Precision LOGARITHMIC AND LOG RATIO AMPLIFIER

Transcription

1 LOG0 LOG0 SBOSA MAY 00 REVISED JULY 00 Precision LOGARITHMIC AND LOG RATIO AMPLIFIER FEATURES EASY-TO-USE COMPLETE CORE FUNCTION HIGH ACCURACY: 0.0% FSO Over Decades WIDE INPUT DYNAMIC RANGE: 7. Decades, 00pA to.ma LOW QUIESCENT CURRENT: ma WIDE SUPPLY RANGE: ±.V to ±V APPLICATIONS LOG, LOG RATIO, ANTI-LOG COMPUTATION: Communication, Analytical, Medical, Industrial, Test, General Instrumentation PHOTODIODE SIGNAL COMPRESSION AMP ANALOG SIGNAL COMPRESSION IN FRONT OF ANALOG-TO-DIGITAL(A/D) CONVERTER DESCRIPTION The LOG0 is a versatile integrated circuit that computes the logarithm or log ratio of an input current relative to a reference current. The LOG0 is tested over a wide dynamic range of input signals. In log ratio applications, a signal current can come from a photodiode, and a reference current from a resistor in series with a precision external reference. The output signal at is trimmed to 0.V per decade of input current, allowing seven decades of input current, dynamic range. Low DC offset voltage and temperature drift allow accurate measurement of low-level signals over a wide environmental temperature range. The LOG0 is specified over the temperature range C to +7 C, with operation over 0 C to + C. Note: US Patent Pending I = 0. LOG (I /I ) I Q Q LOG0 A A R R GND 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. 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 00, Texas Instruments Incorporated

2 ABSOLUTE MAXIMUM RATINGS () Supply Voltage, to... V Input Voltage... ( 0.) to (+0.V) Input Current... ±0mA Output Short-Circuit ()... Continuous Operating Temperature... 0 C to + C Storage Temperature... C to + C Junction Temperature C Lead Temperature (soldering, 0s) C NOTES: () Stresses above these ratings may cause permanent damage. Exposure to absolute maximum conditions for extended periods may degrade device reliability. () Short-circuit to ground. ELECTROSTATIC DISCHARGE SENSITIVITY 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. PIN DESCRIPTION Top View SO I I NC LOG0 7 NC GND NC = No Internal Connection PACKAGE/ORDERING INFORMATION SPECIFIED PACKAGE TEMPERATURE PACKAGE ORDERING TRANSPORT PRODUCT PACKAGE-LEAD DESIGNATOR () RANGE MARKING NUMBER MEDIA, QUANTITY LOG0AID SO - D C to +7 C LOG0 LOG0AID Rails, 00 " " " " " LOG0AIDR Tape and Reel, 00 NOTE: () For the most current specifications and package information, refer to our web site at. ELECTRICAL CHARACTERISTICS Boldface limits apply over the specified temperature range, T A = C to +7 C. At T A = + C, V S = ±V, R OUT = 0kΩ, unless otherwise noted. LOG0AID PARAMETER CONDITION MIN TYP MAX UNITS CORE LOG FUNCTION I IN / Equation V O = (0.V)log (I /I ) V LOG CONFORMITY ERROR () Initial na to 00µA ( decades) % 00pA to.ma (7. decades) 0.0 % over Temperature na to 00µA ( decades) %/ C 00pA to.ma (7. decades) () %/ C GAIN () Initial Value na to 00µA 0. V/decade Gain Error na to 00µA 0. ± % vs Temperature T MIN to T MAX %/ C INPUT, A and A Offset Voltage ±0. ±. mv vs Temperature T MIN to T MAX ± µv/ C vs Power Supply (PSRR) V S = ±.V to ±V 0 µv/v Input Bias Current ± pa vs Temperature T MIN to T MAX Doubles Every 0 C Voltage Noise f = 0Hz to 0kHz µvrms f = khz 0 nv/ Hz Current Noise f = khz fa/ Hz Common-Mode Voltage Range (Positive) () (). V (Negative) () + () +. V Common-Mode Rejection Ratio (CMRR) 0 db OUTPUT, A ( ) Output Offset, V OSO, Initial ± ± mv vs Temperature T MIN to T MAX ± µv/ C Full-Scale Output (FSO) V S = ±V () +. (). V Short-Circuit Current ± ma LOG0 SBOSA

