1                  L2 - Fundamentals of Amplitude Modulation                               Seneca College                 ...
25.    Mathematical description of AM            Mathematical description of AM        •   The instantaneous value of an u...
3                                        Amplitude Modulation11.    A 1 MHz carrier signal is modulated by a 5 kHz intelli...
4                                            Amplitude Modulation13.     What is Bandwidth of an AM signal?       The tota...
522. Graphical Measurement (see fig 2.8)23.  M = (Emax – Emin) /(Emax + Emin)     Min modulation = 0     Max modulation = ...
6                                        Amplitude Modulation26.   determine the % modulation, and Ei for an un-modulated ...
7                                        Amplitude Modulation38.    A 500 W carrier is to be modulated to a 90% modulation...
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L2 fundamentals of amplitude modulation notes

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L2 fundamentals of amplitude modulation notes

  1. 1. 1 L2 - Fundamentals of Amplitude Modulation Seneca College Prof Kris Pillay AM Introduction1. Why do we use modulation? a. Antenna size and efficient transmission and reception at higher frequencies. b. Only one transmission and reception of voice can take place and transmission and reception of 2nd signal would result in the interference being at the same frequency.2. What is Modulation and Demodulation? Modulation is a process of impressing (or translating) a low frequency intelligence signal onto a higher frequency carrier signal. Demodulation is the reverse process where the received modulated signal is transformed back to its original low frequency audio signal. Amplitude Modulation3. What is Amplitude Modulation? In Amplitude Modulation the amplitude of the carrier frequency is changed in accordance with the amplitude.4. Figure 2.4 shows the AM wave forms under varying intelligence conditions.
  2. 2. 25. Mathematical description of AM Mathematical description of AM • The instantaneous value of an unmodulated carrier is ec = Ec sin 2 fc t Where Ec = peak carrier amplitude fc = Carrier frequency • The instantaneous value of an intelligence signal ei = Ei sin 2 fi t Where Ei = peak intelligence amplitude fi = Intelligence frequency6. The instantaneous value of an unmodulated carrier is ec = Ec sin 2 fc t Where Ec = peak carrier amplitude fc = Carrier frequency7. The instantaneous value of an intelligence signal ei = Ei sin 2 fi t Where Ei = peak intelligence amplitude fi = Intelligence frequency Mathematical description of AM8. Since the amplitude of the am signal varies in accordance with the amplitude of the intelligence signal eAM = (Ec +Ei sin 2 fi t) sin 2 fc t eAM = Ec sin 2 fc t +Ei sin 2 fi t x sin 2 fc t9. The second part is the multiplication of the signals in the frequency domain results in amplitude modulation10. Since sin A X sin B = 0.5{cos (A-B) – cos (A+B)} eAM = Ec sin 2 fc t +Ei sin 2 fi t x sin 2 fc t eAM = Ec sin 2 fc t +mEc sin 2 fi t x sin 2 fc t [where Ei =mEc ] eAM = Ec sin 2 fc t +0.5 mEc {cos 2 (fc - fi )t – cos 2(fc + fi )t}
  3. 3. 3 Amplitude Modulation11. A 1 MHz carrier signal is modulated by a 5 kHz intelligence signal. Determine the frequency components of the resulting AM signal and draw the frequency domain representation. Amplitude Modulation12. A 30 MHz carrier signal is modulated by a 10 kHz intelligence signal. Determine the frequency components of the resulting AM signal, draw the frequency domain representation, and determine the bandwidth.
