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19-3070; Rev 1; 6/04
Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range
General Description
The MAX4207 logarithmic amplifier computes the log ratio of an input current relative to a reference current (externally or internally generated) and provides a corresponding voltage output with a default -0.25V/decade scale factor. The device operates from dual 2.7V to 5.5V supplies and is capable of measuring five decades of input current across a 10nA to 1mA range. The MAX4207's uncommitted op amp can be used for a variety of functions, including filtering noise, adding offset, and adding additional gain. A 0.5V reference is also included to generate an optional precision current reference using an external resistor, which adjusts the log intercept of the MAX4207. The output-offset voltage and the adjustable scale factor are also set using external resistors. The MAX4207 is available in a space-saving 16-pin thin QFN package (4mm x 4mm x 0.8mm), and is specified for operation over the -40C to +85C extended temperature range.
KIT ATION EVALU ABLE AVAIL
Features
2.7V to 5.5V Dual-Supply Operation 5 Decades of Dynamic Range (10nA to 1mA) Monotonic Over a 1nA to 1mA Range -0.25V/Decade Internally Trimmed Output Scale Factor Adjustable Output Scale Factor Adjustable Output Offset Voltage Internal 10nA to 10A Reference Current Source Input Amplifiers Summing Nodes at Ground Small 16-Pin Thin QFN Package (4mm x 4mm x 0.8mm) -40C to +85C Operating Temperature Range Evaluation Kit Available (Order MAX4206EVKIT)
MAX4207
Applications
Photodiode Current Monitoring Portable Instrumentation Medical Instrumentation Analog Signal Processing
PART MAX4207ETE
Ordering Information
TEMP RANGE -40C to +85C PIN-PACKAGE 16 Thin QFN-EP*
*EP = Exposed paddle.
Typical Operating Circuit
VCC
Pin Configuration
REFIOUT TOP VIEW (LEADS ON BOTTOM)
IIN
0.1F
VCC LOGV2 LOGIIN
VOUT
LOGIIN
CMVIN
REFIIN
CCOMP REFIOUT RCOMP CCOMP REFIIN SCALE
R2
16
15
14
13
R1
N.C. REFVOUT GND VEE
1 2 3 4
12 11
CMVOUT REFISET VCC N.C.
RCOMP
MAX4207
LOGV1
MAX4207
10 9
CMVIN CMVOUT
REFVOUT R3 OSADJ VEE R4 VEE 0.1F
5 LOGV1
6
OSADJ
7 SCALE
8 LOGV2
RSET
REFISET GND
THIN QFN
________________________________________________________________ Maxim Integrated Products
1
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
ABSOLUTE MAXIMUM RATINGS
(All voltages referenced to GND, unless otherwise noted.) VCC ...........................................................................-0.3V to +6V VEE............................................................................-6V to +0.3V Supply Voltage (VCC to VEE) .............................................. +12V REFVOUT ....................................................(VEE - 0.3V) to +3.0V OSADJ, SCALE, REFISET ...........................(VEE - 0.3V) to +5.5V REFIIN, LOGIIN ........................................(VEE - 0.3V) to VCMVIN LOGV1, LOGV2, CMVOUT, REFIOUT ......................................(VEE - 0.3V) to (VCC + 0.3V) CMVIN............................................................(VEE - 0.3V) to +1V Continuous Current (REFIIN, LOGIIN) ................................10mA Continuous Power Dissipation (TA = +70C) 16-Pin Thin QFN (derate 16.9mW/C above +70C) ...1349mW Operating Temperature Range ...........................-40C to +85C Junction Temperature .....................................................+150C Storage Temperature Range .............................-65C to +150C Lead Temperature (soldering, 10s) .................................+300C
Stresses beyond those listed under "Absolute Maximum Ratings" may cause permanent damage to the device. These are stress ratings only, and functional operation of the device at these or any other conditions beyond those indicated in the operational sections of the specifications is not implied. Exposure to absolute maximum rating conditions for extended periods may affect device reliability.
