LOG102 LOG 102 SBOS211A – MARCH 2002 Precision LOGARITHMIC AND LOG RATIO AMPLIFIER FEATURES DESCRIPTION ● EASY-TO-USE COMPLETE LOG RATIO FUNCTION The LOG102 is a versatile integrated circuit that computes the logarithm or log ratio of an input current relative to a reference current. ● 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 ● LOW QUIESCENT CURRENT: 1.25mA 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. ● 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 ● LOG, LOG RATIO COMPUTATION: Communication, Analytical, Medical, Industrial, Test, General Instrumentation 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 temperature range, 0°C to +70°C, with operation over –40°C to +85°C. ● PHOTODIODE SIGNAL COMPRESSION AMP NOTE: U.S. Patent Pending. ● ONET, OPTICAL POWER METERS ● ANALOG SIGNAL COMPRESSION IN FRONT OF A/D CONVERTER ● ABSORBANCE MEASUREMENT ● OPTICAL DENSITY MEASUREMENT R1 VLOG OUT = LOG (I1/I2) VOUT3 = G • LOG (I1/I2), G = 1 +R2/R1 CC I2 V+ VLOG OUT 6 I1 5 14 1 Q1 R2 +IN3 –IN3 3 4 Q2 A3 7 VOUT3 A2 A1 12 A4 9 10 11 8 +IN4 VOUT4 A4 can be used as comparator for signal loss detect. GND –IN4 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. Copyright © 2001, 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. www.ti.com PIN DESCRIPTION ABSOLUTE MAXIMUM RATINGS(1) 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 I1 1 14 I2 Storage Temperature ..................................................... –55°C to +125°C NC 2 13 NC Lead Temperature (soldering, 10s) ............................................... +300°C +IN3 3 12 +IN4 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. –IN3 4 Vlog out 5 10 GND V+ 6 9 V– VOUT3 7 8 VOUT4 Junction Temperature .................................................................... +150°C ELECTROSTATIC DISCHARGE SENSITIVITY LOG102 11 –IN4 NC = No Internal Connection 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. 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. PACKAGE/ORDERING INFORMATION SPECIFIED TEMPERATURE RANGE PACKAGE MARKING ORDERING NUMBER TRANSPORT MEDIA, QUANTITY LOG102AID LOG102AIDR Rails, 58 Tape and Reel, 2500 PRODUCT PACKAGE-LEAD PACKAGE DESIGNATOR(1) LOG102AID SO -14 D 0°C to +70°C LOG102A " " " " " NOTES: (1) For the most current specifications and package information, refer to our web site 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 = 10kΩ, unless otherwise noted. LOG102AID PARAMETER CONDITION MIN CORE LOG FUNCTION IIN / VLOG OUT Equation LOG CONFORMITY ERROR(1) Initial over Temperature GAIN(2) Initial Value Gain Error vs Temperature INPUT, A1 and A2 Offset Voltage vs Temperature vs Power Supply (PSRR) Input Bias Current vs Temperature Voltage Noise Current Noise Common-Mode Voltage Range (Positive) (Negative) CMRR OUTPUT, A2 (VLOGOUT) Output Offset, VOSO, Initial vs Temperature Full-Scale Output (FSO) Short-Circuit Current 2 TYP MAX UNITS ±0.3 % % %/ °C %/ °C VO = log (I1/I2) 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 1nA to 100µA (5 decades) 1nA to 100µA (5 decades) TMIN to TMAX 1 0.15 0.025 TMIN to TMAX VS = ±4.5V to ±18V TMIN to TMAX f = 10Hz to 10kHz f = 1kHz f = 1kHz ±0.3 ±2 5 ±5 Doubles Every 10°C 3 30 4 (V+) – 2 (V+) – 1.5 (V–) + 2 (V–) + 1.2 90 105 ±3 TMIN to TMAX VS = ±5V Supplies ±1 0.05 (V–) + 1.2 ±18 ±1.5 50 ±55 25 (V+) – 1.5 V/decade % %/ °C mV µV/°C µV/V pA µVrms nV/√Hz fA/√Hz V V dB mV µV/°C V mA LOG102 www.ti.com SBOS211A ELECTRICAL CHARACTERISTICS (Cont.) Boldface limits apply over the specified temperature range, TA = 0°C to +70°C. At TA = +25°C, VS = ±5V, RL = 10kΩ, unless otherwise noted. LOG102AID PARAMETER TOTAL Initial CONDITION ERROR(3)(4) vs Temperature vs Supply FREQUENCY RESPONSE, core log (5) BW, 3dB I2 = 10nA I2 = 1µA I2 = 10µA I2 = 1mA Step Response Increasing I2 = 1µA to 1mA (3 decade) I2 = 100nA to 1µA (1 decade) I2 = 10nA to 100nA (1 decade) Decreasing I2 = 1mA to 1µA (3 decade) I2 = 1µA to 100nA (1 decade) I2 = 100nA to 10nA (1 decade) OP AMPS, A3 AND A4 Input Offset Voltage vs Temperature vs Power Supply Input Bias Current(5) Input Offset Current Input Voltage Range Common-Mode Rejection 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 POWER SUPPLY Operating Range Quiescent Current MIN TYP MAX UNITS ±55 ±30 ±25 ±20 ±25 ±30 ±37 I1 or I2 remains fixed while other varies min to max 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 = 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 = 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 ±0.15 ±0.15 ±0.25 ±0.2 ±0.2 ±0.15 ±0.25 mV mV mV mV mV mV mV 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 CC = 4500pF CC = 150pF CC = 150pF CC = 50pF 0.1 38 40 45 kHz kHz kHz kHz CC = 150pF CC = 150pF CC = 150pF 11 7 110 µs µs µs CC = 150pF CC = 150pF CC = 150pF 45 20 550 µs µs µs TMIN to TMAX VS = ±4.5V to ±18V ±175 ±2 10 –10 ±0.5 ±0.4 ±0.07 ±0.07 ±0.07 ±0.07 ±0.07 ±0.4 (V–) G = 1, 2.5V step G = 1, 2.5V Step, CL =100pF VS = 5V, RL = 10kΩ ±750 50 (V+) – 1.5 86 1 28 88 1.4 0.5 16 (V–) + 1.5 –ISC /+ISC (V+) – 0.9 –36 /+60 VS IO = 0 TEMPERATURE RANGE Specified Range, TMIN to TMAX Operating Range Storage Range Thermal Resistance, θJA SO-14 ±4.5 1.25 0 –40 –40 100 µV µV/ °C µV/V nA nA V dB µVp-p nV/√Hz dB MHz V/µs µs V mA ±18 2 V mA 70 +85 +125 °C °C °C °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 SBOS211A www.ti.com 3 TYPICAL CHARACTERISTICS At TA = +25°C, VS = ±5V, RL = 10kΩ, unless otherwise noted. ONE CYCLE OF NORMALIZED TRANSFER FUNCTION NORMALIZED TRANSFER FUNCTION 3 VOUT = 1V • Log I1 I2 0.9 Normalized Output Voltage (V) Normalized Output Voltage (V) 1 2 1 0 –1 –2 –3 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.001 0.01 0.1 1 10 100 1000 1 2 I Current Ratio, 1 I2 3 6 4 10 8 I Current Ratio, 1 I2 TOTAL ERROR vs INPUT CURRENT GAIN ERROR vs TEMPERATURE 0.35 60 0.30 50 40 30 70°C 0°C 0.20 Gain Error (%) Total Error (mV) 0.25 20 0.15 0.10 0.05 0.00 25°C 10 –0.05 0 –0.10 1nA 10nA 100nA 1µA 10µA 100µA 1mA –60 –40 –20 Input Current (I1 or I2) 1000 I1 = 10nA CC (pF) I1 = 1µA I1 = 10µA I1 = 1mA I1 = 100µA 10 Values below 2pF may be ignored. 