TI LOG112AID Logarithmic and log ratio amplifier Datasheet

LOG
LOG112
LOG2112
2112
LOG
112
SBOS246C – JUNE 2002 – REVISED APRIL 2003
Precision
LOGARITHMIC AND LOG RATIO AMPLIFIERS
FEATURES
DESCRIPTION
● EASY-TO-USE COMPLETE FUNCTION
The LOG112 and LOG2112 are versatile integrated circuits
that compute the logarithm or log ratio of an input current
relative to a reference current. VLOGOUT of the LOG112 and
LOG2112 are trimmed to 0.5V per decade of input current,
ensuring high precision over a wide dynamic range of input
signals.
● OUTPUT SCALING AMPLIFIER
● ON-CHIP 2.5V VOLTAGE REFERENCE
● HIGH ACCURACY: 0.2% FSO Over 5 Decades
● WIDE INPUT DYNAMIC RANGE:
7.5 Decades, 100pA to 3.5mA
The LOG112 and LOG2112 features a 2.5V voltage reference that may be used to generate a precision current
reference using an external resistor.
● LOW QUIESCENT CURRENT: 1.75mA
● WIDE SUPPLY RANGE: ±4.5V to ±18V
Low DC offset voltage and temperature drift allow accurate
measurement of low-level signals over the specified temperature range of –5°C to +75°C.
● PACKAGES: SO-14 (narrow) and SO-16
APPLICATIONS
● LOG, LOG RATIO:
Communication, Analytical, Medical, Industrial,
Test, General Instrumentation
● PHOTODIODE SIGNAL COMPRESSION AMP
● ANALOG SIGNAL COMPRESSION IN FRONT
OF ANALOG-TO-DIGITAL (A/D) CONVERTER
● ABSORBANCE MEASUREMENT
● OPTICAL DENSITY MEASUREMENT
R1
R2
VLOGOUT = (0.5V)LOG (I1/I2)
VO3 = K (0.5V)LOG (I1/I2), K = 1 + R2/R1
CC
V+
VLOGOUT
I1
Q1
–IN3
LOG112
Q2
A2
A1
I2
+IN3
RREF
A3
VREF
VO3
VREF
VREF – GND VCM
GND
V–
NOTE: Internal resistors are used to compensate gain change over temperature.
The VCM pin is internally connected to GND in the LOG2112.
Please be aware that an important notice concerning availability, standard warranty, and use in critical applications of
Texas Instruments semiconductor products and disclaimers thereto appears at the end of this data sheet.
Copyright © 2002-2003, Texas Instruments Incorporated
PRODUCTION DATA information is current as of publication date.
Products conform to specifications per the terms of Texas Instruments
standard warranty. Production processing does not necessarily include
testing of all parameters.
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ELECTROSTATIC
DISCHARGE SENSITIVITY
ABSOLUTE MAXIMUM RATINGS(1)
Supply Voltage, V+ to V– .................................................................. ±18V
Inputs ................................................................................................. ±18V
Input Current ................................................................................... ±10mA
This integrated circuit can be damaged by ESD. Texas Instruments recommends that all integrated circuits be handled with
appropriate precautions. Failure to observe proper handling
and installation procedures can cause damage.
Output Short-Circuit Current(2) ................................................ Continuous
Operating Temperature .................................................... –40°C to +85°C
Storage Temperature ..................................................... –55°C to +125°C
Junction Temperature .................................................................... +150°C
Lead Temperature (soldering, 10s) ............................................... +300°C
ESD damage can range from subtle performance degradation
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 its published
specifications.
NOTES: (1) Stresses above these ratings may cause permanent damage.
Exposure to absolute maximum conditions for extended periods may degrade
device reliability. (2) One output per package.
PACKAGE/ORDERING INFORMATION
PRODUCT
PACKAGE-LEAD
PACKAGE
DESIGNATOR(1)
SPECIFIED
TEMPERATURE
RANGE
PACKAGE
MARKING
ORDERING
NUMBER
TRANSPORT
MEDIA, QUANTITY
SO-14
D
–5°C to +75°C
LOG112A
"
"
"
"
SO-16
DW
–5°C to +75°C
LOG2112A
"
"
"
"
LOG112AID
LOG112AIDR
LOG2112AIDW
LOG2112AIDWR
Rails, 250
Tape and Reel, 2500
Rails, 250
Tape and Reel, 2500
LOG112
"
LOG2112
"
NOTE: (1) For the most current specifications and package information, refer to our web site at www.ti.com.
