FM Generation and Detection Analog and Digital Communications Autumn 2005-2006

Oct 11, 2005 CS477: Analog and Digital Communications 1

FM Bandwidth

Consider Tone Modulation Observation for м э 1 jJ n ( м )j  falls off quickly for jn= м j > 1 Consider components only for jnj ф м Significant frequency components lie within f c ж м f m Observation for м ь 1 jJ n ( м )j  is insignificant for jnj > 1 Consider components only for jnj = 1 Significant frequency components lie within f c ж f m Oct 11, 2005 CS477: Analog and Digital Communications 2

FM Bandwidth: Single Tone

B = 2M ( м )f m ; M ( м ) х 1 M ( м ) depends upon the allowable distortion level Usually approximated by M ( м ) = м + 2; м > 2 B = 2( м + 2) f m = 2(A For worst case, use: m A m f 4 + 2f = 1; f m m ) = W B T = 2(f É + 2W); м > 2 What is the corresponding value of м ?

Is this the maximum value?

( м = f W Й ) B T Oct 11, 2005 CS477: Analog and Digital Communications 3

FM Bandwidth: Generic Signal

Estimate BW using worst case tone modulation!

Define Deviation ratio:

Approximations:

B T = 2DW = 2f 2W; f Й W ) B T É ; = 2M (D)W D D ь э 1 1

Carson’s rule:

B T щ 2(f É + W) = 2(D + 1)W Carson’s rule is applied for extreme values of deviation ratio. It underestimates the BW for practical systems.

Use B T щ 2(f É + 2W) = 2(D + 2)W; D > 2 (Do Example 5.2-1 and Exercise 5.2-1 in text) Oct 11, 2005 CS477: Analog and Digital Communications 4

Transmission BW: Summary

Condition(s) Single Tone Generic Signal D э 1; мэ 1 Carson’s Rule D; м extreme Practical designs 2 м f m 2DW 2f m 2W 2( м + 1)f m 2(D + 1)W 2( м + 2)f m 2(D + 2)W Oct 11, 2005 CS477: Analog and Digital Communications 5

Generating NBFM Signals

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Direct method

   Use a voltage-controlled oscillator  Output frequency is proportional to input voltage  Use information signal as the input voltage Restricted to low power applications Most circuits unstable at carrier frequency  Not suitable for commercial FM broadcast  Require sophisticated feedback control Oct 11, 2005 CS477: Analog and Digital Communications 6

Generating NBFM Signals Indirect method:

x c (t) щ A c cos2 щ f c t а A c ю (t) sin 2 щ f c t (NBPM/NBFM) þ(t) = þ É x(t) x c (t) (NBPM) 90 0 A c cos2ùf c t Input Oct 11, 2005 1 T R NBPM Modulator þ É = 2ùTf É NBFM Output CS477: Analog and Digital Communications 7

Generating WBFM Signals

Direct Method  Use a VCO (as in case of NBFM) Indirect Method  Generate NBFM first NBFM Modulator Non-linear Device Bandpass Filter Frequency Multiplier Frequency Converter ì " ; f c " ; f m unchanged Frequency converter might be needed if the multiplier produces a carrier at a frequency different from the desired carrier frequency!

Oct 11, 2005 CS477: Analog and Digital Communications 8

FM Detection

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Four primary methods

 Differentiator with envelope detector  FM to AM conversion    Phase-shift discriminator  Approximates the differentiator Zero-crossing detector Frequency feedback  Phase lock loops (PLL) Oct 11, 2005 CS477: Analog and Digital Communications 9

FM Detection: FM to AM

Differentiate the FM signal to get an AM signal!

x c (t) = A c cos(2 щ f c t + ю (t)) = A c cos т c (t) x c (t) = A c cos(2 щ f dx c (t) dt = а 2 щ A c (f c c t + 2 + f É щ f É R x( ь )d ь t x(t)) sin т c (t) ) Then use an Envelope Detector!

Amplitude Limiter Signal Differentiator Envelope Detector DC Block Oct 11, 2005 CS477: Analog and Digital Communications 10

FM Detection: Discriminator

ю (t) а ю (t а t 1 ) щ Can we produce t 1 юз (t) = 2 щ f ю (t) а ю (t а t É t 1 x(t) 1 )?

Amplitude Limiter+BPF cos(2ùf c t + þ(t )) LPF y D (t ) ù K D f É x(t) Phase-shift Network sin(2ùf c t + þ(t à t 1 )) For small values of t 1 y D (t) = sin( ю (t) а ю (t а t 1 )) щ ю (t) а ю (t а t 1 ) Oct 11, 2005 CS477: Analog and Digital Communications 11

FM Detection: Zero crossing detector

Idea: Produce a pulse at each zero crossing; Integrate over a suitable period Higher frequencies produce more pulses; More pulses result in higher output values; Output values are proportional to message W ь 1 T ь f c Want to track message but not the carrier!

Oct 11, 2005 CS477: Analog and Digital Communications 12

FM Detection: Phase Lock Loops

Basic Task of PLL: Lock the instantaneous angle of a VCO with the instantaneous angle of an external signal. i.e., lock (or track) the phase and frequency.

x c (t ) = A c cosò c (t) e(t ) LPF K a y(t ) = 1 2 A c A v K a sin ï (t ) v(t) = A v cosò v (t ) VCO y(t) = = 1 2 A c A v K a cos[ т c (t) а т v (t)] 1 2 A c A v K a cos[ п (t) а 90 î ] = 1 2 A c A v K a sin п (t) Oct 11, 2005 CS477: Analog and Digital Communications 13