LOG100
Precision
LOGARITHMIC AND LOG RATIO AMPLIFIER
resistors. The resistors are laser-trimmed for maxi-
mum precision. FET input transistors are used for the
amplifiers whose low bias currents (1pA typical) per-
mit signal currents as low as 1nA while maintaining
guaranteed total errors of 0.37% FSO maximum.
Because scaling resistors are self-contained, scale
factors of 1V, 3V or 5V per decade are obtained
simply by pin selections. No other resistors are re-
quired for log ratio applications. The LOG100 will
meet its guaranteed accuracy with no user trimming.
Provisions are made for simple adjustments of scale
factor, offset voltage, and bias current if enhanced
performance is desired.
DESCRIPTION
The LOG100 uses advanced integrated circuit tech-
nologies to achieve high accuracy, ease of use, low
cost, and small size. It is the logical choice for your
logarithmic-type computations. The amplifier has guar-
anteed maximum error specifications over the full six-
decade input range (1nA to 1mA) and for all possible
combinations of I
1
and I
2
. Total error is guaranteed so
that involved error computations are not necessary.
The circuit uses a specially designed compatible thin-
film monolithic integrated circuit which contains am-
plifiers, logging transistors, and low drift thin-film
PDS-437E
FEATURES
q
ACCURACY
0.37% FSO max Total Error
Over 5 Decades
q
LINEARITY
0.1% max Log Conformity
Over 5 Decades
q
EASY TO USE
Pin-selectable Gains
Internal Laser-trimmed Resistors
q
WIDE INPUT DYNAMIC RANGE
6 Decades, 1nA to 1mA
q
HERMETIC CERAMIC DIP
APPLICATIONS
q
LOG, LOG RATIO AND ANTILOG
COMPUTATIONS
q
ABSORBANCE MEASUREMENTS
q
DATA COMPRESSION
q
OPTICAL DENSITY MEASUREMENTS
q
DATA LINEARIZATION
q
CURRENT AND VOLTAGE INPUTS
International Airport Industrial Park Mailing Address: PO Box 11400 Tucson, AZ 85734 Street Address: 6730 S. Tucson Blvd. Tucson, AZ 85706
Tel: (520) 746-1111 Twx: 910-952-1111 Cable: BBRCORP Telex: 066-6491 FAX: (520) 889-1510 Immediate Product Info: (800) 548-6132
7
A
2
A
1
1
14
I
1
9
V
CC
6
+V
CC
10
Com
I
2
Q
1
Q
2
V
OUT
3
K = 1
4
K = 3
5
K = 5
2
Scale
Factor
Trim
39k
24k
7.5k
270
220
Resistor values nominal only;
laser-trimmed for precision gain.
V
OUT
= K LOG
I
1
I
2
1981 Burr-Brown Corporation
PDS-437E
Printed in U.S.A. January, 1995
LOG100
2
SPECIFICATIONS
ELECTRICAL
T
A
= +25
C and
V
CC
=
15V, after 15 minute warm-up, unless otherwise specified.
LOG100JP
PARAMETER
CONDITIONS
MIN
TYP
MAX
UNITS
TRANSFER FUNCTION
V
OUT
= K Log (I
1
/I
2
)
Log Conformity Error
(1)
Either I
1
or I
2
Initial
1nA to 100
A (5 decades)
0.04
0.1
%
1nA to 1mA (6 decades)
0.15
0.25
%
Over Temperature
1nA to 100
A (5 decades)
0.002
%/
C
1nA to 1mA (6 decades)
0.001
%/
C
K Range
(2)
1, 3, 5
V/decade
Accuracy
0.3
%
Temperature Coefficient
0.03
%/
C
ACCURACY
Total Error
(3)
K = 1,
(4)
Current Input Operation
Initial
I
1
, I
2
= 1mA
55
mV
I
1
, I
2
= 100
A
30
mV
I
1
, I
2
= 10
A
25
mV
I
1
, I
2
= 1
A
20
mV
I
1
, I
2
= 100nA
25
mV
I
1
, I
2
= 10nA
30
mV
I
1
, I
2
= 1nA
37
mV
vs Temperature
I
1
, I
2
= 1mA
0.20
mV/
C
I
1
, I
2
= 100
A
0.37
mV/
C
I
1
, I
2
= 10
A
0.28
mV/
C
I
1
, I
2
= 1
A
0.033
mV/
C
I
1
, I
2
= 100nA
0.28
mV/
C
I
1
, I
2
= 10nA
0.51
mV/
C
I
1
, I
2
= 1nA
1.26
mV/
C
vs Supply
I
1
, I
2
= 1mA
4.3
mV/V
I
1
, I
2
= 100
A
1.5
mV/V
I
1
, I
2
= 10
A
0.37
mV/V
I
1
, I
2
= 1
A
0.11
mV/V
I
1
, I
2
= 100nA
0.61
mV/V
I
1
, I
2
= 10nA
0.91
mV/V
I
1
, I
2
= 1nA
2.6
mV/V
INPUT CHARACTERISTICS (of Amplifiers A
1
and A
2
)
Offset Voltage
Initial
0.7
5
mV
vs Temperature