PIN CONFIGURATION
Top View
SO
I1
1
14 I2
I1A
1
16 I1B
NC
2
13 VCM – IN
I2A
2
15 I2B
+IN3
3
12 NC
+IN3A
3
14 +IN3B
–IN3
4
11 VREF – GND
–IN3A
4
LOG112
13 –IN3B
LOG2112
VLOGOUT
5
10 GND
V+
6
9
V–
VO3
7
8
VREF
VLOGOUTA
5
12 VLOGOUTB
V+
6
11 V–
VO3A
7
10 V03B
GND
8
9
VREF
NC = No Internal Connection
2
LOG112, 2112
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SBOS246C
ELECTRICAL CHARACTERISTICS
Boldface limits apply over the specified temperature range, TA = –5°C to +75°C.
At TA = +25°C, VS = ±5V, and ROUT = 10kΩ, unless otherwise noted.
LOG112, LOG2112
PARAMETER
CONDITION
CORE LOG FUNCTION
VIN / VOUT Equation
LOG CONFORMITY ERROR(1)
Initial
over Temperature
GAIN(2)
Initial Value
Gain Error
vs Temperature
INPUT, A1A and A1B, A2A, A2B
Offset Voltage
vs Temperature
vs Power Supply (PSRR)
Input Bias Current
vs Temperature
Voltage Noise
Current Noise
Common-Mode Voltage Range (Positive)
(Negative)
Common-Mode Rejection Ratio (CMRR)
OUTPUT, (VLOG OUT) A2A, A2B
Output Offset, VOSO, Initial
vs Temperature
Full-Scale Output (FSO)
Short-Circuit Current
TOTAL ERROR(3)(4)
Initial
vs Temperature
vs Supply
MIN
TYP
MAX
VLOGOUT = (0.5V)LOG (I1/I2)
1nA to 100µA (5 decades)
100pA to 3.5mA (7.5 decades)
1nA to 100µA (5 decades)
100pA to 3.5mA (7.5 decades)
0.01
0.13
0.0001
0.005
1nA to 100µA
1nA to 100µA
TMIN to TMAX
0.5
0.10
0.003
TMIN to TMAX
VS = ±4.5V to ±18V
TMIN to TMAX
f = 10Hz to 10kHz
f = 1kHz
f = 1kHz
±3
TMIN to TMAX
VS = ±5V
I1 or I2 remains fixed while other varies.
Min to Max
I1 or I2 = 5mA (VS ≥ ±6V)
I1 or I2 = 3.5mA
I1 or I2 = 1mA
I1 or I2 = 100µA
I1 or I2 = 10µA
I1 or I2 = 1µA
I1 or I2 = 100nA
I1 or I2 = 10nA
I1 or I2 = 1nA
I1 or I2 = 350pA
I1 or I2 = 100pA
I1 or I2 = 3.5mA
I1 or I2 = 1mA
I1 or I2 = 100µA
I1 or I2 = 10µA
I1 or I2 = 1µA
I1 or I2 = 100nA
I1 or I2 = 10nA
I1 or I2 = 1nA
I1 or I2 = 350pA
I1 or I2 = 100pA
I1 or I2 = 3.5mA
I1 or I2 = 1mA
I1 or I2 = 100µA
I1 or I2 = 10µA
I1 or I2 = 1µA
I1 or I2 = 100nA
I1 or I2 = 10nA
I1 or I2 = 1nA
I1 or I2 = 350pA
I1 or I2 = 100pA
±10
(V–) + 1.2
V
0.2
±1
0.01
±0.3
±2
5
±5
Doubles Every 10°C
3
30
4
(V+) – 2
(V+) – 1.5
(V–) + 2
(V–) + 1.2
10
±1.5
20
±3.0
±0.1
±0.1
±0.1
±0.1
±0.1
±0.1
±0.25
±0.1
±0.1
%
%
%/ °C
%/ °C
V/decade
%
%/ °C
mV
µV/°C
µV/V
pA
µVrms
nV/√Hz
fA/√Hz
V
V
µV/V
±15
mV
µV/°C
(V+) – 1.5
V
mA
±150
±75
±20
±20
±20
±20
±20
±20
±20
±20
±20
mV
mV
mV
mV
mV
mV
mV
mV
mV
mV
mV
mV/ °C
mV/ °C
mV/ °C
mV/ °C
mV/ °C
mV/ °C
mV/ °C
mV/ °C
mV/ °C
mV/ °C
mV/ V
mV/ V
mV/ V
mV/ V
mV/ V
mV/ V
mV/ V
mV/V
mV/ V
mV/ V
±18
±1.2
±0.4
±0.1
±0.05
±0.05
±0.09
±0.2
±0.3
±0.1
±0.3
UNITS
NOTES: (1) Log Conformity Error is the peak deviation from the best-fit-straight line of VO versus LOG (I1/I2) curve expressed as a percent of peak-to-peak fullscale output. K, scale factor, equals 0.5V output per decade of input current. (2) Scale factor of core log function is trimmed to 0.5V output per decade change of
input current. (3) Worst-case Total Error for any ratio of I1/I2, as the largest of the two errors, when I1 and I2 are considered separately. (4) Total Error includes offset
voltage, bias current, gain, and log conformity. (5) Bandwidth (3dB) and transient response are a function of both the compensation capacitor and the level of input
current.