1 1nA 10nA 100nA 1µA 10µA 100µA 1mA 100k 80 1k F 0p 100µA 100µA CC 1nA =1 1µA 1mA to 10µA 0 00 CC =1 I1 = 1nA CC 10nA 100nA 10nA pF 0.1 1nA A I1 = 1nA 10 10mA 1µ to µA 0 1 10nA 10nA 100 1 100µA 100µA 1mA I1 = 1mA 1µA 10k 100nA 1µA µF =1 10µA 100µA 1mA I2 I2 4 60 10µA I1 = 1nA I1 = 100nA 100 40 1M 3dB Frequency Response (Hz) Select CC for I1 min and I2 max 20 3dB FREQUENCY RESPONSE MINIMUM VALUE OF COMPENSATION CAPACITOR 10000 0 Temperature (°C) LOG102 www.ti.com SBOS211A TYPICAL CHARACTERISTICS (Cont.) At TA = +25°C, VS = ±5V, RL = 10kΩ, unless otherwise noted. LOG CONFORMITY vs VLOGOUT 5 LOG CONFORMITY vs TEMPERATURE 300 4 Log Conformity (m%) Log Conformity (mV) 70°C 3 2 1 0 25°C –1 200 6 Decades (1nA to 1mA) 100 5 Decades (1nA to 100µA) –2 0°C 0 –3 –3 –2 –1 1 0 2 3 0 10 20 VLOGOUT (V) 30 40 50 60 70 Temperature (°C) TOTAL ERROR vs TEMPERATURE 60 50 Total Error (mV) 1nA 40 1mA 30 20 10 10nA to 100µA 0 0 10 20 30 40 50 60 70 Temperature (°C) LOG102 SBOS211A www.ti.com 5 APPLICATION INFORMATION R2 10kΩ 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. 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 capacitor, as shown in Figure 1. Connecting the capacitors as close to the LOG102 as possible will contribute to noise reduction as well. V+ VOUT = G • VLOGOUT 12 VOUT I1 LOG102 14 9 CC V– R2' 10kΩ V+ FIGURE 2. Bias Current Nulling. 14 3 VLOGOUT 8 (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: R1 5 11 VLOGOUT = (1V) • log (I1/I2) 4 LOG102 R2 CC RREF = 2.5V/10nA = 250MΩ Amplifier A4 not being used. 10µF V– IREF Unused amplifiers should have positive inputs grounded and negative inputs tied to their respective outputs. 2N2905 RREF INPUT CURRENT RANGE 3.6kΩ 2N2905 +15V FIGURE 1. Basic Connections with Output Gain Factor of the LOG102. 6V IN834 –15V IREF = 6V RREF 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 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. 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. 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. 6 10 R1' > 1MΩ I2 VOUT 7 10 1000pF 5 VLOGOUT is expressed as: 6 1 9 6 1 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 I2 R1 1MΩ SETTING THE REFERENCE CURRENT 10µF I1 V– V+ VREF = 100mV R1 R3 14 +5V R2 VOS + – IREF A1 R3 >> R2 FIGURE 4. T Network for Reference Current. LOG102 www.ti.com SBOS211A Figure 5 shows a low-level current source using a series resistor. The low offset op-amp reduces the effect of the LOG102’s input offset voltage. V+ 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+ I1 = 2.5nA to 1mA REF3025 6 2.5V 1 5 VLOGOUT 1GΩ to 2.5kΩ LOG102 100kΩ I2 = 2.5nA 10MΩ +25mV +2.5V 100Ω 5 CC QA IIN 14 9 QB National LM394 10 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 Characteristic 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 The transient response of the LOG102 is 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 LOG102. 1/2 OPA2335 1.5kΩ 1.5kΩ 10nA to 1mA FREQUENCY COMPENSATION In an application, highest overall bandwidth can be achieved by detecting the signal level at VOUT, then switching in appropriate values of compensation capacitors. 