So I have been trying to work out the equation that Robin Mitchell used on his AAC project "DIY synth series: Part 1" to calculate the exponential voltage. Here is a link:

https://www.allaboutcircuits.com/projects/diy-synth-series-vco/ on his AAC used to calculate

I understand that the transistor Ic equation has exponential properties, but what equation did he use to calculate the required expo voltage? given the linear input voltage and frequency required. I want to know this since I am trying to include an exponential voltages in the code of a micro controller for a MIDI to CV to then power a Synth. Thanks for any help

 

Robin's article provides a link to a web page, here, that does a good job with the mathematics. Also, THATcorp.com, a firm that manufactures ICs used in professional audio processing, has an application note that provides similar information.

 

But surely both of these sources are demonstrating the method of obtaining the desired exponential characteristics. My point is, before considering how it can be obtained. Is there a mathematical formula that shows what we are after? which then allows us to consider ways of achieving it.

 

Mmmm... I guess I just don't get what you're asking, what distinction you're making. Both those references are pretty clear on the relation between temperature, ΔVbe and ΔIc, leading to (at 300 °K) every 60 mV change in Vbe causing a 10:1 change in collector current, a relation which holds true over many decades of Ic.

 

There’s no explicit formula given, but the key is the statement “

• The larger VEXPO is, the quicker C2 charges.”

That’s how most musical VCO’s work. The linear voltage gets converted to an exponential current which charges a capacitor according to the usual capacitor current/voltage equation. Then something discharges the capacitor. The linked circuit discharges at an equal rate to the charging (triangle wave). Others discharge very quickly (saw wave), The final voltage-frequency equation depends on the current level, capacitor value, and discharge trip point.