LOG112, 2112
SBOS246C
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3
ELECTRICAL CHARACTERISTICS (Cont.)
Boldface limits apply over the specified temperature range, TA = –5°C to +75°C.
At TA = +25°C, VS = ±5V, and RL = 10kΩ, unless otherwise noted.
LOG112, LOG2112
PARAMETER
FREQUENCY RESPONSE, CORE LOG(5)
BW, 3dB
I2 = 10nA
I2 = 1µA
I2 = 10µA
I2 = 1mA
Step Response
Increasing
I1 = 10nA to 100nA
I1 = 1µA to 100µA
I1 = 1µA to 1mA
Decreasing
I1 = 100nA to 10nA
I1 = 100µA to 1µA
I1 = 1mA to 1µA
Increasing
I2 = 10nA to 100nA
I2 = 1µA to 100µA
I2 = 1µA to 1mA
Decreasing
I2 = 100nA to 10nA
I2 = 100µA to 1µA
I2 = 1mA to 1µA
OP AMP, A3
Input Offset Voltage
vs Temperature
vs Supply
Input Bias Current
Input Offset Current
Input Voltage Range
Input Noise, f = 0.1Hz to 10Hz
f = 1kHz
Open-Loop Voltage Gain
Gain-Bandwidth Product
Slew Rate
Settling Time, 0.01%
Rated Output
Short-Circuit Current
VOLTAGE REFERENCE
Bandgap Voltage
Error, Initial
vs Temperature
vs Supply
vs Load
Short-Circuit Current
POWER SUPPLY
Operating Range
Quiescent Current
LOG112
LOG2112
CONDITION
MIN
TYP
MAX
UNITS
CC = 4500pF
CC = 150pF
CC = 150pF
CC = 50pF
0.1
38
40
45
kH
kH
kH
kHz
CC = 120pF, I2 = 31.6nA
CC = 375pF, I2 = 10µA
CC = 950pF, I2 = 31.6µA
1.1
1.6
1.5
ms
µs
µs
CC = 120pF, I2 = 31.6nA
CC = 375pF, I2 = 10µA
CC = 950pF, I2 = 31.6µA
2.1
31.2
39
ms
µs
µs
CC = 125pF, I1 = 31.6nA
CC = 750pF, I1 = 10µA
CC = 10.5nF, I1 = 31.6µA
2.6
113
1.2
ms
µs
ms
CC = 125pF, I1 = 31.6nA
CC = 750pF, I1 = 10µA
CC = 10.5nF, I1 = 31.6µA
630
6.6
13.3
µs
µs
µs
VS
+250
±2
5
–10
±0.5
TMIN to TMAX
= ±4.5V to ±18V
(V–)
±1000
50
(V+) – 1.5
1
28
88
1.4
0.5
16
G = –1, 3V Step, CL = 100pF
(V–) + 1.5
(V+) – 0.9
±4
2.5
±0.05
±25
±10
±600
16
TMIN to TMAX
VS = ±4.5V to ±18V
ILOAD = 10mA
VS
IO = 0
TEMPERATURE RANGE
Specified Range, TMIN to TMAX
Operating Range
Storage Range
Thermal Resistance, θJA SO-14
SO-16
±4.5
±1.25
±2.5
–5
–40
–55
110
80
±0.5
µV
µV/°C
µV/V
nA
nA
V
µVp-p
nV/ √Hz
dB
MHz
V/µs
µs
V
mA
V
%
ppm/°C
ppm/V
ppm/mA
mA
±18
V
±1.75
±3.5
mA
mA
75
85
125
°C
°C
°C
°C/W
°C/W
NOTES: (1) Log Conformity Error is the peak deviation from the best-fit-straight line of VO vs LOG(I1/I2) curve expressed as a percent of peak-to-peak full-scale
output. K, scale factor, equals 0.5V output per decade of input current. (2) Scale factor of core log function is trimmed to 0.5V output per decade change of input
current. (3) Worst-case Total Error for any ratio of I1/I2, as the largest of the two errors, when I1 and I2 are considered separately. (4) Total Error includes offset
voltage, bias current, gain, and log conformity. (5) Bandwidth (3dB) and transient response are a function of both the compensation capacitor and the level of input
current.