  4. 4. 4 Amplitude Modulation13. What is Bandwidth of an AM signal? The total Bandwidth of the AM signal is defined as the difference between the upper and the lower side frequencies.14. BW = fUSF- fLSF15. A closer look at the result reveals that the BW = 2 fi Amplitude Modulation16. A 1000 kHz carrier is modulated by a music signal that has frequency range from 20 Hz to 20 kHz. a. Determine the range of frequencies generated for the upper sideband and lower sidebands. b. Determine the BW c. Can the music signal be processed in an AM system without distortion? Amplitude Modulation17. Solution a. fUSBmax=fC+ fimax= 1000 kHz + 20 kHz = 1020 kHz b. fUSBmin=fC+ fimin= 1000 kHz + 20 Hz = 1000.02 kHz c. fLSBmax=fC- fimax= 1000 kHz - 20 kHz = 980 kHz d. fLSBmin=fC- fimin= 1000 kHz + 20 Hz = 999.98 kHz18. BW =fUSBmax-fLSBmax= 1020 kHz -980 kHz =2 x fimax = 2x 20 kHz = 40 kHz19. AM designated BW = 10 kHz, hence only frequencies below 5 kHz will be processed and all fi > 5 kHz will be distorted. No wonder on AM radio music does not sound as good as an FM band. Modulation index20. What is modulation index? A measure of the extent to which the amplitude of the carrier is varied by the intelligence is expressed in terms of the modulation index m.21. Modulation index is given by M = Ei/Ec = (Emax – Emin) /(Emax + Emin) where m = modulation index Ei = Peak amp of intelligence signal Ec = Peak amp of carrier signal
  5. 5. 522. Graphical Measurement (see fig 2.8)23. M = (Emax – Emin) /(Emax + Emin) Min modulation = 0 Max modulation = 100 Over - Modulation24. What is over modulation? modulation index = m = Ei/Ec If Ei = 0, this results in 0% modulation If Ei = Ec, this results in 100% modulation25. If E > Ec, this results in over modulation, If this occurs the modulated carrier will be more than double its un modulated value but will fall to zero for an interval of time as shown in fig 2.9
  6. 6. 6 Amplitude Modulation26. determine the % modulation, and Ei for an un-modulated carrier peak to peak amplitude of 80 V that reaches its max and min values as shown below S No Emax (V) Emin (V) m% Ei (V) a. 100 60 25 20 b. 125 35 56.2 45 c. 160 0 100 80 d. 180 0 ? 90 e. 135 25 68.7 55 AM Analaysis27. The am signal is given by eAM = Ec sin 2 fc t +0.5 mEc {cos 2 (fc - fi )t – cos 2(fc + fi )t} eAM=Ec sin 2 fc t +0.5 mEc cos 2 (fc - fi )t – 0.5 mEc cos 2(fc + fi )t28. Inference: The AM wave consists of carrier, USF and LSF The amplitude of the side frequencies is 0.5mEc29. In AM transmission the carrier amplitude Ec and carrier frequency fc always remain constant , whilst the intelligence amplitude Ei and the intelligence frequencies keep changing and hence the side bands amplitude and the frequencies keep changing.30. The carrier contains no intelligence, however max power goes to it.31. The side bands carry the intelligence and if more power goes to the side bands that contain info the transmission becomes more efficient. That is why the m is always set to maximum, but not higher than 100%. AM power distribution32. Power distribution in AM signal The amplitude of the am wave is eAM=Ec sin 2 fc t +0.5 mEc cos 2 (fc - fi )t – 0.5 mEc cos 2(fc + fi )t Eam = Ec + 0.5mEc + 0.5 mEc Pam = Pc + PLSB + PLSB Since power is proportional to the swquare of the voltage, the power can be expressed as Pam = Pc + 0.25m2 Pc+ 0.25m2 Pc33. PT =Pam = Pc + 0.25m2 Pc+ 0.25m2 Pc = Pc (1 + m2 /2)34. Power is side band is PLSB =PLSB = Pc ( m2 /4) AM power distribution35. Power in side band is PLSB =PLSB = Pc ( m2 /2)36. The effect of m over the power in side bands?37. Most modulators are set for 90 to 95% modulation to transmit max intelligence power and at the same time do not exceed 100% modulation.
  7. 7. 7 Amplitude Modulation38. A 500 W carrier is to be modulated to a 90% modulation level. Determine the – The total transmitted power39. – The upper side band and lower side band power Solution40. PT =Pc (1 + m2 /2) = 500 (1 + .92 /2) = 702.541. Power in side band is PLSB =PLSB = Pc ( m2 /4) = 500 ( .92 /4) = 101.25 Amplitude Modulation42. An AM broadcast station operates at its max allowed tatal output of 50 kw and at 95% modulation. Calcualte the – Carrier power43. – Sideband power Solution PT =Pc (1 + m2 /2) 50 =Pc (1 + 0.952 /2) = Pc(1 + .857 /2) = 1.429 Pc 50 = 1.429 Pc 1.429 Pc = 50 kW Carrier Power Pc = 50 / 1.429 kW = 34.99 kw sideband power = Pc ( 0.952 /2) = Pc(.857 /2) = 0.429 Pc = 15.01 kw AM Transmitter system44. Microphone sound to modulating signal45. Intelligence signal is amplified.46. The oscillator generates the carrier frequency47. The oscillator buffer ensues stability and then amplified48. The modulator modulates the signal and transmits to the antenna49. The impedance of the antenna is to be properly matched
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