80
V/
C
Bias Current
Initial
1
5
(5)
pA
vs Temperature
Doubles Every 10
C
Voltage Noise
10Hz to 10kHz, RTI
3
Vrms
Current Noise
10Hz to 10kHz, RTI
0.5
pArms
AC PERFORMANCE
3dB Response
(6)
, I
2
= 10
A
1nA
C
C
= 4500pF
0.11
kHz
1
A
C
C
= 150pF
38
kHz
10
A
C
C
= 150pF
27
kHz
1mA
C
C
= 50pF
45
kHz
Step Response
(6)
Increasing
C
C
= 150pF
1
A to 1mA
11
s
100nA to 1
A
7
s
10nA to 100nA
110
s
Decreasing
C
C
= 150pF
1mA to 1
A
45
s
1
A to 100nA
20
s
100nA to 10nA
550
s
OUTPUT CHARACTERISTICS
Full Scale Output (FSO)
10
V
Rated Output
Voltage
I
OUT
=
5mA
10
V
Current
V
OUT
=
10V
5
mA
Current Limit
Positive
12.5
mA
Negative
15
mA
Impedance
0.05
LOG100
3
LOG100JP
PARAMETER
CONDITIONS
MIN
TYP
MAX
UNITS
POWER SUPPLY REQUIREMENTS
Rated Voltage
15
VDC
Operating Range
Derated Performance
12
18
VDC
Quiescent Current
7
9
mA
AMBIENT TEMPERATURE RANGE
Specification
0
+70
C
Operating Range
Derated Performance
25
+85
C
Storage
40
+85
C
SPECIFICATIONS
(CONT)
ELECTRICAL
T
A
= +25
C and
V
CC
=
15V, after 15 minute warm-up, unless otherwise specified.
NOTES: (1) Log Conformity Error is the peak deviation from the best-fit straight line of the V
OUT
vs Log I
IN
curve expressed as a percent of peak-to-peak full scale
output. (2) May be trimmed to other values. See Applications section. (3) The worst-case Total Error for any ratio of I
1
/I
2
is the largest of the two errors when
I
1
and I
2
are considered separately. (4) Total Error at other values of K is K times Total Error for K = 1. (5) Guaranteed by design. Not directly measurable due to
amplifier's committed configuration. (6) 3dB and transient response are a function of both the compensation capacitor and the level of input current. See Typical
Performance Curves.
PIN CONFIGURATION
K, V/DECADE
CONNECTIONS
5
5 to 7
3
4 to 7
1.9
4 and 5 to 7
1
3 to 7
0.85
3 and 5 to 7
0.77
3 and 4 to 7
0.68
3 and 4 and 5 to 7
SCALE FACTOR PIN CONNECTIONS
ABSOLUTE MAXIMUM RATINGS
Supply ................................................................................................
18V
Internal Power Dissipation .............................................................. 600mV
Input Current ..................................................................................... 10mA
Input Voltage Range ..........................................................................
18V
Storage Temperature Range ........................................... 40
C to +85
C
Lead Temperature (soldering, 10s) ............................................... +300
C
Output Short-circuit Duration .................................. Continuous to ground
Junction Temperature ...................................................................... 175
C
FREQUENCY COMPENSATION
1
C
C
14
9
6
7
10
5
4
3
LOG100
Bottom View
NC = No Connection
I
1
Input
Scale Factor Trim
K = 1
K = 3
K = 5
+V
CC
Output
I
2
Input
NC
NC
NC
Common
V
CC
NC
1
2
3
4
5
6
7
14
13
12
11
10
9
8
ORDERING INFORMATION
SPECIFIED
TEMPERATURE
MODEL
PACKAGE
RANGE
LOG100JP
14-Pin Hermetic Ceramic DIP
0
C to +70
C
ELECTROSTATIC
DISCHARGE SENSITIVITY
Any integral circuit can be damaged by ESD. Burr-Brown
recommends that all integrated circuits be handled with
appropriate precautions. Failure to observe proper handling
and installation procedures can cause damage.
ESD damage can range from subtle performance degrada-
tion to complete device failure. Precision integrated circuits
may be more susceptible to damage because very small
parametric changes could cause the device not to meet
published specifications.
