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# Amplitude modulation

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### Amplitude modulation

1. 1. Analog Modulation Analog-to-analog conversion is the representationAnalog-to-analog conversion is the representation of analog information by an analog signal. Oneof analog information by an analog signal. One may ask why we need to modulate an analogmay ask why we need to modulate an analog signal; it is already analog. Modulation is neededsignal; it is already analog. Modulation is needed if the medium is bandpass in nature or if only aif the medium is bandpass in nature or if only a bandpass channel is available to us.bandpass channel is available to us.
2. 2. 5.2 Types of analog-to-analog modulation
3. 3. Analog Modulation – Amplitude Modulation: changes the amplitude. – Frequency Modulation: changes the frequency. – Phase Modulation: changes the phase.
4. 4. 5.4 Amplitude Modulation • A carrier signal is modulated only in amplitude value • The modulating signal is the envelope of the carrier • The required bandwidth is 2B, where B is the bandwidth of the modulating signal • Since on both sides of the carrier freq. fc, the spectrum is identical, we can discard one half, thus requiring a smaller bandwidth for transmission.
5. 5. 5 AM Modulation/Demodulation Modulator Demodulator Baseband Signal with frequency fm (Modulating Signal) Bandpass Signal with frequency fc (Modulated Signal) Channel Original Signal with frequency fm Source Sink fc >> fm Voice: 300-3400Hz GSM Cell phone: 900/1800MHz
6. 6. CSULB May 22, 2006 6 Amplitude Modulation • The amplitude of high-carrier signal is varied according to the instantaneous amplitude of the modulating message signal m(t). Carrier Signal: or Modulating Message Signal: or The AM Signal: cos(2 ) cos( ) ( ): cos(2 ) cos( ) ( ) [ ( )]cos(2 ) c c m m AM c c f t t m t f t t s t A m t f t π ω π ω π= +
7. 7. 7 AM Signal Math Expression • Mathematical expression for AM: time domain • expanding this produces: • In the frequency domain this gives: ( ) (1 cos ) cosAM m cS t k t tω ω= + ( ) cos cos cosc cAM mS t t k t tω ω ω= + [ ])cos()cos(coscos:using 2 1 BABABA ++−= 2 2( ) cos cos( ) cos( )c c c k k AM m mS t t t tω ω ω ω ω= + − + + frequency k/2 k/2 Carrier, A=1. upper sideband lower sideband Amplitude fcfc-fm fc+fm
8. 8. CSULB May 22, 2006 8 AM Power Frequency Spectrum • AM Power frequency spectrum obtained by squaring the amplitude: • Total power for AM: . 2 2 2 2 4 4 1 2 k k A k = + + = + freq k2 /4k2 /4 Carrier, A2 =12 = 1 Power fcfc-fm fc+fm
9. 9. 9 Amplitude Modulation • The AM signal is generated using a multiplier. • All info is carried in the amplitude of the carrier, AM carrier signal has time-varying envelope. • In frequency domain the AM waveform are the lower-side frequency/band (fc - fm), the carrier frequency fc, the upper-side frequency/band (fc + fm).
10. 10. CSULB May 22, 2006 10 AM Modulation – Example • The information signal is usually not a single frequency but a range of frequencies (band). For example, frequencies from 20Hz to 15KHz. If we use a carrier of 1.4MHz, what will be the AM spectrum? • In frequency domain the AM waveform are the lower-side frequency/band (fc - fm), the carrier frequency fc, the upper-side frequency/band (fc + fm). Bandwidth: 2x(25K-20)Hz. frequency 1.4 MHz 1,385,000Hz to 1,399,980Hz 1,400,020Hz to 1,415,000Hz fc
11. 11. CSULB May 22, 2006 11 Modulation Index of AM Signal m c A k A = )2cos()( tfAtm mm π= Carrier Signal: cos(2 ) DC:c Cf t Aπ For a sinusoidal message signal Modulation Index is defined as: Modulated Signal: ( ) [ cos(2 )]cos(2 ) [1 cos(2 )]cos(2 ) AM c m m c c m c S t A A f t f t A k f t f t π π π π = + = + Modulation index k is a measure of the extent to which a carrier voltage is varied by the modulating signal. When k=0 no modulation, when k=1 100% modulation, when k>1 over modulation.