DC ELECTRICAL CHARACTERISTICS--Dual-Supply Operation
(VCC = +5V, VEE = -5V, GND = 0, IREF = 1A, ILOG = 10A, LOGV2 = SCALE, LOGV1 = OSADJ, CMVIN = CMVOUT, RSET > 1M, TA = -40C to +85C. Typical values are at TA = +25C, unless otherwise noted.) (Note 1)
PARAMETER Supply Voltage Supply Current LOGIIN Current Range (Notes 3, 4) REFIIN Current Range (Notes 3, 4) Common-Mode Voltage Common-Mode Voltage Input Range SYMBOL VCC VEE ICC ILOG IREF VCMVOUT VCMVIN IREF = 10nA, ILOG= 10nA to 1mA, K = -0.25V/decade (Note 4) TA = +25C TA = -40C to +85C TA = -40C to +85C TA = +25C, |VCMVIN - VREFIIN|, |VCMVIN - VLOGIIN| |VCMVIN - VREFIIN|, |VCMVIN - VLOGIIN| TA = +25C TA = -40C to +85C (Note 4) 1.218 1.195 TA = +25C TA = -40C to +85C -237.5 -231.25 80 -250 0 2 (Note 2) (Note 2) TA = +25C TA = -40C to +85C Minimum Maximum Minimum Maximum 0 0.5 5 mV 10 -262.5 -268.75 mV/ decade V/ decade/ C 5 mV V/C 1.258 1.275 V 10 1 10 1 CONDITIONS MIN 2.7 -2.7 5 TYP MAX 5.5 -5.5 6 7.5 UNITS V mA nA mA nA mA V V
Log Conformity Error
VLC
Logarithmic Slope (Scale Factor) Logarithmic Slope (Scale Factor) Temperature Drift Input Offset Voltage Input Offset Voltage Temperature Drift Voltage Reference Output
K
VIO VIOS VREFVOUT
0.6 6 1.238
2
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range
DC ELECTRICAL CHARACTERISTICS--Dual-Supply Operation (continued)
(VCC = +5V, VEE = -5V, GND = 0, IREF = 1A, ILOG = 10A, LOGV2 = SCALE, LOGV1 = OSADJ, CMVIN = CMVOUT, RSET > 1M, TA = -40C to +85C. Typical values are at TA = +25C, unless otherwise noted.) (Note 1)
PARAMETER Voltage Reference Output Current Current Reference Output Voltage LOGV2 BUFFER Input Offset Voltage Input Bias Current VIO IB VOH Output Voltage Range VOL Output Short-Circuit Current Slew Rate Unity-Gain Bandwidth IOUT+ IOUTSR GBW RL to GND = 2k Sourcing Sinking VEE + 0.2 VEE + 0.08 34 58 12 5 mA V/s MHz TA = +25C TA = -40C to +85C (Note 4) (Note 4) RL to GND = 2k 0.01 VCC 0.2 0.4 2 6 1 VCC 0.3 V mV nA SYMBOL IREFVOUT VREFISET TA = +25C TA = -40C to +85C (Note 4) 490 482 CONDITIONS MIN TYP 1 500 510 518 MAX UNITS mA mV
MAX4207
AC ELECTRICAL CHARACTERISTICS--Dual-Supply Operation
(VCC = +5V, VEE = -5V, GND = 0, IREF = 1A, ILOG = 10A, LOGV2 = SCALE, LOGV1 = OSADJ, CMVIN = CMVOUT, RSET > 1M, TA = +25C, unless otherwise noted.)
PARAMETER LOGV2 Total Noise LOGV2 Spot Noise Density REFVOUT Total Noise REFVOUT Spot Noise Density REFISET Total Noise REFISET Spot Noise Density Small-Signal Unity-Gain Bandwidth SYMBOL CONDITIONS 0.1Hz to 10Hz, total output-referred noise, IREF = 10nA, ILOG = 100nA f = 5kHz, IREF = 10nA, ILOG = 100nA 1Hz to 10Hz, total output-referred noise f = 5kHz 1Hz to 10Hz, total output-referred noise f = 5kHz IREF = 1A, ILOG = 10A, RCOMP = 300, CCOMP = 32pF MIN TYP 17 0.8 3.3 266 0.67 23 1 MAX UNITS VRMS V/Hz VRMS nV/Hz VRMS nV/Hz MHz
Note 1: Note 2: Note 3: Note 4:
All devices are 100% production tested at TA = +25C. All temperature limits are guaranteed by design. Guaranteed and functionally verified. Log conformity error less than 5mV with scale factor = 0.25V/decade. Guaranteed by design.
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Typical Operating Characteristics
(VCC = +5V, VEE = -5V, GND = 0V, IREF = 1A, ILOG = 10A, LOGV2 = SCALE, LOGV1 = OSADJ, CMVIN = CMVOUT, RSET > 1M, TA = +25C, unless otherwise noted.)
