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LOG104

8

SBOS243C

A

2

A

1

I

1

Q

1

Q

2

V

OUT = (0.5V) LOG

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

OUT = 05

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

:

k = Boltzmann’s constant = 1.381 • 10–23

T = Absolute temperature in degrees Kelvin

q = Electron charge = 1.602 • 10–19 Coulombs

IC = Collector current

IS = Reverse saturation current

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

VTI = VT2, then (3) becomes:

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

FIGURE 13. Transfer Function with Varying I2 and I1.

(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

I 2 =

100pA

I 2 =

1nA

I 2 =

10nA

I 2 =

100nA

I 2 =

1µ

A

I 2 =

10

µA

I 2 =

100

µA

I 2 =

1m

A

I

1

V

OUT = (0.5V) • LOG (I1/I2)

DEFINITION OF TERMS

TRANSFER FUNCTION

The ideal transfer function is:

VOUT = 0.5V • logI1/I2

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.