Appendix A Advanced Filters - Stanford Research Systems SR865A Operation Manual

Appendix A
Advanced Filters
Traditionally, analog lock-in amplifier time-constant filters were cascaded single-pole RC
sections. These are easy to construct, require minimal tuning, and have familiar time and
frequency domain characteristics. But with the advent of digital lock-in amplifiers,
anything is possible as far as filters are concerned. So let us consider what is possible,
what is optimal, and what a lock-in user would want in digital filter.
Different filters have different time domain characteristics, such as rise time and
overshoot, and different frequency domain characteristics, such as noise bandwidth and
attenuation slope. These characteristics are inextricably linked. It is impossible to
arbitrarily specify both the frequency response of the filter and its time domain response.
That is why when we impose frequency domain restrictions such as "brick-wall" type
attenuation characteristics they come back to haunt us in the form of poor time domain
behavior, such as large overshoot.
Lock-in outputs are fundamentally time-domain outputs and this limits how aggressively
we can specify the frequency domain characteristics of our time constant filters.
Nevertheless, there are filters other than simple RC filters which offer quantifiable
benefits to lock-in users.
What are these benefits? For two filters with the same noise bandwidth, i.e. whose
outputs would be equally noisy if the input was white noise, a lock-in user would always
prefer a filter with a faster transient response and minimal overshoot. And a lock-in user
would always prefer a filter with higher stop band attenuation to ensure greater
suppression of out-of-band spurs. These are the characteristics we will concentrate on.
To use the advanced filters in place of the RC filters press and hold the [Slope/adv] key
until the
poles from 1 to 4 (6 to 24 dB). Another press and hold of the [Slope/adv] key reverts the
filters back to RC filters and turns off the
Gaussian FIR Filter
When the time constant is 3 s or shorter, an advanced Gaussian FIR filter pole of
equivalent noise bandwidth (ENBW) is substituted for an RC filter pole.
The Gaussian filter has a faster settling time than the RC filter, since it lacks the RC
filter's agonizing "exponential tail". The one-stage Gaussian filter gets to within 1% of its
final value twice as fast as the RC filter!
The Gaussian filter has better rejection of high frequencies than the RC filter. The
Gaussian filter has a constant 11.6 dB more rejection of high frequencies (per stage) than
turns on. Brief presses of [Slope/adv] cycles the number of
Advanced LED
Advanced Filters
Advanced LED .
SR865A DSP Lock-in Amplifier
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