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LOG104

8

SBOS243B

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

V

RR

R

nV

I

I

OUT

L

OUT

T

=

+

=

+

12

1

12

1

1

2

log

VV

I

I

1

2

.

• log

Using the base-emitter voltage relationship of matched

bipolar transistors, the LOG104 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 LOG104

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(9)

(10)

(11)

FIGURE 11. Simplified Model of a Log Amplifier.

(8)

or

(5)

3.0

3.5

2.0

2.5

1.0

1.5

0.5

0.0

–3.0

–3.5

–2.0

–2.5

–1.0

–0.5

–1.5

1nA

10nA

100nA 1µ

A

10µ

A

100

µA

1m

A

10mA

100pA

100pA

1nA

10nA

100nA

1µ

A

10

µA

100

µA

1m

A

I

1

V

DEFINITION OF TERMS

TRANSFER FUNCTION

The ideal transfer function is:

See Figure 12 for the graphical representation of the transfer

over valid operating range for the LOG104.

ACCURACY

Accuracy considerations for a log ratio amplifier are some-

what more complicated than for other amplifiers. This is

because the transfer function is nonlinear and has two

inputs, each of which can vary over a wide dynamic range.

The accuracy for any combination of inputs is determined

from the total error specification.