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LOG101

8

SBOS242B

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

1

2

Using the base-emitter voltage relationship of matched

bipolar transistors, the LOG101 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 LOG101

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(9)

(10)

(11)

FIGURE 11. Simplified Model of a Log Amplifier.

(8)

or

It should be noted that the temperature dependance

tor with the required positive temperature coefficient.

DEFINITION OF TERMS

TRANSFER FUNCTION

The ideal transfer function is:

Figure 12 shows the graphical representation of the transfer

over valid operating range for the LOG101.

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.

(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

1mA

10mA

100pA

100pA

1nA

10

nA

100nA

1µ

A

10

µA

100

µA

1mA

I

1

V