McGill University. Department. of Electrical and Computer Engineering. Communications systems A

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1 McGill University Department. o Electrical and Computer Engineering Communications systems A 1 The Super-heterodyne Receiver 1.1 Principle and motivation or the use o the super-heterodyne receiver The super-heterodyne receiver is a special type o receiver that in addition to demodulating the incoming signal, does carrier-requency tuning(selection o the desired signal), iltering(separation o the desired signal rom intererence) and ampliication. Selectivity is a measure o how well a receiver can select a desired station while excluding all others. By converting the Radio Frequency(RF) signal to a ixed Intermediate Frequency(IF), the super-heterodyne receiver provides improved selectivity. It is much easier, (and much more cost-eective) to implement a band-pass ilter with good selectivity at a ixed center requency, rather than to improve the selectivity o the RF ampliier(which has a variable center requency). 1. AM super-heterodyne Receiver Let us consider, or example, an AM super-heterodyne receiver, depicted in Fig. 1. The desired signal centered at a carrier requency c,is called the Radio Frequency (RF) signal. With this receiver, any signal within a speciied requency band (Radio Frequency signals) can be selected by the user, by simply changing the requency o the local oscillator and o the RF ilter i necessary. The desired signal, together with unwanted signal at requencies other than c, is received by the antenna, then ampliied by the RF ampliier. The ampliier also partially ilters out undesired signals. However, its selectivity is not suicient to eliminate the nearby carriers. In order to improve the selectivity o the receiver, the signal is converted to a ixed Intermediate Frequency (IF) by a mixer, which is cascaded with an IF ampliier, o ixed center requency IF, and a narrow bandwidth. 1

2 The inormation signal s(t) is recovered rom the IF ilter output signal z(t) by using a demodulator and a lowpass ilter(i necessary). Note that the design o the demodulator is also simpliied by the act that z(t) is always centered at the IF. Antenna RF Ampliier x(t) y(t) IF Ampliier z(t) Demodulator B c RF B IF u(t) Common Tuning cos π lt LPF Figure 1: The Super-heterodyne receiver W 1.3 The RF ampliier Let s(t) be the inormation signal as illustrated in Fig.. The AM modulated wave is given S() 1 -W W Figure : Fourier Transorm S() o the inormation signal s(t) by x(t) = A c (1 + ms(t)) cos π c t

3 and illustrated in Fig. 3. The RF ampliier is a bandpass ilter, with a varying center X() A/ ma/ - -W - - +W c c c c -W c c +W Figure 3: Fourier Transorm X() o the modulated signal x(t) requency c, and ixed bandwidth B RF. The center requency is controlled by the choice o the Radio Frequency done by the user o the receiver. The Bandwidth should satisy B < B RF < 4 IF where B is the bandwidth o the modulated signal. For AM, B = W, where W is the bandwidth o the message signal s(t). The upper inequality should hold to eliminate the signal at image requency, im = c + IF. This will be explained in detail in the next subsection. The RF spectrum is illustrated in Fig. 4 and the received signal ater the RF ampliier is illustrated in Fig. 5. Signal to receive Image requency c -W c c +W c+ IF Figure 4: RF spectrum 3

4 The image requency is rejected c -B c c c +W RF / -W c +B RF / 1.4 The mixer The output o the mixer is given by y(t) = x(t) cos π l t Figure 5: Output o RF ampliier = A c (1 + ms(t)) cos π c t cos π l t = A [ c (1 + ms(t)) cos π( c + l )t + cos π( l c )t Most o the super-heterodyne receivers use High-Side Injection(HSI) o the oscillator, i.e. l = c + IF (or Low-Side Injection(LSI), l = c IF ). As the receiver is tuned to the requency o another incoming signal, the requency o the local oscillator is also automatically changed so as to satisy l = c + IF (or HSI). Hence the output o the mixer or HSI is given by y(t) = A [ c (1 + ms(t)) cos π IF t + cos π( c + IF )t + possibly other signals and illustrated in Fig. 6. Y() IF -W IF IF +W c+ IF Figure 6: Fourier transorm Y(): Output o the mixer 4

5 Image response Another signal at im = c + IF, called the image response, can be down converted to the IF i the RF bandpass ilter does not have a good image response. Assume that the RF ampliier is not narrow enough and that there is another signal at im, then the output o the RF ampliier is given by x(t) = A c1 (1 + m 1 s 1 (t)) cos π c t + A c (1 + m s (t)) cos π( c + IF )t The output o the mixer is given by(assuming HSI) y(t) = x(t) cos π l t = A [ c1 (1 + m 1s 1 (t)) cos π( c + l )t + cos π( l c )t + A [ c (1 + m s (t)) cos π( c + IF + l )t + cos π( l c IF )t { Ac1 = (1 + m 1s 1 (t)) + A } c (1 + m s (t)) cos π IF t + A c1 (1 + m 1s 1 (t)) cos π( c + IF )t + A c (1 + m s (t)) cos π( c + 3 IF + l )t We can see that the signal at the image requency gets superimposed with the desired signal at c. To avoid this problem, the RF bandpass ampliier should be narrow enough to reject the image response(i.e. c + B RF < c + IF ). 1.5 The IF ampliier The IF ampliier provides most o the required gain and selectivity. Its bandwidth is equal to B. The output signal o this ilter is and illustrated in Fig. 7. z(t) = A c (1 + ms(t)) cos π IF t 1.6 The Demodulator At the output o the IF ilter, the desired signal z(t) is centered at IF. Theoretically, the output o the demodulator is u(t) = A c (1 + ms(t)) I the demodulator is an envelope detector, the amount o ripples is usually not negligible and can be removed by low-pass iltering when necessary. 5

6 Z() -W +W IF IF IF Figure 7: Fourier transorm Z(): Output o the IF ampliier 6