Precision LOGARITHMIC AND LOG RATIO AMPLIFIER

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Regina French
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1 LOG Precision LOGARITHMIC AND LOG RATIO AMPLIFIER FEATURES ACCURACY.3% FSO max Total Error Over 5 Decades LINEARITY.% max Log Conformity Over 5 Decades EASY TO USE Pin-selectable Gains Internal Laser-trimmed Resistors WIDE INPUT DYNAMIC RANGE Decades, na to ma HERMETIERAMIC DIP DESCRIPTION The LOG uses advanced integrated circuit technologies to achieve high accuracy, ease of use, low cost, and small size. It is the logical choice for your logarithmic-type computations. The amplifier has guaranteed maximum error specifications over the full sixdecade input range (na to ma) and for all possible combinations of and. Total error is guaranteed so that involved error computations are not necessary. The circuit uses a specially designed compatible thinfilm monolithic integrated circuit which contains amplifiers, logging transistors, and low drift thin-film APPLICATIONS LOG, LOG RATIO AND ANTILOG COMPUTATIONS ABSORBANCE MEASUREMENTS DATA COMPRESSION OPTICAL DENSITY MEASUREMENTS DATA LINEARIZATION CURRENT AND VOLTAGE INPUTS resistors. The resistors are laser-trimmed for maximum precision. FET input transistors are used for the amplifiers whose low bias currents (pa typical) permit signal currents as low as na while maintaining guaranteed total errors of.3% FSO maximum. Because scaling resistors are self-contained, scale factors of V, 3V or 5V per decade are obtained simply by pin selections. No other resistors are required for log ratio applications. The LOG will meet its guaranteed accuracy with no user trimming. Provisions are made for simple adjustments of scale factor, offset voltage, and bias current if enhanced performance is desired. Q Q 4 Com A = K LOG Ω A.5kΩ 4kΩ 3 K = 4 K = 3 5 K = 5 3kΩ Scale Factor Trim Ω Resistor values nominal only; laser-trimmed for precision gain. International Airport Industrial Park Mailing Address: PO Box 4 Tucson, AZ 8534 Street Address: 3 S. Tucson Blvd. Tucson, AZ 85 Tel: (5) 4- Twx: -5- Cable: BBRCORP Telex: -4 FAX: (5) 88-5 Immediate Product Info: (8) Burr-Brown Corporation PDS-43E Printed in U.S.A. January, 5 SBFS4

2 SPECIFICATIONS ELECTRICAL T A = 5 C and ±V CC = ±5V, after 5 minute warm-up, unless otherwise specified. LOGJP PARAMETER CONDITIONS MIN TYP MAX UNITS TRANSFER FUNCTION = K Log ( / ) Log Conformity Error () Either or Initial na to µa (5 decades).4. % na to ma ( decades).5.5 % Over Temperature na to µa (5 decades). %/ C na to ma ( decades). %/ C K Range (), 3, 5 V/decade Accuracy.3 % Temperature Coefficient.3 %/ C ACCURACY Total Error (3) K =, (4) Current Input Operation Initial, = ma ±55 mv, = µa ±3 mv, = µa ±5 mv, = µa ± mv, = na ±5 mv, = na ±3 mv, = na ±3 mv vs Temperature, = ma ±. mv/ C, = µa ±.3 mv/ C, = µa ±.8 mv/ C, = µa ±.33 mv/ C, = na ±.8 mv/ C, = na ±.5 mv/ C, = na ±. mv/ C vs Supply, = ma ±4.3 mv/v, = µa ±.5 mv/v, = µa ±.3 mv/v, = µa ±. mv/v, = na ±. mv/v, = na ±. mv/v, = na ±. mv/v INPUT CHARACTERISTICS (of Amplifiers A and A ) Offset Voltage Initial ±. ±5 mv vs Temperature ±8 µv/ C Bias Current Initial 5 (5) pa vs Temperature Doubles Every C Voltage Noise Hz to khz, RTI 3 µvrms Current Noise Hz to khz, RTI.5 parms AC PERFORMANCE 3dB Response (), = µa na = 45pF. khz µa = 5pF 38 khz µa = 5pF khz ma = 5pF 45 khz Step Response () Increasing = 5pF µa to ma µs na to µa µs na to na µs Decreasing = 5pF ma to µa 45 µs µa to na µs na to na 55 µs OUTPUT CHARACTERISTICS Full Scale Output (FSO) ± V Rated Output Voltage I OUT = ±5mA ± V Current = ±V ±5 ma Current Limit Positive.5 ma Negative 5 ma Impedance.5 Ω LOG