4
LOG112, 2112
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SBOS246C
TYPICAL CHARACTERISTICS
At TA = +25°C, VS = ±5V, and RL = 10kΩ, unless otherwise noted.
ONE CYCLE OF NORMALIZED TRANSFER FUNCTION
NORMALIZED TRANSFER FUNCTION
0.50
VLOGOUT = (0.5V)LOG (I1/I2)
1.0
0.5
0
–0.5
–1.0
–1.5
–2.0
0.0001 0.001 0.01
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0
10
100
1k
10k
1
10
Current Ratio, I1/I2
Current Ratio, I1/I2
–10
I1
I2
TOTAL ERROR (70°C)
8
100
80 to 100
60 to 80
40 to 60
20 to 40
0 to 20
–20 to 0
20
40
20
0
0
1mA
100µA
10µA
1µA
100nA
10nA
1µA
10nA
1nA
1nA
I1
–20
100nA
1mA
100µA
10µA
–20
+85°C
+75°C
5
–40°C
4
3
2
1
0
–1
–2
100pA 1nA
I2
–5°C +25°C
10nA 100nA 1µA
10µA 100µA 1mA
10mA
Input Current (I1 or I2)
LOG112, 2112
SBOS246C
Gain Error (%)
40
60
I2
GAIN ERROR (I2 = 1µA)
6
80
Total Error (mV)
Total Error (mV)
60
–20
7
100
80
–15
5 to 10
0 to 5
–5 to 0
1mA
1mA
100µA
10µA
1mA
1µA
10µA
–20
100nA
10nA
1nA
1nA
100nA
10µA
I1
–15
0
–5
–5
–10
–15
–20
100µA
–10
10 to 15
5 to 10
0 to 5
–5 to 0
100µA
–5
–10
–15
–20
5
0
10µA
0
–5
10
1µA
0
15
10
5
100nA
5
20
15
1µA
10
20
100nA
10
5
Total Error (mV)
15
Total Error (mV)
20
15
1mA
Total Error (mV)
20
Total Error (mV)
TOTAL ERROR (25°C)
TOTAL ERROR (–5°C)
10nA
1
10nA
0.1
1nA
1nA
1.5
Normalized Output Voltage (V)
Normalized Output Voltage (V)
2.0
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5
TYPICAL CHARACTERISTICS (Cont.)
At TA = +25°C, VS = ±5V, and RL = 10kΩ, unless otherwise noted.
1M
Select CC for I1 min.
and I2 max. Values
below 2pF may be ignored.
10µA
I1 = 100pA
I1 = 1nA
100k
CC (pF)
1M
3dB Frequency Response (Hz)
10M
3dB FREQUENCY RESPONSE
MINIMUM VALUE OF COMPENSATION CAPACITOR
100M
I1 = 10nA
10k
I1 = 100nA
1µA
1k
100
I1 = 10µA
100µA
1mA
10
1
100pA
1nA
10nA 100nA 1µA
100k
10k
1k
100µA
CC
A
1µA
1mA
to 10µA
10nA
100
I1 = 1nA
10
1
1µ
to
µA
0
1
10nA
CC
=1
00
100nA
10nA
F
0p
CC
=1
I1 = 1nA
µF
0.1
100pA
10µA 100µA 1mA 10mA
1nA
10nA
100nA
1µA
10µA
100µA
1mA
I2
LOG CONFORMITY vs TEMPERATURE
LOG CONFORMITY vs INPUT CURRENT
700
15
600
13
Log Conformity (m%)
Log Conformity (mV)
F
0p 100µA
=1
1nA
I2
17
100µA
100µA
1mA
I1 = 1mA
1µA
+85°C
11
9
7
+75°C
5
–40°C to +25°C
7.5 Decade
500
400
7 Decade
300
6 Decade 5 Decade
200
3
100
1
–1
100pA
0
1nA
10nA
100nA
1µA
10µA
100µA
1mA
Input Current (I1 or I2)
6
–40
–20
0
20
40
60
80
Temperature (°C)
LOG112, 2112
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SBOS246C
INPUT CURRENT RANGE
APPLICATION INFORMATION
The LOG112 is a true logarithmic amplifier that uses the
base-emitter voltage relationship of bipolar transistors to
compute the logarithm, or logarithmic ratio of a current ratio.