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: 1/2 OPA2335 BSH203 10nA to 1mA Pin 1 or Pin 14 LOG102 Photodiode NOTE: OPA2335 Available Q2 2002 FIGURE 7. Precision Current Inverter/Current Source. VOLTAGE INPUTS 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 configuration. (2) LOG102 SBOS211A Back Bias +5V +3.3V 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 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 LOG102 more stable, but will reduce the frequency response. G = 1 + R2/R1 TLV271 or 1 OPA2335 2 +3.3V www.ti.com 7 1.5kΩ 100kΩ 100kΩ +5V 10nA to 1mA +3.3V Back Bias +5V 1/2 OPA2335 +3.3V 1.5kΩ 1/2 OPA2335 Photodiode 1.5kΩ 100kΩ 100kΩ LOG102 10nA to 1mA Pin 1 or Pin 14 NOTE: OPA2335 Available Q2 2002 FIGURE 8. Precision Current Inverter/Current Source. DATA COMPRESSION In many applications the compressive effects of the logarithmic 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. V+ (–VRB) 6 1 5 VOUT I1 Signal LOG102 (–VRB) I2 REF 14 9 CC V+ 10 I1 6 1 5 VOUT V– Sample –VRB λ1 NOTES: (1) –VRB, must be 2.5V more positive than V–. Example, for VRB = –9.5V, V– =12V. (2) Typically, –3.3V bias is used with ±12V supplies. FIGURE 9. Reverse Biased Photodiode Using Pin 10 on LOG102. D1 LOG102 λ 1´ I2 Light Source λ1 D2 14 10 9 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. 8 Absorbance of the sample is A = logλ1´/ λ1 (3) If D1 and D2 are matched A ∝ (1V) logI1 / I2 (4) FIGURE 10. Absorbance Measurement. LOG102 www.ti.com SBOS211A INSIDE THE LOG102 also Using the base-emitter voltage relationship of matched bipolar transistors, the LOG102 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 R1 + R 2 R1 I1 = log I2 VOUT = VL (1) k = Boltzman’s constant = 1.381 • 10–23 VOUT = or T = Absolute temperature in degrees Kelvin (9) (10) R1 + R 2 I n VT log 1 R1 I2 (11) q = Electron charge = 1.602 • 10–19 Coulombs IC = Collector current IS = Reverse saturation current I1 From the circuit in Figure 11, we see that VL = VBE1 – VBE 2 I1 IS1 – VT2 ln + VBE 1 VBE A2 IS 2 VOUT 2 VOUT = (1V) LOG I2 I2 Q2 – A1 I1 I2 I2 (3) R2 VL R1 If the transistors are matched and isothermal and VTI = VT2, then (3) becomes: FIGURE 11. Simplified Model of Log Amplifier. I I VL = VT1 ln 1 – ln 2 IS IS (4) I VL = VT ln 1 and since I2 (5) ln x = 2.3 log10 x (6) I VL = n VT log 1 I2 (7) where n = 2.3 (8) 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 resistor with the required positive temperature coefficient. USING A LARGER REFERENCE VOLTAGE REDUCES OFFSET ERRORS Using a larger reference voltage to create the reference current minimizes errors due to the LOG102’s input offset voltage. Maintaining an increasing output voltage as a function 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 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. The wide dynamic range of the LOG102 is useful for measuring avalanche photodiode current (APD) (see Figure 13). LOG102 SBOS211A – + I1 (2) Substituting (1) into (2) yields VL = VT1 ln Q1 www.ti.com 9 IREF = VREF VOUT = VREF – R1 R2 R3 • LOG ( IREF IPHOTO ) R3 R2 CC VLOGOUT 5 IREF 3 VMIN to VMAX I1 R1 Q1 1 Q2 A3 7 A/D A2 VREF A1 R2 4 IPHOTO I2 R3 14 LOG102 IMIN to IMAX 10 FIGURE 12. Technique for Using Full-Scale Reference Current Such that V OUT Increases with Increasing Photodiode Current. ISHUNT +15V to +60V 500 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 1.2kΩ 1kΩ +5V 6 1 5 Q1 4 Q2 A3 7 VOUT = 2.5V to 0V A2 A1 100µA 3 25kΩ 14 REF3025(1) 2.5V LOG102 SO-14 10 9 –5V NOTE: (1) Available Q2 2002. FIGURE 13. High Side Shunt for Avalanche Photodiode (APD) Measures 3-Decades of APD Current. 