VLOGV1 vs. ILOG
MAX4207 toc01
VLOGV1 vs. ILOG
MAX4207 toc02
VLOGV1 vs. IREF
1.00 0.75 VLOGV1 (V) 0.50 0.25 0 -0.25 ILOG = 1A TA = -40C TO +85C
MAX4207 toc03
0.75 0.50 0.25 VLOGV1 (V)
0.75 0.50 0.25 VLOGV1 (V) 0 -0.25 -0.50 -0.75 TA = -40C TO +85C VCC = +2.7V VEE = -2.7V 1n 10n 100n 1 10 100 1m
1.25
0 -0.25 -0.50 -0.75 -1.00 TA = -40C TO +85C -1.25 1n 10n 100n 1 10 100 ILOG (A) 1m 10m
-1.00 -1.25
-0.50 -0.75 10m 1n 10n 100n 1 10 100 1m 10m
ILOG (A)
IREF (A)
VLOGV1 vs. ILOG
MAX4207 toc04
VLOGV1 vs. IREF
ILOG = 10nA TO 1mA 1.5 1.0 ERROR (mV) VLOGV1 (V) 10A 0.5 0 -0.5 -1.0 100A -1.5 -15 1mA -2.0 -20 1n 10n 100n 1 10 100 IREF (A) 1m 10m 1n 10m 10nA 1m 10A 10nA 100nA 1A
MAX4207 toc05
NORMALIZED LOG CONFORMANCE ERROR vs. ILOG
15 10 5 0 -5 -10 TA = -40C TO +85C 10n 100n 1 10 100 ILOG (A) 1m 10m TA = -40C
MAX4207 toc06
2.0 1mA 1.5 100A 1.0 VLOGV1 (V) 0.5 0 -0.5 -1.0 -1.5 IREF = 10nA TO 1mA -2.0 1n 10n 100n 1 10 100 ILOG (A) 100nA 1A
2.0
20
NORMALIZED LOG CONFORMANCE ERROR vs. ILOG
MAX4207 toc07
NORMALIZED LOG CONFORMANCE ERROR vs. IREF
MAX4207 toc08
NORMALIZED LOG CONFORMANCE ERROR vs. ILOG
15 10 ERROR (mV) 5 0 -5 -10
MAX4207 toc09
20 15 10 ERROR (mV)
20 15 10 ERROR (mV) 5 0 -5 -10 -15 -20 ILOG = 1A TA = -40C TO +85C 1n 10n 100n 1 10 100 IREF (A) 1m TA = -40C
20
5 0 -5 -10 -15 -20 1n TA = -40C TO +85C VCC = +2.7V VEE = -2.7V 10n 100n 1 10 100 ILOG (A) 1m 10m TA = -40C
-15
IREF = 10nA, 100nA, 1A, 10A, 100A, 1mA
-20 10m 1n 10n 100n 1 10 100 ILOG (A) 1m 10m
4
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Typical Operating Characteristics (continued)
(VCC = +5V, VEE = -5V, GND = 0V, IREF = 1A, ILOG = 10A, LOGV2 = SCALE, LOGV1 = OSADJ, CMVIN = CMVOUT, RSET > 1M, TA = +25C, unless otherwise noted.)
NORMALIZED LOG CONFORMANCE ERROR vs. IREF
MAX4207 toc10
NORMALIZED LOG CONFORMANCE ERROR vs. ILOG
15 10 ERROR (mV) 5 0 -5 -10 -15 -20
(VCC = +2.7V, VEE = -2.7V) (VCC = +5V, VEE = -5V) (VCC = +5.5V, VEE = -5.5V)
MAX4207 toc11
INPUT OFFSET VOLTAGE (VLOGIIN - VCMVIN vs. ILOG)
3 2 VLOGIIN - VCMVIN (mV) 1 0 -1 -2 -3 -4 -5
MAX4207 toc12
20
ILOG = 10nA, 100nA, 1A, 10A, 100A, 1mA
20
4
15 10 ERROR (mV) 5 0 -5 -10 -15 -20 1n 10n 100n 1 10 100 IREF (A) 1m
10m
1n
10n 100n
1 10 100 ILOG (A)
1m
10m
1n
10n 100n
1 10 100 ILOG (A)
1m
10m
ILOG PULSE RESPONSE (IREF = 1A)
MAX4207 toc13
IREF PULSE RESPONSE (ILOG = 1A)
MAX4207 toc14
+0.25V 0V 0V -0.25V -0.25V -0.50V -0.50V -0.75V 20s/div
1A TO 100nA
0.75V 0.50V
100A TO 1mA
10A TO 1A
0.50V 0.25V
10A TO 100A
100A TO 10A
0.25V 0V
1A TO 10A
1mA TO 100A
0V -0.25V 20s/div
100nA TO 1A
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Typical Operating Characteristics (continued)
(VCC = +5V, VEE = -5V, GND = 0V, IREF = 1A, ILOG = 10A, LOGV2 = SCALE, LOGV1 = OSADJ, CMVIN = CMVOUT, RSET > 1M, TA = +25C, unless otherwise noted.)
