a Low Noise, Matched Dual Monolithic Transistor MAT02 PIN CONNECTION FEATURES Low Offset Voltage: 50 mV max Low Noise Voltage at 100 Hz, 1 mA: 1.0 nV/√Hz max High Gain (hFE): 500 min at I C = 1 mA 300 min at IC = 1 mA Excellent Log Conformance: rBE . 0.3 V Low Offset Voltage Drift: 0.1 mV/8C max Improved Direct Replacement for LM194/394 Available in Die Form TO-78 (H Suffix) NOTE Substrate is connected to case on TO-78 package. Substrate is normally connected to the most negative circuit potential, but can be floated. PRODUCT DESCRIPTION ABSOLUTE MAXIMUM RATINGS 1 The design of the MAT02 series of NPN dual monolithic transistors is optimized for very low noise, low drift, and low rBE. Precision Monolithics’ exclusive Silicon Nitride “TriplePassivation” process stabilizes the critical device parameters over wide ranges of temperature and elapsed time. Also, the high current gain (hFE) of the MAT02 is maintained over a wide range of collector current. Exceptional characteristics of the MAT02 include offset voltage of 50 µV max (A/E grades) and 150 µV max F grade. Device performance is specified over the full military temperature range as well as at 25°C. Collector-Base Voltage (BVCBO) . . . . . . . . . . . . . . . . . . . . 40 V Collector-Emitter Voltage (BVCEO) . . . . . . . . . . . . . . . . . . 40 V Collector-Collector Voltage (BVCC) . . . . . . . . . . . . . . . . . . 40 V Emitter-Emitter Voltage (BVEE) . . . . . . . . . . . . . . . . . . . . . 40 V Collector Current (IC) . . . . . . . . . . . . . . . . . . . . . . . . . . 20 mA Emitter Current (IE) . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 mA Total Power Dissipation Case Temperature ≤ 40°C2 . . . . . . . . . . . . . . . . . . . . . 1.8 W Ambient Temperature ≤ 70°C3 . . . . . . . . . . . . . . . . 500 mW Operating Temperature Range MAT02A . . . . . . . . . . . . . . . . . . . . . . . . . . –55°C to +125°C MAT02E, F . . . . . . . . . . . . . . . . . . . . . . . . . –25°C to +85°C Operating Junction Temperature . . . . . . . . . . –55°C to +150°C Storage Temperature . . . . . . . . . . . . . . . . . . . –65°C to +150°C Lead Temperature (Soldering, 60 sec) . . . . . . . . . . . . . +300°C Junction Temperature . . . . . . . . . . . . . . . . . . –65°C to +150°C Input protection diodes are provided across the emitter-base junctions to prevent degradation of the device characteristics due to reverse-biased emitter current. The substrate is clamped to the most negative emitter by the parasitic isolation junction created by the protection diodes. This results in complete isolation between the transistors. The MAT02 should be used in any application where low noise is a priority. The MAT02 can be used as an input stage to make an amplifier with noise voltage of less than 1.0 nV/√Hz at 100 Hz. Other applications, such as log/antilog circuits, may use the excellent logging conformity of the MAT02. Typical bulk resistance is only 0.3 Ω to 0.4 Ω. The MAT02 electrical characteristics approach those of an ideal transistor when operated over a collector current range of 1 µA to 10 mA. For applications requiring multiple devices see MAT04 Quad Matched Transistor data sheet. NOTES 1 Absolute maximum ratings apply to both DICE and packaged devices. 2 Rating applies to applications using heat sinking to control case temperature. Derate linearly at 16.4 mW/°C for case temperature above 40°C. 3 Rating applies to applications not using a heat sinking; devices in free air only. Derate linearly at 6.3 mW/°C for ambient temperature above 70°C. ORDERING GUIDE1 Model VOS max Temperature (TA = +258C) Range Package Option MAT02AH2 MAT02EH MAT02FH 50 µV 50 µV 150 µV TO-78 TO-78 TO-78 –55°C to +125°C –55°C to +125°C –55°C to +125°C NOTES 1 Burn-in is available on commercial and industrial temperature range parts in TO-can packages. 