Digital Signal Processing Reference
In-Depth Information
1.6
Input Noise Var 0.28 deg sqr
Var 0.028 deg sqr
Var 2.8 deg sqr
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Normalized Premixing Filter Cut-off
,
F
in
Normalized Pre-mixing Filter Cut-off,
F
in
Figure 7.30
Noise performance of PM Hilbert demodulator Scheme 1.
7.10.4
Noise Performance of PM Demodulation Scheme 1
The mixing concepts discussed earlier could be applied to the PM demodulation
Scheme 1. However, because of the symmetry of the data paths, there is a
significant amount of correlation between data on the in-phase and quadrature
channels. If the correlation between these channels is
and the input phase noise
on the
c
- and
s
-channels are respectively, and , then the output phase noise
power
ρ
2
2
s
σ
σ
ϕ
c
ϕ
2
is given by
σ
ϕ
2
2
2
σ
≈
2
F
(
−
ρ
)(
F
σ
+
F
σ
)
(7.40)
ϕ
1
1
ϕ
s
2
ϕ
c
where
F
1
is the premixing cut-off frequency of the input filters, and all bandwidths
are assumed to be identical. If the input phase noise powers on the
s-
and
c-
channels are identical, so that
σ
=
σ
=
σ
, and
F
in
=
F
1,
then
ϕ
s
ϕ
c
ε
2
2
σ
≈
4
F
(
−
ρ
)
σ
(7.41)
ϕ
in
ε
σ
2
/
σ
2
Figure 7.30 shows a plot of against
F
in
using (7.41), where the
modulation frequency was set at
F
in
/2 for each premixing bandwidth,
F
in
. The
coefficient
ϕ
ε
was found from the simulations to be 0.62, and is applicable to most
practical instrumentation situations where the input phase noise bears close
resemblance to white Gaussian noise. Equations (7.40) and (7.41) are valid for all
ρ
