4 and the time-constants R 3 –C 3 and R 4 –C 4 are chosen to smooth out the half-wave pulses but follow any slow changes in the envelope (amplitude) of the half-wave pulses. These slow changes represent low (audio) frequency. Before proceeding to the analysis of the circuit, it is in the interest of simplicity, to make three assumptions: (1) The impedance of the coupling capacitance C c is small enough to be considered as a short-circuit, at the frequency of operation. (2) The impedance of the RFC is an open-circuit at the high frequency f o but a short-circuit at the low (audio) frequency. (3) The neutral node of the envelope discriminators can be considered to be grounded since the secondary circuit, including the envelope discriminators, is symmetric. Now, all that needs to be demonstrated is that, when a signal of frequency f o Æ Df is applied to the circuit, the amplitude of the voltage appearing across the inputs of the envelope detectors will vary proportionally to ÆDf . The tuned circuits L 1 –C 1 and L 2 –C 2 are both high Q factor circuits but their mutual coupling coefficient, M, is low. This means that the secondary load coupled into the primary circuit is negligible. The primary current is I 1 % V 1 joL 1 : ð5:2:1Þ The voltage induced in the secondary is 2V 2 ¼ÆjoMI 1 ð5:2:2Þ where the Æ sign depends on the relative directions of the primary and secondary windings. Assuming the positive sign and substituting for I 1 2V 2 ¼ MV 1 L 1 : ð5:2:3Þ Since the secondary circuit is tuned to resonance, the secondary current is I 2 ¼ MV 1 R 2 L 1 ð5:2:4Þ where R 2 is the series resistance of the secondary circuit. 150 THE FREQUENCY MODULATED RADIO RECEIVER The voltage across the capacitor C 2 is 2V 2 ¼ I 2 jo 0 C 2 : ð5:2:5Þ Substituting for I 2 , 2V 2 ¼ MV 1 jo 0 C 2 R 2 L 1 : ð5:2:6Þ The secondary voltage applied to one envelope discriminator is given by V 2 ¼ M j2o 0 C 2 R 2 L 1 V 1 : ð5:2:7Þ It is now clear that, at resonance, the primary voltage V 1 is at right angles to the secondary voltage V 2 . The phasor diagram of the voltage applied to the inputs of the envelope discriminators is as shown in Figure 5.3(a). This can be modified by reversing the direction of one of the phasors representing V 2 as shown in Figure 5.3(b). The discriminator input voltage phasors V 3 and V 4 are equal in magnitude and since the outputs of the envelope discriminators are proportional to the magnitude of the applied voltages, when the output is taken differentially, it is zero. This means that the Foster–Seeley discriminator has zero volts output at the resonant frequency. The impedance of the secondary tuned circuit, at any given frequency o,is Z 2 ¼ R 2 þ j oL 2 À 1 oC 2  : ð5:2:8Þ Figure 5.3. (a) The basic phasor diagram of the discriminator. (b) The phasor diagram when the FM carrier is unmodulated. 5.2 COMPONENT DESIGN 151 But at resonance C 2 ¼ 1 o 2 0 L 2 : ð5:2:9Þ Eliminating C 2 from Equation (5.2.8) gives Z 2 ¼ R 2 þ j oL 2 À o 2 0 L 2 o  : ð5:2:10Þ If we now define the Q factor at resonance as Q 0 ¼ o 0 L 2 R 2 ð5:2:11Þ then Equation (5.2.10) can be written as Z 2 ¼ R 2 þ jo 0 L 2 o o 0 À o 0 o  : ð5:2:12Þ Now consider relatively small changes of frequency about the resonant frequency o o and define ‘‘fractional detuning’’ d as d ¼ o À o 0 o 0 ð5:2:13Þ then o o 0 ¼ 1 þ d ð5:2:14Þ hence o o 0 À o 0 o ¼ 1 þ d À 1 1 þ d ¼ d 2 þ d 1 þ d  : ð5:2:15Þ For a high Q factor circuit at a frequency near the resonance, the fractional detuning d is much smaller than 1, therefore o o 0 À o 0 o % 2d: ð5:2:16Þ Substituting into Equation (5.2.12) Z 2 ¼ R 2 ð1 þ j2QdÞ: ð5:2:17Þ 152 THE FREQUENCY MODULATED RADIO RECEIVER [...]... communication system in which it is used, giving the relevant details An incoming signal in a communication receiver is given by vðtÞ ¼ 1 b½cosðoc À om Þt À cosðoc þ om ÞtŠ 2 P5: 1Þ where oc is the carrier angular frequency and om is the modulating signal angular frequency What do you need to demodulate the signal and how would you carry out the demodulation? Support your answer with suitable diagrams and derived... 2nd Ed., Rinehart Press, San Francisco, 1972 6 Stark, H and Tuteur, F B., Modern Electrical Communications, Prentice-Hall, Englewood Cliffs, NJ, 1979 PROBLEMS 159 PROBLEMS 5.1 A bipolar transistor operating at a frequency of 100 MHz has the following Y parameters: y11 ¼ 9:84 þ j9:1; y12 ¼ 0:01 À j0:68; y21 ¼ 60:7 À j95:8 and y22 ¼ 0:60 þ j1:8, measured in mSi in the common emitter configuration with 0.6... junction Using this device, design an oscillator to supply maximum power to a suitable conductive load What modifications would you make to the oscillator to obtain a local oscillator for an FM receiver operating in the range 88– 108 MHz? 5.2 An FM receiver is tuned to a transmitter at 100 MHz The modulation is sinusoidal at a frequency of 15 kHz The intermediate frequency is 10.7 MHz and the Q factor of the... the stereophonic spectrum has a larger bandwidth – more than three times larger At the receiver, the signal is demodulated and the baseband information is recovered Figure 5.9 shows a scheme for separating the left, LðtÞ, and right, RðtÞ, information and passing them on to their respective loudspeakers The first bandpass filter has a passband 23–53 kHz and it is used to separate the double-sideband-suppressed... block diagram, giving all the necessary details to achieve your wish What would be the advantages and disadvantages of your new receiver? 5.6 The dual-gate FET (whose characteristics are given in Figure P5. 1) is to be used in the design of a frequency changer in a commercial FM receiver whose 160 THE FREQUENCY MODULATED RADIO RECEIVER intermediate frequency is 10.7 MHz The output of the radio-frequency... (3) À3 dB bandwidth, 240 kHz Choose all the other values and in every case justify your choice Calculate the ratio of the intermediate-frequency power output to the radio-frequency power input Figure P5- 1 5.7 The purpose of the discriminator in an FM receiver is to convert variation in frequency to variation in amplitude Describe the operation of the Foster– Seeley discriminator and demonstrate its . amplitude of the modulating signal. In frequency modulation, the amplitude of the carrier is kept constant and its frequency is changed in accordance with the amplitude of the modulating signal. It. is given by vðtÞ¼ 1 2 b½cosðo c À o m Þt À cosðo c þ o m Þt P5: 1Þ where o c is the carrier angular frequency and o m is the modulating signal angular frequency. What do you need to demodulate. to remember is that an antenna is a reciprocal device, that is, it can be used both for transmitting signals as well as for receiving them. An antenna structure that produces a good ground wave