3 ELECTRICAL CHARACTERISTICS (Cont.) Boldface limits apply over the specified temperature range, T A = C to +7 C. At T A = + C, V S = ±V, R L = 0kΩ, unless otherwise noted. LOG0AID PARAMETER CONDITION MIN TYP MAX UNITS TOTAL ERROR ()() I or I remains fixed while other varies. Initial Min to Max I or I =.ma ±7 mv I or I = ma ±0 mv I or I = 00µA ±0 mv I or I = 0µA ±0 mv I or I = µa ±0 mv I or I = 00nA ±0 mv I or I = 0nA ±0 mv I or I = na ±0 mv I or I = 0pA ±0 mv I or I = 00pA ±0 mv vs Temperature I or I =.ma ±. mv/ C I or I = ma ±0. mv/ C I or I = 00µA ±0. mv/ C I or I = 0µA ±0.0 mv/ C I or I = µa ±0.0 mv/ C I or I = 00nA ±0.09 mv/ C I or I = 0nA ±0. mv/ C I or I = na ±0. mv/ C I or I = 0pA ±0. mv/ C I or I = 00pA ±0. mv/ C vs Supply I or I =.ma ±.0 mv/ V I or I = ma ±0. mv/ V I or I = 00µA ±0. mv/ V I or I = 0µA ±0. mv/ V I or I = µa ±0. mv/ V I or I = 00nA ±0. mv/ V I or I = 0nA ±0. mv/ V I or I = na ±0. mv/v I or I = 0pA ±0. mv/ V I or I = 00pA ±0. mv/ V FREQUENCY RESPONSE, CORE LOG () BW, db I = 0nA = 00pF 0. khz I = µa = 0pF khz I = 0µA = 0pF 0 khz I = ma = 0pF khz Step Response Increasing I = µa to ma = 0pF µs I = 00nA to µa = 0pF 7 µs I = 0nA to 00nA = 0pF 0 µs Decreasing I = ma to µa = 0pF µs I = µa to 00nA = 0pF 0 µs I = 00nA to 0nA = 0pF 0 µs POWER SUPPLY Operating Range V S ±. ± V Quiescent Current I O = 0 ± ±. ma TEMPERATURE RANGE Specified Range, T MIN to T MAX 7 C Operating Range 0 C Storage Range C Thermal Resistance, θ JA SO- 0 NOTES: () Log Conformity Error is peak deviation from the best-fit straight line of versus log (I /I ) curve expressed as a percent of peak-to-peak full-scale. () May require higher supply for full dynamic range. () Output core log function is trimmed to 0.V output per decade change of input current. () Worst-case Total Error for any ratio of I /I is the largest of the two errors, when I and I are considered separately. () Total I + I should be kept below.ma on ±V supply. () Bandwidth (db) and transient response are a function of both the compensation capacitor and the level of input current. LOG0 SBOSA

