LOG102AIDRG4 [TI]

LOG OR ANTILOG AMPLIFIER, 1.4MHz BAND WIDTH, PDSO14, GREEN, PLASTIC, MS-012AB, SOIC-14;
LOG102AIDRG4
型号: LOG102AIDRG4
厂家: TEXAS INSTRUMENTS    TEXAS INSTRUMENTS
描述:

LOG OR ANTILOG AMPLIFIER, 1.4MHz BAND WIDTH, PDSO14, GREEN, PLASTIC, MS-012AB, SOIC-14

放大器 光电二极管
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LOG102  
L
O
G
1
0
2
SBOS211B – DECEMBER 2001– REVISED APRIL 2005  
Precision  
LOGARITHMIC AND LOG RATIO AMPLIFIER  
FEATURES  
DESCRIPTION  
The LOG102 is a versatile integrated circuit that computes  
the logarithm or log ratio of an input current relative to a  
reference current.  
EASY-TO-USE COMPLETE LOG RATIO FUNCTION  
OUTPUT AMPLIFIERS FOR SCALING AND  
SIGNAL LOSS INDICATION  
The LOG102 is tested over a wide dynamic range of input  
signals. In log ratio applications, a signal current can be  
generated by a photodiode, and a reference current from a  
resistor in series with a precision external voltage reference.  
HIGH ACCURACY: 0.15% FSO Total Error Over  
6 Decades  
WIDE INPUT DYNAMIC RANGE:  
6 Decades, 1nA to 1mA  
In the block diagram shown below, A3 and A4 are identical,  
uncommitted op amps that can be used for a variety of  
functions, such as filtering, offsetting, adding gain or as a  
comparator to detect loss of signal.  
LOW QUIESCENT CURRENT: 1.25mA  
SO-14 PACKAGE  
The output signal at VLOG OUT is trimmed to 1V per decade of  
input current. It can be scaled with an output amplifier, either  
A3 or A4.  
APPLICATIONS  
ONET, OPTICAL POWER METERS  
Low dc offset voltage and temperature drift allow accurate  
measurement of low-level signals over a wide environmental  
temperature range. The LOG102 is specified over the tem-  
perature range, 0°C to +70°C, with operation over –40°C to  
+85°C.  
LOG, LOG RATIO COMPUTATION:  
Communication, Analytical, Medical, Industrial,  
Test, General Instrumentation  
PHOTODIODE SIGNAL COMPRESSION AMP  
NOTE: U.S. Patent Pending.  
ANALOG SIGNAL COMPRESSION IN FRONT  
OF A/D CONVERTER  
ABSORBANCE MEASUREMENT  
OPTICAL DENSITY MEASUREMENT  
R1  
R2  
VLOG OUT = LOG (I1/I2)  
VOUT3 = G LOG (I1/I2), G = 1 +R2/R1  
CC  
I2  
V+  
6
VLOG OUT  
+IN3  
3
IN3  
5
4
14  
I1  
1
Q1  
Q2  
7
A3  
VOUT3  
+IN4  
A2  
A1  
12  
8
A4  
VOUT4  
A4 can be used  
as comparator for  
signal loss detect.  
9
10  
11  
IN4  
GND  
V–  
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.  
All trademarks are the property of their respective owners.  
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.  
Copyright © 2001-2005, Texas Instruments Incorporated  
www.ti.com  
ABSOLUTE MAXIMUM RATINGS(1)  
PIN DESCRIPTION  
Supply Voltage, V+ to V.................................................................... 36V  
Top View  
SO  
Input Voltage ....................................................... V(0.5) to V+ (+0.5V)  
Input Current................................................................................... ±10mA  
Output Short-Circuit(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  
I1  
NC  
1
2
3
4
5
6
7
14 I2  
13 NC  
12 +IN4  
11 IN4  
10 GND  
+IN3  
LOG102  
IN3  
NOTES: (1) Stresses above these ratings may cause permanent damage.  
Exposure to absolute maximum conditions for extended periods may degrade  
device reliability. (2) Short circuit to ground, one amplifier per package.  
Vlog out  
V+  
9
8
V–  
VOUT3  
VOUT4  
ELECTROSTATIC  
DISCHARGE SENSITIVITY  
NC = No Internal Connection  
This integrated circuit can be damaged by ESD. Texas Instru-  
ments 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 its  
published specifications.  
