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The short-circuit collector current of many silicon transistors is proportional to the exponential of the emitter-base voltage over 9 decades of collector current ( 10^{-11} a to 10^{-2} a ). Such a transistor may be connected as a three-terminal feedback network in an operational amplifier to obtain accurate logarithmic transfer response over a dynamic range of 9 decades.

A synthesis procedure that can realize any RCrealizable rational transfer function as the open-circuit-voltage transfer ratio of a nonuniform, passive RC distributed circuit is presented. The resulting circuits have a simple, standardized topology and can be readily constructed by thin-film techniques. The synthesis procedure has been completely programmed on a digital computer. From the specification of the transfer function and the electrical properties of the construction materials, the computer produces the complete geometry for the construction of the distributed circuit.