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Tue Jan 18 23:25:09 EST 2011

Translinear Principle

I can't remember running into the Translinear Principle (TLP)
before[1], especially not in school.  ( Of course I did run into
log/antilog converters and current mirrors. )

The TLP is a product rule for currents through translinear elements
(TE).  To simplify, a TE is a forward biased PN junction, i.e. a diode
or BJT BE junction.

It's quite nifty:

  * Construct a loop that goes through TEs traversing each element
    forward or backward.  A loop needs to contain an equal amount of
    TEs traversed in the 2 opposite directions: clockwise (CW) and
    counter clockwise (CCW).

  * By Kirchoff's law, the sum of all the forward voltages of CC TEs
    equals the sum of all the forward voltages of the CCW TEs.

  * By the exponential V->I law, this implies that the product of the
    forward currents through all the CC TEs equals the product of all
    the forward currents through all the CCW TEs.



[1] http://en.wikipedia.org/wiki/Translinear_circuit





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