3 SPECIFICATIONS (CONT) ELECTRICAL T A = 5 C and ±V CC = ±5V, after 5 minute warm-up, unless otherwise specified. LOGJP PARAMETER CONDITIONS MIN TYP MAX UNITS POWER SUPPLY REQUIREMENTS Rated Voltage ±5 VDC Operating Range Derated Performance ± ±8 VDC Quiescent Current ± ± ma AMBIENT TEMPERATURE RANGE Specification C Operating Range Derated Performance 5 85 C Storage 4 85 C NOTES: () Log Conformity Error is the peak deviation from the best-fit straight line of the vs Log I IN curve expressed as a percent of peak-to-peak full scale output. () May be trimmed to other values. See Applications section. (3) The worst-case Total Error for any ratio of / is the largest of the two errors when and are considered separately. (4) Total Error at other values of K is K times Total Error for K =. (5) Guaranteed by design. Not directly measurable due to amplifier s committed configuration. () 3dB and transient response are a function of both the compensation capacitor and the level of input current. See Typical Performance Curves. ABSOLUTE MAXIMUM RATINGS PIN CONFIGURATION Supply... ±8V Internal Power Dissipation... mv Input Current... ma Input Voltage Range... ±8V Storage Temperature Range... 4 C to 85 C Lead Temperature (soldering, s)... 3 C Output Short-circuit Duration... Continuous to ground Junction Temperature... 5 C Bottom View Input NC NC NC Input Scale Factor Trim K = K = 3 SCALE FACTOR PIN CONNECTIONS K, V/DECADE CONNECTIONS 5 5 to 3 4 to. 4 and 5 to 3 to.85 3 and 5 to. 3 and 4 to.8 3 and 4 and 5 to FREQUENCY COMPENSATION 4 LOG Common NC 8 NC = No Connection 5 K = 5 Output ELECTROSTATIC DISCHARGE SENSITIVITY Any integral circuit can be damaged by ESD. Burr-Brown 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 published specifications. ORDERING INFORMATION SPECIFIED TEMPERATURE MODEL PACKAGE RANGE LOGJP 4-Pin Hermetic Ceramic DIP C to C PACKAGE INFORMATION PACKAGE DRAWING MODEL PACKAGE NUMBER () LOGJP 4-Pin Hermetic Ceramic DIP 48 () NOTES: () For detailed drawing and dimension table, please see end of data sheet, or Appendix D of Burr-Brown IC Data Book. () During 4, the package was changed from plastic to hermetic ceramic. Pinout, model number, and specifications remained unchanged. The metal lid of the new package is internally connected to common, pin. 3 LOG

4 TYPICAL PERFORMANCE CURVES T A = 5 C, V CC = ±5VDC, unless otherwise noted. Normalized Output Voltage (V) 3 (K) (K) (K) (K) (K) (K) 3 (K) NORMALIZED TRANSFER FUNCTION = K Log... I Current Ratio, Normalized Output Voltage (V) (K). (K).8 (K). (K). (K).5 (K).4 (K).3 (K). (K). (K) ONE CYCLE OF NORMALIZED TRANSFER FUNCTION Current Ratio, Maximum Total Error (mv) ±5 ±5 ±5 TOTAL ERROR vs INPUT CURRENT Trimmed Output Error (mv) TRIMMED OUTPUT ERROR vs INPUT CURRENT Gain Error and Offset Error Trimmed to Zero na na µa ma Input Current ( or ) na na µa ma Input Current ( or ) Compensation Capacitor, (pf) M k k k na MINIMUM VALUE OF COMPENSATION CAPACITOR Select for min and max Values below pf may be ignored. = µa na = µa = na na µa µa Input Current, = na = na = µa to ma µa ma 3dB Frequency Response (Hz) M k k k. na na µa 3dB FREQUENCY RESPONSE na µa = pf na na µa µa µa ma µa µa = na = µf na = pf µa to µa µa µa ma = ma µa ma to µa na na = na LOG 4

