• Use the Ps command to examine the frequency spectrum of the pulse. You should see
a main energy lobe that is 4 MHz wide and centered at the radars IF. There should also
be weaker lobes spaced 2 MHz apart on both sides of the main lobe. If the lobe spacing
does not look quite right, it may be because the signal generator has slightly shortened
or lengthened the trigger gate.
• Continue using Ps to examine filters that are 4 MHz, 2 MHz, and 1 MHz wide at their 3
dB points. You should see filter losses reported that are very close to the theoretical
values for the ideal band pass filter.
In the above analysis we assume that S(f) is the idealized power spectrum of a continuous
time signal. Of course, the RVP900 filter loss algorithm can only work from an estimate of
S(f) that is obtained from a finite number of samples. The filter loss calculation becomes
more complicated than the above example in which we integrated an idealized filter
response over an idealized power spectrum.
Let
denote the estimated power spectrum of the continuous-time Tx burst waveform,
for which we have only a finite number of discrete samples {b
n
}. For purposes of this
discussion we can assume that the frequency variable f is continuous. Furthermore, let
denote a power spectrum estimate that is derived in an identical manner using the same
number of samples, but of a pure sine wave at the radar's IF. The RVP900 determines
according to its sampled measurement of the transmitted waveform; however it can
calculate
internally based on an idealized sinusoid. The reported filter loss is then:
= 10log
10
2
ⅆ
ⅆ
÷
2
ⅆ
ⅆ
Where |H(f)|
2
is the spectral response of the RVP900 IF filter, and the integrals are
performed over the Nyquist frequency band that is implied by the IFDR sampling rate. Note
that the two integrals involving
have a constant value and need only be computed
once. They serve to normalize the
integrals in such a way that the filter loss evaluates
to 0 dB when the transmit burst is a pure tone at IF.
This normalization is necessary for the
filter loss values to be meaningful. Regardless of the
bandwidth and center frequency of H(f) , the
filter loss should be reported as 0 dB when the
Tx waveform appears to have zero spectral width, that is, is indistinguishable from a pure IF
sinusoid. Of course, the real Tx waveform has only
finite duration, and should never look like
a pure tone as long as RVP900 can "see" the entire Tx envelope. For this reason, it is
important that the
filter's impulse response length be set long enough (using the Pb plot) to
insure that all of the details of the Tx waveform are being captured. If the entire Tx envelope
does not
fit within the FIR filter, then the filter loss is underestimated because the Tx
spectrum appears to be narrower than it really is.
The RVP900 calculation of digital
filter loss is similar to how the loss of an analog filter
would be measured on a test bench. Suppose we are given an analog band pass filter and
are asked to determine its spectral loss when a given waveform is presented. We could use a
power meter to measure the waveform power before and after the
filter is inserted, and
compute the ratio of these two numbers. This corresponds to the first integral ratio in the
above equation. However, this is not by itself an accurate measure of
filter loss because it
does not take into account the bandwidth-independent insertion loss. Put another way, a
flat 3 dB pad would seem to produce a 3 dB filter loss in the above measurement, but that is
RVP900 User Guide M211322EN-J
146
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