PACKAGE/ORDERING INFORMATION(1)  
PACKAGE  
DESIGNATOR  
PACKAGE  
MARKING  
PRODUCT  
PACKAGE-LEAD  
LOG102AID  
SO-14  
D
LOG102A  
NOTES: (1) For the most current package and ordering information, see the Package Option Addendum at the end of this document, or see the TI website at  
www.ti.com.  
ELECTRICAL CHARACTERISTICS  
Boldface limits apply over the specified temperature range, TA = 0°C to +70°C.  
At TA = +25°C, VS = ±5V, RL = 10k, unless otherwise noted.  
LOG102AID  
PARAMETER  
CONDITION  
MIN  
TYP  
MAX  
UNITS  
CORE LOG FUNCTION  
I
IN /VLOG OUT Equation  
VO = log (I1/I2)  
LOG CONFORMITY ERROR(1)  
Initial  
1nA to 100µA (5 decades)  
1nA to 1mA (6 decades)  
1nA to 100µA (5 decades)  
1nA to 1mA (6 decades)  
0.04  
0.15  
0.0002  
0.002  
±0.3  
%
%
%/°C  
%/°C  
over Temperature  
GAIN(2)  
Initial Value  
Gain Error  
vs Temperature  
1nA to 100µA (5 decades)  
1nA to 100µA (5 decades)  
TMIN to TMAX  
1
V/decade  
%
%/°C  
0.15  
0.025  
±1  
0.05  
INPUT, A1 and A2  
Offset Voltage  
±0.3  
±2  
5
±5  
±1.5  
mV  
µV/°C  
µV/V  
pA  
vs Temperature  
vs Power Supply (PSRR)  
Input Bias Current  
vs Temperature  
Voltage Noise  
TMIN to TMAX  
VS = ±4.5V to ±18V  
50  
TMIN to TMAX  
f = 10Hz to 10kHz  
f = 1kHz  
Doubles Every 10°C  
3
30  
4
µVrms  
nV/Hz  
fA/Hz  
V
V
dB  
Current Noise  
Common-Mode Voltage Range (Positive)  
f = 1kHz  
(V+) 2  
(V) + 2  
90  
(V+) 1.5  
(V) + 1.2  
105  
(Negative)  
CMRR  
OUTPUT, A2 (VLOGOUT  
)
Output Offset, VOSO, Initial  
vs Temperature  
Full-Scale Output (FSO)  
Short-Circuit Current  
±3  
±55  
25  
(V+) 1.5  
mV  
µV/°C  
V
TMIN to TMAX  
VS = ±5V Supplies  
(V) + 1.2  
±18  
mA  
LOG102  
2
www.ti.com  
SBOS211B  
ELECTRICAL CHARACTERISTICS (Cont.)  
Boldface limits apply over the specified temperature range, TA = 0°C to +70°C.  
At TA = +25°C, VS = ±5V, RL = 10k, unless otherwise noted.  
LOG102AID  
PARAMETER  
CONDITION  
MIN  
TYP  
MAX  
UNITS  
TOTAL ERROR(3)(4)  
Initial  
I1 or I2 remains fixed while other varies  
min to max  
I1 or I2 = 1mA  
±55  
±30  
±25  
±20  
±25  
±30  
±37  
mV  
mV  
mV  
mV  
mV  
I1 or I2 = 100µA  
I1 or I2 = 10µA  
I1 or I2 = 1µA  
I1 or I2 = 100nA  
I1 or I2 = 10nA  
I1 or I2 = 1nA  
mV  
mV  
vs Temperature  
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  
±0.4  
±0.07  
±0.07  
±0.07  
±0.07  
±0.07  
±0.4  
±0.15  
±0.15  
±0.25  
±0.2  
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  
vs Supply  
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  
±0.2  
±0.15  
±0.25  
FREQUENCY RESPONSE, core log(5)  
BW, 3dB  
I2 = 10nA  
I2 = 1µA  
I2 = 10µA  
I2 = 1mA  
CC = 4500pF  
CC = 150pF  
CC = 150pF  
CC = 50pF  
0.1  
38  
40  
45  
kHz  
kHz  
kHz  
kHz  
Step Response  
Increasing  
I2 = 1µA to 1mA (3 decade)  
I2 = 100nA to 1µA (1 decade)  
I2 = 10nA to 100nA (1 decade)  
