Lecture Aims To examine modulation process Baseband and bandpass - PDF document

EE1: Introduction to Signals and Communications Professor Kin K. Leung EEE and Computing Departments Imperial College kin.leung@imperial.ac.uk Lecture Three Lecture Aims ● To examine modulation process ● Baseband and bandpass signals ● Double Sideband Suppressed Carrier (DSB-SC) Modulation - Demodulation - ● One of various modulators Switching modulator - 2

Modulation ● Modulation is a process that causes a shift in the range of frequencies in a signal. ● Two types of communication systems Baseband communication: communication that does not use modulation - Carrier modulation: communication that uses modulation - ● The baseband is used to designate the band of frequencies of the source signal. (e.g., audio signal 4kHz, video 4.3MHz) 3 Modulation (continued) In analog modulation the basic parameter such as amplitude, frequency or phase of a sinusoidal carrier is varied in proportion to the baseband signal m ( t ) . This results in amplitude modulation (AM) or frequency modulation (FM) or phase modulation (PM). The baseband signal m ( t ) is the modulating signal. The sinusoid is the carrier or modulator. 4

Why modulation? ● To use a range of frequencies more suited to the medium ● To allow a number of signals to be transmitted simultaneously (frequency division multiplexing) ● To reduce the size of antennas in wireless links 5 Amplitude Modulation    A cos( t ) ● Carrier c c  c  0 Phase is constant - Frequency is constant - m ( t ) ● Modulating signal ● With amplitude spectrum 6

Modulated signal m ( t )cos  c t ● Modulated signal: 7 Modulated signal m ( t )cos  c t ● Modulated signal: 8

Modulated signal BHz ● Baseband spectrum: ● M (  ) is shifted to M (  +  c ) and M (  -  c ) 9 Demodulation of DSB signal m ( t )cos  c t ● Process modulated signal cos  c t ● Multiply modulated signal with 1        2 e t ( ) m t ( )cos t m t ( ) m t ( )cos2 t c c 2 1 1              E ( ) M ( ) M ( 2 ) M ( 2 ) c c 2 4 10

Demodulation of DSB signal m ( t )cos  c t ● Process modulated signal 11 Example: AM of a cosine signal ● Modulating signal m ( t )=cos  m t ● Carrier cos  c t ● Modulated signal ϕ ( t ) = m ( t ) cos  c t = cos  m t cos  c t 12

Amplitude spectrum ● Baseband signal   M             ( ) ( ) ( ) m m 1            ( ) t cos( ) t cos( ) t  DSB SC c m c m 2  (  c   m ) 13 Demodulation of DSB signal m ( t )cos  c t ● Process modulated signal 14

Modulators ● We need to implement multiplication m ( t ) cos  c t ● Among various methods, we can use Switching modulators - ● Switching modulators can be implemented using diodes (not included in your exam) - 15 Switching modulator using square pulses ● Consider a square pulse train ● The Fourier series for this periodic waveform is   1 2 1 1         w t ( ) cos t cos3 t cos5 t     c c c 2  3 5  ● The signal m ( t ) w ( t ) is  1 2 1       m t w t ( ) ( ) m t ( ) m t ( )cos t m t ( )cos3 t   c c  2  3 16

Switching modulator 17 Double Sideband Suppressed Carrier ● A receiver must generate a carrier in frequency and phase synchronism with the carrier at the transmitter ● This calls for sophisticated receiver and could be quite costly ● An alternative is for the transmitter to transmit the carrier along with the modulated signal ● In this case the transmitter needs to transmit much larger power 18

Amplitude Modulation A cos(  c t   c ) ● Carrier  c  0 Phase is constant - Frequency is constant. - m ( t ) ● Modulation signal ● With amplitude spectrum ● Full AM signal is      ( ) t A cos t m t ( )cos t AM c c      A m t ( ) cos t c ● Spectrum of full AM signal 1                         ( ) t M ( ) M ( ) A ( ) ( ) AM c c c c 2 19 Full AM Modulated signal ● DSB Modulated signal: ● Full AM signal 20

