Reference stabilizes exponential current

In an antilog converter, the difference between the base voltages of two transistors sets the ratio of their collector currents:

The use of matched transistors balances the first-order temperature coefficient but leaves a temperature-dependent gain term, q/kT. Classic antilog circuits use a thermistor in the drive circuitry to correct this temperature dependency. However, if the control input is a fraction of some reference voltage, as when you use a manual potentiometer or a DAC, you can achieve an exact temperature correction by adding a second reference transistor. Figure 1 shows three of the five transistors in a CA3046 array. Q₁ is the exponential current source, and Q₂ is the conventional reference transistor. IC₂ forces Q₂'s collector to ground so its collector current, 1 mA in this example, is simply the reference voltage divided by R₃. Typically, this current equals the maximum output required from Q₁; lower currents result from negatively driving the transistor's base.

The attenuator on the base of Q₁, R₁, and R₂ reduces the effects of IC₁'s offset voltage. IC₃ drives the base of Q₃ via a second attenuator, R₄ and R₅, forcing its collector to ground. The reference current through Q₃ is a fraction of the main reference—one-tenth in this example. Despite the chip temperature, the base voltage of Q₃ is exactly the value you need to generate a 1-to-10 current ratio. Because IC₃'s output supplies the reference voltage for the potentiometer, the ratio of the two attenuators defines the full-scale-current-adjustment range. If the ratio is 4 to 1, the output current has a four-decade tuning range that's independent of temperature. The circuit in Figure 1 is dynamically stable, using either low-power or fast op amps.

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