LOG112, 2112

11

SBOS246C

www.ti.com

also

VV

RR

R

OUT

L

=

+

12

1

(9)

V

RR

R

nV

I

I

OUT

T

=

+

12

1

1

2

log

(10)

or

V

V LOG

I

I









(.

)

05

1

2

(11)

Using the base-emitter voltage relationship of matched

bipolar transistors, the LOG112 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

:

(1)

T = Absolute temperature in degrees Kelvin

From the circuit in Figure 12:

VV

V

LBE

BE

=

12

–

(2)

Substituting (1) into (2) yields:

VV

I

I

V

I

I

LT

S

T

S

=

1

1

1

2

2

2

ln

–

ln

(3)

If the transistors are matched and isothermal and

VV

I

I

I

I

LT

SS

=













1

12

ln

– ln

(4)

VV

I

I

and

ce

LT

=

ln

sin

1

2

(5)

ln

. log

xx

= 23

10

(6)

Vn V

I

I

LT

=

2

(7)

where n = 2.3

(8)

INSIDE THE LOG112

FIGURE 13. Simplified Model of a Log Amplifier.

A

2

A

1

I

1

Q

1

Q

2

I

2

I

1

I

2

++

––

R

2

V

OUT

V

L

R

1

V

BE1

V

BE2

V

I

1

I

2













over temperature.

DEFINITION OF TERMS

TRANSFER FUNCTION

The ideal transfer function is:

Figure 14 shows the graphical representation of the transfer

over valid operating range for the LOG112 and LOG2112.

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.

TOTAL ERROR

The total error is the deviation (expressed in mV) of the actual

Thus,

(6)

It represents the sum of all the individual components of error

normally associated with the log amp when operated in the

current input mode. The worst-case error for any given ratio

considered separately. Temperature can affect total error.

3.0

3.5

2.0

2.5

1.0

1.5

0.5

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

10m

A

100pA

100pA

1nA

10nA

100nA

1µ

A

10

µA

100

µA

1m

A

I

1

V