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Phase/Frequency Modulators. Frequency Modulation using a Voltage Controlled Oscillator (VCO). v o (t) = V c cos{2 p [f c +k 0 v m (t)]t} k 0 v m (t) = D f(t). f out. f c , k o (Hz/v) VCO. v m (t). “Modulation Sensitivity”.

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Phase/Frequency Modulators

Frequency Modulation using a Voltage Controlled Oscillator (VCO)

vo(t) = Vccos{2p[fc +k0vm(t)]t}

k0vm(t) = Df(t)

fout

fc ,

ko(Hz/v)

VCO

vm(t)

“Modulation Sensitivity”

This is the only parameter we are interested in! Not the frequency, not the voltage, but the Frequency Deviation. This is the parameter that represents the source information signal; and this is what we recover during demodulation.

fout

fc

ko

“Free Running Frequency” frequency of operation when input voltage is zero.

Df(t)

fout(t)

vm(t)

k0

vm

+

fc


Phase/Frequency Modulators

Reference Phase

Phase Modulation using a Voltage Controlled Phase Shift

fc

vo(t) = Vccos{2pfct+kpvm(t)}

kpvm(t) = F(t)

vm(t)

kp(rad/v)

“Modulation Sensitivity”

Phase Deviation

F

This is the only parameter we are interested in! Not the frequency, not the voltage, but the Phase Deviation. This is the parameter that represents the source information signal; and this is what we recover during demodulation.

vm


Determining modulation sensitivity for a phase modulator
Determining Modulation Sensitivity for a Phase Modulator

Reference Phase

V(t)=I0ZT(t)) = V ejq(t) = V ej(wt+F(t))

i(t)=I0cos(wct)

Phase Deviation


Chain rule
Chain Rule

v0 is the DC bias level which gives zero phase shift.

When v0 is applied to the diode:

C(v0) = C0(1+2v0)-1/2 = Cc

w(v0)= wc

S(v0) = 0



Limit of Linearity: How good is good enough?

DF

s

se

Phase Error

DFe

se

s

For a maximum fractional error (distortion) of e, the maximum normalized frequency displacement is:

1

If e < 0.05, DFMAX < 0.39R


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