Decreasing  
CC = 150pF  
CC = 150pF  
CC = 150pF  
11  
7
110  
µs  
µs  
µs  
I2 = 1mA to 1µA (3 decade)  
I2 = 1µA to 100nA (1 decade)  
I2 = 100nA to 10nA (1 decade)  
CC = 150pF  
CC = 150pF  
CC = 150pF  
45  
20  
550  
µs  
µs  
µs  
OP AMPS, A3 AND A4  
Input Offset Voltage  
vs Temperature  
±175  
±2  
10  
10  
±0.5  
±750  
µV  
µV/°C  
µV/V  
nA  
nA  
V
TMIN to TMAX  
VS = ±4.5V to ±18V  
vs Power Supply  
50  
Input Bias Current(5)  
Input Offset Current  
Input Voltage Range  
Common-Mode Rejection  
Input Noise, f = 0.1Hz to 10Hz  
f = 1kHz  
(V)  
(V+) 1.5  
86  
1
dB  
µVPP  
nV/Hz  
dB  
MHz  
V/µs  
µs  
28  
88  
1.4  
0.5  
16  
Open Loop Voltage Gain  
Gain-Bandwidth Product  
Slew Rate  
Settling Time, 0.01%  
Rated Output  
G = 1, 2.5V step  
G = 1, 2.5V Step, CL =100pF  
VS = 5V, RL = 10kΩ  
(V) + 1.5  
±4.5  
(V+) 0.9  
V
mA  
Short-Circuit Current  
ISC/+ISC  
36/+60  
POWER SUPPLY  
Operating Range  
Quiescent Current  
VS  
IO = 0  
±18  
2
V
mA  
1.25  
TEMPERATURE RANGE  
Specified Range, TMIN to TMAX  
Operating Range  
0
40  
40  
70  
+85  
+125  
°C  
°C  
°C  
Storage Range  
Thermal Resistance, θJA  
SO-14  
100  
°C/W  
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  
(2) Output core log function is trimmed to 1V output per decade change of input current. (3) Worst-case Total Error for any ratio of I1/I2, is the largest of the two  
errors, when I1 and I2 are considered separately. (4) Total I1 + I2 should be kept below 1.1mA on ±5V supply. (5) Bandwidth (3dB) and transient response are a  
function of both the compensation capacitor and the level of input current. (6) Positive conventional current flows into input terminals.  
LOG102  
SBOS211B  
3
www.ti.com  
TYPICAL CHARACTERISTICS  
At TA = +25°C, VS = ±5V, RL = 10k, unless otherwise noted.  
ONE CYCLE OF NORMALIZED TRANSFER FUNCTION  
NORMALIZED TRANSFER FUNCTION  
I1  
1
0.9  
0.8  
0.7  
0.6  
0.5  
0.4  
0.3  
0.2  
3
2
VOUT = 1V Log  
I2  
1
0
1  
2  
3  
0.1  
0
0.001  
0.01  
0.1  
1
10  
100  
1000  
1
2
3
4
6
8
10  
I1  
I2  
I1  
I2  
Current Ratio,  
Current Ratio,  
TOTAL ERROR vs INPUT CURRENT  
GAIN ERROR vs TEMPERATURE  
0.35  
60  
50  
40  
30  
20  
10  
0
0.30  
0.25  
0.20  
0.15  
0.10  
0.05  
0.00  
0.05  
0.10  
70°C  
25°C  
0°C  
1nA  
10nA  
100nA  
1µA  
10µA  
100µA  
1mA  
60  
40  
20  
0
20  
40  
60  
80  
Input Current  
(I1 or I2)  
Temperature (°C)  
3dB FREQUENCY RESPONSE  
MINIMUM VALUE OF COMPENSATION CAPACITOR  
1M  
10000  
1000  
100  
10  
Select CC for I1 min  
and I2 max  
10µA  
1µA  
100µA  
100µA  
1mA  
100k  
I1 = 1nA  
I1 = 10nA  
I
= 1mA  
1
10k  
1k  
100µA  
100µA  
I1 = 100nA  
1 = 1µA  
1µA  
1nA  
I
10nA  
1mA  
to 10µA  
10nA  
I
1 = 10µA  
100  
10  
100nA  
10nA  
I1 = 1nA  
I1 = 1mA  
I1 = 100µA  
I
= 1nA  
1
1
Values below 2pF  
may be ignored.  
