Analog linear interpolation of AC signals

Question

I have two AC signals in audio range \$V_1\$ and \$V_2\$, both around \$2\,\mathrm{V}\$ p.p.. I need to interpolate between the two linearly through some external control voltage \$V_c\$ (ideally also in audio range, but can be slower if it's not feasible) that varies between \$0\,\mathrm{V}-3\,\mathrm{V}\$, something like

$$V_{out}=\left(1-\frac{V_c}{3\,\mathrm{V}}\right)V_1+\frac{V_c}{3\,\mathrm{V}}V_2.$$

I, however, have no idea how to approach this. I'd bodge a solution by figuring out some sort of voltage controlled potentiometer, but I don't really know of anything of the sort either.

Answer 1

in effect you need to multiply one signal by the control input (scaled to be a number between 0 and 1), and multiply the other input by 1- the control input, then add the two together.

There's two basic approaches, either you buy an expensive multiplier chip, or you convert the control input into a fast PWM signal and use that to drive an analogue multiplexer (like CD4053 / HEF4053) then filter out the PWM frequency.

Answer 2

Sounds like an application for analog multipliers: For example, the AD633

You could need two, plus a 3.0V reference voltage. If you need the exact transfer function you state, you'd also have to multiply the result by 3.33 (so an op-amp and a couple resistors).

So you'd feed Vc into X2, 3.0V into X1, 0V into Y2, V1 into Y1, 0V into Z on the first. Output from W is (3-Vc)*V1/10

Then on the second

Vc into X1, 0V into X2, 0V into Y2, V2 into Y1, W (from the first one) into Z and take the output from W.

Output from W is \$V_{W2} = (0.1)(V_CV_2 + (3-V_C)V_1)\$

Then a simple non-inverting amplifier with two resistors to bring the output up to the desired level.

The downsides are these parts are rather expensive, and they are not terribly accurate. You could consider doing it digitally, which is quite practical at audio frequencies with a 32-bit micro.

Or with a digital pot that can handle bipolar signals, connect one side to each of the inputs and feed it a digital control signal that results from converting the 0-1V input to 0..xx where xx is the maximum setting of the digital pot. Eg. AD5121

Also, for actual audio applications, OTAs such as LM13700 are used, but don't expect much in the way of DC accuracy or stability.

Answer 3

The old-style canonical way to do this was with VCA. But, with good performance, they are horribly expensive. If you need it directly controlled by an analog voltage that's IMHO the only way to do it.

Just be careful since most VCA have logarithmic scale while you said you need a linear scale (it's a crossfader). A cheap way would be to use a JFET as an attenuator; it's routinely done in audio AGCs but it's… well… difficult to control without a feedback loop. Here you can find some pointers:

https://www.sound-au.com/articles/vca-techniques.html

and this is an example design. Note that is using a longtail so you need matched transistor to make it work well:

https://kassu2000.blogspot.com/2015/10/vca.html

Another way to do that would be using analog multipliers. out=af+b(1-f). Even more horribly expensive. AFAIK only analog device still makes them.

Now. In 2021. Pick a cheap DSP of your liking (or a small FPGA) and just do it in digital domain. Audio frequencies can be even handled by dsPICs and you have no drifting/offset/distortion issue, just use some decent converter (the builtin ones are usually subpar)