2 For devices processed in total compliance to MIL-STD-883, add /883 after part number. Consult factory for 883 data sheet. REV. C Information furnished by Analog Devices is believed to be accurate and reliable. However, no responsibility is assumed by Analog Devices for its use, nor for any infringements of patents or other rights of third parties which may result from its use. No license is granted by implication or otherwise under any patent or patent rights of Analog Devices. One Technology Way, P.O. Box 9106, Norwood, MA 02062-9106, U.S.A. Tel: 617/329-4700 Fax: 617/326-8703 MAT02–SPECIFICATIONS ELECTRICAL CHARACTERISTICS (@ V CB = 15 V, IC = 10 mA, TA = 258C, unless otherwise noted.) Parameter Symbol Conditions Current Gain hFE Current Gain Match Offset Voltage Offset Voltage Change vs. VCB Offset Voltage Change vs. Collector Current Offset Current Change vs. VCB Bulk Resistance Collector-Base Leakage Current Collector-Collector Leakage Current Collector-Emitter Leakage Current Noise Voltage Density ∆hFE VOS ∆VOS/∆VCB IC = 1 mA1 IC = 100 µA IC = 10 µA IC = 1 µA 10 µA ≤ IC ≤ 1 mA2 VCB = 0, 1 µA ≤ IC ≤ 1 mA3 0 ≤ VCB ≤ VMAX,4 1 µA ≤ IC ≤ 1 mA3 VCB = 0 V 1 µA ≤ IC ≤ 1 mA3 Collector Saturation Voltage Input Bias Current Input Offset Current Breakdown Voltage Gain-Bandwidth Product Output Capacitance Collector-Collector Capacitance ∆VOS/∆IC MAT02A/E Min Typ Max Min 500 500 400 300 400 400 300 200 605 590 550 485 0.5 10 10 10 5 5 MAT02F Typ Max Units 2 50 25 25 25 25 605 590 550 485 0.5 80 10 10 5 5 4 150 50 50 50 50 % µV µV µV µV µV ∆IOS/∆VCB rBE 0 ≤ VCB ≤ VMAX 10 µA ≤ IC ≤ 10 mA5 30 0.3 70 0.5 30 0.3 70 0.5 pA/V Ω ICBO VCB = VMAX 25 200 25 400 pA ICC VCC = VMAX5, 6 VCE = VMAX5, 6 VBE = 0 IC = 1 mA, VCB = 07 fO = 10 Hz fO = 100 Hz fO = 1 kHz fO = 10 kHz 35 200 35 400 pA 35 200 35 400 pA 1.6 0.9 0.85 0.85 2 1 1 1 1.6 0.9 0.85 0.85 3 2 2 2 nV/√Hz nV/√Hz nV/√Hz nV/√Hz VCE(SAT) IB IOS BVCEO fT COB IC = 1 mA, IB = 100 µA IC = 10 µA IC = 10 µA 0.05 0.1 25 0.6 0.05 0.2 34 1.3 IC = 10 mA, VCE = 10 V VCB = 15 V, IE = 0 200 23 200 23 V nA nA V MHz pF CCC VCC = 0 35 35 pF ICES en 40 40 NOTES 1 Current gain is guaranteed with Collector-Base Voltage (V CB) swept from 0 to V MAX at the indicated collector currents. 100 (∆IB) (hFE min) 2 Current gain match (∆hFE) is defined as: ∆hFE = IC 3 Measured at IC = 10 µA and guaranteed by design over the specified range of I C. 4 This is the maximum change in V OS as VCB is swept from 0 V to 40 V. 5 Guaranteed by design. 6 ICC and ICES are verified by measurement of I CBO. 7 Sample tested. Specifications subject to change without notice. –2– REV. C MAT02 ELECTRICAL CHARACTERISTICS (V CB = 15 V, –258C ≤ TA ≤ +858C, unless otherwise noted.) MAT02E Min Typ Max Parameter Symbol Conditions Offset Voltage VOS VCB = 0 1 µA ≤ IC ≤ 1 mA1 Average Offset Voltage Drift TCVOS Input Offset Current Input Offset Current Drift Input Bias Current Current Gain Collector-Base Leakage Current Collector-Emitter Leakage Current Collector-Collector Leakage Current MAT02F Min Typ Max 220 10 µA ≤ IC ≤ 1 mA, 0 ≤ VCB ≤ VMAX2 VOS Trimmed to Zero3 IC = 10 µA 0.08 0.3 0.03 0.1 8 0.08 1 0.03 0.3 13 µV/°C 40 40 pA/°C nA ICBO IC = 10 µA4 IC = 10 µA IC = 1 mA5 IC = 100 µA IC = 10 µA IC = 1 µA VCB = VMAX ICES ICC IOS TCIOS IB hFE 300 250 200 150 3 nA VCE = VMAX, VBE = 0 3 4 nA VCC = VMAX 3 4 nA CB = 15 V, –558C ≤ TA ≤ +1258C, unless otherwise noted.) Conditions Offset Voltage VOS VCB = 0 1 µA ≤ IC ≤ 1 mA1 Average Offset Voltage Drift TCVOS 10 µA ≤ IC ≤ 1 mA, 0 ≤ VCB ≤ VMAX2 VOS Trimmed to Zero3 IC = 10 µA IC = 10 µA4 IC = 10 µA IC = 1 mA5 IC = 100 µA IC = 10 µA IC = 1 µA VCB = VMAX TA = 125°C VCE = VMAX, VBE = 0 TA = 125°C VCC = VMAX TA = 125°C Collector-Base Leakage Current Collector-Emitter Leakage Current Collector-Collector Leakage Current IOS TCIOS IB hFE ICBO ICES ICC Min MAT02A Typ Max Units 80 µV 0.08 0.03 0.3 0.1 9 µV/°C µV/°C nA 40 90 60 pA/°C nA 275 225 125 150 15 nA 50 nA 30 nA NOTES 1 Measured at IC = 10 µA and guaranteed by design over the specified range of I C. Guaranteed by V OS test (TCVOS ≅ 150 50 nA 2 Symbol Input Offset Current Input Offset Current Drift Input Bias Current Current Gain 90 45 325 275 225 200 Parameter V OS for VOS ! VBE) T = 298°K for TA = 25°C. T 3 The initial zero offset voltage is established by adjusting the ratio of IC1 to IC2 at T A = 25°C. This ratio must be held to 0.003% over the entire temperature range. Measurements are taken at the temperature extremes and 25 °C. 4 Guaranteed by design. 