Synthesis of the Campbell Ladder Filter


(A Human-Competitive Result Produced by Genetic Programming)


The Result

Genetic programming evolved a lowpass filter circuit as described in Section 25.15.1 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999). This circuit was produced in a run of genetic programming on October 31, 1995 and established the principle that it is possible to synthesize both the topology and sizing of an analog electrical circuit using genetic programming. This circuit appears as Figure 25.57 in Genetic Programming III.


Basis for Claim of Human-Competitiveness

The circuit in the figure has the recognizable features of the circuit for which George Campbell of American Telephone and Telegraph received U.S. patent 1,227,113 (Campbell 1917a). As Campbell said, in describing his patent entitled “Electric Wave Filter,”

“My invention in one or more of its embodiments has important applications in connection with wireless telegraphy, wireless telephony, multiplex high frequency wire telephony, composite telegraph and telephone lines, and in particular with telephone repeater circuits, wherein it is highly important that means be provided for selecting a range or band of frequencies, such as, for instance, the range or band of frequencies necessary for intelligible telephonic transmission of speech, while at the same time excluding from the receiving or translating device currents of all other frequencies.”

Claim 2 of patent 1,227,113 covered

“An electric wave filter consisting of a connecting line of negligible attenuation composed of a plurality of sections, each section including a capacity element and an inductance element, one of said elements of each section being in series with the line and the other in shunt across the line, said capacity and inductance elements having precomputed values dependent upon the upper limiting frequency and the lower limiting frequency of a range of frequencies it is desired to transmit without attenuation, the values of said capacity and inductance elements being so proportioned that the structure transmits with practically negligible attenuation sinusoidal currents of all frequencies lying between said two limiting frequencies, while attenuating and approximately extinguishing currents of neighboring frequencies lying outside of said limiting frequencies.”

An examination of the evolved circuit shows that it indeed consists of "a plurality of sections" (specifically, seven). In the figure, "each section includ[es] a capacity element and an inductance element." Specifically, the first of the seven sections consists of inductor L5 and capacitor C12, the second section consists of inductor L10 and capacitor C24, and so forth. Moreover, "one of said elements of each section [is] in series with the line and the other in shunt across the line." As can be seen in the figure, inductor L5 of the first section is indeed "in series with the line" and capacitor C12 is "in shunt across the line." This is also the case for the remaining six sections of the evolved circuit. Furthermore, the figure here exactly matches Figure 7 of Campbell's 1917 patent. In addition, this circuit's frequency domain behavior confirms the fact that the values of the inductors and capacitors are such as to transmit "with practically negligible attenuation sinusoidal currents" of the passband frequencies "while attenuating and approximately extinguishing currents" of the stopband frequencies. In short, the evolved circuit has all the features contained in claim 2 of Campbell's 1917 patent. But for the fact that this patent has long since expired, this evolved circuit would infringe that patent.

In addition to possessing the topology of the Campbell filter, the evolved circuit also approximately possesses the numerical values described in Campbell's 1917 patent (Campbell 1917a). In fact, this evolved circuit is almost equivalent to what is now known as a cascade of six identical symmetric π-sections (Johnson l950).

It is important to note that when we performed the preparatory steps for applying genetic programming to this problem of synthesizing a lowpass filter, we did not employ any significant domain knowledge from the field of filter design or electrical engineering. In fact, we explicitly inventoried our use of information and knowledge about electrical engineering as we performed each of the preparatory steps for this problem (Section 25.14 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999). The ladder topology emerged during this run of genetic programming as a natural consequence of the problem's fitness measure and natural selection—not because we primed the run with domain knowledge about electrical engineering in general or information from Campbell's 1917 patent in particular. That is, the evolutionary process opportunistically reinvented the Campbell filter in this run because it was helpful in solving the problem at hand. Thus, in spite of the absence of explicit domain knowledge about electrical engineering and filters, genetic programming evolved a 100%-compliant circuit that is well known in the field of electrical engineering.

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 the Campbell filter 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 is equal to or better than a result that was considered an achievement in its field at the time it was first discovered.


Campbell, George A. 1917a. Electric Wave Filter. U.S. Patent 1,227,113. Filed July 15, 1915. Issued May 22, 1917.

Johnson, Walter C. 1950. Transmission Lines and Networks. New York: McGraw-Hill.

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.

· The home page of Genetic Programming Inc. at

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· 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.

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Last updated on December 28, 2003