5 THEORY OF OPERATION The base-emitter voltage of a bipolar transistor is I C KT V BE = V T l n where: V T = () q I S K = Boltzman s constant =.38 x 3 T = Absolute temperature in degrees Kelvin q = Electron charge =. x Coulombs I C = Collector current I S = Reverse saturation current From the circuit in Figure, we see that ' = V BE V BE () Substituting () into () yields ' = V T ln V T ln (3) I S If the transistors are matched and isothermal and V T = V T, then (3) becomes: ' = V T [ l n l n ] (4) I S ' = V T ln and since (5) I S I S It should be noted that the temperature dependance associated with V T = KT/q is compensated by making R a temperature sensitive resistor with the required positive temperature coefficient. DEFINITION OF TERMS TRANSFER FUNCTION The ideal transfer function is = K log I where: K = the scale factor with units of volts/decade = numerator input current = denominator input current. ACCURACY Accuracy considerations for a log ratio amplifier are somewhat more complicated than for other amplifiers. The reason is that 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. ln x =.3 log x () ' = n V T log () where n =.3 (8) also R = ' R () R R = R I n V T log () R or (V) na na na K = 5 µa µa µa ma = K LOG = µa Fixed value of. K = 3 K = = K log () FIGURE. Transfer Function with Varying K and. A Q Q V BE V BE = K LOG A R (V) 8 4 na na na = na = µa = µa µa µa µa ma R 4 8 = K LOG K = 3 Fixed value of K. FIGURE. Simplified Model of Log Amplifier. FIGURE 3. Transfer Function with Varying and. 5 LOG

6 TOTAL ERROR The total error is the deviation (expressed in mv) of the actual output from the ideal output of = K log ( / ). 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 / is the largest of the two errors when and are considered separately. Example: varies over a range of na to µa and varies from na to µa. What is the maximum error? Table I shows the maximum errors for each decade combination of and. (maximum error) () Since the largest value of / is and the smallest is., K is set at 3V per decade so the output will range from 3V to V. The maximum total error occurs when = na and is equal to K x 3mV. This represents a.5% of peak-topeak FSO error 3 x.3/ x % =.5% where the full scale output is V (from 3V to V). 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. Refer to: Yu Jen Wong and William E. Ott, Function Circuits: Design & Applications, McGraw-Hill Book,. LOG CONFORMITY Log conformity corresponds to linearity when is plotted versus / on a semilog 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 na 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. (maximum error) () na na µa (3mV) (5mV) (mv) na. (5mV) (3mV) (5mV) (5mV) µa.. (mv) (3mV) (5mV) (mv) µa... (5mV) (3mV) (5mV) (5mV) NOTE: () Maximum errors are in parenthesis. TABLE I. / and Maximum Errors. LOG Log conformity is defined as the peak deviation from the best-fit straight line of the versus log ( / ) curve. This is expressed as a percent of peak-to-peak full scale output. Thus, the nonlinearity error expressed in volts over m decades is (NONLIN) = K Nm V () where N is the log conformity error, in percent. INDIVIDUAL ERROR COMPONENTS The ideal transfer function with current input is = K Log (3) The actual transfer function with the major components of error is = K ( ± K) log I B ±K Nm ± V OS OUT (4) I B The individual component of error is K = scale factor error (.3%, typ) I B = bias current of A (pa, typ) I B = bias current of A (pa, typ) N = log conformity error (.5%,.%, typ) V OS OUT = output offset voltage (mv, typ) m = number of decades over which N is specified:.5% for m = 5,.% for m = Example: what is the error with K = 3 when = µa and = na = 3( ±.3) log ±3()(.5)5±mV (5) 3. log.5. () = 3. ().5. () = 3.5V (8) Since the ideal output is 3.V, the error as a percent of reading is.5 % error = 3 x % =.83% () For the case of voltage inputs, the actual transfer function is = K( ± K) log V R V R I B ± I B ± E OS R E OS ±K Nm ±V OS OUT () FREQUENCY RESPONSE The 3dB frequency response of the LOG is a function of the magnitude of the input current levels and of the value of the frequency compensation capacitor. See Typical Performance Curves for details. R

