Z87200
Zilog Spread-Spectrum Transceiver
4-43
The spectrum of a real input signal with center (I.F.) fre-
quency of f1 and signal bandwidth B is shown in line 1 of
Figure 13. The bandwidth B is the two-sided bandwidth,
corresponding to a PN chip rate of 1/2 B Mcps. Note that
throughout this discussion it is assumed that the signal
bandwidth does not exceed 1/2f
SA
; that is, B < 1/2f
SA
. Oth-
erwise, the mixing and sampling processes to be de-
scribed will result in destructive in-band aliasing. Also,
clearly, the I.F. frequency must be able to support the sig-
nal bandwidth; that is, 1/2B<f1.
The input signal is sampled at the frequency f
SA
, where the
sampling spectrum is shown in line 2 and the resulting
spectrum is shown in line 3. As can be seen, the funda-
mental and harmonics of the sampling frequency result in
images of the input signal spectrum at other frequencies,
where here the images are centered about multiples of the
sampling frequency. In other words, the spectrum of the
sampled signal shown in line 3 contains aliases of the input
signal at frequencies f1 ± n f
SA
, where n can assume both
positive and negative integer values. Since the sampling
process is linear, no spectral inversion occurs; that is, the
original spectrum is translated along the frequency axis
with no mirror reflections of the input spectrum created.
The Z87200’s NCO provides a quadrature (sine and co-
sine) output that defines a complex signal. Line 4 shows its
spectrum as an impulse at frequency -f1, where the minus
sign reflects the signal’s use in downconversion and the
absence of a positive impulse at frequency +f1 results be-
cause the NCO output is truly complex. Aliases of this im-
pulse are shown offset by integer multiples of f
SA
to reflect
the sampled nature of the NCO output. When the input
sampled signal of line 3 is then modulated with the com-
plex signal of the Z87200’s quadrature NCO of line 4, the
signal spectrum after mixing is as shown in line 5. The sec-
tions shown inside the shaded areas are the aliases of the
baseband signal beyond the Nyquist frequency and are
not of concern. The signals inside the primary baseband
Nyquist region (| f |<1/2 f
SA
) consist of the desired signal
and a spectrally reversed or inverted image signal with
center frequency separated from that of the desired signal
by 2 f1, twice the I.F. frequency before sampling. This im-
age signal can be removed by a subsequent ideal low-
pass filter as shown in line 6.
In Figure 13, the input signal is shown at a low I.F. frequen-
cy such that f1 < 1/2 f
SA
; that is, the signal is only defined
inside the primary Nyquist region. Provided, however, that
B < 1/2 f
SA
, that condition need not be true as long as the
input spectrum is only defined for frequencies within a non-
primary Nyquist region; that is, defined only over frequen-
cies f such that
(n–1/2)f
SA
<|f|<(n+1/2)f
SA
for positive integer n.
Direct I.F. Sampling Mode with this type of signal is shown
in Figure 14, where it can be seen that in line 3 the dia-
gram’s high frequency input has the same spectrum after
sampling as does the low frequency input in Figure 11;
consequently, all subsequent operations are identical to
those in Figure 13.
This result stems from the periodic nature of sampling:
sampling an input frequency f1 is theoretically indistin-
guishable from sampling an input frequency (n f
SA
+ f1) for
positive integer n and positive f1 < 1/2 f
SA
. A slightly differ-
ent result obtains, however, when sampling an input fre-
quency (n f
SA
- f1), again for positive integer n and positive
f1 < 1/2 f
SA
. In this case, the positions of the spectrally in-
verted and spectrally correct aliases will be interchanged
when compared with an input frequency of (n f
SA
+ f1). As
a consequence, the desired baseband signal after down-
conversion and filtering will also be spectrally inverted.
This phenomenon is equivalent to high-side conversion;
that is, downconversion of a signal by means of a local os-
cillator at a frequency higher than the carrier frequency. If
the modulation type is QPSK, demodulation of a spectrally
inverted signal will result in the inversion of the Q channel
data (which can be readily corrected); if the modulation
type is BPSK, there is no effect on the demodulated data.
