Frequency and Phase Modulation Sharlene Katz James Flynn Overview • History • Why FM? Noise problems with linear modulation systems: AMSSBDSB • Definitions: Deviation, WBFM, NBFM • Very popular for VHF voice 101408 2 Definition of an FM Signal • For a baseband signal, x(t): – k f is the frequency deviation constant in Hzvolt – A constant envelope signal with varying frequencyphase – The instantaneous frequency is: – Maximum frequency deviation =Δf= kf|x(t)|max x FM (t) = Ac cos 2πf ct + 2πk f x(τ)dτ −∞ ∫ t fi(t) = fc + k f x(t) 101408 3 FM Signal ‐ Time Domain • For a pulse train baseband signal: Baseband signal, x(t) FM signal 101408 4 FM Signal ‐ Time Domain • For a sinusoidal baseband signal: Baseband signal, x(t) FM signal 101408 5 FM Signal – Frequency Domain • For a 1 KHz sinusoidal baseband signal (tone modulation) and 10 KHz carrier f (Hz) 10 KHz Spacing = 1 KHz Wider than an AM or DSB signal 101408 6 Deviation and Bandwidth • Instantaneous Frequency: fc + kfx(t) • Frequency deviation: Δf=kfx(t) • Maximum frequency deviation, Δf = kf|x(t)|max – For tone modulation: Δf = k fAm • Deviation Ratio, D = ΔfW – For tone modulation: Modulation index, b = Dffm – b 1: wideband FM, WBFM • Bandwidth, BW = 2(D+1)W, or BW = 2(b+1)fm 101408 7 FM MODULATION • Spectrum vs. modulation index, β – Spectra have a typical trapezoidal shape in linear frequency and amplitude in decibels. carrier 2 x deviation ≈ ‐3 to ‐6dB per fm ≈ ‐3 to ‐6dB per fm FM MODULATION FM MODULATION FM MODULATION demos FM MODULATION • Comparison to AMSSBDSB AM DSB SSB FM BANDWIDTH 2 f m 2 fm fm 2 (β+1)fm SNR LINEAR LINEAR LINEAR NON‐ LINEAR EFFICIENCY 33% 50% 100% ≤ 100% COMPLEXITY LOW MODERATE MODERATE HIGH FM MODULATION • Threshold Effect • Capture effect: Signals more than 6dB down will not interfere. FM MODULATION • SDR Program for NBFM GUI INTERFACE (ptt _block) TRANSMIT transmit_path RECEIVE receive_path USRP FM MODULATION • TRANSMIT PATH (always running) Audio Source Audio Gain 32 Resampler 48kSs 48kSs 32kSs 320kSs FM Modulator Transmit Gain Transmit Enable from GUI 320kSs To USRP FM MODULATION • RECEIVE PATH (always running) 256kSs from USRP Low Pass Filter 64kSs FM Demodulator 32kSs Squelch 32kSs Audio Gain Receive Enable from GUI 23 32kSs Resampler Audio 48kSs Sink Definition of a PM Signal • For a baseband signal, x(t): – k p is the frequency deviation constant in radvolt – A constant envelope signal with varying frequencyphase – The instantaneous phase is: – The instantaneous frequency is: x PM (t) = Ac cos2πf ct + k p x(t) θ i(t) = 2πfct + kpx(t) fi(t) = fc + k p 2π dx(t) dt 101408 17 PM Signal ‐ Time Domain • For a pulse train baseband signal: Baseband signal, x(t) PM signal 101408 18 PM Signal ‐ Time Domain • For a sinusoidal baseband signal: Baseband signal, x(t) PM signal 101408 19 PM Signal – Frequency Domain • For a 1 KHz sinusoidal baseband signal (tone modulation) and 10 KHz carrier f (Hz) 10 KHz Spacing = 1 KHz Wider than an AM or DSB signal 101408 20 Bandwidth Comparison for FMPM • Bandwidth, BW = 2(D+1)W, or BW = 2(b+1)fm • FM: • For tone modulation: Modulation index, b = Df f m • BW = 2(kfAm + fm) • PM: • For tone modulation: Modulation index, b = k pAm • BW = 2(kpAm+1)fm • Increasing frequency has a more profound effect on the BW of PM 101408 21
