ENSC327 Communications Systems 4. Double Sideband

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ENSC327Communications Systems4. Double Sideband ModulationJie LiangSchool of Engineering ScienceSimon Fraser University1

Outline DSB:Modulator Spectrum Coherent Demodulator: Threemethods Quadrature-carrierMultiplexing2

Double Sideband Modulation (DSB) AM:s (t ) Ac [1 k a m(t )]cos(2πf c t ) DSB:s (t ) Ac m(t ) cos(2πf c t ) No carrier component in the DSB signal. Input:DSB Output:Envelope is no longer the input, Cannot use envelope detector as demodulation. 3

Spectrum of DSBThe FT of DSB signal isS( f ) Ac[M ( f f c ) M ( f f c )]2Proof:4

Spectrum of DSB Upper Sideband and Lower Sideband Upper Sideband (USB): [fc, fc W], [- fc – W, -fc].Lower Sideband (LSB): [fc - W, fc], [- fc, -fc W].LSBUSBLSBUSB-fcfcf2W Bandwidth: 2W (same as AM)No component at carrier frequency, unless m(t) has a DC: DSB is also called suppressed carrier DSB (DSB-SC) Better power efficiency The price paid is more complicated demodulation.5

Modulator & Demodulator of DSB Modulator: The generation of DSB signal is straightforward,Just multiply the message with the carrier.This is also called Product ModulatorS(t)s (t ) Ac m(t ) cos(2πf c t )Demodulator: The demodulation is more complicated than theAM, because the envelop detector cannot be used in DSB. The key idea of DSB demodulation: the trigonometric identity cos 2 (2πf c t ) 6

Coherent Detection (SynchronousDemodulation) Assuming a coherent or synchronized carrier signal is available at thereceiver, the message can be recovered by multiplying the received signalwith the coherent carrier, followed by a lowpass filter.S(t)vo(t)v(t)Ac ' cos( 2πf c t ) After multiplying with coherent carrier: V(f) f After lowpass filter:7

Example Modulation:s (t ) Ac m(t ) cos(2πf c t )m(t)Ac cos(2πf c t ) Demodulation:s(t)v(t ) Ac ' cos( 2πf c t )LPFAc Ac 'm(t )[1 cos(4πf ct )]2Freq is higher than in s(t).Sign of v(t) is same as m(t).Ac Ac ' m(t ) / 28

Phase Error of the Demodulator So far we assume the demodulator has a carrier thathas the same frequency and phase as the transmitter If a phase error exists at the receiver:After LPF: If the phase error is constant: Otherwise:9

DSB: Generation of Coherent Carrier Methodsto generate a phase coherent carrier: Method 1. Costas receiver Invented by John Costas at General Electric in the 1950s. Also known as Costas Phase Locked Loop (PLL): A negative feedback system that generates a signal, whosephase is locked to the phase of an input or "reference" signal. Accomplished by a voltage controlled oscillator (VCO) Method2. Squaring the received signal Method 3. Transmitting Used in stereo FMpilot signal10

3.4 Costas ReceiverI-channelQ-channel Two local oscillator signals that are in quadrature: cos(2πf c t φ )o with 90 phase differencesin( 2πf c t φ )These local carriers are used by two coherent detectors: In-phase coherent detector (also known as I-channel) Quadrature-phase coherent detector (or Q-channel)11

3.4 Costas Receiver The I-channel output is The Q-channel product modulator output: The output after lowpass filter:12

3.4 Costas ReceiverVCO When phase error is 0: I-channel output: Q-channel output:If the phase of the local carrier drifts by a small value φ : I-channel output: Q-channel output:13

αφ The phase discriminator consists of a multiplierfollowed by a time-averaging unit: Multiplier output: Time averaging output (which is input of VCO): The phase discriminator output is proportional to VCO is a negative feedback system: The VCO will drive the local carrier phase to 0.Synchronization with the input is thus achieved. 14

DSB: Generation of Coherent Carrier Method 2. Squaring the received signals (t ) Ac cos(2πf ct )m(t ) A coherent carrier can be obtained by:15

DSB: Generation of Coherent Carrier Method 3. Transmitting a pilot signal outside the passband ofthe modulated signal: The pilot is a low-power sinusoidal wave whose freq and phase arerelated to the carrier wave (e.g., divide by 2)Receiver uses a narrowband bandpass filter to extract the pilot signal,and then converts it to the correct frequency (e.g., double the freq)Example: Stereo FM (page 183)Single-sided spectrum ofFM baseband signal. Carrier: 38 kHz. Pilot: 19 kHz16

Outline DSB:Modulator Spectrum Coherent Demodulator: Threemethods Quadrature-carrierMultiplexing17

3.5 Quadrature-Carrier Multiplexing Also known as Quadrature-amplitude modulation (QAM): Transmit two DSB-SC signals in the same spectrum region.Use two modulators with quadrature phases.Transmitted signal:s (t ) 18

3.5 Quadrature-Carrier Multiplexing Demodulator: two coherent detectors with 90 degree phase shiftOutput of the top product demodulator:After LPF:Similarly, m2(t) can be recovered by the 2nd detector.19

3.5 Quadrature-Carrier Multiplexing It is important to maintain the synchronization of the oscillatorsat the transmitter and at the receiver.This can be achieved using the Costas Receiver or the pilotsignal method.20

Demodulator : The demodulation is more complicated than the AM, because the envelop detector cannot be used in DSB. The key idea of DSB demodulation: the trigonometric identi

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