User`s guide

FM Discriminator Fundamentals 9
Agilent E5505A User’s Guide 247
The double-balanced mixer, acting as a phase detector, transforms the
instantaneous phase fluctuations into voltage fluctuations ( ). With the
two input signals 90° out of phase (phase quadrature), the voltage out is
proportional to the input phase fluctuations. The voltage fluctuations can then
be measured by the baseband analyzer and converted to phase noise units.
The discriminator transfer response
The important equation is the final magnitude of the transfer response.
Where represents the voltage fluctuations out of the discriminator and
represents the frequency fluctuations of the DUT. is the phase
detector constant (phase to voltage translation). is the amount of delay
provided by the delay line and is the frequency offset from the carrier that
the phase noise measurement is made.
System sensitivity
A frequency discriminator’s system sensitivity is determined by the transfer
response. As shown below, it is desirable to make both the phase detector
constant and the amount of delay large so that the voltage fluctuations
out of a frequency discriminator will be measurable for even small
fluctuations .
The magnitude of the sinusoidal output term or the frequency discriminator is
proportional to . This implies that the output response will have
peaks and nulls, with the first null occurring at . Increasing the rate of
a modulation signal applied to the system will cause nulls to appear at
frequency multiples of (Figure 179).
Δφ ΔV→
ΔVf
m
() K
φ
2πτ
d
Δff
m
()
πf
m
τ
d
()sin
πf
m
τ
d
()
-----------------------------
=
ΔVf
m
()
Δffm()
Kφ
τd
f
m
Kφ
τd
ΔV
Δf
ΔVf
m
() K
φ
2πτ
d
πf
m
τ
d
()sin
πf
m
τ
d
()
-----------------------------
Δffm()()=
NOTE
The system sensitivity is independent of carrier frequency .
f
o
πf
m
τ
d
()πf
m
τ(⁄n
m 1 τd⁄=
1 τd⁄