# [sdiy] 1-quadrant multiplier with 2164

Neil Johnson neil.johnson71 at gmail.com
Tue Jan 18 12:23:27 CET 2022

```Hi Rutger,

David's solution is a good approach, simple.

The idea of quadrants is a 2-dimensional XY graph (there can be more
dimensions, but let's stick to 2D for now).

If you draw a big "+" on a sheet of paper, with the middle crossing as "0",
then -x to +x on the horizontal, and -y to +y on the vertical, you now have

- if both inputs are unipolar then the output will be unipolar and the
- if one input is bipolar, e.g., typical audio signal with no DC, then the
- if both inputs are bipolar, then the output will occupy all four

And yes, the input of the 2164 is a virtual ground summing node, as long as
you don't overdrive it (limit is around +/- 1mA peak for the SSI2164, less
for the original SSM and CoolAudio's V versions).

Neil

On Tue, 18 Jan 2022 at 10:45, Rutger Vlek via Synth-diy <
synth-diy at synth-diy.org> wrote:

> Hi all,
>
> @David: thanks for the quick and detailed solution! I'm glad you took into
> account the linearization as well, as I'll need that too. One thing in your
> solution caught my eye, and that is that you're summing signals in front of
> the 2164's input. I know you can sum signals on the input of the I-V
> convertor, but did not know it could be done even earlier, before the 2164.
> Are you sure it would not cause interactions between the summed signals
> (i.e. can the input of the 2164 also be considered virtual ground)?
>
> @cheater00 & Matthew Skala: good point about the definition of N-quadrant
> multipliers. Here's how I understand it:
>
> - A 4-quadrant multiplier is capable of taking into account the magnitude
> and sign (+ or -) of both (biplolar) inputs and flip the output according
> to both signs (as in normal math multiplications). This would be the case
> for a ring modulator
>
> - A 2-quadrant multiplier can take into account the magnitude of both
> inputs, but only the sign of 1 input (the second input should be unipolar
> and cannot sign-flip the output). This would be the case for a normal audio
> VCA.
>
> - A 1-quadrant multiplier can take into account only the magnitude of both
> inputs, and not deal with either of the signs to cause sign-flipping of the
> output. In the common case this requires two unipolar signals, but I feel
> my case of a bipolar wave of which the amplitude is decreased up to it's
> lower bound also fits this... what do you think?
>
> Rutger
>
>
>
> Op di 18 jan. 2022 om 02:48 schreef David G Dixon <dixon at mail.ubc.ca>:
>
>> Hi Rutger,
>>
>> It is really easy to do what you want to do.
>>
>> If I understand you correctly, for an input signal of 10Vpp centred on
>> 0V, you basically want the output signal to grow from a baseline of -5V, so
>> that when the VCA is off, the output is -5V DC, at 50% gain, the output is
>> 5Vpp from -5V to 0V, and at 100% the output is 10Vpp from -5V to +5V.
>>
>> Let's assume that you have built the standard linearized VCA circuit and
>> that you have good 5V and -5V reference voltages available.  Presuming that
>> your input resistor into the amplifying 2164 VCA is 30k, and the feedback
>> resistor on the I-V converting opamp is also 30k, then all you have to do
>> is this:  Sum -5V into the 2164 VCA, in parallel with the input signal,
>> through a 30k resistor, and sum +5V into the I-V converter also through a
>> 30k resistor.  The +5V into the I-V converter will apply a constant bias of
>> -5V to the output signal.  The -5V into the VCA will counteract this bias
>> in proportion to the VCA's gain, such that, then the VCA is off, the bias
>> is -5V, and when the VCA is at unity gain, the bias is 0V.
>>
>> Easy peasy, lemon squeezy.  Schematic attached.
>>
>> Cheers,
>> Dave Dixon
>> ------------------------------
>> *From:* Synth-diy [mailto:synth-diy-bounces at synth-diy.org] *On Behalf Of
>> *Rutger Vlek via Synth-diy
>> *Sent:* Monday, January 17, 2022 1:04 PM
>> *To:* SDIY List
>> *Subject:* [sdiy] 1-quadrant multiplier with 2164
>>
>> [*CAUTION:* Non-UBC Email]
>> Dear all,
>>
>> I think i need a bit of wisdom from the 2164 guru's around here. The case
>> is as follows:
>> I'm in need of a 1-quadrant multiplier (VCA) that works on a bipolar
>> signal. The input would be a 10Vpp triangle wave centered around 0V. The
>> output should be the same with the VCA fully open, but... when closing I
>> would like to reduce the level with respect to the -5V power bound, so that
>> a VCA half-open would result in a triangle of half the amplitude, sitting
>> between -5V and 0V and a fully closed VCA would give -5V DC.
>>
>> Of course I could level-shift both input and output of a 2164 bases VCA,
>> but I feel it could be simpler. Would it work to connect a -5V signal to
>> the ground pin of a 2164? And would that also require a shifted control
>> voltage?
>>
>> Regards,
>>
>> Rutger
>>
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