Frequency Stability  f 0 /f 0 Usually Specified in ppm over a given environmental range. Temperature Altitude (pressure) Age Broadcast FM requires +/-20 ppm stability Cannot be achieved without Crystal Control Crystal oscillators cannot be FM’ed Need method to combine stability of XO with modulation sensitivity of VCO

Phase Locked Loop VCO f 0, k o,  f 0 vmvm 1/N FM out Crystal Oscillator f 0 /N LPF ~ 5 Hz + + Phase Error We will Study Phase Locked Loop dynamics in detail in Advanced Comm. This is the primary method for performing “coherent” demodulation. “Average” Phase Error

FM Automatic Frequency Control VCO f o, k o,  f o v in f out v out kdkd f discr f in v in koko fofo f out fofo  f discr Frequency Discriminator f discr, k d,  f discr v out f in koko v in f out fofo fofo kdkd  f discr f discr f in v out + _ _ ++ + Practical frequency control hardware always exhibits measurable frequency error,  f.

Crosby Method of AFC VCO f o, k o,  f o vmvm N1N1 N2N2 f out Crystal Oscillator f xo,  f xo f test = N 1 f 0 LPF ~ 5 Hz BPF ~ f discr + + f* Low pass filter prevents correction voltage from trying to follow the audio frequencies in the modulation voltage Band pass filter, centered on f discr, selects only the “difference” frequency coming out of the mixer Frequency Discriminator f discr, k d,  f discr Node variables are voltages Node Variables are frequencies

Crosby Loop Analysis koko fofo fofo kdkd  f discr f discr vmvm N1N1 N2N2 f out f test = N 1 f 0  f xo f xo _ + _ _ + f* VCO Frequency Discriminator Must find transfer function(s) in order to determine effect of drift (  f) terms on f out. f d = (f xo  f xo ) – f*

koko fofo fofo kdkd  f discr f discr vmvm N1N1 N2N2 f out f test = N 1 f 0  f xo f xo _ + _ _ + f* There are seven inputs to the loop, therefore there are seven Transfer Functions! …(f o, f d, and f xo are constants, so we don’t care about theirs) G i is forward gain from input i to output (f out ). L is Loop Gain: Total Drift of f out is the sum of the magnitudes of the drifts of f out due to each  f term.

koko fofo fofo kdkd  f discr f discr vmvm N1N1 N2N2 f out f test = N 1 f o  f xo f xo _ _ _ f* To find “open loop” responses to drift terms (“ before correcting for feedback improvement”), place the switch in the test position. Now the response to each  f term is just the forward gain from it’s input to f out.