12. 12. CSULB May 22, 2006 12 Modulation Index of AM SignalModulation Index of AM Signal
13. 13. CSULB May 22, 2006 13 Modulation Index of AM SignalModulation Index of AM Signal
14. 14. CSULB May 22, 2006 14 Modulation Index of AM SignalModulation Index of AM Signal
15. 15. 15 Example • Determine the maximum sideband power if the carrier output is 1 kW and calculate the total maximum transmitted power. • Max sideband power occurs when k = 1. At this percentage modulation each side frequency is ½ of the carrier amplitude. Since power is proportional to the square of the voltage, each has ¼ of the carrier power. ¼ x 1kW = 250W Total sideband power = 2 x 250 = 500W. Total transmitted power = 1kW + 500W = 1.5kW
16. 16. 16 Demodulation of AM Signals Demodulation extracting the baseband message from the carrier. •There are 2 main methods of AM Demodulation: • Envelope or non-coherent detection or demodulation. • Synchronised or coherent demodulation.
17. 17. Envelope/Diode AM Detector When an AM signal is received, the receiver must perform a converse process to get the original signal (Information Signal ) back . This process is known as detection or demodulation, the simplest process which is used widely in AM radios is the Envelop Detector . Envelop Detector is an electronic circuit which is used to recover ( Demodulate ) the original signal in AM systems, its constructed from just one diode, one capacitor and one resistor . This is essentially just a halfwave rectifier which charges a capacitor to a voltage = the peak voltage of the AM signal .
18. 18. CSULB May 22, 2006 19 Envelope/Diode AM Detector If the modulation depth is > 1, the distortion below occurs K>1
19. 19. Envelope/Diode AM Detector • The output of the detector follows the envelop of the modulated signal. On the positive cycles of the input signal, the diode conducts and the capacitor charges up to the peak voltage of the input signal. As the input falls below this peak value, the diode is cut off, because the capacitor voltage is greater than the input signal voltage, thus causing the diode to open. The capacitor now discharges through the resistor at slow rate. The discharge process continues until the nest positive half-cycle. When the input signal becomes greater than the output across the capacitor, the diode conducts again and the process is repeated.
20. 20. CSULB May 22, 2006 21 Synchronous or Coherent Demodulation This is relatively more complex and more expensive. The Local Oscillator (LO) must be synchronised or coherent, i.e. at the same frequency and in phase with the carrier in the AM input signal.
21. 21. Synchronous or Coherent Demodulation If the AM input contains carrier frequency, the LO or synchronous carrier may be derived from the AM input.
22. 22. Synchronous or Coherent Demodulation If we assume zero path delay between the modulator and demodulator, then the ideal LO signal is cos(ωct). Analysing this for a AM input =  ( )( ) ( )tωtm+V cDC cos
23. 23. CSULB May 22, 2006 24 Exercises: Draw the Spectrums a) cos(ωct)cos(ω1t) from cosAcosB= 1/2[cos(A-B)+cos(A+B)] we get: cos(ωct)cos(ω1t)=1/2[cos(ωc-ω1)t + cos(ωc+ω1)t] Hence the spectrum of this is: b) cos2 ωt from cos2 A=1/2[1+cos2A] we get: cos2 ωt=1/2[1+cos2ωt] The spectrum is thus: ωc-ω1 ωc+ω1 1/2 1/2 frequency amplitude 1/2 freq 2ω 1/2 DC=0Hz
24. 24. Demerits of AM DSB FC An unmodulated RF carrier requires narrow bandwidth Modulation results in creation of a carrier and 2 Sidebands. This requires more power. Moreover carrier contains no information.
25. 25. Why DSB SC?  The carrier contains no information.  So we can think of avoiding or suppressing
26. 26. Why SSB?  The carrier contains no audio information. The sidebands contains duplicated information