Multiplication and Logarithmic Conversion by Operational Amplifier-Transistor Circuits

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Abstract
Multiplier and log converter circuits in the literature which are based on junction diodes have in common the requirement that the junction employed have a constant slope of the log I vs V characteristic. When current components of the Cutler‐Bath and Sah‐Noyce‐Shockley types are considered, it is found that the range over which any one component becomes dominant, permitting application of the junction for logarithmic conversion, is narrow. The transfer conductance yFB of silicon diffused transistors is shown to exhibit the desired logarithmic characteristic over many decades. The use of an operational amplifier to impose the required bias conditions is discussed, together with performance limitations imposed by the amplifier. Circuits are given illustrating the application of the technique to vacuum gauges, transistor testing, and to an analog multiplier having a dynamic output range of five decades. A commercial electrometer is converted to logarithmic indication by the addition of only two components.

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