Figure 1 and Figure 2 show the basic connections required
for operation of the LOG112 and LOG2112. In order to
reduce the influence of lead inductance of power-supply
lines, it is recommended that each supply be bypassed with
a 10µF tantalum capacitor in parallel with a 1000pF ceramic
capacitor, as shown in Figure 1 and Figure 2. Connecting
the capacitors as close to the LOG112 and LOG2112 as
possible will contribute to noise reduction as well.
To maintain specified accuracy, the input current range of the
LOG112 and LOG2112 should be limited from 100pA to
3.5mA. Input currents outside of this range may compromise
the LOG112 performance. Input currents larger than 3.5mA
result in increased nonlinearity. An absolute maximum input
current rating of 10mA is included to prevent excessive power
dissipation that may damage the input transistor.
On ±5V supplies, the total input current (I1 + I2) is limited to
4.5mA. Due to compliance issues internal to the LOG112 and
LOG2112, to accommodate larger total input currents, supplies
should be increased.
SETTING THE REFERENCE CURRENT
V+
10µF
When the LOG112 and LOG2112 are used to compute logarithms, either I1 or I2 can be held constant to become the
reference current to which the other is compared.
1000pF
VLOGOUT is expressed as:
6
1
8
11
14
9
I2
VLOGOUT
5
LOG112
I1
VLOGOUT = (0.5V)LOG (I1/IREF)
VREF
10
VREF – GND
13
IREF can be derived from an external current source (such as
that shown in Figure 3), or it may be derived from a voltage
source with one or more resistors. When a single resistor is
used, the value may be large depending on IREF. If IREF is
10nA and +2.5V is used:
VCM – IN
RREF = 2.5V/10nA = 250MΩ
CC
1000pF
10µF
2N2905
FIGURE 1. Basic Connections of the LOG112.
RREF
V+
–15V
6V
IN834
6V
RREF
FIGURE 3. Temperature Compensated Current Source.
CCA
6
2
5
VLOGOUTA
1
9
VREF
I1A
LOG2112
16
12
15
11
IREF =
1000pF
10µF
I2B
3.6kΩ
2N2905
+15V
I1B
(2)
IREF
V–
I2A
(1)
A voltage divider may be used to reduce the value of the
resistor, as shown in Figure 4. When using this method, one
must consider the possible errors caused by the amplifier’s
input offset voltage. The input offset voltage of amplifier A1
has a maximum value of 1.5mV, making VREF a suggested
value of 100mV.
VLOGOUTB
VREF = 100mV
R1
8
R3
1
+5V
CCB
R2
10µF
VOS
+
–
IREF
A1
R3 >> R2
1000pF
V–
FIGURE 2. Basic Connections of the LOG2112.
FIGURE 4. T Network for Reference Current.
LOG112, 2112
SBOS246C
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7
Figure 5 shows a low-level current source using a series
resistor. The low offset op amp reduces the effect of the
LOG112 and LOG2112’s input offset voltage.
VREF
I1 = 2.5nA to 1mA
V+
8
6
5
1
VLOGOUT
100kΩ
LOG112
I2 = 2.5nA
10MΩ
+25mV
14
+2.5V
100Ω
9
CC
FREQUENCY COMPENSATION
Frequency compensation for the LOG112 is obtained by
connecting a capacitor between pins 5 and 14. Frequency
compensation for the LOG2112 is obtained by connecting a
capacitor between pins 2 and 5, or 15 and 12. The size of the
capacitor is a function of the input currents, as shown in the
Typical Characteristic curves (Minimum Value of Compensation Capacitor). For any given application, the smallest value
of the capacitor which may be used is determined by the
maximum value of I2 and the minimum value of I1. Larger
values of CC make the LOG112 and LOG2112 more stable,
but reduce the frequency response.
In an application, highest overall bandwidth can be achieved
by detecting the signal level at VOUT, then switching in
appropriate values of compensation capacitors.
10 GND
V–
OPA335 Chopper Op Amp
NEGATIVE INPUT CURRENTS
The LOG112 and LOG2112 function only with positive input
currents (conventional current flows into input current pins).
In situations where negative input currents are needed, the
circuits in Figures 6, 7, and 8 may be used.
–2.5V
FIGURE 5. Current Source with Offset Compensation.
FREQUENCY RESPONSE
The frequency response curves seen in the Typical Characteristic curves are shown for constant DC I1 and I2 with a
small-signal AC current on one input.