0.1  
1
1nA  
10nA  
100nA  
1µA  
10µA  
100µA  
1mA  
1nA  
10nA 100nA 1µA  
10µA 100µA 1mA  
10mA  
I2  
I2  
LOG102  
4
www.ti.com  
SBOS211B  
TYPICAL CHARACTERISTICS (Cont.)  
At TA = +25°C, VS = ±5V, RL = 10k, unless otherwise noted.  
LOG CONFORMITY vs VLOGOUT  
5
LOG CONFORMITY vs TEMPERATURE  
300  
200  
100  
0
4
70°C  
3
2
1
6 Decades (1nA to 1mA)  
0
25°C  
1  
5 Decades (1nA to 100µA)  
2  
0°C  
3  
3  
2  
1  
0
1
2
3
0
10  
20  
30  
40  
50  
60  
70  
VLOGOUT (V)  
Temperature (°C)  
TOTAL ERROR vs TEMPERATURE  
60  
50  
40  
30  
20  
10  
0
1nA  
1mA  
10nA to 100µA  
50 60 70  
0
10  
20  
30  
40  
Temperature (°C)  
LOG102  
SBOS211B  
5
www.ti.com  
R2  
10kΩ  
APPLICATION INFORMATION  
V–  
V+  
The LOG102 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.  
With two uncommitted on-chip operational amplifiers, the  
LOG102 provides design flexibility and simplicity.  
R1  
1MΩ  
6
1
5
VOUT  
I1  
LOG102  
Figure 1 shows the basic connections required for operation  
of the LOG102 with a gain factor. 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 capaci-  
tor, as shown in Figure 1. Connecting the capacitors as close  
to the LOG102 as possible will contribute to noise reduction  
as well.  
14  
10  
R1'  
> 1MΩ  
9
I2  
CC  
V–  
R2'  
10kΩ  
V+  
FIGURE 2. Bias Current Nulling.  
V+  
SETTING THE REFERENCE CURRENT  
10µF  
When the LOG102 is used to compute logarithms, either I1 or  
I2 can be held constant and becomes the reference current to  
which the other is compared.  
1000pF  
VOUT = G VLOGOUT  
6
VLOGOUT is expressed as:  
1
12  
7
VOUT  
VLOGOUT = (1V) log (I1/I2)  
(1)  
10  
4
I
REF can be derived from an external current source (such as  
LOG102  
R1  
5
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:  
14  
3
VLOGOUT  
I1  
I2  
R2  
9
11  
CC  
8
RREF = 2.5V/10nA = 250MΩ  
Amplifier A4 not being used.  
1000pF  
10µF  
V–  
Unused amplifiers should  
have positive inputs grounded  
and negative inputs tied to  
their respective outputs.  
IREF  
2N2905  
RREF  
3.6k  
2N2905  
+15V  
15V  
FIGURE 1. Basic Connections with Output Gain Factor of the  
LOG102.  
6V  
IN834  
6V  
IREF  
=
RREF  
INPUT CURRENT RANGE  
FIGURE 3. Temperature Compensated Current Source.  
To maintain specified accuracy, the input current range of the  
LOG102 should be limited from 1nA to 1mA. Input currents  
outside of this range may compromise LOG102 performance.  
Input currents larger than 1mA result in increased nonlinearity.  
An absolute maximum input current rating of 10mA is included  
to prevent excessive power dissipation that may damage the  
logging transistor.  
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 amplifiers  
input offset voltage. The input offset voltage of amplifier A1  
has a maximum value of 1.5mV, making VREF a suggested  
value of 100mV.  
On ±5V supplies the total input current (I1 + I2) is limited to  
1.1mA. Due to compliance issues internal to the LOG102, to  
accommodate larger total input currents, supplies should be  
increased.  
VREF = 100mV  
R1 R3  
VOS  
+
14  
+5V  
Currents smaller than 1nA will result in increased errors due  
the input bias currents of op amps A1 and A2 (typically 5pA).  
