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LOG102

11

SBOS211A

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 LOG102.

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

Thus,

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; and is shown in Table I. Temperature

can affect total error.

ERRORS RTO AND RTI

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

tion itself 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

corresponds to a constant percent of the input regardless of

the actual input level.

LOG CONFORMITY

For the LOG102, log conformity is calculated the same as

applications, log conformity is the most important specifica-

tion. This is true because bias current errors are negligible

(1pA compared to input currents of 1nA 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:

where N is the log conformity error, in percent.

INDIVIDUAL ERROR COMPONENTS

The ideal transfer function with current input is:

VV

I

I

1

1

2

log

The actual transfer function with the major components of

error is:

VV

K

II

II

Nm

V

OUT

B

B

OS OUT

=

(

)

±±

11

2

1

1

2

2

∆ log

–

–

The individual component of error is:

∆K = gain accuracy (0.3%, typ), as specified in

specification table.

N = log conformity error (0.04%, 0.15%, typ)

0.04% for n = 5, 0.15% for n = 6

n = number of decades over which N is specified:

Example: what is the error when

VmV

(

)

±±

10 003

10

5 10

10

5 10

2 0 0004 5

0 3

612

712

.

log

–•

–•

()( .

)

.

––

––

10nA

100nA

1

(30mV)

(25mV)

(20mV)

100nA

(25mV)

30mV

25mV

25mV

1

µA

(20mV)

30mV

25mV

20mV

10

µA

(25mV)

30mV

25mV

25mV

NOTE: (1) Maximum errors are in parenthesis.

(maximum

(5)

3

2

1

0

–3

1

µA10µA 100µA

1mA

100nA

10nA

V

Dashed Line = Greater

Supply Voltage Requirement

I

1

I

2

10nA

100nA

1nA

1µ

A

100

µA

10

µA

1mA

I

1

(5)

(6)

(7)

(8)

(9)