frequency stability f 0 /f 0 usually specified in ppm over a given environmental range. temperature...
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Frequency Stability
f0/f0
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
VCOf0, ko, f0
vm
1/N
FMout
Crystal Oscillator
f0 /N
LPF ~ 5 Hz
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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
VCOfo, ko, fo
vin fout
vout
kd
fdiscr
fin
vin
ko
fo
fout
fo
fdiscr
Frequency Discriminatorfdiscr , kd , fdiscr
vout
fin
ddindout fffkv
kovin fout
fo
fo
kd
fdiscr
fdiscr
fin vout
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_
_+ +
+
Practical frequency control hardware always exhibits measurable frequency error, f.
out o in o of k v f f
Crosby Method of AFC
VCOfo, ko, fo
vm N1 N2fout
Crystal Oscillator
fxo , fxo
ftest = N1f0
LPF ~ 5 Hz
BPF ~ fdiscr
+
+
f*
Low pass filter prevents correction voltage from trying to follow the audio frequencies in the modulation voltage
Band pass filter, centered on fdiscr , selects only the “difference” frequency coming out of the mixer
Frequency Discriminatorfdiscr , kd , fdiscr
Node variables are voltages
Node Variables are frequencies
Crosby Loop Analysis
out d in discr discrv k f f f
ko
fo
fo
kd
fdiscr
fdiscr
vm N1 N2fout
ftest = N1f0
fxo
fxo
++
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_+
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f*
VCO
Frequency Discriminator
Must find transfer function(s) in order to determine effect of drift (f) terms on fout.
fd = (fxo fxo) – f*
out o in o of k v f f
ko
fo
fo
kd
fdiscr
fdiscr
vm N1 N2fout
ftest = N1f0
fxo
fxo
++
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+
_
+_
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f*
There are seven inputs to the loop, therefore there are seven Transfer Functions!…(fo, fd, and fxo are constants, so we don’t care about theirs)
1i
i
GT
L
• Gi is forward gain from input i to output (fout).
• L is Loop Gain: 1 o dL N k k
Total Drift of fout is the sum of the magnitudes of the drifts of fout due to each f term.
ko
fo
fo
kd
fdiscr
fdiscr
vm N1 N2fout
ftest = N1fo
fxo
fxo
++
+
+
_ _
_
+
+
+
+
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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 fout.