PACKAGE INFORMATION
PACKAGE DRAWING
MODEL
PACKAGE
NUMBER
(1)
LOG100JP
14-Pin Hermetic Ceramic DIP
148
(2)
NOTES: (1) For detailed drawing and dimension table, please see end of data
sheet, or Appendix D of Burr-Brown IC Data Book. (2) During 1994, the package
was changed from plastic to hermetic ceramic. Pinout, model number, and
specifications remained unchanged. The metal lid of the new package is
internally connected to common, pin 10.
LOG100
4
3dB FREQUENCY RESPONSE
I
2
3dB Frequency Response (Hz)
0.1
1nA
1M
100k
10k
1k
100
10
1
10nA
100nA
1A
10A
100A
1mA
100A
100A
1mA
I
1
= 1mA
1A
1mA
to 10A
100nA
10nA
I
1
= 1nA
10nA
10nA
1A
10A
100A
C
C
= 1F
C
C
= 1000pF
10A to 1A
C
C
= 10pF
I
1
= 1nA
1nA
100A
MINIMUM VALUE OF COMPENSATION CAPACITOR
Input Current, I
2
Compensation Capacitor, C
C
(pF)
1
1nA
1mA
100nA
10A
1M
100k
10k
1k
100
10
100A
1A
10nA
Select C
C
for
I
1
min and I
2
max
Values below 2pF
may be ignored.
I
1
= 1nA
I
1
= 10nA
I
1
= 100nA
I
1
= 1A
I
1
= 10A
I
1
= 100A to 1mA
TRIMMED OUTPUT ERROR vs INPUT CURRENT
Trimmed Output Error (mV)
1nA
60
50
40
30
20
10
0
10
Input Current (I
1
or
I
2
)
100nA
10A
1mA
20
60
50
40
30
20
10
0
10
20
I
1
I
2
Gain Error and
Offset Error Trimmed
to Zero
TOTAL ERROR vs INPUT CURRENT
Input Current ( I
1
or I
2
)
Maximum Total Error (mV)
1nA
75
50
25
100nA
10A
1mA
0
0
ONE CYCLE OF NORMALIZED TRANSFER FUNCTION
Normalized Output Voltage (V)
1 (K)
0.9 (K)
0.8 (K)
0.7 (K)
0.6 (K)
0.5 (K)
0.4 (K)
0.3 (K)
0.2 (K)
0.1 (K)
2
6
1
10
3
Current Ratio,
I
1
I
2
4
8
NORMALIZED TRANSFER FUNCTION
Normalized Output Voltage (V)
0.001
3 (K)
2 (K)
1 (K)
0 (K)
1 (K)
2 (K)
3 (K)
0.01
1
100
Current Ratio,
0.1
10
1000
I
1
I
2
I
1
I
2
V
OUT
= K Log
TYPICAL PERFORMANCE CURVES
T
A
= +25
C, V
CC
=
15VDC, unless otherwise noted.
LOG100
5
THEORY OF OPERATION
The base-emitter voltage of a bipolar transistor is
V
BE
= V
T
n where: V
T
=
(1)
K = Boltzman's constant = 1.381
x
10
23
T = Absolute temperature in degrees Kelvin
q = Electron charge = 1.602
x
10
19
Coulombs
I
C
= Collector current
I
S
= Reverse saturation current
From the circuit in Figure 1, we see that
V
OUT
' = V
BE1
V
BE2
(2)
Substituting (1) into (2) yields
V
OUT
' = V
T1
n V
T2
n
(3)
If the transistors are matched and isothermal and V
T1
= V
T2
,
then (3) becomes:
V
OUT
' = V
T
[ n n ]
(4)
V
OUT
' = V
T
n and since
(5)
n
x
= 2.3 log
10
x
(6)
V
OUT
' = n V
T
log
(7)
where n = 2.3
(8)
also
V
OUT
= V
OUT
'
(9)
= n V
T
log
(10)
or
V
OUT
= K log
(11)
FIGURE 1. Simplified Model of Log Amplifier.
I
2
I
1
R
1
+
R
2
R
1
R
1
+
R
2
R
1
I
2
I
1
FIGURE 2. Transfer Function with Varying K and I
1
.
FIGURE 3. Transfer Function with Varying I
2
and I
1
.
KT
q
A
2
A
1
I
1
Q
1
Q
2
V
OUT
= K LOG
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
OUT
= K log
where:
K = the scale factor with units of volts/decade
I
1
= numerator input current
I
2
= denominator input current.
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
1A
10A
100A
1mA
100nA
10nA
1nA
V
OUT
= K LOG
I
1
I
2
I
2
= 1A
Fixed value of I
2
.
V
OUT
(V)
K = 5
K = 3
K = 1
I
1
10
8
6
4
2
0
2
4
6
8
10
1A
10A 100A
1mA
100nA
10nA
1nA
V
OUT
= K LOG
I
1
I
2
K = 3
Fixed value of K.
V
OUT
(V)
I
2
= 10nA
I
2
= 1A
I
2
= 100A
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
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