Lecture 7 AM and FM Signal Demodulation Introduction Demodulation of AM signals Demodulation of FM Signals Regeneration of Digital Signals and Bias Distortion Noise and Transmission Line Capacity Channel capacity Conclusion 1 Introduction The goal of demodulation. Demodulation Regeneration can exactly reproduce the original digital signal. An AM signal preserves the frequency domain information of the baseband signal in each sideband, Two methods for demodulation of an AM signal: Envelope detection (for DSBTC AM signal) Synchronous detection (coherent or homodyne) 2 FM signal demodulation It is more resistant to noise than an AM signal.

filtering and Limiting the transmitted signal. Differentiation to obtain the phase information in the modulated signal. There are four ways to implement differentiation: Phase-Locked Loop Zero-Crossing Detection FM-to-AM Conversion Phase-Shift or Quadrature Detection 3 Envelope detection circuit. Low-pass filter Half-wave rectifier C R2 Diode R1 S( t ) R Sr ( t ) Operational Amplifier

Sf ( t ) 4 Half-wave rectification and filtration of DSBTC AM signal. Baseband signal Sm ( t ) Modulated signal S ( t ) Rectified signal Sr ( t ) Filtered signal Sf ( t ) 5 Circuit diagram of the low-pass filter. C R2 eout ge ; g 106 to 108 -g R1 ein e R Operational Amplifier

eout 6 ein e e eout d ( e eout ) e 0 C R1 R2 dt R In the limit as | g | , the voltage, ein eout deout C R1 R2 dt R2 F ein R1 or e 0 otherwise eout = -g e

deout R2 ein eout R 2 C R1 dt R2 R U in ; F eout U out ; 1 de F R 2 C out R 2 C j U out ( j ) dt R2 U out 1 H j R 1 1 j R 2 C U in H j R2 1 2 R1 1 R 2C

( ) tan 1 R 2 C 7 20 log10 R 1 2 H ( j ) 20 log10 2 R1 1 R C 2 R 2 20 log10 2 10log10 1 R 2 C R1

1 : R 2C 1 : R 2C 1 : R 2C 20 log H j 20 log H j 20 log H j R2 10 log10 1 20 log10 R1 R

20 log10 2 R1 R 20 log10 2 10 log10 2 R1 R 20 log10 2 3.01 dB R1 R 2 20 log10 2 10 log10 R 2 C R1 R 20 log10 2 20 log10 R 2 C R1 tan 1 R 2 C 1 R 2C c 1 R 2C

( ) R 2 C ( ) 4 ( ) 2 8 20log10 | H( j ) | c = 20log10 R2 R1 1 R2 C plot of 20log10 R2 -20log10 ( R2 C ) R1 -3 dB gain?1 =

1 R1 C (a) Amplitude Bode plot (in decibels) () c = - - 1 R2 C 4 2 constant time delay RC (b) Phase Bode plot (in radians) 9 Synchronous Demodulation of AM signals S t Ac Ac S m t cos 2 f c t S demod t k1 A2 c Ac S m t cos 2 f c t cos 2 f c t

k1 A2 c Ac S m t cos2 2 f c t 1 A c Ac S m t 1 cos 2 2 f c t 2 Ac3 A2 c 1 2 S m t A c Ac S m t cos 4 f c t 2k 2k 2k 1 k 2 1 cos 1 cos 2 2 2 A2 c S demod t S m t 2k 10 Block diagram of synchronous demodulator. Sc ( t )

S(t) Multiplier Sdemod( t ) Low-pass filter Sm ( t ) 11 Demodulation of FM Signal 1 - filter the signal in order to eliminate all noise outside of the signal band. Broadcast FM signals are filtered by a band-pass filter prior to transmitting. 2 - Modulated FM signal is to pass it through a limiter. This will restrict the signal amplitude to the range -VL to +VL . The output is a series of nearly rectangular pulses. 3 - low-pass filter eliminates the higher frequency components from these pulses to obtain a signal which very closely resembles the transmitted FM signal: 12 Sf t 4 g filter VL cos c t t

gfilter : gain of low-pass filter (ratio of R2 to R1 ) This amplitude variation in the received signal does not appear at the output of the low-pass filter, but the phase function ( t ) is preserved. After the added noise is removed, the demodulator must restore the original signal Sm ( t ). It is possible to accomplish this by differentiating the filtered output signal with respect to time: (Af : amplitude of filter output, Af gfilter VL) t S ( t ) Ac cos 2 f c t k S m ( ) d d d (t ) A f cos c t t A f c sin c t t dt dt 13 Data

