Stanford Research Systems SR865A Operation Manual page 174

156 Advanced Filters
the RC filter. Thus, a four-stage Gaussian filter rejects high frequencies 4*11.6 dB = 46
dB better than a four-stage RC filter.
The Gaussian filter has a flatter pass band than the RC filter. The −3dB bandwidth of the
Gaussian filter is 1.5 times greater than that of the RC filter.
One disadvantage of the Gaussian filter is the increased latency as more stages are added.
When 4 stages of Gaussian filtering are used, there is seemingly no response for several
time constants before the output quickly rises.
Lock-in users have long complained that traditional RC filters are "slow", i.e. for a given
width in the frequency domain they take the longest time to reach a given percentage of
their final value. Notice that the FIR filter reaches 99% of its final value more than twice
as fast as the RC filter. The FIR filter also attenuates signals above f
The FIR filter is ideal when the experiment is sweeping a parameter and faster response
time translates to faster sweeping, better peak definition and peak symmetry.
What's the drawback? The FIR f
dc might not be attenuated as much as the RC filter.
The SR865A implements multiple poles of FIR filtering by simply adding identical poles
in succession. Because the Gaussian filter is computationally intensive it is not available
for time constants longer than 3s.
Linear Phase Filter
For time constants of 10 s through 30000 s, the advanced filter is a Linear Phase IIR filter
with same attenuation slope as the RC filters of the same time constant and number of
poles. In other words, the Linear Phase filter's stop band is aligned with the
corresponding RC filter.
For 1 pole of filtering, the Linear Phase and RC filter are identical.
For a given stop band attenuation, the 2 pole Linear Phase filter reaches 99% of its final
value almost twice as fast as the RC filter. There is slight penalty in ENBW and
overshoot but at these longer time constants, the long wait times of the RC filter can
make the experiment exceptionally arduous.
In Real Life
In an actual experimental situation, the signal is never simple. If the goal is to read a
static output value, then longer time constants will achieve that. If the output value is
changing because of parameter sweeping or a signal turning on and off, then the
advanced filters can be of great help. In practice it is simple to try these filters, at various
time constants and number of poles, in comparison with RC filters. They often yield
better results in less time.
Closed Loop Applications
If the lock-in output X is used in a feedback loop, the filter should always be a single RC
pole. Advanced filtering may lead to oscillations in the loop.
SR865A DSP Lock-in Amplifier
is 50% greater than the RC. This means signals near
3dB
Appendix A
much more.
3dB