When a difference amplifier with reference voltage VREF is implemented to compare the outputs of two

logarithmic amplifiers with input currents I1 and I2,

VOUT2−VOUT1= kTq ln I1IS1 − kTq ln I2IS2

(3)

As IS1 is approximately equivalent to IS2 by design, this equation is equivalent to:

VOUT2−VOUT1= kTq ln I1I2 = kT0.434q log10 I1I2

(4)

+

–

+

–

+

–

V

LOGOUT

V

REF

V

CM

I1

I2

R

3

R

4

R

2

R

1

U

1

U

2

U

3

V

OUT1

V

OUT2

Figure 7-2. LOG200 Difference Amplifier

In the LOG200, the internal input resistors of the difference amplifier have a positive temperature coefficient to

compensate for the temperature dependence of the above expression. The difference amplifier also gains up the

nominal output, such that the output of the LOG200 is:

VLOGOUT=K×log10 I1I2 +VREF

(5)

where K is the device scaling factor, nominally 250mV/decade. Thus, for each decade or order of magnitude

shift in the difference of I1 and I2, the device output is correspondingly shifted by 250mV (such as by 250mV for

I1 = 10µA and I2 = 1µA, or by –500mV for I1 = 10nA and I2 = 1µA).

LOG200

SBOSA28A – AUGUST 2023 – REVISED DECEMBER 2024

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