Dan McMahill wrote:
H. Jones I believe. Bob Widlar didn't design that particular cell structure nor specifically generalize the trans-linear principle early on, but he was among the first to design circuits that actually used the translinear behavior of monolithic transistors.
Bonus points to anyone who can name the real inventor of the mixer in question here. Hint: It wasn't Gilbert even though it's called a Gilbert cell.
Of course the Is's need not be identical, just ratiometrically matched (I know you know that Dan, but maybe not others here). Ratios in Is can be achieved through scaling emitter areas, or more precise retios through paralleling devices. One key point is that this really only works well in a monolothic design where tight thermal and doping matching can be achieved. For non-constant Is, the equation above is just I1/Is1 * I2/Is2 = I3/Is3 * I4/Is4.
sum( Vbe_cw ) = sum( Vbe_ccw)
where Vbe_cw = junctions where the voltage is positive in the clockwise direction and Vbe_ccw = junctions where the voltage is positive in the counter clockwise direction.
Now assume all the Is are the same and some simple math shows that
product( Ic_cw ) = product( Ic_ccw )
For example, you can build a circuit where I1 * I2 = I3 * I4
Cheers, harry
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