11 Nov 2017
In many situations, when you want to filter noise out of a signal, a simple RC-filter will do the trick. The key conditionto being able to get by with this simple circuit is that there is a large spectral 'distance' between the signal you want to see, and the noise you don't. If the signal and the noise are too close together, the RC filter can be less than fully effective (to put it kindly).
Figure - Simple RC Filter
One thing you might try to improve an RC filter's performance is to just cascade a bunch of them together, as shown below.
Figure - Cascade of RC filters.
While a cascade of RC sections (below, red trace) does give more high-frequency attenuation than a single RC section (below green trace), and the attenuation rolls off faster with increasing frequency, the roll-off rate near the corner frequency is still painfully slow.
Figure - Single RC Section (Green) vs. Cascaded RC filter (Red)
One technique for improving the roll-off near the corner is to use a combination of gain, and positive feedback in what is known as an active filter. A stylized design for an active filter using a gain of '2' (Controlled source) is shown below. Note that it still uses a cascade of RC sections, but they are set to different corner frequencies, and the middle section's capacitor is connected to the output of the gain stage instead of being returned to ground.
Figure - 3rd-order Active Filter
As you can see below, the active filter (red trace) has a much sharper and more crisp transition around the corner frequency than the 3-section RC cascade (green). It also has more attenuation overall in its stop-band.
Figure - Active filter (red) vs RC Cascade (green)
I thoght it would be a fun exercise to make a generalized implementation - a 3rd-order active filter where the user can select the corner frequency over several decades. In the circuit below, one switch selects the range (10Hz, 100Hz, 1kHz, 10kHz), thile the other selects a multiplier (1,2,5,7). In this way, the user can select corner frequencies from 10Hz-70kHz. This board also has options for handingle +/-10V signals while operating from a single +5V supply - the optional DC-DC in the upper left corner furnishes +/-15V for this purpose. Input and output connections can be made either with screw termianls or BCN connectors (both installed here)
Figure - My 3rd-order LPF implementation
Below are some time-domain tests on what changing the corner does to a 1kHz square wave. Yellow is the input, and cyan is the output.
1kHz Corner - What comes out is pretty sinusoidal
2kHz Corner - Still Sine-y 5kHz - Square-ish
7kHz - More Square-ish 10kHz - Very Square-ish
