Digital Signal Processing Reference
In-Depth Information
which means that
R
x
=
GA
⋅
R
out
(4.17)
R
y
=
GA
⋅
R
/(
GA
−
1
out
(4.18)
The circuit of Figure 4.2 shows one stage of the new configuration with the
voltage divider output. If the input signal level is very high, we might choose to
use the voltage divider on the first stage of the filter in order to reduce distortion
in the filter.
Figure 4.2
Active filter with voltage divider output.
Before we consider how to implement an odd-order approximation function,
we need to consider whether the gain adjustment technique is appropriate for all
applications. In many cases, amplification is a required part of the filtering system,
and therefore the differences in gain can be factored into the overall gain
requirement. For example, if the overall system gain required is 60 dB, and the
filter is producing a gain of 20 dB in the passband, a more efficient solution would
be to design the remaining amplifiers to provide 40 dB of gain. This design would
be more power efficient, use fewer components, and have better dynamic range.
However, the preceding technique can be used if an exact gain is required from
the filter.
If an odd-order approximation factor is to be implemented, an odd-order stage
as shown in Figure 4.3 can be used as the first stage of the active filter. This
simple RC filter is followed by a buffer amp so that the output impedance of
the RC combination will not affect the input to the next active filter stage.
However, if an op-amp is going to be required to implement this first-order factor,
we might consider adding a few more components and implementing a second-
order stage instead. In many cases, additional attenuation in the stopband would
be welcome, and the additional cost is slight.
