1. ECE 4710: Lecture #22 1 Frequency Modulation  FM spectrum is very difficult to calculate in general  Useful to develop simple approximations when the modulation index,  , is small or large  Recall that  “small”   so   F  B / 5  Narrowband FM  “large”   so   F > 5 B  Wideband FM  FM complex envelope where

2. ECE 4710: Lecture #22 2 Narrowband FM  Narrowband FM = NBFM  Restrict phase angle to small value  For small values the exponential function in complex envelope can be approximated using first two terms of Taylor series expansion   So  NBFM signal at Tx output

3. ECE 4710: Lecture #22 3 Narrowband FM  NBFM signal at Tx output (continued)  Carrier Term  does NOT depend on  (t) modulation »Just like large carrier (LC) in AM  Sideband Term  depends on  (t) modulation and is 90° out of phase with respect to carrier »Note that  (t) is modulating amplitude of sine !! »Different than AM where sidebands are in phase with LC Carrier Term Sideband Term

4. ECE 4710: Lecture #22 4 NBFM Spectrum Carrier Sidebands LCDSB

5. ECE 4710: Lecture #22 5 NBFM Tx LC DSB

6. ECE 4710: Lecture #22 6 Wideband FM  FM  instantaneous frequency of s(t) varies in direct proportion to modulating signal voltage m(t)  If m(t) stays at one particular voltage more than another then s(t) will spend more time at one particular frequency  PSD of s(t) should have more power at frequencies associated with m(t) voltages that are more likely  Probability Density Function (PDF) of m(t) can be used to approximate PSD for s(t) for wideband FM (WBFM)

7. ECE 4710: Lecture #22 7 Wideband FM Equal probability for any voltage between  V p and + V p  Uniform PDF for m(t) and rectangular spectrum for WBFM Triangle Modulating m(t) PDF of m(t) Approximate WBFM spectrum for triangle modulation

8. ECE 4710: Lecture #22 8 Wideband FM Tx VCO = Voltage Controlled Oscillator Phase Lock Loop (PLL) configuration produces DC output at LPF to ensure stable carrier when center frequency of VCO drifts away from f c

9. ECE 4710: Lecture #22 9 Digital FM Signals  What happens if a digital waveform is used for m(t) in an FM system??  Instantaneous frequency of s(t) varies in time about assigned carrier frequency in direct proportion to modulating signal voltage m(t)  Two voltage states (± A c )  two discrete frequency values ( f H, f L ) @ output of FM Tx +Ac+Ac VCO AcAc

10. ECE 4710: Lecture #22 10 Digital FM Signals VCO Binary Frequency Shift Keying (BFSK) +Ac+Ac AcAc 1 0 1 0 1 0  special case of WBFM with digital m(t)

11. ECE 4710: Lecture #22 11 BFSK Signal Spectrum Binary Digital m(t) PDF of m(t) Approximate WBFM spectrum for BFSK

12. ECE 4710: Lecture #22 12 Digital AM & FM BPSK Signal Polar Modulation BFSK Signal Special Case of DSB-SC Special Case of FM 1 0 1 0 1 0

13. ECE 4710: Lecture #22 13 FDM  Frequency Division Multiplexing = FDM  Technique to transmit multiple messages simultaneously over a wideband channel  Modulate multiple messages onto subcarriers »Composite baseband signal formed from multiple signals  Composite signal spectrum most not have overlapping spectrum  message “crosstalk” (interference)  Composite signal modulated onto main RF carrier  Any type of modulation can be used for carrier and sub- carriers (AM, FM, DSB, etc.) »Different modulation types can be used within same FDM system »Example: DSB-SC for subcarriers and FM for carrier  FM Stereo

14. ECE 4710: Lecture #22 14 FDM Tx Transmitter Composite Baseband Signal Spectrum

15. ECE 4710: Lecture #22 15 FDM Rx Receiver 1. Received FDM signal demodulated to recover composite baseband signal 2. Passed thru multiple bandpass filters to separate individual subcarriers 3. Subcarriers demodulated to recover multiple message signals

16. ECE 4710: Lecture #22 16 FM Stereo Broadcast  FM Stereo Broadcast in U.S. is FDM system  FM carrier modulation  DSB-SC sub-carrier modulation  Left & Right ( L / R ) audio channels for stereo signal  L + R signal used to allow mono Rx (outdated) »15 kHz baseband audio signal BW  L - R signal modulated on 38 kHz DSB-SC sub-carrier »38 kHz sub-carrier signal BW (2 x 15 kHz) »38 / 2 = 19 kHz pilot tone for coherent demodulation of sub-carrier  Rx uses sum & difference of L + R and L - R to recover L and R channels for stereo speakers

17. ECE 4710: Lecture #22 17 FM Stereo Tx Transmitter Composite Baseband Signal Spectrum 23 kHz 53 kHz f L + R Composite Baseband Signal Spectrum 23 kHz 53 kHz L + R DSB-SC Spectrum L  R

18. ECE 4710: Lecture #22 18 FM Stereo Rx L + R L  R f p = 19 kHz f VCO = 38 kHz

19. ECE 4710: Lecture #22 19 FM Stereo Broadcast  FCC can authorize FM station for subsidiary communication authorization (SCA)  Up to 4 SCA channels authorized  First SCA subcarrier is usually 67 kHz »Second analog audio program »Background “elevator” music  Musac service  Secondary service of FM station for revenue generation  Other subcarriers used for data or analog audio »Radio Broadcast Data System (RBDS)  57 kHz subcarrier with 1200 bps data  Auxillary text information (music titles, artist, traffic reports, etc.)

20. ECE 4710: Lecture #22 20 FM Stereo Spectrum f Composite Baseband Signal Spectrum with SCA Channels 23 kHz 53 kHz L + R DSB-SC Spectrum L  R 67 kHz 57 kHz 2 nd Audio “Musac” Data 75 kHz 59 kHz 1. Non-Commercial Stations  88.1 to 91.9 MHz 2. Commercial Stations  92.1 to 107.9 MHz 3. RF Channel BW = 200 kHz 4.  F = 75 kHz from RF channel carrier frequency 5. 2  F = 150 kHz < 200 kHz channel BW  guard BW to minimize interference between stations