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LOG102

9

SBOS211A

A

2

A

1

I

1

Q

1

Q

2

V

I

1

I

2

I

2

I

1

I

2

++

––

R

2

V

OUT

V

L

R

1

V

BE1

V

BE2

also

VV

RR

R

I

I

V

RR

R

nV

I

I

OUT

L

OUT

T

=

+

=

=

+

12

1

2

12

1

2

1

1

log

log

Using the base-emitter voltage relationship of matched

bipolar transistors, the LOG102 establishes a logarith-

mic function of input current ratios. Beginning with the

base-emitter voltage defined as

VV

I

I

where V

kT

q

BE

T

C

S

T

==

ln

:

T = Absolute temperature in degrees Kelvin

From the circuit in Figure 11, we see that

VV

V

LBE

BE

=

12

–

Substituting (1) into (2) yields

VV

I

I

V

I

I

LT

S

T

S

=

1

1

1

2

2

2

ln

–

ln

If the transistors are matched and isothermal and

VV

I

I

I

I

VV

I

I

and

ce

xx

Vn V

I

I

LT

SS

LT

LT

=













=

=

=

1

12

1

2

10

1

2

23

ln

– ln

ln

sin

ln

. log

log

where n = 2.3

INSIDE THE LOG102

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(9)

(10)

(11)

FIGURE 11. Simplified Model of Log Amplifier.

(8)

or

It should be noted that the temperature dependance

tor with the required positive temperature coefficient.

USING A LARGER REFERENCE VOLTAGE

REDUCES OFFSET ERRORS

Using a larger reference voltage to create the reference

current minimizes errors due to the LOG102’s input offset

voltage. Maintaining an increasing output voltage as a func-

tion of increasing photodiode current is also important in

many optical sensing applications. All zeros from the A/D

converter output represent zero or low scale photodiode

maximum photodiode current is accomplished using this

requirement. The LOG102 configured with the reference

with inverting gain and is used to scale the photodiode

current directly into the A/D input voltage range.

The wide dynamic range of the LOG102 is useful for measuring

avalanche photodiode current (APD) (see Figure 13).