The input bias currents may be compensated for, as shown in  
Figure 2. The input stages of the amplifiers have FET inputs,  
with input bias current doubling every 10°C, which makes the  
nulling technique shown practical only where the temperature  
is fairly stable.  
A1  
IREF  
R2  
R3 >> R2  
FIGURE 4. T Network for Reference Current.  
LOG102  
6
www.ti.com  
SBOS211B  
Figure 5 shows a low-level current source using a series  
resistor. The low offset op-amp reduces the effect of the  
LOG102s input offset voltage.  
NEGATIVE INPUT CURRENTS  
The LOG102 will function only with positive input currents  
(conventional current flow into pins 1 and 14). In situations  
where negative input currents are needed, the circuits in  
Figures 6, 7, 8, and 9, may be used.  
V+  
V+  
I1 = 2.5nA to 1mA  
6
2.5V  
1
5
REF3025  
VLOGOUT  
1Gto 2.5kΩ  
I2 = 2.5nA  
LOG102  
100kΩ  
100Ω  
QA  
QB  
IIN  
1MΩ  
14  
+2.5mV  
National  
LM394  
5
9
10  
+2.5V  
CC  
V–  
D1  
D2  
OPA335 Chopper Om Amp  
2.5V  
OPA703  
IOUT  
FIGURE 5. Current Source with Offset Compensation.  
FREQUENCY RESPONSE  
The 3dB frequency response of the LOG102 is a function of  
the magnitude of the input current levels and of the value of  
the frequency compensation capacitor. See Typical Charac-  
teristic Curves for details.  
FIGURE 6. Current Inverter/Current Source.  
The frequency response curves are shown for constant DC  
I1 and I2 with a small signal AC current on one of them.  
+5V  
1
2
OPA2335  
TLV271 or  
The transient response of the LOG102 is different for in-  
creasing 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 LOG102.  
+3.3V  
1/2 OPA2335  
1.5kΩ  
1.5kΩ  
+5V  
BSH203  
1/2 OPA2335  
Back Bias  
+3.3V  
10nA to 1mA  
FREQUENCY COMPENSATION  
LOG102  
10nA to 1mA  
Pin 1 or Pin 14  
Frequency compensation for the LOG102 is obtained by  
connecting a capacitor between pins 5 and 14. The size of  
the capacitor is a function of the input currents, as shown in  
the Typical Characteristic Curves (Minimum Value of Com-  
pensation 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 LOG102 more stable, but will  
reduce the frequency response.  
Photodiode  
FIGURE 7. Precision Current Inverter/Current Source.  
VOLTAGE INPUTS  
In an application, highest overall bandwidth can be achieved  
by detecting the signal level at VOUT, then switching in  
appropriate values of compensation capacitors.  
The LOG102 gives the best performance 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 (14) applies to this configura-  
tion.  
As seen on front page diagram, the voltage output of VLOGOUT  
can be scaled by increasing or decreasing the resistor ratio  
connected to pins 4 and 7. The gain, G, can be set according  
to the following equation:  
G = 1 + R2/R1  
(2)  
LOG102  
SBOS211B  
7
www.ti.com  
1.5kΩ  
100kΩ  
100kΩ  
+5V  
10nA to 1mA  
Back Bias  
+3.3V  
+3.3V  
+5V  
1.5kΩ  
1.5kΩ  
1/2 OPA2335  
1/2 OPA2335  
Photodiode  
100kΩ  
100kΩ  
10nA to 1mA  
LOG102  
Pin 1 or Pin 14  
FIGURE 8. Precision Current Inverter/Current Source.  
DATA COMPRESSION  
V+  
6
In many applications the compressive effects of the logarith-  
mic transfer function are useful. For example, a LOG102  
preceding a 12-bit Analog-to-Digital (A/D) converter can  
produce the dynamic range equivalent to a 20-bit converter.  
(VRB  
)
1
5
VOUT  
I1  
Signal  
LOG102  
(VRB  
)
14  
I2  
REF  
V+  
9
10  
CC  
6
I1  
1
5
VOUT  
D1  
Sample  
λ1´  
VRB  
V–  
LOG102  
λ1  
NOTES: (1) VRB, must be 2.5V more positive than V. Example, for  
RB = 9.5V, V=12V. (2) Typically, 3.3V bias is used with ±12V supplies.  