QB
National
LM394
The 3dB frequency response of the LOG112 and LOG2112 are
a function of the magnitude of the input current levels and of the
value of the frequency compensation capacitor. See typical
characteristic curve “3dB Frequency Response” for details.
The transient response of the LOG112 and LOG2112 are
different for increasing and decreasing signals. This is due to
the fact that a log amp is a nonlinear gain element and has
different gains at different levels of input signals. Smaller
input currents require greater gain to maintain full dynamic
range, and will slow the frequency response of the LOG112
and LOG2112.
QA
IIN
D1
D2
OPA703
IOUT
FIGURE 6. Current Inverter/Current Source.
+5V
TLV271 or 1/2 OPA2335
+3.3V
1/2
OPA2335
1.5kΩ
1kΩ
10nA to 1mA
Back Bias
+5V
1/2
OPA2335
BSH203
+3.3V
10nA to 1mA
Pin 1 or Pin 14
LOG112
Photodiode
FIGURE 7. Precision Current Inverter/Current Source.
8
LOG112, 2112
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SBOS246C
VOLTAGE INPUTS
age to VCM of at least +1V and up to 2.5V, brings the log
transistors out of saturation and reduces output error to
approximately 10%. To avoid forward biasing a photodiode,
return the cathode to the VCM pin, as shown in Figure 9. To
reverse bias the photodiode, apply a more positive voltage to
the cathode than the anode.
The LOG112 and LOG2112 give the best performances with
current inputs. Voltage inputs may be handled directly with
series resistors, but the dynamic input range is limited to
approximately three decades of input voltage by voltage
noise and offsets. The transfer function of Equation 13
applies to this configuration.
APPLICATION CIRCUITS
ACHIEVING HIGHER ACCURACY WITH HIGHER
INPUT CURRENTS
LOG RATIO
One of the more common uses of log ratio amplifiers is
to measure absorbance. See Figure 10 for a typical application.
As input current to the LOG112 increases, output accuracy
degrades. For a 4.5mA input current on ±5V supplies and a
10mA input current on ±12V supplies, total output error can
be between 15% and 25%. Applying a common-mode volt-
Absorbance of the sample is A = logλ1´/ λ1
(3)
If D1 and D2 are matched A ∝ (0.5V) logI1 / I2
(4)
1kΩ
100kΩ
100kΩ
+5V
10nA to 1mA
+3.3V
Back Bias
Photodiode
1/2
OPA2335
+5V
+3.3V
1.5kΩ
1/2
OPA2335
1.5kΩ
100kΩ
100kΩ
LOG112
10nA to 1mA
Pin 1 or Pin 14
FIGURE 8. Precision Current Inverter/Current Source.
R1
R2
CC
V+ = +5V
6
I1
1
Q1
+2.5V
100kΩ
+IN3
3 4
–IN3
LOG112
Q2
A2
A1
I2
RREF
VLOGOUT
5
14
8
VREF
A3
7
VO3
VREF
11
13
VREF – GND
VCM
10
9
GND
V– = –5V
150kΩ
+1.5V
FIGURE 9. Extending Input Current Level and Improving Accuracy by Applying a Common-Mode Voltage.
LOG112, 2112
SBOS246C
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9
DATA COMPRESSION
MEASURING AVALANCHE PHOTODIODE CURRENT
In many applications, the compressive effects of the logarithmic transfer function are useful. For example, a LOG112
preceding a 12-bit A/D converter can produce the dynamic
range equivalent to a 20-bit converter.
The wide dynamic range of the LOG112 and LOG2112 is
useful for measuring avalanche photodiode current (APD), as
shown in Figure 12.
OPERATION ON SINGLE SUPPLY
Single Supply +5V
Many applications do not have the dual supplies required to
operate the LOG112 and LOG2112. Figure 11 shows the
LOG112 and LOG2112 configured for operation with a single
+5V supply.
6
5
1
I1
VLOGOUT
LOG112
10
14
V+
I1
6
1
VLOGOUT
5
9
I2
CC
D1
Sample
λ1
1µF
LOG112
λ 1´
I2
Light λ 1
Source
14
3
10
2
9
D2
5
TPS(1)
1µF
CC
1
–5V
1µF
4
NOTE: (1) TPS60402DBV
negative charge pump.
V–
FIGURE 11. Single +5V Power-Supply Operation.
FIGURE 10. Absorbance Measurement.
