®

LOG100

5

THEORY OF OPERATION

The base-emitter voltage of a bipolar transistor is

V

n

where: V

(1)

T = Absolute temperature in degrees Kelvin

I

I

From the circuit in Figure 1, we see that

V

(2)

Substituting (1) into (2) yields

V

n

– V

T2

n

(3)

If the transistors are matched and isothermal and V

then (3) becomes:

V

n

–

n

]

(4)

V

n

and since

(5)

n x = 2.3 log

(6)

V

(7)

where n = 2.3

(8)

also

V

(9)

=

n V

(10)

or

V

(11)

FIGURE 1. Simplified Model of Log Amplifier.

I

2

I

1

R

R

1

R

R

1

I

2

I

1

FIGURE 2. Transfer Function with Varying K and I

FIGURE 3. Transfer Function with Varying I

KT

q

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

OUT

R

1

V

BE1

V

BE2

It should be noted that the temperature dependance associ-

ated with V

T

= KT/q is compensated by making R

1

a

temperature sensitive resistor with the required positive

temperature coefficient.

DEFINITION OF TERMS

TRANSFER FUNCTION

The ideal transfer function is V

where:

K = the scale factor with units of volts/decade

I

I

ACCURACY

Accuracy considerations for a log ratio amplifier are some-

what more complicated than for other amplifiers. The reason

is that 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.

I

2

I

1

10

8

6

4

2

0

–2

–4

–6

–8

–10

1µA

10µA

100µA

1mA

100nA

10nA

1nA

V

I

1

I

2

I

Fixed value of I

K = 5

K = 3

K = 1

I

1

10

8

6

4

2

0

–2

–4

–6

–8

–10

1µA

10µA 100µA

1mA

100nA

10nA

1nA

V

I

1

I

2

K = 3

Fixed value of K.

I

I

I

I

1

l

I

2

I

1

l

I

S

I

C

l

I

S1

I

1

l

I

S2

I

1

l

l

I

S

I

1

I

S

I

2

l

I

2

I

1