VLOGV2 VOLTAGE-NOISE DENSITY vs. FREQUENCY
MAX4207 toc15
TOTAL WIDEBAND VOLTAGE NOISE AT VLOGV2 vs. ILOG
f = 1Hz TO 1MHz IREF = ILOG VOLTAGE NOISE (mVRMS) 4
VMAX4207 toc16
LOGARITHMIC SLOPE DISTRIBUTION
MAX4207 toc17
10 10nA NOISE DENSITY (V/Hz) 100nA 1 1A
5
35 30 25
3
COUNT (%)
20 15 10
10A 0.1
2
1 IREF = ILOG 0.01 1 10 100 1k 10k 100k 1M 10M FREQUENCY (Hz) 0 10n 100n 1 10 100 1m ILOG (A)
5 0 240 245 250 255 260 SLOPE (mV/DECADE)
VREFVOUT DISTRIBUTION
MAX4207 toc18
INPUT OFFSET VOLTAGE DISTRIBUTION
MAX4207 toc19
OFFSET VOLTAGE vs. TEMPERATURE
16 12 8 VLOGV1 (mV) IREF = 1A ILOG = 1A
MAX4207 toc20
30
RL = 100k
25
INPUT OFFSET VOLTAGE = VLOGIIN - VCMVIN
20
25 20 COUNT (%) 15 10 5 0 1.232
20 COUNT (%)
15
4 0 -4 -8
10
5
-12 -16
0 1.234 1.236 1.238 1.240 1.242 1.246 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 VREFVOUT (V) INPUT OFFSET VOLTAGE (mV)
-20 -50 -25 0 25 50 75 100 TEMPERATURE (C)
REFERENCE OUTPUT VOLTAGE (VREFVOUT) vs. TEMPERATURE
MAX4207 toc21
REFERENCE OUTPUT VOLTAGE (VREFVOUT) vs. LOAD CURRENT
1.29 REFERENCE OUTPUT VOLTAGE (V) 1.28 1.27 1.26 1.25 1.24 1.23 1.22 1.21 1.20
MAX4207 toc22
1.30 1.29 REFERENCE OUTPUT VOLTAGE (V) 1.28 1.27 1.26 1.25 1.24 1.23 1.22 1.21 1.20 -50 -25 0 25 50 75
1.30
100
-1.0
-0.5
0
0.5
1.0
TEMPERATURE (C)
LOAD CURRENT (mA)
6
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Typical Operating Characteristics (continued)
(VCC = +5V, VEE = -5V, GND = 0V, IREF = 1A, ILOG = 10A, LOGV2 = SCALE, LOGV1 = OSADJ, CMVIN = CMVOUT, RSET > 1M, TA = +25C, unless otherwise noted.)
REFERENCE OUTPUT VOLTAGE (VREFVOUT) vs. SUPPLY VOLTAGE (VCC - VEE)
MAX4207 toc23
REFERENCE POWER-SUPPLY REJECTION RATIO vs. FREQUENCY
-10 -20 REFERENCE PSRR (dB) -30 -40 -50 -60 -70 -80 -90 -100 VREFVOUT 200mV/div
CREFVOUT = 0.1F IREFVOUT = 1mA
MAX4207 toc24
REFERENCE LINE-TRANSIENT RESPONSE
MAX4207 toc25
1.250 1.245 REFERENCE OUTPUT VOLTAGE (V) 1.240 1.235 1.230 1.225 1.220 1.215 1.210 1.205 1.200 5 6 7 8 9 10
0
VCC - VEE 5V/div 0V
1.238V
CREFVOUT = 0F
11
10
100
1k
10k
100k
1M
10s/div
SUPPLY VOLTAGE (V)
FREQUENCY (Hz)
REFERENCE LOAD-TRANSIENT RESPONSE
MAX4207 toc26
REFERENCE TURN-ON TRANSIENT RESPONSE
MAX4207 toc27
SMALL-SIGNAL AC RESPONSE (ILOG TO VLOGV1)
ILOG = 100A 0 NORMALIZED GAIN (dB)
MAX4207 toc28
10
IREFVOUT 1mA/div
0mA
VCC - VEE 5V/div 0V
-10 -20 -30 -40 -50 -60 CCOMP = 33pF RCOMP = 330 IREF = 10A 100 1k
ILOG = 1mA ILOG = 10A ILOG = 1A ILOG = 100nA
VREFVOUT 100mV/div
CREFVOUT = 0F
1.24V
VREFVOUT 500mV/div 0V
CREFVOUT = 0F
100s/div
10s/div
10k
100k
1M
10M
FREQUENCY (Hz)
SMALL-SIGNAL AC RESPONSE (ILOG TO VLOGV1)
MAX4207 toc29
SMALL-SIGNAL AC RESPONSE OF BUFFER
AV = 1V/V 0 NORMALIZED GAIN (dB) AV = 2V/V -3 AV = 4V/V -6
MAX4207 toc30