I2  
V
14  
10  
λ1  
Light  
Source  
9
D2  
FIGURE 9. Reverse Biased Photodiode Using Pin 10 on  
LOG102.  
CC  
V–  
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 10.  
FIGURE 10. Absorbance Measurement.  
Absorbance of the sample is A = logλ1´/ λ1  
(3)  
If D1 and D2 are matched A (1V) logI1/I2  
(4)  
LOG102  
8
www.ti.com  
SBOS211B  
INSIDE THE LOG102  
also  
Using the base-emitter voltage relationship of matched  
bipolar transistors, the LOG102 establishes a logarith-  
mic function of input current ratios. Beginning with the  
base-emitter voltage defined as  
R1 + R2  
VOUT = VL  
= log  
(9)  
R1  
I1  
IC  
IS  
kT  
q
(10)  
VBE = VT ln  
where : VT =  
(1)  
I2  
k = Boltzmanns constant = 1.381 1023  
T = Absolute temperature in degrees Kelvin  
q = Electron charge = 1.602 1019 Coulombs  
IC = Collector current  
R1 + R2  
I1  
I2  
or  
VOUT  
=
n VT log  
(11)  
R1  
IS = Reverse saturation current  
I2  
Q1  
Q2  
I1  
From the circuit in Figure 11, we see that  
VOUT  
+
+
A2  
VBE VBE  
1
2
I1  
VL = VBE VBE  
1
2
(2)  
(3)  
A1  
I1  
I2  
R2  
VL  
R1  
VOUT = (1V) LOG  
Substituting (1) into (2) yields  
I2  
I2  
I1  
VL = VT1 ln  
VT2 ln  
IS1  
IS2  
If the transistors are matched and isothermal and  
VTI = VT2, then (3) becomes:  
FIGURE 11. Simplified Model of Log Amplifier.  
I1  
VL = VT1 ln ln  
IS  
I2  
(4)  
(5)  
IS  
It should be noted that the temperature dependance  
associated with VT = kT/q is internally compensated on  
the LOG102 by making R1 a temperature sensitive resis-  
tor with the required positive temperature coefficient.  
I1  
VL = VT ln  
and since  
I2  
ln x = 2.3log10  
I1  
x
(6)  
(7)  
VL = n VT log  
I2  
where n = 2.3  
(8)  
USING A LARGER REFERENCE VOLTAGE  
REDUCES OFFSET ERRORS  
IREF such that it is as large or larger than the expected  
maximum photodiode current is accomplished using this  
requirement. The LOG102 configured with the reference  
current connecting I1 and the photodiode current connecting  
to I2 is shown in Figure 12. A3 is configured as a level shifter  
with inverting gain and is used to scale the photodiode  
current directly into the A/D input voltage range.  
Using a larger reference voltage to create the reference  
current minimizes errors due to the LOG102s input offset  
voltage. Maintaining an increasing output voltage as a func-  
tion of increasing photodiode current is also important in  
many optical sensing applications. All zeros from the A/D  
converter output represent zero or low scale photodiode  
current. Inputting the reference current into I1, and designing  
The wide dynamic range of the LOG102 is useful for measuring  
avalanche photodiode current (APD) (see Figure 13).  
LOG102  
SBOS211B  
9
www.ti.com  
VREF  
R1  
R2  
R3  
IREF  
IREF  
=
VOUT = VREF  
LOG  
( )  
R2  
R3  
IPHOTO  
CC  
VLOGOUT  
5
3
VMIN to VMAX  
IREF  
R1  
I1  
Q1  
Q2  
7
1
A3  
A/D  
A2  
VREF  
A1  
R2  
R3  
4
IPHOTO  
I2  
14  
LOG102  
I
MIN to IMAX  
10  
FIGURE 12. Technique for Using Full-Scale Reference Current such that VOUT Increases with Increasing Photodiode Current.  
ISHUNT  
+15V to +60V  
500  
Irx = 1µA to 1mA  
Receiver  
5kΩ  
5kΩ  
10gbits/sec  
+5V  
APD  
I to V  
Converter  
INA168  
SOT23-5  
IOUT = 0.1 ISHUNT  
1
2
IOUT  
CC  
1.2kΩ  
1kΩ  
+5V  
6
5
4
1
Q1  
Q2  
7
3
A3  
VOUT = 2.5V to 0V  
A2  
A1  
100µA  
25kΩ  
14  
REF3025(1)  
2.5V  
LOG102  
SO-14  
9
10  
5V  
NOTE: (1) Available Q2 2002.  
