Z87200
Spread-Spectrum Transceiver Zilog
4-44
THEORY OF OPERATION (Continued)
The above discussion has assumed ideal low-pass filter-
ing to recover the desired signal at baseband, but, in the
Z87200’s Downconverter, an ideal low-pass filter is not
available. The quadrature Integrate and Dump filter of the
Downconverter serves this purpose instead. The Down-
converter’s Integrate and Dump filter is a decimation filter,
integrating input samples over a programmable number of
sample periods, N, so that the output sampling rate is
(1/N)th of the input sampling rate and the I.F. sampling rate
fSA is decimated to the baseband sampling rate. Since the
Z87200’s PN Matched Filter requires two samples per
chip, the baseband sampling rate must be at twice the PN
chip rate and N must equal f
SA
/B. When the sampling rate
is much greater than the signal bandwidth (or, equivalent-
ly, the chip rate), the Integrate and Dump filter is most ef-
fective in attenuating the unwanted aliased image. This
performance can be seen from the transfer function G(w)
of a decimation filter, where:
G(w) = sin(w’)/w’ and w’ = (2 πNf)/f
SA
.
Figure 13 shows a plot of the gain of this transfer function
as a function of the normalized frequency (N f/F
SA
). To ef-
fect the desired low-pass filter and eliminate the aliased
image in the baseband Nyquist region appearing in line 5
of Figure 11, the attenuation must be suitably high for fre-
quencies greater than, in the worst case, 1/2 B. Given a
defined signal bandwidth B, however, judicious choice of
f1 and f
SA
allows a higher break frequency to be chosen,
as will be discussed.
As an extreme worst case, if f1 = 1/4f
SA
and B=1/2f
SA
, cor-
responding to the highest chip rate that can be handled for
a given value of f
SA
, then the break frequency must be
1/2B (equal to 1/4f
SA
). In this example, then, N = f
SA
/B=2
and the attenuation provided by the Integrate and Dump fil-
ter is given by the curve of Figure 13 for values of (N f/f
SA
)
greater than 1/2. As can be seen, the attenuation will be at
least equal to the peak of the corresponding lobe or at
least ~13 dB. This sidelobe peak is a worst case, and
much of the alias energy outside the desired band will be
attenuated by more than 13 dB. Nonetheless, the pres-
ence of unattenuated energy from the unwanted alias de-
grades performance. It is for this reason that Direct I.F.
Sampling Mode is only recommended for received PN chip
rates less than 1/8 f
SA
; in other words, for B<1/4 f
SA
. The
attenuation realized by the Integrate and Dump filter is
then further determined by the choice of the I.F. frequency
f
1
and the I.F. sampling rate f
SA
.
Figure 12. Direct I.F. Sampling Mode with I.F. Frequency (f
SA
+f
1
) > Sampling Frequency f
SA
FREQ.
INPUT SPECTRUM
BANDWIDTH: B
0
FREQ.
0
FREQ.
SPECTRUM
AFTER A/D
0
SPECTRUM OF
SAMPLING PROCESS
1
2
3
–f
SA
– f
1
f
SA
+ f
1
f
SA
–f
SA
f
SA
–f
SA
–f
1
f
1
