MAT02

–9–

REV. C

Ω for the MAT02 and assum-

ing a collector current range of up to 200

µA, then a peak error

the MAT02. Total error is dependent on the specific application

configuration (multiply, divide, square, etc.) and the required

duce the maximum collector current, but then op amp offsets

and leakage currents become a limiting factor at low input lev-

els. A design range of no greater than 10

µA to 1 mA is generally

recommended for most nonlinear function circuits.

sistor base. For this circuit:

(10)

Ω,

Ω and R

In more complex circuits, such as the circuit in Figure 19, it

may be inconvenient to apply a compensation voltage to each

individual base. A better approach is to sum all compensation to

±0.1% is readily achievable with

this compensation technique.

Operational amplifier offsets are another source of error. In Fig-

ure 20, the input offset voltage and input bias current will cause

amp, such as the OP07 with less than 75

µV of V

less than

±3 nA, is recommended. The OP22/OP32, a program-

mable micropower op amp, should be considered if low power

consumption or single-supply operation is needed. The value of

amp frequency response and peak collector current. Typical val-

. . .

FOUR-QUADRANT MULTIPLIER

A simplified schematic for a four-quadrant log/antilog multiplier

is shown in Figure 21. As with the previously discussed one-

This positive offset is then subtracted out at the output stage.

Assuming ideal op amps, the currents are:

+

+

(11)

+

+

+

2

(12)

Figure 20. Compensation of Bulk Resistance Error

Extrinsic resistive terms and the early effect cause departure

these effects can be lumped together as a total effective bulk re-

than 0.5

Ω and ∆r

Returning to the multiplier/divider circuit of Figure 1 and using

Equation (4):

If the transistor pairs are held to the same temperature, then:

kT

q

In

=

kT

q

In

(6)

If all the terms on the right-hand side were zero, then we would

the desired result:

(7)

Note that this relationship is temperature independent. The

right-hand side of Equation (6) is near zero and the output cur-

as the right-hand side terms of Equation (6):

ø = In

+

q

kT

(8)

ø,

= 1 + ø

(9)

(1 – ø)

±0.6% from each pair when using the MAT02, and this gain

more troublesome because they vary with signal levels and

are multiplied by absolute temperature. At 25

°C, kT/q is