4 TYPICAL CHARACTERISTICS At T A = + C, V S = ±V, R L = 0kΩ, unless otherwise noted. Normalized Output Voltage (V) NORMALIZED TRANSFER FUNCTION = 0.V LOG (I /I ) Normalized Output Voltage (V) ONE CYCLE OF NORMALIZED TRANSFER FUNCTION k 0k Current Ratio, I /I Current Ratio, I /I Total Error (mv) TOTAL ERROR vs INPUT CURRENT +7 C Gain Error (%)..... GAIN ERROR (I = µa) + C +7 C + C C to 0 C 0 + C C pA na 0nA 00nA µa 0µA 00µA ma 0mA Input Current (I or I ) 0. 00pA na 0nA 00nA µa 0µA 00µA ma 0mA Input Current (I or I ) (pf) 00M 0M M 00k 0k k MINIMUM VALUE OF COMPENSATION CAPACITOR Select for I min. and I max. Values below pf may be ignored. I = na I = 0nA I = 00nA µa I = 00pA 00 I = 0µA 0 00µA ma 00pA na 0nA 00nA µa 0µA 00µA ma 0mA I db Frequency Response (Hz) M 00k 0k k na 00µA db FREQUENCY RESPONSE 0nA = 000pF µa = 0pF = µf 0µA to µa 0nA 00pA na 0nA 00nA µa 0µA 00µA ma I 0µA 00µA I = na 00µA 00µA ma I = ma µa ma to 0µA 00nA 0nA I = na LOG0 SBOSA

5 TYPICAL CHARACTERISTICS (Cont.) At T A = + C, V S = ±V, R L = 0kΩ, unless otherwise noted. 7 LOG CONFORMITY vs INPUT CURRENT 0 LOG CONFORMITY vs TEMPERATURE Log Conformity (mv) + C C 0 C to + C 00pA na 0nA 00nA µa 0µA 00µA ma Input Current (I or I ) Log Conformity (m%) Decades (00pA to ma) Decades (na to ma) Decades (na to 00µA) Temperature ( C) APPLICATION INFORMATION The LOG0 is a true logarithmic amplifier that uses the base-emitter voltage relationship of bipolar transistors to compute the logarithm, or logarithmic ratio of a current ratio. Figure shows the basic connections required for operation of the LOG0. In order to reduce the influence of lead inductance of power-supply lines, it is recommended that each supply be bypassed with a 0µF tantalum capacitor in parallel with a 000pF ceramic capacitor, as shown in Figure. Connecting the capacitors as close to the LOG0 as possible will contribute to noise reduction as well. 0µF 000pF INPUT CURRENT RANGE To maintain specified accuracy, the input current range of the LOG0 should be limited from 00pA to.ma. Input currents outside of this range may compromise LOG0 performance. Input currents larger than.ma result in increased nonlinearity. An absolute maximum input current rating of 0mA is included to prevent excessive power dissipation that may damage the logging transistor. On ±V supplies, the total input current (I + I ) is limited to.ma. Due to compliance issues internal to the LOG0, to accommodate larger total input currents, supplies should be increased. Currents smaller than 00pA will result in increased errors due the input bias currents of op amps A and A (typically pa). The input bias currents may be compensated for, as shown in Figure. The input stages of the amplifiers have FET inputs, with input bias current doubling every 0 C, which makes the nulling technique shown practical only where the temperature is fairly stable. LOG0 R 0kΩ I I R MΩ I LOG0 0µF 000pF I R ' > MΩ GND FIGURE. Basic Connections of the LOG0. R ' 0kΩ FIGURE. Bias Current Nulling. LOG0 SBOSA