ISHUNT
+15V to +60V
500Ω
Irx = 1µA to 1mA
5kΩ
Receiver
5kΩ
+5V
10Gbits/sec
APD
INA168
SOT23-5
I-to-V
Converter
IOUT = 0.1 • ISHUNT
1
2
IOUT
CC
10kΩ
16.7kΩ
+5V
6
4
5
1
Q2
Q1
A3
7
V03 = 2.5V to 0V
A2
A1
14
100µA
25kΩ
8
VREF
LOG112
SO-14
9
11
13
10
3
–5V
FIGURE 12. High-Side Shunt for APD Measures 3 Decades of APD Current.
10
LOG112, 2112
www.ti.com
SBOS246C
INSIDE THE LOG112
Using the base-emitter voltage relationship of matched
bipolar transistors, the LOG112 establishes a logarithmic function of input current ratios. Beginning with the
base-emitter voltage defined as:
VBE = VT ln
IC
IS
where : VT =
kT
q
also
VOUT = VL
(10)
I 
VOUT = (0.5V)LOG  1 
 I2 
k = Boltzman’s constant = 1.381 • 10–23
or
T = Absolute temperature in degrees Kelvin
(9)
R1 + R2
I
n VT log 1
R1
I2
VOUT =
(1)
R1 + R2
R1
(11)
q = Electron charge = 1.602 • 10–19 Coulombs
IC = Collector current
IS = Reverse saturation current
From the circuit in Figure 12:
VL = VBE1 – VBE 2
(2)
VL = VT1 ln
IS1
–
+
VOUT
+
1
I1
I2
Q2
–
VBE
A2
VBE
2
A1
Substituting (1) into (2) yields:
I1
Q1
I1
– VT2 ln
I2
IS 2
I 
VOUT = (0.5V)LOG  1 
 I2 
(3)
R2
VL
I2
R1
If the transistors are matched and isothermal and
VTI = VT2, then (3) becomes:
 I
I 
VL = VT1 ln 1 – ln 2 
I
I
S
 S
VL = VT ln
I1
and since
I2
ln x = 2.3 log10 x
(4)
NOTE: R1 is a metal resistor used to compensate for gain
over temperature.
(5)
(6)
I1
I2
(7)
where n = 2.3
(8)
VL = n VT log
FIGURE 13. Simplified Model of a Log Amplifier.
DEFINITION OF TERMS
3.5
TRANSFER FUNCTION
3.0
The ideal transfer function is:
2.0
VLOGOUT = (0.5V)LOG (I1/I2)
1.5
Figure 14 shows the graphical representation of the transfer
over valid operating range for the LOG112 and LOG2112.
0.5
VOUT (V)
1.0
0
–0.5
–1.0
ACCURACY
–1.5
Accuracy considerations for a log ratio amplifier are somewhat 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 actual
output from the ideal output of VLOGOUT = (0.5V)LOG (I1/I2).
Thus,
VLOGOUT(ACTUAL) = VLOGOUT(IDEAL) ± Total Error
–2.0
–2.5
–3.0
100
pA
1nA
10n
A
0n
10
I 2 = µA
1
I 2 = 0µA
1
=
I 2 00µA
1
I 2 = mA
1
=
I2
A
100
nA µA
1
1 0µ
A
100
µA
1m
A
A
10m
I1
VLOGOUT = (0.5V)LOG (I1/I2)
–3.5
FIGURE 14. Transfer Function with Varying I2 and I1.
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. Temperature can affect total error.
(6)
LOG112, 2112
SBOS246C
A
0p
10
I 2 = nA
1
I 2 = 0nA
1
=
I2
2.5
www.ti.com
11
ERRORS RTO AND RTI
The individual component of error is:
∆K = gain error (0.10%, typ), as specified in the specification table.
As with any transfer function, errors generated by the function 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.
IB1 = bias current of A1 (5pA, typ)
IB2 = bias current of A2 (5pA, typ)
N = log conformity error (0.01%, 0.13%, typ)
0.01% for m = 5, 0.13% for m = 7.5
LOG CONFORMITY
For the LOG112 and LOG2112, log conformity is calculated
the same as linearity and is plotted I1 /I2 on a semi-log scale.
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
fit straight line of the VLOGOUT versus log (I1/I2) curve. This is
expressed as a percent of ideal full-scale output. Thus, the
nonlinearity error expressed in volts over m decades is:
VLOGOUT
(NONLIN)
= 0.5V/dec • 2NmV
(7)
where N is the log conformity error, in percent.
