LOG
LOG112
LOG2112
2112
LOG
112
SBOS246B – JUNE 2002 – REVISED NOVEMBER 2002
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)
CC
VO3 = K LOG (I1/I2), K = 1 + R2/R1
V+
VLOGOUT
I1
Q1
–IN3
LOG112
Q2
A2
A1
I2
+IN3
RREF
A3
VREF
VO3
VREF
VREF – GND VCM
GND
V–
NOTE: R1 and R2 are metal resistors used to compensate gain change over temperature.
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, 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
"
"
"
"
LOG112AID
LOG112AIDR
Rails, 250
Tape and Reel, 2500
SO -16
DW
–5°C to +75°C
LOG2112A
"
"
"
"
LOG2112AIDW
LOG2112AIDWR
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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SBOS246B
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
MIN
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
TYP
MAX
VO = (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
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
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
105
±3
TMIN to TMAX
VS = ±5V
±10
(V–) + 1.2
±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
dB
±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 peak deviation from the best-fit-straight line of VO versus 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.
LOG112, 2112
SBOS246B
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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 = 1µA to 1mA
I1 = 100µA to 1µA
I1 = 10nA to 100nA
Decreasing
I1 = 1mA to 1mA
I1 = 1µA to 100nA
I1 = 100µA to 10nA
I2 = 1µA to 1nA
I2 = 100µA to 1µA
I2 = 10nA to 100nA
Decreasing
I2 = 1mA to 1µA
I2 = 1µA to 100nA
I2 = 100µA to 10nA
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
kHz
kHz
kHz
kHz
CC = 950pF, I2 = 31.6µA
CC = 375pF, I2 = 10µA
CC = 120pF, I2 = 31.6nA
1.5
1.6
1.1
µs
µs
ms
CC = 950pF, I2 = 31.6µA
CC = 375pF, I2 = 10µA
CC = 150pF, I2 = 31.6nA
39
31.2
2.1
µs
µs
ms
CC = 10.5nF, I1 = 31µA
CC = 750pF, I1 = 10µA
CC = 125pF, I1 = 31.6nA
1.2
113
2.6
ns
µs
ns
CC = 10.5nF, I1 = 31µA
CC = 750pF, I1 = 10µA
CC = 125pF, I1 = 31.6nA
13.3
6.6
629
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 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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SBOS246B
TYPICAL CHARACTERISTICS
At TA = +25°C, VS = ±5V, and RL = 10kΩ, unless otherwise noted.
ONE CYCLE OF NORMALIZED TRANSFER FUNCTION
NORMALIZED TRANSFER FUNCTION
2.0
VOUT = 0.5V LOG (I1/I2)
Normalized Output Voltage (V)
Normalized Output Voltage (V)
1.5
0.50
1.0
0.5
0.0
–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
0.00
0.1
1
10
100
1k
10k
1
2
Current Ratio, I1/I2
+75°C
Gain Error (%)
Total Error (mV)
+75°C
6
300
250
200
150
+25°C
100
5
–40°C
4
3
2
1
0
–5°C
50
–1
1nA 10nA 100nA
1µA
–5°C +25°C
–2
100pA 1nA
10µA 100µA 1mA 10mA
10nA 100nA 1µA
Input Current (I1 or I2)
CC (pF)
3dB FREQUENCY RESPONSE
10µA
Select CC for I1 min.
and I2 max. Values
below 2pF may be ignored.
I1 = 100pA
I1 = 1nA
100k
I1 = 10nA
10k
I1 = 100nA
1µA
1k
100
I1 = 10µA
100µA
1mA
10
1
100pA
1nA
10nA 100nA 1µA
100k
10k
1k
100µA
100µA
1mA
I1 = 1mA
1µA
100µA
CC
F
0p 100µA
=1
1
1nA
to
A
1µ
1µA
1mA
to 10µA
10nA
10nA
100
I1 = 1nA
10
1
A
0µ
CC
=
0
10
0
100nA
10nA
pF
CC
I1 = 1nA
µF
=1
0.1
10µA 100µA 1mA 10mA
100pA
1nA
10nA
100nA
1µA
10µA
100µA
1mA
I2
I2
LOG112, 2112
SBOS246B
10mA
1M
3dB Frequency Response (Hz)
1M
10µA 100µA 1mA
Input Current (I1 or I2)
MINIMUM VALUE OF COMPENSATION CAPACITOR
100M
10
+85°C
7
0
100pA
8
GAIN ERROR (I2 = 1µA)
8
350
10M
6
4
Current Ratio, I1/I2
TOTAL ERROR vs INPUT CURRENT
400
3
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5
TYPICAL CHARACTERISTICS (Cont.)
At TA = +25°C, VS = ±5V, and RL = 10kΩ, unless otherwise noted.