6 SETTING THE REFERENCE CURRENT When the LOG0 is used to compute logarithms, either I or I can be held constant and becomes the reference current to which the other is compared. is expressed as: = (0.V) log (I /I ) () I REF can be derived from an external current source (such as shown in Figure ), 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 I REF. If I REF is 0nA and +.V is used: R REF =.V/0nA = 0M () R REF N90.kΩ N90 +V V V IN V I REF = R REF I REF FIGURE. Temperature Compensated Current Source. A voltage divider may be used to reduce the value of the resistor (as shown in Figure ). When using this method, one must consider the possible errors caused by the amplifier s input offset voltage. The input offset voltage of amplifier A has a maximum value of.mv, making V REF a suggested value of 00mV. +V R >> R V REF = 00mV R R R I REF + V OS FIGURE. T Network for Reference Current. A.V REF0 +mv 00kΩ 00Ω I =.na to ma I =.na 0MΩ +.V OPA.V GΩ to.kω Chopper Op Amp LOG0 GND FIGURE. Current Source with Offset Compensation. 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 LOG0. FREQUENCY COMPENSATION Frequency compensation for the LOG0 is obtained by connecting a capacitor between pins and. 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 I and the minimum value of I. Larger values of will make the LOG0 more stable, but will reduce the frequency response. In an application, highest overall bandwidth can be achieved by detecting the signal level at, then switching in appropriate values of compensation capacitors. NEGATIVE INPUT CURRENTS The LOG0 will function only with positive input currents (conventional current flows into pins and ). In situations where negative input currents are needed, the circuits in Figures, 7, and may be used. Figure shows a low-level current source using a series resistor. The low offset op-amp reduces the effect of the LOG0 s input offset voltage. FREQUENCY RESPONSE The frequency response curves seen in the Typical Characteristics Curves are shown for constant DC I and I with a small-signal AC current on one input. The db frequency response of the LOG0 is a function of the magnitude of the input current levels and of the value of the frequency compensation capacitor. See Typical Characteristic Curve db Frequency Response for details. The transient response of the LOG0 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 I IN D OPA70 Q A Q B FIGURE. Current Inverter/Current Source. National LM9 D I OUT LOG0 SBOSA

7 VOLTAGE INPUTS The LOG0 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 () applies to this configuration. Sample λ λ D I LOG0 +.V +V / OPA TLV7 or OPA Light Source λ D I.kΩ.kΩ +V FIGURE 9. Absorbance Measurement. 0nA to ma Back Bias +.V Photodiode BSH0 / OPA LOG0 0nA to ma Pin or Pin OPERATION ON SINGLE SUPPLY Many applications do not have the dual supplies required to operate the LOG0. Figure 0 shows the LOG0 configured for operation with a single +V supply. FIGURE 7. Precision Current Inverter/Current Source. Single Supply +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 9. Absorbance of the sample is A = logλ / λ () I I LOG0 If D and D are matched A (0.V) logi /I () DATA COMPRESSION In many applications the compressive effects of the logarithmic transfer function are useful. For example, a LOG0 preceding a -bit A/D converter can produce the dynamic range equivalent to a 0-bit converter. µf µf TPS () V µf () TPS00DBV negative charge pump. FIGURE 0. Single +V Power-Supply Operation..kΩ +V 00kΩ 00kΩ 0nA to ma Back Bias +.V +.V / OPA +V.kΩ Photodiode / OPA.kΩ 00kΩ NOTE: OPA Available Q kΩ 0nA to ma Pin or Pin LOG0 FIGURE. Precision Current Inverter/Current Source. LOG0 7 SBOSA

8 INSIDE THE LOG0 Using the base-emitter voltage relationship of matched bipolar transistors, the LOG0 establishes a logarithmic function of input current ratios. Beginning with the base-emitter voltage defined as: IC VBE = VT ln where : VT = IS kt q k = Boltzman s constant =. 0 T = Absolute temperature in degrees Kelvin () also or V V R + R OUT = L R V OUT R + R = R nv T I log I V = 0 I OUT. V log I (9) (0) () q = Electron charge = Coulombs I C = Collector current I S = Reverse saturation current From the circuit in Figure, we see that: VL = VBE V BE () I I A Q Q + + V BE V BE I A Substituting () into () yields: = (0.V) LOG I I R I I VL = VT ln V T ln I S I S () I V L R If the transistors are matched and isothermal and V TI = V T, then () becomes: I I VL = VT ln ln IS IS I VL = VT ln I and since ln x =. log x V L = nv T 0 I log I where n =. () () () (7) () FIGURE. Simplified Model of a Log Amplifier. DEFINITION OF TERMS TRANSFER FUNCTION The ideal transfer function is: = 0.V logi /I See Figure for the graphical representation of the transfer over valid operating range for the LOG0. ACCURACY 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. () (V) pA na I = 00nA I = µa I = 0µA I = 00µA I = ma 0nA 00nA µa I = 00pA I = na I = 0nA 0µA 00µA ma = (0.V) LOG (I /I ) FIGURE. Transfer Function with Varying I and I. 0mA I LOG0 SBOSA