10 0 NORMALIZED GAIN (dB) -10 -20 -30 -40 -50 -60 100 1k 10k 100k CCOMP = 100pF RCOMP = 100 IREF = 10A ILOG = 100A ILOG = 10A ILOG = 1A
ILOG = 1mA
3
ILOG = 100nA
-9
-12 1M 10M 10k 100k 1M FREQUENCY (Hz) 10M 100M FREQUENCY (Hz)
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Pin Description
PIN 1, 9 2 3 4 5 6 7 8 10 11 12 13 14 15 16 NAME N.C. REFVOUT GND VEE LOGV1 OSADJ SCALE LOGV2 VCC REFISET CMVOUT REFIOUT REFIIN LOGIIN CMVIN No Connection. Not internally connected. 1.238V Reference Voltage Output. Bypass REFVOUT to GND with a 0 to 1F capacitor (optional). Ground Negative Power Supply. Bypass VEE to GND with a 0.1F capacitor. Logarithmic Amplifier Voltage Output 1. The output scale factor of LOGV1 is -0.25V/decade. Offset Adjust Input. Apply a voltage at OSADJ to adjust the LOGV2 output offset voltage (see the Output Offset section). Scale Factor Input. Adjust the output scale factor for LOGV2 using a resistive divider (see the Scale Factor section). Logarithmic Amplifier Voltage Output 2. Adjust the output scale factor for LOGV2 using a resistive divider between SCALE, GND, and LOGV2 (see the Scale Factor section). Positive Power Supply. Bypass VCC to GND with a 0.1F capacitor. Current Reference Adjust Input. A resistor (RSET), from REFISET to GND, adjusts the current at REFIOUT (see the Adjusting the Logarithmic Intercept section). 0V Common-Mode Voltage Reference Output Current Reference Output. The internal current reference output is available at REFIOUT. Current Reference Input. Apply an external reference current at REFIIN. IREFIIN is the reference current used by the logarithmic amplifier when generating LOGV1. Current Input to Logarithmic Amplifier. LOGIIN is typically connected to a photodiode anode or other external current source. Common-Mode Voltage Input. VCMVIN is the common-mode voltage for the input and reference amplifiers (see the Common Mode section). FUNCTION
VCC
REFVOUT
CMVOUT
CURRENT MIRROR VCC LOGIIN CURRENT CORRECTION 1.238V VCC
REFIOUT
0.5V CMVIN VEE VCC REFIIN SUMMING AMPLIFIER AND TEMPERATURE COMPENSATION VCC REFISET LOGV2 SCALE
OSADJ VEE
VEE GND
MAX4207
LOGV1
Figure 1. Functional Diagram 8 _______________________________________________________________________________________
Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
VOUT = VBE1 - VBE2 kT I kT I = ln LOG - ln REF q IS q IS ILOG IREF kT = ln - ln I q IS S kT I = ln LOG q IREF I kT = ( ln(10))log10 LOG q IREF ILOG = K x log10 (see Figure 3) IREF where: k = scale factor (V/decade) ILOG = the input current at LOGIIN IREF = the reference current at REFIIN The MAX4207 uses internal temperature compensation to virtually eliminate the effects of the thermal voltage, (kT/q), on the amplifier's scale factor, maintaining a constant slope over temperature.
