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431/531 Class Notes 11
8 Radio Basics
In this section we will discuss some basic concepts concerning signal mo dulation, generation, receiving, and demo dulation. Some of these concepts are quite general and see applications in many areas. However, the most familiar p erhaps is that of broadcast radio generation and receiving, hence the title of the section. We will b egin with a simpli ed discussion of amplitude mo dulation (AM). From this, we can see how to carry over many of the concepts to other forms of signal mo dulation and reception of signals.
8.1 The Case for Mo dulation
Consider the familiar example of radio signals which carry audio information. The audio itself has a typical frequency range of
20Hz < faudio < 20kHz
Hence, audio has an e ective bandwidth of ab out 20 kHz. Even if it were p ossible to broadcast signals of such low frequency in the electromagnetic sp ectrum, there would b e a multitude of confusion resulting from the interference b etween comp eting broadcasts. On the other hand, electromagnetic signals in the radio-frequency (RF) range, have frequencies roughly from several hundred kHz to several hundred MHz. An audio signal which mo dulates an RF \carrier" of, say, 1 Mhz, uses only the range 20 : 00 0 : 02 MHz. Another broadcast \channel" with a carrier frequency only 100 kHz removed will have give interference with its own signal at 20 : 10 0 : 02 MHz. We will lo ok at several techniques for signal mo dulation, b eginning with amplitude mo d- ulation. It is imp ortant to rememb er that the signals do not have to b e audio, that is only a familiar example. They could, represent any information which can b e converted to an electromagnetic signal. Another familiar example is the mo dulation of computer-generated signals for transmission over telephone lines.
8.2 Amplitude Mo dulation
Figure 43 gives the general scheme. Each frequency which is to carry information, !m = 2 fm , is \mixed" with the high-frequency carrier frequency, !c = 2 fc , to pro duce an output signal of the form Vs (t) = A [1 + m cos !m t] cos !c t (45)
where A is a constant and the constant m 1 is known as the mo dulation index. We see that the carrier amplitude A cos(!c t) is mo dulated by the factor 1 + m cos (!m t), where m = 0 represents the limit of no mo dulation and m = 1 is a miximally mo dulated signal. By using the identity
cos x cos y =
[cos (x + y ) + cos(x y )]
f c
fm
Vs
Figure 43: Schematic of mo dulation.
we can do a \p o or man's" Fourier transform of Vs :
Vs (t) = A cos !c t +
Am [cos ((!c + !m )t) + cos ((!c !m )t)] (46)
So we have a central carrier frequency plus two side-bands at fc fm.
8.3 Detection of AM
8.3.1 Hetero dyne Detection
We rst consider the simple, but subtle, radio receiver shown in Fig. 44. A real receiver might include at the input an antenna followed by an LC bandpass lter, with tunable capacitor. The lter is a resonant circuit with a sharp p eak at the carrier frequency of the broadcast !c = 1 =
p LC. The Q of the lter is set so that the width of the p eak of the transfer function matches the bandwidth ! of the mo dulating signal, roughly from !c !m to !c + !m. With this addition, and without the ampli ed output, the passive \crystal" radio receiver lo oks like this.
IN (^) OUT
a R
C
r
G
Figure 44: Simple AM receiver.
The resistor R and capacitor clearly form a low-pass lter. The cuto frequency would b e set b etween !m and !c in order to keep the information enco ded by the low-frequency mo dulations, and remove the carrier. However, without the dio de, the e ect would b e to throw away all of the information, to o, since as we saw from Eqn. 46, all of the frequencies of interest are actually in a narrow band cenetered ab out the carrier frequency. Without the dio de, the system is linear, and no signal will b e present at the output.
consider the mo dulation of the carrier to b e a phase shift (by amount !m t), the output of the PLL can then pro duce a voltage signal prop ortional to these phase shifts, which in turn is used to provide active recti cation of the input at the frequency of the mo dulation. The essential non-linear b ehavior of the dio de discussed ab ove is provided in this case by an active voltage multiplier. This typ e of PLL circuit is actually more relevant to FM detection, discussed b elow.
