®

LOG100

6

Log conformity is defined as the peak deviation from the

best-fit straight line of the V

is expressed as a percent of peak-to-peak full scale output.

Thus, the nonlinearity error expressed in volts over m

decades is

V

(12)

where N is the log conformity error, in percent.

INDIVIDUAL ERROR COMPONENTS

The ideal transfer function with current input is

V

(13)

The actual transfer function with the major components of

error is

V

±K 2Nm ± V

OS OUT

(14)

The individual component of error is

∆K = scale factor error (0.3%, typ)

I

I

N = log conformity error ( 0.05%, 0.1%, typ)

V

m = number of decades over which N is specified:

0.05% for m = 5, 0.1% for m = 6

Example: what is the error with K = 3 when

I

V

±3(2)(0.0005)5±1mV

(15)

≈ 3.009 log

+ 0.015 + 0.001

(16)

= 3.009 (1) + 0.015 + 0.001

(17)

= 3.025V

(18)

Since the ideal output is 3.000V, the error as a percent of

reading is

% error =

x 100% = 0.83%

(19)

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

V

±K 2Nm ±V

OS OUT

(20)

FREQUENCY RESPONSE

The 3dB frequency response of the LOG100 is a function of

the magnitude of the input current levels and of the value of

the frequency compensation capacitor. See Typical Perfor-

mance Curves for details.

TOTAL ERROR

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

actual output from the ideal output of V

Thus,

V

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 of I

considered separately.

Example:

I

100nA to 10

µA. What is the maximum error?

Table I shows the maximum errors for each decade combi-

nation of I

Since the largest value of I

K is set at 3V per decade so the output will range from +3V

to –9V. The maximum total error occurs when I

is equal to K x 30mV. This represents a 0.75% of peak-to-

peak FSO error 3 x 0.030/12 x 100% = 0.75% where the full

scale output is 12V (from +3V to –9V).

ERRORS RTO AND RTI

As with any transfer function, errors generated by the

function itself may be Referred-to-Output (RTO) or Re-

ferred-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.

Refer to: Yu Jen Wong and William E. Ott, “Function

Circuits: Design & Applications”, McGraw-Hill Book, 1976.

LOG CONFORMITY

Log conformity corresponds to linearity when V

ted versus I

conformity is the most important specification. 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.

I

2

I

1

I

I

TABLE I. I

I

(1)

NOTE: (1) Maximum errors are in parenthesis.

10nA

100nA

1

µA

(30mV)

(25mV)

(20mV)

100nA

0.1

1

10

(25mV)

(30mV)

(25mV)

(25mV)

1

µA

0.01

0.1

1

(20mV)

(30mV)

(25mV)

(20mV)

10

µA

0.001

0.01

0.1

(25mV)

(30mV)

(25mV)

(25mV)

R

1

– I

R

1

V

1

R

2

– I

R

2

V

2

E

OS1

E

OS2

3

0.025