Digital Signal Processing Reference
In-Depth Information
fundamental frequencies are close to each other, it follows that the spurs will
also be located close to the fundamental frequency. As a result, the transfer
function from node
d
to the output
y
of the system should thus be evaluated
at the fundamental frequency. The expression for frequency dependent third-
order intermodulation distortion is now given by (A.49):
Third-order frequency dependent intermodulation
distortion
3
1
im
3,cl
(jω)
=
3
·
hd
3,ol
·
(A.49)
1
+
F(jω)a
1
H
For the lower end of the frequency band, the approximation im
3
·
hd
3
still holds. For higher frequencies, the hd
3
expression (A.47) exhibits a pole
located at one third of the closed-loop pole. In case of intermodulation, this
pole must be relocated to the cut-off frequency of the closed-loop system. For
the same amplifier, the intermodulation performance will be 19 dB worse com-
paredtothehd
3
characteristic at the higher end of the spectrum. In a practical
application, if the bandwidth of the waveform that is applied to the input is kept
below the cut-off frequency of the closed-loop system, the error on the approxi-
mation im
3
=
=
3
·
hd
3
is much less pronounced. Summarizing plot (Figure A.14)
shows that this error can indeed be safely ignored. The reader should be aware
3
|
[
H
3,CL
(f) [dB]
Third-order distortion
keeps rising very fast
beyond closed-loop cut-off!
open-loop
ω
p1
a
1
a
1
H
ω
p1
closed-loop
20
1/H
3*HD
3,OL
HD
3,OL
HD
3,OL
/3
1+a
1
H
0
−
20
(1+a
1
H)
3
For high suppression ratios,
effects such as the linearity
of H become important.
−
40
3*HD
3,OL
/(1+a
1
H)
3
HD
3,OL
/(1+a
1
H)
3
−
60
10
-1
10
0
10
1
frequency [GHz]
Figure A.14.
Frequency dependent third-order harmonic distortion suppression in a
feedback system. Note that only the effects originating from the third-
order coefficient a
3
of the active element in the forward path were taken
into account by this figure.