ILOG LOGIIN
VCC
VBE1
CMVIN VEE VBE2
IREF REFIIN
VCC
VEE
Figure 2. Simplified Model of a Logarithmic Amplifier
Detailed Description
Theory
Figure 2 shows a simplified model of a logarithmic amplifier. Two transistors convert the currents applied at LOGIIN and REFIIN to logarithmic voltages according to the following equation: kT I VBE = ln C q IS where: VBE = base-emitter voltage of a bipolar transistor k = 1.381 x 10-23 J/K T = absolute temperature (K) q = 1.602 x 10 -19 C IC = collector current IS = reverse saturation current The logarithmic amplifier compares VBE1 to the reference voltage VBE2, which is a logarithmic voltage for a known reference current, IREF. The temperature dependencies of a logarithmic amplifier relate to the thermal voltage, (kT/q), and IS. Matched transistors eliminate the IS temperature dependence of the amplifier in the following manner:
Definitions
Transfer Function The ideal logarithmic amplifier transfer function is: I VIDEAL = K x log10 LOG IREF Adjust K (see the Scale Factor section) to increase the transfer-function slope as illustrated in Figure 3. Adjust IREF using REFISET (see the Adjusting the Logarithmic Intercept section) to shift the logarithmic intercept to the left or right as illustrated in Figure 4. Log Conformity Log conformity is the maximum deviation of the MAX4207's output from the best-fit straight line of the VLOGV1 versus log (ILOG/IREF) curve. It is expressed as a percent of the full-scale output or an output voltage. Referred-to-Input and Referred-to-Output Errors The log nature of the MAX4207 insures that any additive error at LOGV1 corresponds to multiplicative error at the input, regardless of input level.
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
IDEAL TRANSFER FUNCTION WITH VARYING K
MAX4207 fig03
IDEAL TRANSFER FUNCTION WITH VARYING IREF
K = -0.25 1.0 OUTPUT VOLTAGE (V) IREF = 100A 0.5 0 -0.5 -1.0 IREF = 10nA -1.5
MAX4207 fig04
4 NORMALIZED OUTPUT VOLTAGE (V) 3 2 1 0 -1 -2 -3 -4 0.001 K = -0.25 K = -0.5 K = -1 VOUT = K LOG (ILOG/IREF) K=1 K = 0.5 K = 0.25
1.5
IREF = 1A 100n 1 ILOG (A) 10 100 1m
0.01
0.1
1
10
100
1000
1n
10n
CURRENT RATIO (ILOG/IREF)
Figure 3. Ideal Transfer Function with Varying K
Figure 4. Ideal Transfer Function with Varying IREF
Total Error Total error (TE) is defined as the deviation of the output voltage, VLOGV1, from the ideal transfer function (see the Transfer Function section): VLOGV1 = VIDEAL TE TE is a combination of the associated gain, input offset current, input bias current, output offset voltage, and transfer characteristic nonlinearity (log conformity) errors:
I -I VLOGV 2 = K(1 K)log10 LOG BIAS1 4( VLC VOSOUT ) IREF - IBIAS2
I I VLOGV 2 K log10 LOG KK log10 LOG IREF IREF 4K(1 + K)( VLC VOSOUT ) The first term of this expression is the ideal component of VLOGV1. The remainder of the expression is the TE: I TE KK log10 LOG 4K(1 + K)( VLC VOSOUT ) IREF In the second term, one can generally remove the products relating to K, because K is generally much less than 1. Hence, a good approximation for TE is given by: I TE K K log10 LOG 4( VLC VOSOUT ) IREF As an example, consider the following situation: Full-scale input = 5V ILOG = 100A IREF = 100nA K = 1 5% V/decade (note that the uncommitted amplifier is configured for a gain of 4) VLC = 5mV (obtained from the Electrical Characteristics table) VOSOUT = 2mV (typ), and TA = +25C.
where VLC and VOSOUT are the log conformity and output offset voltages, respectively. Output offset is defined as the offset occurring at the output of the MAX4207 when equal currents are presented to ILOG and IREF. Because the MAX4207 is configured with a gain of K = -0.25V/decade, a 4 should multiply the (VLC VOSOUT) term, if VLC and VOSOUT were derived from this default configuration. IBIAS1 and IBIAS2 are currents in the order of 20pA, significantly smaller than ILOG and IREF, and can therefore be eliminated: I VLOGV 2 K(1 K)log10 LOG 4( VLC VOSOUT ) IREF Expanding this expression:
10
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Substituting into the TE approximation, TE (1V/decade)(0.05 log10 (100A/100nA) 4 (5mV 2mV) = [0.15V 4(7mV)] As a worst case, one finds TE 178mV or 3.6% of full scale. When expressed as a voltage, TE increases in proportion with an increase in gain as the contributing errors are defined at a specific gain. Calibration using a look-up table eliminates the effects of gain and output offset errors, leaving conformity error as the only factor contributing to total error. For further accuracy, consider temperature monitoring as part of the calibration process.
Adjusting the Logarithmic Intercept
Adjust the logarithmic intercept by changing the reference current, IREF. A resistor from REFISET to GND (see Figure 5) adjusts the reference current, according to the following equation: V RSET = REFISET 10 x IREF where VREFISET is 0.5V. Select RSET between 5k and 5M. REFIOUT current range is 10nA to 10A only.
