This document summarizes key concepts in analog modulation techniques including amplitude modulation (AM), frequency modulation (FM), and their performance in the presence of noise. It discusses topics such as modulation indices, signal-to-noise ratios, threshold effects, and techniques to improve noise performance like pre-emphasis/de-emphasis and phase-locked loop demodulation.

1. Modulación Analógica (AM-FM) Cx Eléctricas 09 – E.Tapia

2. Modulación de Onda CC (CW) Representación en dominios t-f Efectos del ruido en los receptores correspondientes

3. Modulation -Demodulation Ix transmission in presence of noise Ix bearing signals or baseband signals Transmitter-Channel-Receiver Frequency shifting on Tx – Modulation using a carrier Frequency shift back on Rx –Demodulation

4. Modulation Carrier is sinusoidal wave Amplitude, frequency, or phase are varied with a modulating wave - signal

5. Amplitude Modulation Message signal m(t) and carrier c(t) are independent Carrier amplitude is varied about a mean value (Ac), linearly with m(t) K a is the modulation sensiviy measured in 1/volt

6. Some issues on AM Overmodulation Leads to envelope distortion. The demodulator will track a false envelope and information will be lost. f c >>>> W – the message bandwidth Easy envelope visualization and tracking

7. Frequency Domain

8. Note that Mod-Demod are implemented using non-linear devices Demod are often envelope detectors AM Power and AM Bandwith Not efficient at power use (tx of c(t)) Sidebands are related each other >>>> just one is needed Hence >>>> avoid c(t) transmission and duplicate sidebands

9. Linear Modulation

10. DSB-SC- (Double SideBand-Supressed Carrier)

11. Coherent Detection

12. Note that Non coherent detection may lead to null quadrature effect Need coherent local oscillator at demodulation >> complexity >> the price

13. SSB MOdulation DSB-SC + Filtering for Sideband Removal Highly selective filters from cristal oscillators Coherent detector >> low power pilot carrier addition is added at transmission

14. VSB – Vestigial Sideband Modulation

15. More on VSB

16. Frequency Modulation (FM)  f is the frequency deviation  is the modulation index defined as  f /f m

17. Which is the FM angle?  << 1 radian is known as narrowband FM  >> 1 radian is known as wideband FM

18. Noise in CW Modulation Chanel Model is AWGN Power spectral density is N o /2 Receiver model defined by a bandpass filter and a demodulator model

19. SNRs SNR I (Input) Ratio of the average power of the modulated signal s(t) to the average power of the filtered noise SNR o (Output) Ratio of the averaged power of the demodulated signal to the power of noise measured at the receiver output SNR c (Channel) Ratio of the averaged power of the modulated signal to the average power of noise in the message bandwith both at the receiver input

20. Noise in DSB Coherent Detection s(t) is the DSB component of x(t) C is system dependent scaling factor m(t) sample from stationary process of zero mean and S(f) Hence compute SNR C, DSB

21. Figure of Merit in Coherent Detection The quadrature component of noise is rejected in coherent detection The average power of filtered noise n(t) is Same for n I (t)

22. Figure …. The same holds for SSB NO way to improve SNR by increasig bandwith use in DSB w.r.t SSB The effect of modulation is just frequenxy shifting

23. Noise in AM From the SNR at the channel (C, AM) we desire the SNR at the output , demodulator – envelope

24. Phasorial Analysis

25. Figures of Merit Always << 1for AM envelope receivers Equal to 1 for DSB, SSB Caused by waste of power on carrir transmission Existence of threshold effect

26. Threshold effect in AM Detectors

27. Noise Effects in FM Limiter: clipp and round so that amplitude is independent of the carrier amplitude at the receiver input.

28. Noise Model for FM R(t) is Rayleigh Phase is uniform

29. Signal Model for FM

30. Signal and Noise in FM

31. Discriminator Output Provided the carrier to noise is high

32. FM Discriminator: S2N

33. Cont’ The carrier power has noise quoting effect in FM Recall that The average signal transmitted power is k f 2 P

34. How can we improve S2N in FM?

35. The conclusion FM provides a mechanism for the exchange of improved noise performance by increased transmission bandwidth FM can also reject other FM signals closed to the carrier frequency provided interferent signal are weaker w.r.t. the target FM input

36. Threshold Effect in FM Assumption Carrier to Noise ratio at the discriminator input >> 1 Violation to this assumption FM receiver breaks. From breaks to sputtering sounds. The formula does not hold.

37. No signal but Noise Ac >> n I , n Q Ac << n I , n Q P 1 noves to the origin and random phase is observed is around

38. Alternatevely Clicks are heard after the low pass filter

39. Threshold Effect As  is decreased the rate of clicks grows Rate of clicks is high threshold occurs

40. Designing an FM System Given D (  ) Compute B T Given B T and N 0 (Noise power per unit bandwidth) Determine A C to keep above the threshold

41. FM Threshold Reduction FM demodulator with negative feeback (FMFB) or PLL

42. FM Threshold Reduction The VCO output The phase comparator output

43. FM Threshold Reduction (cont)

44. FM Threshold Reduction (cont)

45. FM Threshold Reduction (cont)

46. Linear Model of the PLL-FM Demodulator

47. PreEmphasis - Deemphasis Pre at transmitter De- at the receiver

48. Pre-emphasis & De-emphasis Pre at transmitter De- at the receiver

49. Conclusions