FIGURE 13. High Side Shunt for Avalanche Photodiode (APD) Measures 3 Decades of APD Current.  
LOG102  
10  
www.ti.com  
SBOS211B  
ERRORS RTO AND RTI  
DEFINITION OF TERMS  
TRANSFER FUNCTION  
As with any transfer function, errors generated by the func-  
tion itself may be Referred-to-Output (RTO) or Referred-to-  
Input (RTI). In this respect, log amps have a unique property:  
The ideal transfer function is:  
Given some error voltage at the log amps output, that error  
corresponds to a constant percent of the input regardless of  
the actual input level.  
VOUT = 1V logI1/I2  
(5)  
Figure 14 shows the graphical representation of the transfer  
over valid operating range for the LOG102.  
LOG CONFORMITY  
For the LOG102, 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 specifica-  
tion. 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.  
3
2
1
10nA  
100nA  
1µA  
10µA 100µA  
1mA I1  
0
Dashed Line = Greater  
Supply Voltage Requirement  
I1  
VOUT = (1V) LOG  
I2  
3  
Log conformity is defined as the peak deviation from the best  
fit straight line of the VOUT 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:  
FIGURE 14. Transfer Function with Varying I2 and I1.  
ACCURACY  
(6)  
VOUT (NONLIN) = 1V/dec 2Nm V  
Accuracy considerations for a log ratio amplifier are some-  
what 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.  
where N is the log conformity error, in percent.  
INDIVIDUAL ERROR COMPONENTS  
The ideal transfer function with current input is:  
I1  
(7)  
VOUT = 1V log  
(
)
I2  
TOTAL ERROR  
The actual transfer function with the major components of  
error is:  
The total error is the deviation (expressed in mV) of the  
actual output from the ideal output of VOUT = 1V log(I1/I2).  
I1 IB1  
Thus,  
(8)  
VOUT = 1V 1± ∆K log  
± 2Nm ± VOS OUT  
(
)
(
)
I2 IB2  
The individual component of error is:  
(5)  
VOUT (ACTUAL) = VOUT (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; this case is shown in Table I. Tem-  
perature can affect total error.  
K = gain accuracy (0.3%, typ), as specified in  
specification table.  
IB1 = bias current of A1 (5pA, typ)  
IB2 = bias current of A2 (5pA, typ)  
N = log conformity error (0.04%, 0.15%, typ)  
0.04% for n = 5, 0.15% for n = 6  
I1 (maximum error)(1)  
I2  
(maximum  
VOS OUT = output offset voltage (1mV, typ)  
n = number of decades over which N is specified:  
Example: what is the error when  
10nA  
(30mV)  
100nA  
(25mV)  
1µA  
(20mV)  
error)(1)  
100nA  
(25mV)  
30mV  
30mV  
30mV  
25mV  
25mV  
25mV  
25mV  
20mV  
25mV  
1µA  
(20mV)  
I1 = 1µA and I2 = 100nA  
(9)  
10µA  
(25mV)  
NOTE: (1) Maximum errors are in parenthesis.  
TABLE I. I1/I2 and Maximum Errors.  
LOG102  
SBOS211B  
11  
www.ti.com  
For the case of voltage inputs, the actual transfer function is  
(14)  
106  
107  
(10)  
1.003 log  
+ 0.004 + 0.003  
EOS  
V1  
R1  
V2  
1
IB1  
±
R1  
(11)  
(12)  
= 1.003 (1) + 0.004 + 0.0003  
= 1.0073V  
VOUT = 1V 1± ∆K log  
± 2Nn ± VOS OUT  
(
)
(
)
EOS  
R2  
2
IB2  
±
R2  
Since the ideal output is 1.000V, the error as a percent of  
reading is  
(15)  
E
EOS2  
R2  
OS1 and  
0.0073  
(13)  
Where  
are considered to be zero for large  
R1  
% error =  
100% = 0.73%  
1
values of resistance from external input current sources.  