Dual-Supply Operation
The MAX4207 operates only from dual 2.7 to 5.5V supplies. The relationship of inputs to outputs is a function of IREF, relative to ILOG, and the configuration of the uncommitted amplifier. The uncommitted amplifier can be configured in either inverting or noninverting mode. In an inverting configuration, the uncommitted amplifier output, LOGV2, is positive and LOGV1 is negative when ILOG exceeds IREF. When operating in a noninverting configuration, LOGV2 and LOGV1 are both negative when ILOG exceeds IREF (see Table 1). An inverting configuration of the uncommitted buffer is recommended when large output offset voltage adjustments are required using OSADJ. By connecting CMVOUT and CMVIN, the log and reference amplifier inputs (LOGIIN and REFIIN) are biased at 0V. Applying the external voltage (0 to 0.5V) to CMVIN optimizes the application's performance.
VCC IIN 0.1F LOGIIN REFIOUT CCOMP 32pF RCOMP 330 CMVIN CMVOUT REFISET RSET 50k OSADJ GND VEE R4 REFIIN VCC LOGV2 VOUT R2 4k SCALE R1 10k LOGV1 REFVOUT R3
Applications Information
Input Current Range
Five decades of input current across a 10nA to 1mA range are acceptable for ILOG and IREF. The effects of bias currents increase as I LOG and I REF fall below 10nA. Bandwidth decreases at low ILOG values (see the Frequency Response and Noise Considerations section). As ILOG and IREF increase to 1mA or higher, transistors become less logarithmic in nature. The MAX4207 incorporates leakage current compensation and high-current correction circuits to compensate for these errors.
Frequency Compensation
The MAX4207's frequency response is a function of the input current magnitude and the selected compensation network at LOGIIN and REFIIN. The compensation network comprised of CCOMP and RCOMP ensures stability over the specified range of input currents by introducing an additional pole/zero to the system. For the typical application, select CCOMP = 32pF and RCOMP = 330. Frequency Response and Noise Considerations The MAX4207 bandwidth is proportional to the magnitude of the IREF and I LOG currents, whereas the noise is inversely proportional to IREF and ILOG currents.
CCOMP 32pF RCOMP 330
MAX4207
Common Mode
A 0V common-mode input voltage, VCMVOUT, is available at CMVOUT and can be used to bias the logging and reference amplifier inputs by connecting CMVOUT to CMVIN. A voltage between 0 and 0.5V, connected to CMVIN, may be used to bias the logging and reference transistor collectors, thereby optimizing performance.
VEE
0.1F
Figure 5. Typical Operating Circuit
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Table 1. MAX4207 Example Configurations
LOGV2 AMPLIFIER CONFIGURATION Inverting Noninverting INPUT CONDITIONS ILOG > IREF (constant) ILOG < IREF (constant) ILOG > IREF (constant) ILOG < IREF (constant) VLOGV1 Negative Positive Negative Positive VLOGV2 Positive Negative Negative Positive
Output Offset The inverting configuration utilized by the MAX4207 facilitates large output-offset voltage adjustments. The magnitude of the offset voltage is given by the following equation: R VOS = VOSADJ 1 + 2 R1 A resistive divider between REFVOUT, OSADJ, and GND can be used to adjust VOSADJ (see Figure 5). R4 VOSADJ = VREFOUT R3 + R4 Scale Factor The scale factor, K, is the slope of the logarithmic output. For the LOGV1 amplifier, K = -0.25V/decade. Adjust the overall scale factor for the MAX4207 using the uncommitted LOGV2 amplifier and the following equation, which refers to Figure 5: R2 = R1 K
- 0.25
Photodiode Current Monitoring
Figure 6 shows the MAX4207 in an optical-power measurement circuit, common in fiberoptic applications. The MAX4007 current monitor converts the sensed APD current to an output current that drives the MAX4207 LOGIIN input (APD current is scaled by 0.1). The MAX4007 also buffers the high-voltage APD voltages from the lower MAX4207 voltages. The MAX4207's internal current reference sources 10nA (RSET = 5M) to the REFIIN input. This configuration sets the logarithmic intercept to 10nA, corresponding to an APD current of 100nA. The unity-gain configuration of the output buffer maintains the -0.25V/decade gain present at the LOGV1 output.