8.3.4 Sup erhetero dyne Detection
This technique is illustrated in the text, pages 895-6. This is essentially a fancy version of our simple hetero dyne detector ab ove. In this case, the simple passive LC bandpass lter at the input is replaced by a lo cal oscillator and mixer. An example is given in Figure 13 : 41 of the text. Consider an input carrier of frequency 10 MHz which has amplitude mo dulated at some much lower frequency. This signal is mixed with a lo cal oscillator of xed frequency greater that the carrier. In the example of the text, the lo cal oscillator has frequency tuned to b e fLO = 10 : 455 MHz, exactly 455 kHz greater than the carrier. As with our earlier dio de example, the mixed signal includes the di erence frequency, in this case 455 kHz, which in turn has nearby sideband frequencies which di er from 455 kHz by the audio mo dulation frequencies. From this p oint on, the detection is carried out as in the simple hetero dyne example. One advantage here is that a relatively high-frequency carrier, which in general will b e dicult to condition using conventional electronics is e ectively reduced to a more manageable frequency, in the example from 10 MHz to 455 kHz. The other advantage is that the band-pass tuning which follows the mixer is always centered at a constant 455 kHz. So the tuning is accomplished by adjusting the oscillator, rather than the lter.
8.4 Other Mo dulation Schemes
Recall from Eqn. 45 that for AM the amplitude is mo dulated by varying the frequency !m. However, to preserve the information, the generation and receipt of the amplitude must b e linear. In addition, most noise sources will naturally app ear as voltages, and hence will add to the AM signal. On the other hand, phase and frequency mo dulation (FM) do not su er from these complications. Hence, where delity is imp ortant, these schemes have intrinsic advantages. Radio broadcast by FM also has the additional advantage, by dint of historical accident, of o ccupying a higher frequency band, thus allowing easy accomo dation of a full audio bandwidth. However, unlike the AM radio band, the FM band signals do not re ect from the ionosphere, and therefore can not b e transmitted over very large distances (at night).
8.4.1 Phase Mo dulation
A carrier of frequency !c is phase modulated if the resulting signal has the form
V (t) = V 0 cos (!c t + Ap cos !m t) (47)
where V 0 and Ap are constants and !m is the mo dulating frequency, as b efore. This can b e expanded, and for Ap 1 can also b e simpli ed:
V (t)=V 0 = cos !c t cos(Ap cos !m t) sin !c t sin(Ap cos !m t) cos !c t Ap sin !c t cos !m t
= cos !c t
Ap [sin((!c + !m )t) + sin((!c !m )t)] (48)
As for AM, two new sidebands have app eared, but now they are 90 out of phase with resp ect to the carrier.
8.4.2 Frequency Mo dulation
The phase of a sinusoidal function, when frequency is a function of time, can in general b e expressed as
=
Z
! dt
Now supp ose the frequency is mo dulated by a frequency! ab out some central carrier fre- quency ! = !c + Af cos !m t
where Af is a constant. Then the phase b ecomes
= !c t +
Af !m
sin !m t
Here, Af is called the frequency deviation and Af =!m is the modulation index for FM. Carrying out steps analogous to those for Eqn. 48 gives the following expression for the FM signal:
V (t)=V 0 = cos = cos !c t +
Af 2 !m
[cos((!c + !m )t) cos ((!c !m )t)] (49)
So again the Fourier sp ectrum is similar to what we found for AM, except now one of the two sidebands has amplitude of opp osite sign.
8.5 FM Detection
In the AM detection schemes discussed ab ove, the dio de or other non-linear element is used to extract an output signal prop ortional to cos !m t, and hence provide a repro duction of the original mo dulation, for example in the form of an audio signal. For FM detection we need to replace the dio de with something which can provide a voltage output prop ortional to the input frequency mo dulated signal. We explored such a technique in Lab 5 in the form of the phase-lo cked lo op circuit. The PLL scheme is repro duced in Fig. 45. (In this application, the counter can b e omitted.) Recall that the signal b efore the VCO, lab elled Vout , is prop ortional to input phase shifts. This is exactly what we need to detect the phase shift intro duced by FM. All that is left is to feed Vout to a low-pass lter and ampli er, as b efore. An apparent practical limitation of this technique for FM radio reception is that PLLs do
not op erate at these high frequencies ( 100 MHz). This is overcome by using the technique
discussed ab ove at the front-end of the sup erhetero dyne receiver. The input is mixed using a lo cal oscillator and the resulting lower frequency (455 kHz in our example) mo dulated signal is then input to the PLL. Another technique, called quadrature detection is brie y discusses in the text, page 652.