7 The frequency response curves are shown for constant DC and with a small signal AC current on one of them. The transient response of the LOG 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. Frequency response decreases as the gain increases. GENERAL INFORMATION INPUT CURRENT RANGE The stated input range of na to ma is the range for specified accuracy. Smaller or larger input currents may be applied with decreased accuracy. Currents larger than ma result in increased nonlinearity. The ma absolute maximum is a conservative value to limit the power dissipation in the output stage of A and the logging transistor. Currents below na will result in increased errors due to the input bias currents of A and A (pa typical). These errors may be nulled. See Optional Adjustments section. FREQUENCY COMPENSATION Frequency compensation for the LOG is obtained by connecting a capacitor between pins and 4. The size of the capacitor is a function of the input currents as shown in the Typical Performance Curves. For any given application, the smallest value of the capacitor which may be used is determined by the maximum value at and the minimum value of. Larger values of will make the LOG more stable, but will reduce the frequency response. SETTING THE REFERENCE CURRENT When the LOG is used as a straight log amplifier is constant and becomes the reference current in the expression A voltage divider may be used to reduce the value of the resistor. When this is done, one must be aware of possible errors caused by the amplifier s input offset voltage. This is shown in Figure 5. In this case the voltage at pin 4 is not exactly zero, but is equal to the value of the input offset voltage of A, which ranges from zero to ±5mV. V T must be kept much larger than 5mV in order to make this effect negligible. This concept also applies to pin. V T R R 3 V REF R I REF V OS FIGURE 5. T Network for Reference Current. OPTIONAL ADJUSTMENTS 4 The LOG will meet its specified accuracy with no user adjustments. If improved performance is desired, the following optional adjustments may be made. INPUT BIAS CURRENT The circuit in Figure may be used to compensate for the input bias currents of A and A. Since the amplifiers have FET inputs with the characteristic bias current doubling every C, this nulling technique is practical only where the temperature is fairly stable. R kω A = K log () I REF I REF can be derived from an external current source (such as shown in Figure 4), or it may be derived from a voltage source with one or more resistors. When a single resistor is used, the value may be quite large when I REF is small. If I REF is na and 5V is used R kmω 4 LOG R REF = 5V na = 5MΩ. R ' kmω V R REF N5 V IN834 N5 I REF = V R REF I REF 3.kΩ 5V FIGURE 4. Temperature-Compensated Current Reference. R ' kω FIGURE. Bias Current Nulling. OUTPUT OFFSET The output offset may be nulled with the circuit in Figure. and are set equal at some convenient value in the range of na to µa. R is then adjusted for zero output voltage. LOG

8 kω R kω LOG LOG = FIGURE 8. Reverse Polarity Protection. FIGURE. Output Offset Nulling. ADJUSTMENTS OF SCALE FACTOR K The value of K may be changed by increasing or decreasing the voltage divider resistor normally connected to the output, pin. To increase K put resistance in series between pin and the appropriate scaling resistor pin (3, 4 or 5). To decrease K place a parallel resistor between pin and either pin 3, 4 or 5. APPLICATION INFORMATION WIRING PRECAUTIONS In order to prevent frequency instability due to lead inductance of the power supply lines, each power supply should be bypassed. This should be done by connecting a µf tantalum capacitor in parallel with a pf ceramic capacitor from the and pins to the power supply common. The connection of these capacitors should be as close to the LOG as practical. CAPACITIVE LOADS Stable operation is maintained with capacitive loads of up to pf, typically. Higher capacitive loads can be driven if a Ω carbon resistor is connected in series with the LOG s output. This resistor will, of course, form a voltage divider with other resistive loads. CIRCUIT PROTECTION The LOG can be protected against accidental power supply reversal by putting a diode (N4 type) in series with each power supply line as shown in Figure 8. This precaution is necessary only in power systems that momentarily reverse polarity during turn-on or turn-off. If this protection circuit is used, the accuracy of the LOG will be degraded slightly by the voltage drops across the diodes as determined by the power supply sensitivity specification. The LOG uses small geometry FET transistors to achieve the low input bias currents. Normal FET handling techniques should be used to avoid damage caused by low energy electrostatic discharge (ESD). LOG RATIO One of the more common uses of log ratio amplifiers is to measure absorbance. A typical application is shown in Figure. λ ' Absorbance of the sample is A = log () If λ = λ and D and D are matched A K log. (3) Light Source Sample λ λ λ D D FIGURE. Absorbance Measurement. 4 LOG DATA COMPRESSION In many applications the compressive effects of the logarithmic transfer function is useful. For example, a LOG preceding an 8-bit analog-to-digital converter can produce equivalent -bit converter operation. SELECTING OPTIMUM VALUES OF AND K In straight log applications (as opposed to log ratio), both K and are selected by the designer. In order to minimize errors due to output offset and noise, it is normally best to λ LOG 8

