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1 Contemporary Communication Systems using MATLAB Chapter 3: Analog Modulation 2013 Cengage Learning Engineering. All Rights Reserved.

2 3.1 Preview In this chapter we study analog modulation & demodulation, with or without additive noise. Systems covered in this chapter include 3 major categories: amplitude modulation (AM), e.g. DSB-AM, SSB-AM, and conventional AM; frequency modulation (FM); phase modulation (PM). FM and PM are also called angle modulation schemes. AM, FM and PM share these common & interdependent properties: 1. Time-domain representation of the modulated signal 2. Frequency-domain representation of the modulated signal 3. Bandwidth of the modulated signal 4. Power content of the modulated signal 5. Signal-to-noise ratio (SNR) after demodulation Properties 1 and 2 are related by FT. Also, the bandwidth (Property 3) of a signal is typically dependent upon its frequency characteristics Cengage Learning Engineering. All Rights Reserved. 2

3 3.2 Analog Modulation (AM) Also referred to as linear modulation, AM is the family of modulation schemes in which the amplitude of a sinusoidal carrier changes as a function of the modulating signal (a.k.a. the message signal). The AM family, or class, of schemes includes: 1. Double-sideband AM (DSB-AM) 2. Single-sideband AM (SSB-AM) 3. Vestigial-sideband AM (VSB-AM) 4. Conventional AM Dependence between the modulating signal and the amplitude of The modulated carrier varies from simple, e.g. DSB-AM, to highly Complex, e.g. SSB-AM & VSB-AM. AM communication exhibits lower bandwidth requirement and less power efficiency, compared to FM and PM systems Cengage Learning Engineering. All Rights Reserved. 3

4 3.2.1 DSB-AM DSB-AM means the amplitude of modulated signal is to the message signal. In time domain, this means the modulated signal is: where c(t) = A c cos(2πf c t) is the carrier, and m(t) is the message signal. Taking FT of u(t) we get the transform of the DSB-AM signal as: where M(f) is the FT of m(t). As we can see, the frequency spectrum of m(t) is scaled by A c /2 and shifted by ±f c with DSB-AM modulation. The transmission bandwidth, B T, is 2x that of m(t). Figure 3.1 shows a typical m(t) and its u(t) Cengage Learning Engineering. All Rights Reserved. 4

5 2013 Cengage Learning Engineering. All Rights Reserved. 5

6 Given Figure 3.1, the power of the modulated signal u(t) is: where P m is the power of the message signal m(t). (Can you work the math?)

7 Note that, since m(t) is a low-pass signal with frequency contents much less than 2f c, i.e. the frequency content of cos(4πf c t), the integral: in Eq. (3.2.5) goes to 0 as T. The SNR for DSB-AM is equal to the base-band SNR, given by: where P R is the power of u(t) at the receiver, a.k.a. received power. N 0 /2 is the noise power spectral density (for white noise). W is the bandwidth of m(t). See IP 3.1 & 3.2 for more details Cengage Learning Engineering. All Rights Reserved. 7

8 3.2.2 Conventional AM Conventional AM is similar in many ways to DSB-AM. Recall that for DSB-AM, from Eq. (3.2.1), With conventional AM, m(t) is replaced with [1+am n (t)], where m n (t) is the normalized message signal, i.e. m n (t) 1, and a is called index of Modulation, and 0 a 1. Thus, for u(t) and U(f) we get: We note that [1+am n (t)] is always positive. This enables much easier demodulation using envelope detectors Cengage Learning Engineering. All Rights Reserved. 8

9 Eq. (3.2.15) shows that in U(f) there are sinusoidal components at frequency f c, i.e. the two δ(f - f c ) and δ(f + f c ) components. This means we are spending power transmitting the carrier besides the message. This shows DSB-AM is more power efficient than conventional AM. However, the B T is the same for both conventional AM and DSB-AM, at 2W. See Figure 3.4 below. Doesn t this look the same as Figure 3.1? 2013 Cengage Learning Engineering. All Rights Reserved. 9

10 If m(t) is a zero-mean signal (uniformly distributed between limits), the power of modulated signal U(f) is given by: A c2 /2 denotes the power in the carrier. The second term denotes the power for the message-bearing part of U(f). Modulation efficiency is defined as the ratio between the second term and the total: Because m n (t) 1 and 0 a 1, we always have η 0.5. Generally, η 0.1. The SNR is given by: 2013 Cengage Learning Engineering. All Rights Reserved. 10

11 Eq. (3.2.19) shows that the SNR is reduced by η compared to the DSB-AM whose SNR is given by Eq. (3.2.8) below. This reduction results from the power spent in the carrier (the δ s in the spectrum), which does not carry any information and is filtered out at the receiver. See IP 3.3 for more details on conventional AM Cengage Learning Engineering. All Rights Reserved. 11

