Wide-Range Stable Exponential Generator

The following circuit is an adaption of  A Temperature Conpensated Exponential Function Generator, by R. A. Barham, IEEE JOURNAL OF SOLID-STATE CIRCUITS, MARCH 1968, pp 34-5.

Over three decades, I’ve invested a lot of research into these types of circuits, and also developed many alternative methods for exponential generation. Including giving up, and just using an A/D, ROM, and power-of-2 D/A feeding an MDAC; or using a DDS after the ROM.

This circuit is very favorable for electronic music applications, for a number of reasons:

1. It is an all-transistor circuit, with integral current regulator, and does not require several op amps in the exponentiation circuitry. The circuit is cleverly designed so as to not even require precision resistors for precise exponential current output.
2. The simple current regulating feedback loop holds the exponentiation action stable for a very wide variety of input frequencies. Literally, programmed for 1V/octave, the exponential output holds constant for a full 0 to -10V input up to 20 KHz and beyond. This means exponential FM modulation would function significantly more accurately and responsively than typical circuits used in electronic music.
3. Wideband operation is possible, because there is no complex current-dependent op amp phase margin to compensate for. This is possible in part because a larger current referrence is use, as described next.
4. Instead of multiplying a small reference current of 10 μA or 100 μA by powers-of-2 (e.g. octaves) for each -1.000V of  input, this circuit divides larger reference current of 1 mA by powers-of-2. This inversion of direction is very favorable for accurate pitch tuning. When there is no input (e.g. the input control voltage is 0V), the exponential output is trimmed for precise full scale; then the frequency of oscillation for a VCO is trimmed for some precise maximun frequency. The scale adjustment is unaffected by this peak calibration! The scale can subsequently be adjusted independently.
5. The originator of the circuit already obtained a very wide dynamic range of 9 decades of current with very good large range temperature stability, using a +3300 ppm thermistor and the pair of 2N4250 PNP transistors. 9 decades is far in excess of what is needed for electronic music applications, so less of the full performance available is even needed. More particularly, the modern PN4250A PNP transistor appears to have high-β at low currents, and all the data sheets show ruler flat logarithmic conformance of Ic vs. Vbe. As well, the high-β aspect appears to deal well with Is variation from device-to-device. The circuit provided precise exponential generation without even requiring matched pair transistors! The article also deals with this issue, indicating good performance across a wide variety of units of the same device type.