Transmitter 1. Rectangular pulses are generated. 2. High-frequency components are removed and the wave is given a more suitable shape for modulation. FM Modulator 3. Frequency of sine wave carrier is varied by the data signal. Band Pass Filter 4. Sidebands with low data content are removed. Pulse Generator Low Pass Filter Sine Wave Generator

Noise Transmission Medium Receiver Band Pass Filter Limiter Sine Wave Generator Data FM Demodulator 1. Components and noise outside the transmitted signal bandwidth are removed. 2. Signal is converted into a nearly rectangular wave so that amplitude distortions can be ignored 3. Demodulation recovers the data signal. Regenerator 4.

Data signal converted to rectangular pulses. 14 +VL Received signal S ( t ) +VL +VL Limited signal SL ( t ) +VL Filtered signal Sf ( t ) 15 The DC offset can be removed with a capacitor placed in series to the differentiator. The varying portion of the signal is proportional to the original signal: By passing the differentiated signal through an ideal envelope detector and low-pass filter, we can recover the original signal. The carrier frequency determines the DC offset of this signal, which will be much larger than the varying portion of the signal: d t d t S env t A f c A A f c f

dt dt Af d K S m t ; S env t A f c Sm t dt K A. B. C. D. There are four ways to implement a differentiator: Phase-Locked Loop (PLL) Zero-Crossing Detection FM-to-AM Conversion (also called a slope detector) Phase Shift or Quadrature Detection 16 Phase-Locked Loop (PLL) - negative feedback. The PLL consists of three basic components: A. Phase detector (PD) B. Low-pass filter (LPF) C. Voltage controlled oscillator (VCO) Sf ( t )

Phase Detector Sphase( t ) Low-pass filter Sout ( t ) SVCO ( t ) Voltage Controlled Oscillator (VCO) Sf ( t ) = Af cos [ c t + ( t )] SVCO ( t ) = AVCO sin [ 0 t + 0( t )] 17 Demodulation by Zero Crossing Detection Zero crossing detector Positive voltage. Negative voltage. Pulse generator. low-pass filter. The advantage of zero crossing detection (and

FM-to-AM conversion) is that no source of the carrier frequency is required to demodulate the signal. A digital signal can easily be recovered from a FM signal in this manner. Decoding an analog signal may be difficult by this method, since the signal at the low-pass filter output does not closely resemble the baseband signal. 18 Received signal S ( t ) Limited and filtered signal Sf ( t ) Zero Crossing Detection Fully rectified signal Pulse Generator Low Pass Filter Regenerator Threshold Regenerated baseband signal Sm ( t ) 19 Regeneration of Digital Signals and Bias Distortion To produce rectangular pulses, we send the demodulated signal to a regenerator, which detects whether the signal level is above a certain threshold. A poorly adjusted regenerator threshold can cause bias

distortion, where the digital signal produced is not identical to the original signal. BD 1 reg orig 20 mark space mark space mark space Original digital signal Demodulated signal Regenerator threshold is too high Regenerated signal with positive bias distortion mark space

mark space mark space mark space Regenerator threshold is too low Regenerated signal with negative bias distortion mark space mark space 21 Noise is any signal that interferes with a transmitted signal. It can be another message signal, a random fluctuation in the amount of signal attenuation, environmental noise, or additional voltages introduced by the transmitting or receiving equipment. N = kTW k: the Boltzmann constant = 1.3710 10-23 Joules per degree Kelvin T: temperature degrees Kelvin; W: bandwidth in Hertz The channel capacity is the maximum rate at which data can be

accurately transmitted over a given communication link (transmission line or radio link) under a given set of conditions. Shannon proved that if signals are sent with power S over a transmission line perturbed by AWGN of power N, the upper limit to the channel capacity in bits per second is: S C W log 2 1 N W: S: N: bandwidth of the channel in Hertz power of the signal in the transmission bandwidth power of the noise in the transmission bandwidth 22