Isolated potentiometer design (Part 2)

In Part 1 of this series, the current sources used in the isopot—both Howland and op-amp V/I—were explained. We now get to the heart of the isopot circuits: the multipliers. The two multipliers comprise the LM13700 dual translinear amplifier. Detailed design derivations and application now proceed, followed by prototype build and testing. The isopot circuit diagram is repeated at the end of this second part of the article.

LM13700 translinear amplifier
The simplified circuit diagram of the repeated half of the LM13700 is shown below.

Diodes Q11, Q12 match Q1, Q2 and form a translinear gain cell. (BJTs are used as diodes for better junction matching.) It has the property that the ratios of currents in the diodes equal the ratio of BJT currents. This is evident when KVL is applied to the diode loop and the BJT input loop. Let i(Q11) = i_D鈭? and i(Q12) = i_D+. Then

Also, for a perfect current mirror, i(Q3) = I_Y = i(Q1) + i(Q2), for 伪 = 1 (尾 >> 1). The diff-amp output current is differential and is:

Then with this nomenclature, applying KVL to the diode loop,

For matched BJT b-e junctions, I_s values match and cancel. Then

Then equating and solving for the current ratios,

It can be shown algebraically that if

then