9 scale the log amp to use as much of the ±V output range as possible. Thus, with the range of from MIN to MAX ; For MAX V = K log MAX / (4) For MIN V = K log MIN / (5) Addition of these two equations and solving for shows that its optimum value, OPT, is the geometric mean of MAX and MIN. OPT = MAX x MIN () I IN Q A Q B D D National LM34 I OUT K OPT = () log MAX OPT Since K is selectable in discrete steps, use the largest value of K available which does not exceed K OPT. FIGURE. Current Inverter. ANTILOG CONFIGURATION (an implicit technique) NEGATIVE INPUT CURRENTS The LOG will function only with positive input currents (conventional current flow into pins and 4). Some current sources (such as photomultiplier tubes) provide negative input currents. In such situations, the circuit in Figure may be used. () I REF 4 LOG VOLTAGE INPUTS The LOG 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. V IN = I REF R Antilog V IN K R =.µf K = when V IN connected to pin 3. K = 3 when V IN connected to pin 4. K = 5 when V IN connected to pin 5. NOTE: () More detailed information may be found in Properly Designed Log Amplifiers Process Bipolar Input Signals by Larry McDonald, EDN, 5 Oct. 8, pp. FIGURE. Connections for Antilog Function. The information provided herein is believed to be reliable; however, BURR-BROWN assumes no responsibility for inaccuracies or omissions. BURR-BROWN assumes no responsibility for the use of this information, and all use of such information shall be entirely at the user s own risk. Prices and specifications are subject to change without notice. No patent rights or licenses to any of the circuits described herein are implied or granted to any third party. BURR-BROWN does not authorize or warrant any BURR-BROWN product for use in life support devices and/or systems. LOG

10 IMPORTANT NOTICE Texas Instruments and its subsidiaries (TI) reserve the right to make changes to their products or to discontinue any product or service without notice, and advise customers to obtain the latest version of relevant information to verify, before placing orders, that information being relied on is current and complete. All products are sold subject to the terms and conditions of sale supplied at the time of order acknowledgment, including those pertaining to warranty, patent infringement, and limitation of liability. TI warrants performance of its semiconductor products to the specifications applicable at the time of sale in accordance with TI s standard warranty. Testing and other quality control techniques are utilized to the extent TI deems necessary to support this warranty. Specific testing of all parameters of each device is not necessarily performed, except those mandated by government requirements. Customers are responsible for their applications using TI components. In order to minimize risks associated with the customer s applications, adequate design and operating safeguards must be provided by the customer to minimize inherent or procedural hazards. TI assumes no liability for applications assistance or customer product design. TI does not warrant or represent that any license, either express or implied, is granted under any patent right, copyright, mask work right, or other intellectual property right of TI covering or relating to any combination, machine, or process in which such semiconductor products or services might be or are used. TI s publication of information regarding any third party s products or services does not constitute TI s approval, warranty or endorsement thereof. Copyright, Texas Instruments Incorporated

High Accuracy INSTRUMENTATION AMPLIFIER

INA High Accuracy INSTRUMENTATION AMPLIFIER FEATURES LOW DRIFT:.µV/ C max LOW OFFSET VOLTAGE: µv max LOW NONLINEARITY:.% LOW NOISE: nv/ Hz HIGH CMR: db AT Hz HIGH INPUT IMPEDANCE: Ω -PIN PLASTIC, CERAMIC