LOG102  
12  
www.ti.com  
SBOS211B  
PACKAGE OPTION ADDENDUM  
www.ti.com  
16-Feb-2009  
PACKAGING INFORMATION  
Orderable Device  
LOG102AID  
Status (1)  
ACTIVE  
ACTIVE  
ACTIVE  
ACTIVE  
Package Package  
Pins Package Eco Plan (2) Lead/Ball Finish MSL Peak Temp (3)  
Qty  
Type  
Drawing  
SOIC  
D
14  
14  
14  
14  
50 Green (RoHS & CU NIPDAU Level-3-260C-168 HR  
no Sb/Br)  
LOG102AIDG4  
LOG102AIDR  
SOIC  
SOIC  
SOIC  
D
D
D
50 Green (RoHS & CU NIPDAU Level-3-260C-168 HR  
no Sb/Br)  
2500 Green (RoHS & CU NIPDAU Level-3-260C-168 HR  
no Sb/Br)  
LOG102AIDRG4  
2500 Green (RoHS & CU NIPDAU Level-3-260C-168 HR  
no Sb/Br)  
(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.  
(2)  
Eco Plan - The planned eco-friendly classification: Pb-Free (RoHS), Pb-Free (RoHS Exempt), or Green (RoHS & no Sb/Br) - please check  
http://www.ti.com/productcontent for the latest availability information and additional product content details.  
TBD: The Pb-Free/Green conversion plan has not been defined.  
Pb-Free (RoHS): TI's terms "Lead-Free" or "Pb-Free" mean semiconductor products that are compatible with the current RoHS requirements  
for all 6 substances, including the requirement that lead not exceed 0.1% by weight in homogeneous materials. Where designed to be soldered  
at high temperatures, TI Pb-Free products are suitable for use in specified lead-free processes.  
Pb-Free (RoHS Exempt): This component has a RoHS exemption for either 1) lead-based flip-chip solder bumps used between the die and  
package, or 2) lead-based die adhesive used between the die and leadframe. The component is otherwise considered Pb-Free (RoHS  
compatible) as defined above.  
Green (RoHS & no Sb/Br): TI defines "Green" to mean Pb-Free (RoHS compatible), and free of Bromine (Br) and Antimony (Sb) based flame  
retardants (Br or Sb do not exceed 0.1% by weight in homogeneous material)  
(3)  
MSL, Peak Temp. -- The Moisture Sensitivity Level rating according to the JEDEC industry standard classifications, and peak solder  
temperature.  
Important Information and Disclaimer:The information provided on this page represents TI's knowledge and belief as of the date that it is  
provided. TI bases its knowledge and belief on information provided by third parties, and makes no representation or warranty as to the  
accuracy of such information. Efforts are underway to better integrate information from third parties. TI has taken and continues to take  
reasonable steps to provide representative and accurate information but may not have conducted destructive testing or chemical analysis on  
incoming materials and chemicals. TI and TI suppliers consider certain information to be proprietary, and thus CAS numbers and other limited  
information may not be available for release.  
In no event shall TI's liability arising out of such information exceed the total purchase price of the TI part(s) at issue in this document sold by TI  
to Customer on an annual basis.  
Addendum-Page 1  
PACKAGE MATERIALS INFORMATION  
www.ti.com  
11-Mar-2008  
TAPE AND REEL INFORMATION  
*All dimensions are nominal  
Device  
Package Package Pins  
Type Drawing  
SPQ  
Reel  
Reel  
A0 (mm)  
B0 (mm)  
K0 (mm)  
P1  
W
Pin1  
Diameter Width  
(mm) W1 (mm)  
(mm) (mm) Quadrant  
LOG102AIDR  
SOIC  
D
14  
2500  
330.0  
16.4  
6.5  
9.0  
2.1  
8.0  
16.0  
Q1  
Pack Materials-Page 1  
PACKAGE MATERIALS INFORMATION  
www.ti.com  
11-Mar-2008  
*All dimensions are nominal  
Device  
Package Type Package Drawing Pins  
SOIC 14  
SPQ  
Length (mm) Width (mm) Height (mm)  
346.0 346.0 33.0  
LOG102AIDR  
D
2500  
Pack Materials-Page 2  
IMPORTANT NOTICE  
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and other changes to its products and services at any time and to discontinue any product or service without notice. Customers should  
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TI warrants performance of its hardware products to the specifications applicable at the time of sale in accordance with TI’s standard  
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