VOSO = output offset voltage (3mV, typ)
m = number of decades over which N is specified
For example, what is the error when:
I1 = 1µA and I2 = 100nA
 10−6 − 5 • 10−12 
± 2 0.0001)5 ± 3.0mV
VLOGOUT = (0.5 ± 0.001) log −7
−12  ( )(
 10 − 5 • 10 
= 0.505V
Since the ideal output is 0.5V, the error as a percent of the
reading is:
0.505V
• 100% = 1.01%
(12)
0.5
For the case of voltage inputs, the actual transfer function is:
% error =
(13)
INDIVIDUAL ERROR COMPONENTS
VLOGOUT
The ideal transfer function with current input is:
I 
VLOGOUT = (0.5V)LOG  1 
 I2 
(8)
The actual transfer function with the major components of
error is:
VLOGOUT
12
 I –I 
= (0.5V) (1 ± ∆K ) log 1 B1  ± Nm ± VOSO
 I2 – IB2 
(10)
(11)
Where
EOS1
 V1
 R – IB1 ± R
1
= (0.5V) (1 ± ∆K ) log  1
 V2 – I ± EOS2
B2

R2
 R2


 ± Nm ± VOSO



EOS1
E
and OS2 (offset error) are considered to be
R1
R2
zero for large values of resistance from external input current
sources.
(9)
LOG112, 2112
www.ti.com
SBOS246C
PACKAGE DRAWINGS
D (R-PDSO-G**)
PLASTIC SMALL-OUTLINE PACKAGE
8 PINS SHOWN
0.020 (0,51)
0.014 (0,35)
0.050 (1,27)
8
0.010 (0,25)
5
0.008 (0,20) NOM
0.244 (6,20)
0.228 (5,80)
0.157 (4,00)
0.150 (3,81)
Gage Plane
1
4
0.010 (0,25)
0°– 8°
A
0.044 (1,12)
0.016 (0,40)
Seating Plane
0.010 (0,25)
0.004 (0,10)
0.069 (1,75) MAX
PINS **
0.004 (0,10)
8
14
16
A MAX
0.197
(5,00)
0.344
(8,75)
0.394
(10,00)
A MIN
0.189
(4,80)
0.337
(8,55)
0.386
(9,80)
DIM
4040047/E 09/01
NOTES: A.
B.
C.
D.
All linear dimensions are in inches (millimeters).
This drawing is subject to change without notice.
Body dimensions do not include mold flash or protrusion, not to exceed 0.006 (0,15).
Falls within JEDEC MS-012
LOG112, 2112
SBOS246C
www.ti.com
13
PACKAGE DRAWINGS (Cont.)
DW (R-PDSO-G**)
PLASTIC SMALL-OUTLINE PACKAGE
16 PINS SHOWN
0.050 (1,27)
0.020 (0,51)
0.014 (0,35)
16
0.010 (0,25) M
9
0.419 (10,65)
0.400 (10,15)
0.010 (0,25) NOM
0.299 (7,59)
0.291 (7,39)
Gage Plane
0.010 (0,25)
1
8
0° – 8°
A
0.050 (1,27)
0.016 (0,40)
Seating Plane
0.104 (2,65) MAX
0.012 (0,30)
0.004 (0,10)
PINS **
0.004 (0,10)
16
18
20
24
28
A MAX
0.410
(10,41)
0.462
(11,73)
0.510
(12,95)
0.610
(15,49)
0.710
(18,03)
A MIN
0.400
(10,16)
0.453
(11,51)
0.500
(12,70)
0.600
(15,24)
0.700
(17,78)
DIM
4040000 / E 08/01
NOTES: A.
B.
C.
D.
14
All linear dimensions are in inches (millimeters).
This drawing is subject to change without notice.
Body dimensions do not include mold flash or protrusion not to exceed 0.006 (0,15).
Falls within JEDEC MS-013
LOG112, 2112
www.ti.com
SBOS246C
PACKAGE OPTION ADDENDUM
www.ti.com
3-Oct-2003
PACKAGING INFORMATION
ORDERABLE DEVICE
STATUS(1)
PACKAGE TYPE
PACKAGE DRAWING
PINS
PACKAGE QTY
LOG112AID
ACTIVE
SOIC
D
14
58
LOG112AIDR
ACTIVE
SOIC
D
14
2500
LOG2112AIDW
ACTIVE
SOIC
DW
16
48
LOG2112AIDWR
ACTIVE
SOIC
DW
16
48
(1) The marketing status values are defined as follows:
ACTIVE: Product device recommended for new designs.
LIFEBUY: TI has announced that the device will be discontinued, and a lifetime-buy period is in effect.
NRND: Not recommended for new designs. Device is in production to support existing customers, but TI does not recommend using this part in
a new design.
PREVIEW: Device has been announced but is not in production. Samples may or may not be available.
OBSOLETE: TI has discontinued the production of the device.
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