LOG CONFORMITY vs TEMPERATURE
700
LOG CONFORMITY vs INPUT CURRENT
17
600
Log Conformity (m%)
Log Conformity (mV)
15
13
+85°C
11
9
7
+75°C
5
–40°C to +25°C
3
7.5 Decade
500
400
7 Decade
300
6 Decade 5 Decade
200
100
1
–1
100pA
0
1nA
10nA
100nA
1µA
10µA
100µA
–40
1mA
–20
0
20
40
60
Input Current (I1 or I2)
APPLICATION INFORMATION
V+
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.
CCA
6
I2A
2
5
VLOGOUT A
1
9
VREF
I1A
LOG2112
16
12
15
V+
I1B
8
11
10
VREF
VLOG OUT
VREF – GND
13
VCM – IN
CC
10µF
1000pF
V–
FIGURE 1. Basic Connections of the LOG112.
6
1000pF
V–
5
14
I2
8
CCB
10µF
LOG112
I1
11
I2B
VLOGOUTB
1000pF
6
1
9
1000pF
10µF
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.
10µF
80
Temperature (°C)
FIGURE 2. Basic Connections of the LOG2112.
INPUT CURRENT RANGE
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
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.
LOG112, 2112
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SBOS246B
SETTING THE REFERENCE CURRENT
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.
VREF
I1 = 2.5nA to 1mA
V+
8
6
5
1
VLOGOUT is expressed as:
VLOGOUT
VLOGOUT = (0.5V) • log (I1/IREF)
100kΩ
(1)
IREF can be derived from an external current source (such as
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:
LOG112
I2 = 2.5nA
10MΩ
+25mV
14
+2.5V
100Ω
9
CC
10 GND
V–
OPA335 Chopper Op Amp
RREF = 2.5V/10nA = 250M
(2)
–2.5V
IREF
2N2905
FIGURE 5. Current Source with Offset Compensation.
RREF
3.6kΩ
2N2905
+15V
FREQUENCY RESPONSE
–15V
6V
IN834
IREF =
The frequency response curves seen in the Typical Characteristics Curves are shown for constant DC I1 and I2 with a
small-signal AC current on one input.
6V
RREF
FIGURE 3. Temperature Compensated Current Source.
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.
VREF = 100mV
R1
R3
1
+5V
R2
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.
VOS
+
–
IREF
FREQUENCY COMPENSATION
A1
R3 >> R2
FIGURE 4. T Network for Reference Current.
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.
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 will make the LOG112 and LOG2112 more
stable, but will reduce the frequency response.
LOG112, 2112
SBOS246B
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7
In an application, highest overall bandwidth can be achieved
by detecting the signal level at VOUT, then switching in
appropriate values of compensation capacitors.
QA
IIN
QB
National
LM394
NEGATIVE INPUT CURRENTS
D1
The LOG112 and LOG2112 will 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.
D2
OPA703
IOUT
FIGURE 6. Current Inverter/Current Source.
+5V
+3.3V
1/2
OPA2335
TLV271 or 1 OPA2335
2
1.5kΩ
1kΩ
Back Bias
10nA to 1mA
+5V
BSH203
1/2
OPA2335
+3.3V
10nA to 1mA
Pin 1 or Pin 14
LOG112
Photodiode
FIGURE 7. Precision Current Inverter/Current Source.
1kΩ
100kΩ
100kΩ
+5V
10nA to 1mA
+3.3V
Back Bias
1/2
OPA2335
+5V
+3.3V
1.5kΩ
1/2
OPA2335
Photodiode
1.5kΩ
100kΩ
100kΩ
LOG112
10nA to 1mA
Pin 1 or Pin 14
FIGURE 8. Precision Current Inverter/Current Source.
8
LOG112, 2112
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SBOS246B
VOLTAGE INPUTS
DATA COMPRESSION
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.
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.
OPERATION ON SINGLE SUPPLY
Many applications do not have the dual supplies required to
operate the LOG112 and LOG2112. Figure 10 shows the
LOG112 and LOG2112 configured for operation with a single
+5V supply.
APPLICATION CIRCUITS
LOG RATIO
One of the more common uses of log ratio amplifiers is
to measure absorbance. A typical application is shown in
Figure 9.
Absorbance of the sample is A = logλ1´/ λ1
(3)
If D1 and D2 are matched A ∝ (0.5V) logI1 / I2
(4)
V+
I1
5
LOG112
λ 1´
λ1
VLOGOUT
D1
Sample
I2
Light
Source
6
1
14
10
λ1
9
D2
CC
V–
FIGURE 9. Absorbance Measurement.
Single Supply +5V
6
5
1
I1
VLOGOUT
LOG112
10
14
9
I2
CC
1µF
3
2
1µF
5
TPS(1)
1
4
–5V
1µF
NOTE: (1) TPS60402DBV negative charge pump.
FIGURE 10. Single +5V Power-Supply Operation.
