[sdiy] Single supply op-amp filter biasing question

[Tom Wiltshire]

Hi All,

I have the following situation:

A PIC produces a PWM output representing an LFO waveform. This is then sent to an op-amp MFB filter for smoothing. The circuit looks like this:

	http://www.electricdruid.net/images/SingleSupplyLFO.jpg

If I'm running the PIC on 0-5V, and running the op-amp on 0-9V, the op-amp can't handle the raw PWM output, since it clips below about 1.6V (for the TL07x - other typical op-amps are not terribly dissimiliar). So the PWM signal needs biasing to move it to the correct range.

I found the following useful document discussing biasing, both AC and DC, for the various op-amp configurations:

	https://ocw.mit.edu/courses/media-arts-and-sciences/mas-836-sensor-technologies-for-interactive-environments-spring-2011/readings/MITMAS_836S11_read02_bias.pdf

I've used this guide with success on other circuits. However, in this case I can't make theory and practice match up. For a start, the MFB filter isn't a typical DC-coupled inverting op-amp application, although that's the closest. The filter is inverting and has no overall gain, so gain = -1.

How would I calculate the required bias to get the LFO output signal (0-5V) in the centre of the op-amps range (2-7V)?

I know the answer to this question from practical experiments, but I'd like to know how I'm supposed to derive it from the theory.

Thanks,
Tom