12 3.2.3 SSB-AM This is derived from DSB-AM by eliminating one of sidebands. Thus, SSB-AM uses 1/2 the bandwidth of DSB-AM. Two types of SSB-AM exist: USSB-AM and LSSB-AM. Modulated signal u(t) is given by: The - sign relates to USSB-AM, and the + sign relates to LSSB-AM. m^(t) is the Hilbert transform of m(t), i.e. m^(t) = m(t) 1/(πt) in time and M^(f) = - j sgn(f) M(f) in frequency. Hilbert transform shifts the signal s phase by π/2 in all its frequency components Cengage Learning Engineering. All Rights Reserved. 12

13 Figure 3.7 shows a message signal and its USSB-AM modulated signal. We see that B T for SSB-AM is half that for DSB-AM, i.e. B T = W Cengage Learning Engineering. All Rights Reserved. 13

14 The power of modulated signal U(f) is given by: Compare Eq. (3.2.25) to Eq. (3.2.6), we see that the power of SSB is half that of the DSB, due to half the bandwidth. The noise power at receiver is also half of a comparable DSB signal. Thus the SNR for SSB-AM is the same as DSB-AM. That is, This is the same as Eq. (3.2.8) for DSB-AM. See IP 3.4 for an SSB-AM example Cengage Learning Engineering. All Rights Reserved. 14

15 3.3 Demodulation of AM Signals Demodulation the process of extracting the message signal from the modulated signal. This process depends on the type of modulation used. For DSB-AM and SSB-AM, coherent demodulation is used. This method requires a signal with the same frequency and phase of the carrier at the receiver. For conventional AM, envelope detector is used, where it is not crucial to know precisely the carrier frequency or phase at the receiver. This makes demodulating conventional AM signals easier than DSB-AM and SSB-AM signals. Coherent demodulation for DSB-AM and SSB-AM follows the same procedure as we discussed before, i.e. by multiplying (a.k.a. mixing) the modulated signal with a sinusoid of the same frequency and phase as the carrier, then passing their product through an LPF. We use a local oscillator to generate the required sinusoid at the receiver Cengage Learning Engineering. All Rights Reserved. 15

16 3.3.1 DSB-AM Demodulation For DSB-AM, the modulated signal is given by A c m(t)cos(2πf c t). When mixed with cos(2πf c t), the following product results: Y(f), when passed through the LPF, will have its ±f c components filtered out, leaving us with only A c /2m(t) to be extracted, as below: See IP 3.5 and IP 3.6 for DSB-AM demodulation Cengage Learning Engineering. All Rights Reserved. 16

17 3.3.2 SSB-AM Demodulation Similar to DSB-AM, i.e. mixing followed by LPF. For SSB-AM: The - sign relates to USSB-AM, and the + sign relates to LSSB-AM. Mixing u(t) with the local oscillator output, we obtain: y(t), when passed through the LPF, will have its ±2f c components (the 2nd and 3rd terms in Eq. (3.3.7)) filtered out, leaving us with only A c /4m(t) to be extracted. See Figure 3.13 for the USSB-AM case Cengage Learning Engineering. All Rights Reserved. 17

18 See IP 3.7 and IP 3.8 for SSB-AM demodulation Cengage Learning Engineering. All Rights Reserved. 18

19 3.3.3 Conventional AM Demodulation Conventional AM is inferior to DSB-AM and SSB-AM in power and SNR, because a large portion of the modulated signal power is in the carrier component that does not carry information (i.e. message). In fact, the role of the carrier component is to make it possible to use envelope detection for conventional AM to demodulate. This easier method is widely used in broadcasting to reduce the receiver cost. With this method, the envelope of the modulated signal is detected by using a simple circuit, as depicted below: 2013 Cengage Learning Engineering. All Rights Reserved. 19

20 Mathematically this circuit, given the conventional AM modulated signal, generates the envelope of the signal, which is: However, since 1 + m n (t) 0, we can simplify Eq. (3.3.9) to get: where m n (t) is proportional to m(t), and the 1 corresponds to the carrier component that can be separated by a DC block circuit. Thus, we need not know the phase of the carrier signal. This is why this method is also called noncoherent or asynchronous demodulation Cengage Learning Engineering. All Rights Reserved. 20

21 Recall from Chapter 1 that the envelope of a band-pass signal can be expressed as the magnitude of its low-pass equivalent signal. If u(t) is the band-pass signal with central frequency f c and its low-pass equivalent is u L (t), then the envelope of u(t), denoted by V(t), is: where u c (t) and u s (t) represent the in-phase and quadrature components of the band-pass signal u(t). Thus, to get the envelope of u(t), we just need to obtain the low-pass equivalent of u(t). And the envelope of u(t) is simply the magnitude of the low-pass equivalent signal Cengage Learning Engineering. All Rights Reserved. 21

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