LOG112, 2112

12

SBOS246C

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ERRORS RTO AND RTI

As with any transfer function, errors generated by the func-

tion may be Referred-to-Output (RTO) or Referred-to-Input

(RTI). In this respect, log amps have a unique property: given

some error voltage at the log amp’s output, that error corre-

sponds to a constant percent of the input regardless of the

actual input level.

LOG CONFORMITY

For the LOG112 and LOG2112, log conformity is calculated

In many applications, log conformity is the most important

specification. This is true because bias current errors are

negligible (5pA compared to input currents of 100pA and

above) and the scale factor and offset errors may be trimmed

to zero or removed by system calibration. This leaves log

conformity as the major source of error.

Log conformity is defined as the peak deviation from the best

expressed as a percent of ideal full-scale output. Thus, the

nonlinearity error expressed in volts over m decades is:

(7)

where N is the log conformity error, in percent.

INDIVIDUAL ERROR COMPONENTS

The ideal transfer function with current input is:

V

V LOG

I

I

(

)









05

1

2

.

(8)

The actual transfer function with the major components of

error is:

VV

K

II

II

Nm V

LOGOUT

B

B

OSO

=

(

(

)









±±

05

1

1

1

2

2

.

log

–

–

∆

(9)

The individual component of error is:

∆K = gain error (0.10%, typ), as specified in the specifica-

tion table.

N = log conformity error (0.01%, 0.13%, typ)

0.01% for m = 5, 0.13% for m = 7.5

m = number of decades over which N is specified

For example, what is the error when:

(10)

(11)

VmV

V

(

)

−

−









±

( )(

=

−−

−−

05

0001

10

5 10

10

5 10

2 0 0001 5

3 0

0 505

612

712

.

.

log

•

•

..

.

Since the ideal output is 0.5V, the error as a percent of the

reading is:

%

.

.

%.

%

error

V

=•

=

0 505

05

100

1 01

(12)

For the case of voltage inputs, the actual transfer function is:

(13)

VV

K

V

R

I

E

R

V

R

I

E

R

Nm

V

LOGOUT

B

OS

B

OS

OSO

=

(

(

)

±

±

























±±

05

1

1

11

2

22

1

1

2

2

.

log

–

–

∆

Where

E

R

and

E

R

OS

OS

1

1

2

2

(offset error) are considered to be

zero for large values of resistance from external input current

sources.