Frequency and Phase Modulation Sharlene Katz James Flynn Overview • History • Why FM? Noise problems with linear modulation systems: AM/SSB/DSB • Definitions: Deviation, WBFM, NBFM • Very popular for VHF voice 10/14/08 2 Definition of an FM Signal • For a baseband signal, x(t): [ x FM (t) = Ac cos 2πf c t + 2πk f ∫ x ( τ ) dτ ] t −∞ – kf is the frequency deviation constant in Hz/volt – A constant envelope signal with varying frequency/phase – The instantaneous frequency is: f i (t) = f c + k f x(t) – Maximum frequency deviation =Δf= kf|x(t)|max 10/14/08 3 FM Signal ‐ Time Domain • For a pulse train baseband signal: Baseband signal, x(t) FM signal 10/14/08 4 FM Signal ‐ Time Domain • For a sinusoidal baseband signal: Baseband signal, x(t) FM signal 10/14/08 5 FM Signal – Frequency Domain • For a 1 KHz sinusoidal baseband signal (tone modulation) and 10 KHz carrier Spacing = 1 KHz Wider than an AM or DSB signal f (Hz) 10/14/08 10 KHz 6 Deviation and Bandwidth • Instantaneous Frequency: fc + kfx(t) • Frequency deviation: Δf=kfx(t) • Maximum frequency deviation, Δf = kf|x(t)|max – For tone modulation: Δf = kfAm • Deviation Ratio, D = Δf/W – For tone modulation: Modulation index, = f/fm – 1: wideband FM, WBFM • Bandwidth, BW = 2(D+1)W, or BW = 2( +1)fm 10/14/08 7 FM MODULATION • Spectrum vs. modulation index, β – Spectra have a typical trapezoidal shape in linear frequency and amplitude in decibels. 2 x deviation ≈ ‐3 to ‐6dB per fm ≈ ‐3 to ‐6dB per fm carrier FM MODULATION FM MODULATION FM MODULATION demos FM MODULATION • Comparison to AM/SSB/DSB AM 2 fm DSB 2 fm SSB fm FM 2 (β+1)fm SNR LINEAR LINEAR LINEAR EFFICIENCY 33% 50% 100% NON‐ LINEAR ≤ 100%* COMPLEXITY LOW MODERATE MODERATE HIGH BANDWIDTH FM MODULATION • Threshold Effect • Capture effect: Signals more than 6dB down will not interfere. FM MODULATION • SDR Program for NBFM TRANSMIT transmit_path GUI INTERFACE (ptt _block) USRP RECEIVE receive_path FM MODULATION • TRANSMIT PATH (always running) 48kS/s Audio Gain Audio Source Transmit Enable from GUI 48kS/s 3/2 Resampler 32kS/s FM Modulator 320kS/s Transmit Gain 320kS/s To USRP FM MODULATION • RECEIVE PATH (always running) 256kS/s from USRP Low Pass Filter 64kS/s FM Demodulator 32kS/s Squelch Receive Enable from GUI Audio Sink 48kS/s 2/3 Resampler 32kS/s 32kS/s Audio Gain Definition of a PM Signal • For a baseband signal, x(t): x PM (t) = Ac cos[2πf c t + k p x(t)] – kp is the frequency deviation constant in rad/volt – A constant envelope signal with varying frequency/phase – The instantaneous phase is: θ i (t) = 2πf c t + k p x(t) – The instantaneous frequency is: k p dx(t) f i (t) = f c + 2π dt 10/14/08 17 PM Signal ‐ Time Domain • For a pulse train baseband signal: Baseband signal, x(t) PM signal 10/14/08 18 PM Signal ‐ Time Domain • For a sinusoidal baseband signal: Baseband signal, x(t) PM signal 10/14/08 19 PM Signal – Frequency Domain • For a 1 KHz sinusoidal baseband signal (tone modulation) and 10 KHz carrier Spacing = 1 KHz Wider than an AM or DSB signal f (Hz) 10/14/08 10 KHz 20 Bandwidth Comparison for FM/PM • Bandwidth, BW = 2(D+1)W, or BW = 2( +1)fm • FM: • For tone modulation: Modulation index, = f/ fm • BW = 2(kfAm + fm) • PM: • For tone modulation: Modulation index, = kpAm • BW = 2(kpAm+1)fm • Increasing frequency has a more profound effect on the BW of PM 10/14/08 21