LOG112, 2112
SBOS246B
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9
INSIDE THE LOG112
also
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
I
= VT ln C
IS
kT
where : VT =
q
R1 + R 2
R1
VOUT = VL
VOUT =
(1)
k = Boltzman’s constant = 1.381 • 10–23
R1 + R 2
I
n VT log 1
R1
I2
VOUT = 0.5V • log
or
T = Absolute temperature in degrees Kelvin
(9)
(10)
I1
I2
(11)
q = Electron charge = 1.602 • 10–19 Coulombs
IC = Collector current
IS = Reverse saturation current
Q1
I1
From the circuit in Figure 11, we see that:
VL = VT1 ln
IS1
– VT2 ln
1
2
VOUT = (0.5V) LOG
I2
IS 2
 I
I 
VL = VT1 ln 1 – ln 2 
I
I
S
 S
I1
VL = VT ln
and since
I2
ln x = 2.3 log10 x
I1
I2
where n = 2.3
I1
I2
R2
VL
I2
R1
(3)
If the transistors are matched and isothermal and
VTI = VT2, then (3) becomes:
VL = n VT log
A2
VBE
A1
Substituting (1) into (2) yields:
I1
VOUT
+
VBE
(2)
I2
Q2
–
+
I1
VL = VBE1 – VBE 2
–
FIGURE 11. Simplified Model of a Log Amplifier.
(4)
NOTE: R1 is a metal resistor used to compensate for
gain over temperature.
(5)
(6)
(7)
(8)
DEFINITION OF TERMS
3.5
TRANSFER FUNCTION
3.0
The ideal transfer function is:
2.5
A
0p
10
I 2 = nA
1
I 2 = 0nA
1
I =
2.0
(5)
1.5
Figure 12 shows the graphical representation of the transfer
over valid operating range for the LOG112 and LOG2112.
0.5
ACCURACY
10
100
pA
1nA
0.0
–0.5
–1.0
–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.
2
1.0
VOUT (V)
VLOGOUT = 0.5V • logI1/I2
–2.0
–2.5
–3.0
10n
A
0n
10
I 2 = µA
1
I 2 = 0µA
1
I 2 = 00µA
1
=
I 2 mA
1
I =
A
100
nA µA
1
1 0µ
A
100
µA
1m
A
A
10m
I1
VLOGOUT = (0.5V) • log (I1/I2)
2
–3.5
FIGURE 12. Transfer Function with Varying I 2 and I1.
LOG112, 2112
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SBOS246B
TOTAL ERROR
MEASURING AVALANCHE PHOTODIODE CURRENT
The total error is the deviation (expressed in mV) of the actual
output from the ideal output of VLOGOUT = 0.5V • log (I1/I2).
The wide dynamic range of the LOG112 and LOG2112 is
useful for measuring avalanche photodiode current (APD), as
shown in Figure 13.
Thus,
VLOGOUT(ACTUAL) = VLOGOUT(IDEAL) ± Total Error.
(6)
LOG CONFORMITY
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.
ERRORS RTO AND RTI
As with any transfer function, errors generated by the function itself may be Referred-to-Output (RTO) or Referred-toInput (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.
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.
ISHUNT
+15V to +60V
500Ω
Irx = 1µA to 1mA
Receiver
5kΩ
5kΩ
10Gbits/sec
+5V
APD
INA168
SOT23-5
I-to-V
Converter
IOUT = 0.1 • ISHUNT
1
2
IOUT
CC
10kΩ
16.7kΩ
+5V
6
1
4
5
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 13. High-Side Shunt for Avalanche Photodiode (APD) Measures 3 Decades of APD Current.
LOG112, 2112
SBOS246B
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11
INDIVIDUAL ERROR COMPONENTS
Example: what is the error when
The ideal transfer function with current input is:
VLOGOUT = (0.5V) • log
I1
I2
(8)
The actual transfer function with the major components of
error is:
VLOGOUT = (0.5V) (1 ± ∆K ) log
I1 – IB1
± Nm ± VOSO (9)
I2 – IB2
(11)
VLOGOUT = (0.5 ± 0.001) log
% error =
∆K = gain error (0.10%, typ), as specified in
specification table.
N = log conformity error (0.01%, 0.13%, typ)
0.01% for m = 5, 0.13% for m = 7.5
10 −6 − 5 • 10 −12
10 −7 − 5 • 10 −12
= 0.505V
± (2)(0.0001)5 ± 3.0mV
Since the ideal output is 0.5V, the error as a percent of
reading is
(12)
The individual component of error is:
IB1 = bias current of A1 (5pA, typ)
IB2 = bias current of A2 (5pA, typ)
(10)
I1 = 1µA and I2 = 100nA
0.505V
• 100% = 1.01%
0.5
For the case of voltage inputs, the actual transfer function is
VLOGOUT
VOSO = output offset voltage (3mV, typ)
m = number of decades over which N is specified:
Where
EOS1
(13)
V1
– IB1 ±
R1
R1
= (0.5V) (1 ± ∆K ) log
± Nm ± VOSO
EOS 2
V2
– IB 2 ±
R2
R2
EOS1
E
and OS2
R1
R2
(offset error) are considered to be
zero for large values of resistance from external input current
sources.
12
LOG112, 2112
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SBOS246B
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
SBOS246B
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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
SBOS246B
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