10 LOG102 www.ti.com SBOS211A DEFINITION OF TERMS 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: TRANSFER FUNCTION The ideal transfer function is: VOUT = 1V • logI1/I2 (5) Figure 14 shows the graphical representation of the transfer over valid operating range for the LOG102. 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. LOG CONFORMITY 3 I2 2 1 VOUT (V) nA A 10nA = 1n I2 10 = 100nA 1µA 10µA µA 10 µA 00 mA 100µA 1mA I1 0 A 0n I2 = 10 I2 = A 1µ I2 = I2 = Dashed Line = Greater Supply Voltage Requirement 1 I2 = 1 VOUT = (1V) • LOG I1 I2 –3 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 specification. 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. 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 I 2 and I1. ACCURACY VOUT 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. (NONLIN) = 1V/dec • 2Nm V where N is the log conformity error, in percent. INDIVIDUAL ERROR COMPONENTS The ideal transfer function with current input is: VOUT = (1V) • log TOTAL ERROR The total error is the deviation (expressed in mV) of the actual output from the ideal output of VOUT = 1V • log(I1/I2). I2 (maximum error)(1) VOUT = (1V) (1 ± ∆K ) log (5) 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; and is shown in Table I. Temperature can affect total error. I1 I2 (7) The actual transfer function with the major components of error is: Thus, VOUT (ACTUAL) = VOUT (IDEAL) ± Total Error. (6) I1 – IB1 ± 2Nm ± VOS OUT I2 – IB2 (8) The individual component of error is: ∆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) 10nA (30mV) 100nA (25mV) 1µA (20mV) 100nA (25mV) 30mV 25mV 25mV 1µA (20mV) 30mV 25mV 20mV 10µA (25mV) 30mV 25mV 25mV VOS OUT = output offset voltage (1mV, typ) n = number of decades over which N is specified: Example: what is the error when I1 = 1µA and I2 = 100nA VOUT = (1 ± 0.003) log NOTE: (1) Maximum errors are in parenthesis. 10 –6 – 5 • 10 –12 10 –7 – 5 • 10 –12 (9) ± (2)(0.0004) 5 ± 0.3mV TABLE I. I1 /I2 and Maximum Errors. LOG102 SBOS211A www.ti.com 11 ≈ 1.003 log 10 –6 10 –7 + 0.004 + 0.003 (10) VOUT = 1.003 (1) + 0.004 + 0.0003 (11) = 1.0073V (12) Since the ideal output is 1.000V, the error as a percent of reading is % error = 0.0073 • 100% = 0.73% 1 (13) EOS1 V1 – IB1 ± (14) R1 R1 = (1V) (1 ± ∆K ) log ± 2Nn ± VOS OUT EOS 2 V2 – IB 2 ± R2 R2 (15) EOS1 EOS2 and Where R R 2 are considered to be zero for large 1 values of resistance from external input current sources. For the case of voltage inputs, the actual transfer function is 12 LOG102 www.ti.com SBOS211A PACKAGE DRAWING MSOI002B – JANUARY 1995 – REVISED SEPTEMBER 2001 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 LOG102 SBOS211A www.ti.com 13 PACKAGE OPTION ADDENDUM www.ti.com 3-Oct-2003 PACKAGING INFORMATION ORDERABLE DEVICE STATUS(1) PACKAGE TYPE PACKAGE DRAWING PINS PACKAGE QTY LOG102AID ACTIVE SOIC D 14 58 LOG102AIDR ACTIVE SOIC D 14 2500 (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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