Z87200
Spread-Spectrum Transceiver Zilog
4-50
THEORY OF OPERATION (Continued)
In general, when a DDS is used to generate an unmodu-
lated signal, the stepped sine wave generated by the DDS
has spectral components at integer multiples of the DDS
sampling clock. In other words, the Z87200’s BPSK/QPSK
modulator, when programmed to generate a signal at I.F.
frequency f
OUT
, will produce spectral components at ±f
OUT
as well as at (n
RXIFCLK
± f
OUT
), where n is a positive or
negative integer. Because of these aliases, one generally
cannot program the NCO to provide an output frequency
f
OUT
greater than the Nyquist frequency f
RXIFCLK/2
. When
the I.F. frequency f
OUT
is modulated, however, degrada-
tions to the output signal due to aliasing can result even
when f
OUT
is less than f
RXIFCLK/2
.
In particular, the Z87200’s PN modulation results in a
transmit signal that has a power spectral density charac-
terizable as a sinc function (sin(x)/x) centered about the
I.F. frequency f
OUT
. Nulls of the sinc function occur at inte-
ger multiples of the PN chip rate, and the null-to-null signal
bandwidth of the Z87200’s transmit signal about f
OUT
is
twice the transmit chip rate. The presence of modulation
sidelobes and their interaction with aliases due to sam-
pling, however, will result in distortion of the mainlobe of
the baseband component centered at f
OUT
unless atten-
tion is paid to the interaction of the chip rate, the I.F. fre-
quency f
OUT
, and the sampling rate fRXIFCLK.
In the example of Figure 18, the spectrum drawn in bold
represents a signal where f
OUT
has been programmed to
be (0.4 x f
RXIFCLK
) and has been PN-modulated at a chip
rate of (0.1 x f
RXIFCLK
). The first alias of the negative fre-
quency version of this signal appears centered about (0.6
x f
RXIFCLK
) and is shown as the lighter curve. As can be
seen, energy of the second and third modulation sidelobes
of the first alias is present within the mainlobe of the base-
band component, resulting in distortion. One would typical-
ly filter the digital-to-analog converted output of the
Z87200’s BPSK/QPSK modulator to remove the energy
outside the modulation mainlobe, but such filtering will not
affect any aliasing distortion within the mainlobe as de-
scribed here. Note that the nulls of the modulated signal
aliases in this example coincide here only due to the
choice of values for the I.F. frequency, sampling rate, and
PN chip rate; in general, the nulls will not coincide. Note
also that the filtering effect of sampling has been neglected
in this discussion — in general, the aliases will be sup-
pressed by a second sinc function, sin(f’)/(f’), where f’ =
πf/f
RXIFCLK
, but this effect is not very significant for the
baseband component and first alias.
Figure 16. Spectrum of DDS modulated at 0.1 x f
RXIFCLK
when carrier frequency is set to 0.4 x f
RXIFCLK
