LOG100 Datasheet, PDF (6/9 Pages) Burr-Brown (TI) – Precision LOGARITHMIC AND LOG RATIO AMPLIFIER

TOTAL ERROR
The total error is the deviation (expressed in mV) of the
actual output from the ideal output of V_OUT = K log (I₁/I₂).
Thus,
V_{OUT (ACTUAL)} = V_{OUT (IDEAL)} ± Total Error.
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 I₁/I₂ is the largest of the two errors when I₁ and I₂ are
considered separately.
Example:
I₁ varies over a range of 10nA to 1µA and I₂ varies from
100nA to 10µA. What is the maximum error?
Table I shows the maximum errors for each decade combi-
nation of I₁ and I₂.
100nA
(25mV)
1µA
(20mV)
10µA
(25mV)
I₁ (maximum error)⁽¹⁾
10nA
(30mV)
100nA
(25mV)
0.1
(30mV)
1
(25mV)
0.01
(30mV)
0.1
(25mV)
0.001
(30mV)
0.01
(25mV)
NOTE: (1) Maximum errors are in parenthesis.
TABLE I. I₁/I₂ and Maximum Errors.
1µA
(20mV)
10
(25mV)
1
(20mV)
0.1
(25mV)
Log conformity is defined as the peak deviation from the
best-fit straight line of the V_OUT versus log (I₁/I₂) curve. This
is expressed as a percent of peak-to-peak full scale output.
Thus, the nonlinearity error expressed in volts over m
decades is
V_{OUT (NONLIN)} = K 2Nm V
(12)
where N is the log conformity error, in percent.
INDIVIDUAL ERROR COMPONENTS
The ideal transfer function with current input is
V_OUT = K Log
I₁
I₂
(13)
The actual transfer function with the major components of
error is
I –I
V_OUT = K (1 ± ∆K) log
1 B1
I –I
±K 2Nm ± V_{OS OUT}
(14)
2 B2
The individual component of error is
∆K = scale factor error (0.3%, typ)
I_B1 = bias current of A₁ (1pA, typ)
I_B2 = bias current of A₂ (1pA, typ)
N = log conformity error ( 0.05%, 0.1%, typ)
V_{OS OUT} = output offset voltage (1mV, typ)
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
I₁ = 1µA and I₂ = 100nA
Since the largest value of I₁/I₂ is 10 and the smallest is 0.001,
K is set at 3V per decade so the output will range from +3V
to –9V. The maximum total error occurs when I₁ = 10nA and
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).
V_OUT =
3(1
±
0.003)
log
10^–6 –10^–12
10^–7 –10^–12
±3(2)(0.0005)5±1mV
(15)
≈ 3.009 log
10^–6
+ 0.015 + 0.001
(16)
10^–7
= 3.009 (1) + 0.015 + 0.001
(17)
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:
= 3.025V
(18)
Since the ideal output is 3.000V, the error as a percent of
reading is
% error = ^0.025 x 100% = 0.83%
(19)
3
Given some error voltage at the log amp’s output, that For the case of voltage inputs, the actual transfer function is
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_OUT is plot-
ted versus I₁/I₂ on a semilog scale. In many applications, log
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
V_OUT = K(1 ± ∆K) log
V₁
R₁
– I_B1 ±
E_OS1
R₁
V₂
R₂
– I_B2 ±
E_OS2
R₂
±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.
of error.
®
LOG100
6