9 TOTAL ERROR The total error is the deviation (expressed in mv) of the actual output from the ideal output of = 0.V log(i /I ). Thus, (ACTUAL) = (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 I /I is the largest of the two errors when I and I 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-to- Input (RTI). In this respect, log amps have a unique property: Given some error voltage at the log amp s output, that error corresponds to a constant percent of the input regardless of the actual input level. MEASURING AVALANCHE PHOTODIODE CURRENT The wide dynamic range of the LOG0 is useful for measuring avalanche photodiode current (APD), as shown in Figure. LOG CONFORMITY For the LOG0, log conformity is calculated the same as linearity and is plotted I /I on a semi-log scale. In many applications, log conformity is the most important specification. This is true because bias current errors are negligible (pa compared to input currents of 00pA 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 versus log (I /I ) curve. This is expressed as a percent of ideal full-scale output. Thus, the nonlinearity error expressed in volts over m decades is: (NONLIN) = 0.V/dec Nm V (7) where N is the log conformity error, in percent. +V to +0V 00Ω I SHUNT Irx = µa to ma Receiver +V kω kω APD I to V Converter 0Gbits/sec INA SOT- I OUT = 0. I SHUNT I OUT.kΩ kω +V Q Q A OPA70 =.V to 0V 00µA A kω REF0.V LOG0 SO- V FIGURE. High Side Shunt for Avalanche Photodiode (APD) Measures -Decades of APD Current. LOG0 9 SBOSA

10 INDIVIDUAL ERROR COMPONENTS The ideal transfer function with current input is: V = ( 0 I OUT V ). log I The actual transfer function with the major components of error is: I IB VOUT = ( 0. V) ( ± K) log ± Nm ± V I I B OS O The individual component of error is: K = gain accuracy (0.%, typ), as specified in specification table. I B = bias current of A (pa, typ) I B = bias current of A (pa, typ) N = log conformity error (0.0%, 0.0%, typ) 0.0% for n =, 0.0% for n = 7. V OSO = output offset voltage (mv, typ) m = number of decades over which N is specified: () (9) Example: what is the error when I = µa and I = 00nA V = ( ± ) 0 0 OUT log = 0.0V (0) mV ± ( )( ) ± Since the ideal output is 0.V, the error as a percent of reading is 0. 0 % error = 00% =. % 0. () () For the case of voltage inputs, the actual transfer function is V = ( 0. V) ± K log OUT OS ( ) OS V I R V I R B B E ± R E ± R OS OS ± Nm ± V OSO () Where E R and E R are considered to be zero for large values of resistance from external input current sources. 0 LOG0 SBOSA

11 PACKAGE DRAWING D (R-PDSO-G**) MSOI00B JANUARY 99 REVISED SEPTEMBER 00 PLASTIC SMALL-OUTLINE PACKAGE PINS SHOWN 0.00 (,7) 0.00 (0,) 0.0 (0,) 0.00 (0,) 0. (,0) 0. (,0) 0.00 (0,0) NOM 0.7 (,00) 0.0 (,) Gage Plane A (0,) 0.0 (,) 0.0 (0,0) Seating Plane 0.09 (,7) MAX 0.00 (0,) 0.00 (0,0) 0.00 (0,0) DIM PINS ** A MAX 0.97 (,00) 0. (,7) 0.9 (0,00) A MIN (,0) (,) 0. (9,0) 0007/E 09/0 NOTES: A. All linear dimensions are in inches (millimeters). B. This drawing is subject to change without notice. C. Body dimensions do not include mold flash or protrusion, not to exceed 0.00 (0,). D. Falls within JEDEC MS-0 LOG0 SBOSA

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