
AN168
6
PHASE NOISE CONSIDERATIONS
Noise Sources (See Figure 12)
The noise present at the VCO output originates from three
main sources.
(a) Phase noise in the reference oscillator
θ
r
(b) Phase noise in the detector
θ
d
(c) Phase noise in the VCO
θ
Ο
.
A small sinusoidal frequency modulation of the reference
oscillator for example, with peak phase deviation of
θ
radius
and modulation frequency
ω
m
would produce an output voltage
of :-
V
r
(t) = V cos (
ω
r
t+
θ
r
sin
ω
t)
= V cos (
ω
r
t)- V
θ
r
cos [(
ω
r
+
ω
m
)t] - V
θ
r
cos [(
ω
r
-
ω
m
)t]
2 2
See Figure 13. Many such sidebands will be contributed by
random noise modulation mechanisms in the reference
oscillator such as thermal and schott noise.
Fig.12 System diagram including phase noise
F(s)
1
P*N
1
M
θ
out
θ
o
θ
in
θ
d
θ
r
VCO
REF
OSC
Fig.13 Noise sidebands
f
r
- f
m
f
r
+ f
m
f
r
V
V
θ
r
Noise at Synthesiser Output
The analysis of the System block diagram shows that the
output noise spectrum is determined by :-
θ
out
(
ω
) = A (
ω
)
θ
r
(
ω
) + MA (
ω
)
θ
d
(
ω
) +
θ
O
(
ω
)
Where A(
ω
) is the system frequency response, described
in Appendix 3 (system transfer charateristics) and shown in
Figure 10.
1 - MA (
ω
)
PN
PN
M
PN
M
the noise at the output is :-
PN
M
Noise inside the Loop Bandwidth
The system frequency response inside the loop bandwidth
is approximately given by :-
A (
ω
) =
This is just a statement that the system output frequency is
times bigger than the reference frequency. As a result
θ
out
(
ω
) =
INBAND
θ
r
(
ω
) + PN
θ
d
(
ω
)
Notice that the phase noise due to the phase detector is M
times bigger than the phase noise from the reference oscillator.
Thus the phase detector noise dominates. This noise appears
as a plateau on the spectrum analyser display as shown in
Figure 14. The inband VCO noise meanwhile has been
suppressed by the loop filter. Thus the inband output noise is
determined by the prescaler and programmable divider ratios
and by the noise floor of the detector.
θ
outINBAND
= PN
θ
d
(
ω
)
Noise outside the Loop Bandwidth
The output noise outside the loop bandwidth is
approximately given by :-
θ
outOUTBAND
=
θ
O
(
ω
)
This shows that any noise components due to the VCO
having frequencies outside the loop bandwidth are not
suppressed. Thus the phase noise outside of the loop
bandwidth is determined largely by the performance of the
VCO itself and no improvement of this can be gained by the use
of the synthesiser. See Figure 14.
Example (Low Comparison Frequency Synthesiser)
A synthesiser such as the SP5510 operates with a
comparison frequency of 7.8125 KHz. If an LO of 512 MHz is
to be synthesised then :-
PN =
= 65536
f
out
Synthesized VCO
Unsynthesized VCO
Noise Floor
Fig.14 Output spectrum
512 x 10
6
7.8125 x 10
3