# [sdiy] Digital accumulator VCO core?

Brian Willoughby brianw at audiobanshee.com
Fri Feb 12 07:54:56 CET 2021

On Feb 11, 2021, at 21:48, cheater cheater wrote:
> On Fri, Feb 12, 2021 at 6:41 AM Brian Willoughby wrote:
>> On Feb 11, 2021, at 19:22, cheater cheater wrote:
>>> I hope that when talking about the plan of replacing a single
>>> capacitor with an adc and a microcontroller, when people suggest
>>> improving this design by adding a capacitor, the humor isn't lost on
>>> them.
>>
>> Well, it is you who started chasing his own tail, so you get what you ask for. :)
>>
>>
>>> Anyways, an adc by design measures charge, and a lot of the effort
>>> behind adc design goes into making it appear like it's not measuring
>>> charge, but to instead make it look like it's measuring voltage or
>>> current. It must be natural for there to exist an adc architecture
>>> that measures charge directly - so what is it?
>>
>> No, an ADC by design measures voltage, using a comparator.
>>
>> There are perhaps dozens of different ways to perform ADC - successive approximation, flash conversion, delta-sigma - but I can't recall any that work directly on current.
>>
>> I'm gonna drag you screaming back to the courtroom and ask for a citation here ... again.
>>
>> If someone can point out an analog to digital conversion circuit topology based on current, I'd be very curious to see it.
>
> I didn't say current, I said charge.
>
> Take the Charge-redistribution successive-approximation ADC for
> example. Look at this:
>

The description in that section about how this works uses voltage several times in the text. The relationship between charge and current and voltage is always in play.

Since SAR ADC includes a DAC as part of the circuit, all that architecture is showing is the charge-scaling DAC. The ADC part works the same no matter what kind of DAC is used.

Thanks for that link, though. I didn't realize that folks were using charge-scaling DAC elements in SAR these days.

> what the ADC does is it captures /charge/ into capacitors. That charge
> is then later measured.
>
> The capacitors, however, cannot "capture voltage". A capacitor can
> only capture charge. It's impossible for a capacitor to capture
> voltage. For this reason, any ADC that first captures signal into a
> capacitor of some sort or an S&H (which is capacitor based) by default
> measures /charge/.

There's a very simple formula:

C = Q / V

Capacitance equals charge stored per volt of potential between the plates

Flip that around and Q = CV or V = Q/C

No matter what you do, Voltage is part of the equation.

You're right that capacitors store charge, but you can't force charge to flow into a capacitor from a lower voltage if the capacitor plates have already reached a higher voltage. Instead, charge will leave the capacitor until the voltage matches. I'm just being practical by ignoring charge, because the voltage is what controls what happens.

I'd like to point out that the input to the ADC chip is a voltage, not a charge. Some ADC might use Q=CV to measure that voltage, but it's still measuring a voltage. Just because it uses charge to measure the voltage is not the same as saying that it's measuring charge.

In fact, I still say that you can't measure charge. Not directly.

Also, a S&H works by charging a capacitor until the voltage on the capacitor matches the input voltage. When a S&H switches from Sample mode to Hold mode, it's holding a voltage. Technically, the Capacitor is holding a charge, and that charge produces a Voltage according to the equation V=Q/C, but it's kinda moot to think about it that way because no other part of the circuit can see the charge. The rest of the circuit sees the voltage output by the S&H. The presence of a S&H stage in no way changes ADC from voltage measurement into charge measurement.

I guess what I'm boiling it all down to is this: Circuit design and circuit analysis both use Kirchhoff's laws for current and voltage. Conservation of charge is part of why this works, but nobody calculates or measures charge. It's very difficult to measure charge. It's rather easy to measure voltage (even if that involves charge as part of the capacitor equation).

Brian