# How can I achieve symmetrical analogue low-pass filtering?

I am experimenting with VCFs for an analogue music synthesiser. Initially I tried a 3-stage low-pass filter based on the sinewave-generator circuit in the LM13700 datasheet but having removed the oscillator, as per schematic below:

I find that its effect on a squarewave, as the filter frequency is swept, is not symmetrical. A series of scope traces shows the effect of the sweep:

If the low-pass filter is meant to attenuate higher harmonics, I would expect to see the square soften to a sine whilst retaining its symmetry. Using a Max293 active switched-capacitor filter does give a more symmetrical sweep (ignore the apparent clipping, it's due to the input running to the rails):

Question: Can anyone explain in simple terms why these filters have different effects on the waveshape symmetry (I assume it's something to do with phase shift in the analogue circuit) and whether the asymmetry can be avoided by using a different analogue design rather than having to use an active filter (with its associated downside of the clock frequency breaking through)?

Thanks

• What's the frequency (ies)? None of those 'scope shots looks very good. (slew rate limiting in the second?) You don't need a clock for an active analog filter. See "Art of Electronics" or other electronics text. Usually it's a matter of choosing an opamp that will work. Commented Oct 28, 2014 at 12:22
• The audio signal is just 125Hz - but bear in mind the shots are taken from the filter output with some filtering already applied, showing how the square morphs into a sine as the filter frequency is swept down. The original square is crisp. Re active filter - the Max293 needs its corner frequency defined by inputting a second square wave at around 100 times the frequency of the tone. Commented Oct 28, 2014 at 18:13

The two filters have similar amplitude responses, but different phase responses. In other words, different harmonics of the original square wave are being delayed (phase shifted) by various amounts by the first filter, but they have a more nearly constant delay (linear phase shift) in the second filter.

While the two waveforms look very different on an oscilloscope, they do actually have essentially the same harmonic content, and will sound very similar if not identical to the ear. Human hearing is actually very insensitive to phase relationships of this sort.

It's relatively difficult to build linear-phase filters in the analog domain, while it's quite easy to do in the digital domain, particularly with an FIR filter. But you need to decide whether the results differ enough in your application in order to make the effort.

As to why the first filter has asymmetries in response?

Look no further than the outputs being attached to darlington connected transistors or just the fact that there are transistors there with a weak pull down. The rate at which the output slews from positive to negative is dictated by the weak pull down. Essentially the op-amp looses control of the signal and has to wait until the output catches up.

So some quick screen shots of square wave into 125 Hz, Two pole Low Pass (Bessel)

Frequencies of 50 Hz, 100 Hz, 150 Hz, 200 and 300 Hz.

• Thanks for that - very similar shapes to what I get. Naively I had thought: the filter subtracts the higher harmonics, so as you sweep the filter the waveshape should be similar to the start of the additive series sin(x) + sin(3x)/3... ie rounded progressively rather than becoming lopsided. Commented Oct 28, 2014 at 19:14
• @user2468378, I'm not sure what law it is but the filters are in real time... they need to be casual. (You can't always just think in the frequency domain :^) Commented Oct 28, 2014 at 19:20