Full AM Modulated signal ● Signal ● Modulating signal ● Modulated signal:     A m t ( ) cos t c 21 Envelope detection is not possible when ● Signal ● Modulating signal ● Modulated signal:     A m t ( ) cos t c 22

Envelope detection condition ● Detection condition A + m ( t ) ≥ 0 ● Let m p be the maximum negative value of m ( t ) . This means that m ( t ) ≥ - m p ● When we have A ≥ m p , we can use envelope detector m   p ● The parameter is called the modulation index A ● When 0 ≤ μ ≤ 1 , we can use an envelope detector 23 Envelope detection example   m t ( ) B cos t ● Modulating signal m  m B ● Modulating signal amplitude is p B     B A ● Hence and A ● Modulating and modulated signals are      m t ( ) B cos t A cos t m m              ( ) t A m t ( ) cos t A 1 cos t cos t AM c m c 24

Demodulation of DSB signal   0.5 ● Consider modulation index to be   1 ● For modulation index 25 Sideband and Carrier power ● Consider full AM signal      ( ) t A cos t m t ( )cos t AM c c        carrier sidebands ● Power P c of the carrier A cos  c t 2 2 A ● Power P s of the sideband signals 2 0.5 m t ( ) ● Power efficiency 2 P useful power m t ( )     s 100%  total power P P  2 2 A m t ( ) c s 26

Maximum power efficiency of Full AM    m t ( ) A cos t ● When we have m  2 ( A )  2 m t ( ) ● Signal power is 2 ● When 0 ≤ μ ≤ 1 ● When modulation index is unity, the efficiency is   33% max ● When μ =0.3 the efficiency is   2 0.3    100% 4.3%   2  2 0.3 27 Generation of AM signals ● Full AM signals can be generated using DSB-SC modulators ● But we do not need to suppress the carrier at the output of the modulator, hence we do not need a balanced modulators ● Use a simple diode 28

Simple diode modulator design   c cos t m t ( ) ● Input signal c ● Consider the case c >> m(t) ● Switching action of the diode is controlled by  c cos t c ● A switching waveform is generated. The diode open and shorts periodically with w ( t ) ● The signal is generated      v ' ( ) t c cos t m t ( ) w t ( ) bb c 29 Diode Modulator ● Diode acts as a multiplier      v ( ) t c cos t m t ( ) w t ( ) bb n c     1 2 1 1             c cos t m t ( ) cos t cos3 t cos5 t      c  c c c 2  3 5    c 2      cos t m t ( )cos t other terms c c     2     suppressed by AM bandpass filter 30

Demodulation of AM signals ● Rectifier detector 31 Demodulation of AM signals  R ● Half-wave rectified signal is given by         A m t ( ) cos t w t ( ) R c where w ( t )     1 2 1 1             v A m t ( ) cos t cos t cos3 t cos5 t      R c  c c c 2  3 5    1      A m t ( ) other terms of higher frequencies  32

Demodulation of AM signals using an envelope detector ● Simple detector ● Detector operation 33 Envelope detector example ● For the single tone ● Design envelope detector 34

Double vs Upper/Lower Side Band (USB/LSB) Modulated Signal 35 EE1: Introduction to Signals and Communications Professor Kin K. Leung EEE and Computing Departments Imperial College kin.leung@imperial.ac.uk Lecture Four

Lecture Aims ● Angle Modulation Phase and Frequency modulation - Concept of instantaneous frequency - Examples of phase and frequency modulation - Power of angle-modulated signals - 37 Angle modulation Consider a modulating signal m ( t ) and a carrier v c ( t ) = A cos( ω c t + θ c ) . The carrier has three parameters that could be modulated: the amplitude A (AM) the frequency ω c (FM) and the phase θ c (PM). The latter two methods are closely related since both modulate the argument of the cosine. 38