Measuring Optical Absorbance
A photodiode provides a convenient means of measuring optical power, as diode current is proportional to the incident optical power. Measure absolute optical power using a single photodiode connected at LOGIIN, with the MAX4207's internal current reference driving REFIIN. Alternatively, connect a photodiode to each of the MAX4207's logging inputs, LOGIIN and REFIIN, to measure relative optical power (Figure 7). In absorbance measurement instrumentation, a reference light source is split into two paths. The unfiltered path is incident upon the photodiode of the reference channel, REFIIN. The other path passes through a sample of interest, with the resulting filtered light incident on the photodiode of the second channel, LOGIIN. The MAX4207 outputs provide voltages proportional to the log ratio of the two optical powers--an indicator of the optical absorbance of the sample. In wavelength-locking applications, often found in fiberoptic communication modules, two photodiode currents provide a means of determining whether a given optical channel is tuned to the desired optical frequency. In this application, two bandpass optical filters with overlapping "skirts" precede each photodiode. With proper filter selection, the MAX4207 output can vary monotonically (ideally linearly) with optical frequency.
Select R2 between 1k and 100k. Design Example Desired: Logarithmic intercept: 1A Overall scale factor = +1V/decade 0.5V RSET = = 50k 10 x 1A Select R1 = 10k: R2 = 10k x 1V / decade = 40k - 0.25
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
VCC 2.7V TO 76V 2.2H 2.2F PHOTODIODE BIAS 0.22F BIAS CLAMP REFVOUT 0.1F REFIOUT REFIIN 32pF 330 LOGV2 SCALE 0.1F
VCC OUTPUT
MAX4007
MAX4207
LOGV1 OSADJ REFISET
IAPD REF OUT
IAPD/10 LOGIIN 32pF GND 330 GND TO LIMITING AMPLIFIER VEE CMVOUT CMVIN
5M
FIBER CABLE
APD
TIA HIGH-SPEED DATA PATH
VEE 0.1F
Figure 6. Logarithmic Current-Sensing Amplifier with Sourcing Input
VCC
Capacitive Loads
The MAX4207 drives capacitive loads of up to 50pF. Reactive loads decrease phase margin and can produce excessive ringing and oscillation. Use an isolation resistor in series with LOGV1 or LOGV2 to reduce the effect of large capacitive loads. Recall that the combination of the capacitive load and the small isolation resistor limits AC performance.
VCC REFISET REFIIN 32pF VCC 330
CMVIN CMVOUT REFVOUT LOGV2
MAX4207
SCALE LOGV1 LOGIIN
Power Dissipation
The LOGV1 and LOGV2 amplifiers are capable of sourcing or sinking in excess of 30mA. Ensure that the continuous power dissipation rating for the MAX4207 is not exceeded.
32pF OSADJ REFIOUT 330 GND VEE VEE
TQFN Package
The 16-lead thin QFN package has an exposed paddle that provides a heat-removal path, as well as excellent electrical grounding to the PC board. The MAX4207's exposed pad is internally connected to VEE, and can either be connected to the PC board VEE plane or left unconnected. Ensure that only VEE traces are routed under the exposed paddle.
Figure 7. Measuring Optical Absorbance ______________________________________________________________________________________ 13
Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range MAX4207
Layout and Bypassing
Bypass V CC and V EE to GND with ceramic 0.1F capacitors. Place the capacitors as close to the device as possible. Bypass REFVOUT and/or CMVOUT to GND with a 0.1F ceramic capacitor for increased noise immunity and a clean reference current. For lowcurrent operation, it is recommended to use metal guard rings around LOGIIN, REFIIN, and REFISET. Connect this guard ring to CMVOUT. TRANSISTOR COUNT: 754 PROCESS: BiCMOS
Chip Information
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Precision Transimpedance Logarithmic Amplifier with Over 5 Decades of Dynamic Range
Package Information
(The package drawing(s) in this data sheet may not reflect the most current specifications. For the latest package outline information, go to www.maxim-ic.com/packages.)
MAX4207
PACKAGE OUTLINE 12, 16, 20, 24L THIN QFN, 4x4x0.8mm
21-0139
C
1
2
PACKAGE OUTLINE 12, 16, 20, 24L THIN QFN, 4x4x0.8mm
21-0139
C
2
2
Maxim cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in a Maxim product. No circuit patent licenses are implied. Maxim reserves the right to change the circuitry and specifications without notice at any time.
Maxim Integrated Products, 120 San Gabriel Drive, Sunnyvale, CA 94086 408-737-7600 ____________________ 15 (c) 2004 Maxim Integrated Products Printed USA is a registered trademark of Maxim Integrated Products.
24L QFN THIN.EPS

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