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From: ankleand@athena.mit.edu (Andy Karanicolas)
Newsgroups: sci.electronics,comp.ai,comp.ai.neural-nets
Subject: Re: Sigmoid transfer function
Message-ID: <6577@bloom-beacon.MIT.EDU>
Date: 7 Aug 88 00:04:26 GMT
References: <1945@aecom.YU.EDU>
Sender: daemon@bloom-beacon.MIT.EDU
Reply-To: ankleand@athena.mit.edu (Andy Karanicolas)
Organization: Massachusetts Institute of Technology
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In article <1945@aecom.YU.EDU> krishna@aecom.YU.EDU (Krishna Ambati) writes:
>
>I am looking for a "black box" circuit that has the product transfer
>function:
>
>Output voltage = 0.5 ( 1 + tanh ( Input voltage / "Gain" ) )
>
>	       = 1 / ( 1 + exp ( -2 * Input voltage / "Gain" ) )
>
>When plotted, this function looks like an elongated S
>
>When IV = - infinity, OV = 0
>When IV = + infinity, OV = 1
>When IV = 0         , OV = 0.5
>
>By the way, this question arose in connection with a neural network
>problem.
>
>Thanks.
>
>Krishna Ambati
>krishna@aecom.uucp

The function you are looking for is not too difficult to synthesize from
a basic analog circuit builing block; namely, a differential amplifier.
The accuracy of the circuit will depend on the matching of components, among
other things.  The differential amplifier is discussed in many textbooks
concerned with analog circuits (analog integrated circuits especially).

You can try:

Electronic Principles, Grey and Searle, Wiley 1969.
Bipolar and MOS Analog IC Design, Grebene, Wiley 1984.
Design and Analysis of Analog IC's, Gray and Meyer, Wiley 1984.

Unfortunately, drawing circuits on a text editor is a pain; I'll
attempt it if these or other books are not available or helpful.   


Andy Karanicolas
Microsystems Technology Laboratory

ankleand@caf.mit.edu