Synthesis of a Voltage Reference Circuit


(A Human-Competitive Result Produced by Genetic Programming)


The Result

Genetic programming evolved a voltage reference circuit as described in Section 50.3 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999).



Basis for Claim of Human-Competitiveness

The voltage supplied by all practical sources of electrical power is subject to variation. However, many circuits operate properly only when they are supplied with one or more reference voltages that can be relied upon to vary only slightly from their specified values. Moreover, the behavior of all circuits is subject to variation because of temperature. A voltage reference circuit supplies a prespecified constant voltage (with a small prespecified tolerance) in spite of variation in the incoming power supply and in spite of variation in the ambient temperature.

Since the beginning days of instrumentation in the l9th century, electrical systems have needed a compact source of well-defined potential difference-a voltage-that remains accurate, stable, repeatable, and inexpensive. Although laboratories have used carefully constructed, wet electrochemical cells, called Weston cells, for primary references, these are hopelessly impractical for most systems …”

The legendary, late Bob Widlar (l970) described a reference that simply and cleverly employed the two opposing temperature coefficients together in a mutually canceling way. The resulting device was a bandgap voltage reference, which [David] Fullagar notes was

"one of the most elegant pieces of design work in our industry."


“A voltage reference has a higher ratio of design-in subtlety to the number of active devices than any other linear component. For an IC with just two or three terminals, the voltage reference packs a lot of mystery into its design, packaging, and application.”

Robert C. Dobkin and Robert J. Widlar of National Semiconductor Corporation received U.S. patent 3,617,859 for the voltage reference circuit (Dobkin and Widlar 1971). While the genetically evolved circuit does not employ the cleverness and elegance of the design in the Dobkin-Widlar patent, it achieves the same overall objective. Subsequent to the Dobkin-Widlar patent, other patents have been issued for voltage reference circuits, including U.S. patent 3,743,923 to Goetz Wolfgang Steudel of RCA Corporation (Steudel 1973).

Referring to the eight criteria in chapter 1 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999) for establishing that an automatically created result is competitive with a human-produced result, the automatic synthesis of a voltage gain stage for a voltage reference circuit satisfies the following two criteria:

(A) The result was patented as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention.

(F) The result solves a problem of indisputable difficulty in its field. 


Dobkin, Robert C.; and Widlar, Robert J. 1971. Electrical Regulator Apparatus Including a Zero-Temperature Coefficient Voltage Reference Circuit. U.S. Patent 3,617,859. Filed May 23, 1970. Issued November 2, 1971.

Koza, John R., Bennett III, Forrest H, Andre, David, and Keane, Martin A. 1999a. Genetic Programming III: Darwinian Invention and Problem Solving. San Francisco, CA: Morgan Kaufmann.

Steudel, Goetz Wolfgang. 1973. Reference Voltage Generator and Regulator. U.S. Patent 3,743,923. Filed December 2, 1971. Issued July 3, 1973.

Widlar, Robert J. 1970. New developments in IC voltage regulators. IEEE International Solid-State Circuits Conference. Session FAM 13.3. New York: IEEE Solid State Circuits Council. pp.158-159.

· The home page of Genetic Programming Inc. at

· For information about the field of genetic programming and the field of genetic and evolutionary computation, visit

· The home page of John R. Koza at Genetic Programming Inc. (including online versions of most published papers) and the home page of John R. Koza at Stanford University

· For information about John Koza’s course on genetic algorithms and genetic programming at Stanford University

· Information about the 1992 book Genetic Programming: On the Programming of Computers by Means of Natural Selection, the 1994 book Genetic Programming II: Automatic Discovery of Reusable Programs, the 1999 book Genetic Programming III: Darwinian Invention and Problem Solving, and the 2003 book Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Click here to read chapter 1 of Genetic Programming IV book in PDF format.

· 3,440 published papers on genetic programming (as of November 28, 2003) in a searchable bibliography (with many on-line versions of papers) by over 880 authors maintained by William Langdon’s and Steven M. Gustafson.

· For information on the Genetic Programming and Evolvable Machines journal published by Kluwer Academic Publishers

· For information on the Genetic Programming book series from Kluwer Academic Publishers, see the Call For Book Proposals

· For information about the annual Genetic and Evolutionary Computation (GECCO) conference (which includes the annual GP conference) to be held on June 26–30, 2004 (Saturday – Wednesday) in Seattle and its sponsoring organization, the International Society for Genetic and Evolutionary Computation (ISGEC). For information about the annual Euro-Genetic-Programming Conference to be held on April 5-7, 2004 (Monday – Wednesday) at the University of Coimbra in Coimbra Portugal. For information about the 2003 and 2004 Genetic Programming Theory and Practice (GPTP) workshops held at the University of Michigan in Ann Arbor. For information about Asia-Pacific Workshop on Genetic Programming (ASPGP03) held in Canberra, Australia on December 8, 2003. For information about the annual NASA/DoD Conference on Evolvable Hardware Conference (EH) to be held on June 24-26 (Thursday-Saturday), 2004 in Seattle.

Last updated on December 28, 2003