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In Chapter 2, we did a filter skirt selectivity calculation for two signals
spaced 4 kHz apart, using a 3 kHz analog filter. Let’s repeat that calculation
using digital filters. A good model of the selectivity of digital filters is a
near-Gaussian model:
H(∆f) = –3.01 dB x
[
∆f
]
α
RBW/2
where H(∆f) is the filter skirt rejection in dB
∆f is the frequency offset from the center in Hz, and
α is a parameter that controls selectivity. α = 2 for an ideal
Gaussian filter. The swept RBW filters used in Agilent
spectrum analyzers are based on a near-Gaussian model with an α
value equal to 2.12, resulting in a selectivity ratio of 4.1:1.
Entering the values from our example into the equation, we get:
H(4 kHz) = –3.01 dB x
[
4000
]
2.12
3000/2
= –24.1 dB
At an offset of 4 kHz, the 3 kHz digital filter is down –24.1 dB compared
to the analog filter which was only down –14.8 dB. Because of its superior
selectivity, the digital filter can resolve more closely spaced signals.
The all-digital IF
The Agilent PSA Series spectrum analyzers have, for the first time, combined
several digital techniques to achieve the all-digital IF. The all-digital IF brings
a wealth of advantages to the user. The combination of FFT analysis for
narrow spans and swept analysis for wider spans optimizes sweeps for the
fastest possible measurements. Architecturally, the ADC is moved closer
to the input port, a move made possible by improvements to the A-to-D
converters and other digital hardware. Let’s begin by taking a look at the
block diagram of the all-digital IF in the PSA spectrum analyzer, as shown
in Figure 3-2.
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