5 Current gain is guaranteed with Collector-Base Voltage (V CB) swept from 0 to V MAX at the indicated collector current. Specifications subject to change without notice. REV. C µV 70 ELECTRICAL CHARACTERISTICS (V 2 Units –3– MAT02 WAFER TEST LIMITS (@ 258C for V CB = 15 V and IC = 10 mA, unless otherwise noted.) Parameter Symbol Breakdown Voltage Offset Voltage Input Offset Current Input Bias Current Current Gain BVCEO VOS IOS IB hFE Current Gain Match Offset Voltage Change vs. VCB Offset Voltage Change vs. Collector Current Bulk Resistance Collector Saturation Voltage ∆hFE ∆VOS/∆VCB ∆VOS/∆IC rBE VCE (SAT) Conditions 10 µA ≤ IC ≤ 1 mA1 VCB = 0 V IC = 1 mA, VCB = 0 V IC = 10 µA, VCB = 0 V 10 µA ≤ IC ≤ 1 mA, VCB = 0 V 0 V ≤ VCB ≤ 40 V 10 µA ≤ IC ≤ 1 mA1 VCB = 0 10 µA ≤ IC ≤ 1 mA1 100 µA ≤ IC ≤ 10 mA IC = 1 mA IB = 100 µA MAT02N Limits Units 40 150 1.2 34 400 300 4 50 V min µV max nA max nA max min 50 µV max 0.5 0.2 Ω max V max % max µV max NOTES 1 Measured at lC = 10 µA and guaranteed by design over the specified range of I C. Electrical tests are performed at wafer probe to the limits shown. Due to variations in assembly methods and normal yield loss, yield after packaging is not guaranteed for standard product dice. Consult factory to negotiate specifications based on dice lot qualification through sample lot assembly and testing. TYPICAL ELECTRICAL CHARACTERISTICS (V CB = 15 V, IC = 10 mA, TA = +258C, unless otherwise noted.) MAT02N Limits Units 0.08 µV/°C 40 pA/°C VCE = 10 V, IC = 10 mA 200 MHz 0 ≤ VCB ≤ 40 V 70 pA/V Parameter Symbol Conditions Average Offset Voltage Drift Average Offset Current Drift Gain-Bandwidth Product Offset Current Change vs. VCB TCVOS TCIOS 10 µA ≤ IC ≤ 1 mA 0 ≤ VCB ≤ VMAX IC = 10 µA fT ∆IOS/∆VCB DICE CHARACTERISTICS 1. COLLECTOR (1) 2. BASE (1) 3. EMITTER (1) 4. COLLECTOR (2) 5. BASE (2) 6. EMITTER (2) 7. SUBSTRATE Die Size 0.061 × 0.057 inch, 3,477 sq. mils (1.549 × 1.448 mm, 224 sq. mm) CAUTION ESD (electrostatic discharge) sensitive device. Electrostatic charges as high as 4000 V readily accumulate on the human body and test equipment and can discharge without detection. Although the MAT02 features proprietary ESD protection circuitry, permanent damage may occur on devices subjected to high energy electrostatic discharges. Therefore, proper ESD precautions are recommended to avoid performance degradation or loss of functionality. –4– WARNING! ESD SENSITIVE DEVICE REV. C MAT02 Figure 1. Current Gain vs. Collector Current Figure 4. Base-Emitter-On Voltage vs. Collector Current Figure 7. Saturation Voltage vs. Collector Current REV. C Figure 2. Current Gain vs. Temperature Figure 5. Small Signal Input Resistance vs. Collector Current Figure 8. Noise Voltage Density vs. Frequency –5– Figure 3. Gain Bandwidth vs. Collector Current Figure 6. Small-Signal Output Conductance vs. Collector Current Figure 9. Noise Voltage Density vs. Collector Current MAT02 Figure 10. Noise Current Density vs. Frequency Figure 13. Collector-to-Collector Leakage vs. Temperature Figure 11. Total Noise vs. Collective Current Figure 14. Collector-to-Collector Capacitance vs. Collector-to Substrate Voltage Figure 16. Collector-to-Collector Capacitance vs. Reverse Bias Voltage Figure 12. Collector-to-Base Leakage vs. Temperature Figure 15. Collector-Base Capacitance vs. Reverse Bias Voltage Figure 17. Emitter-Base Capacitance vs. Reverse Bias Voltage –6– REV. C MAT02 Figure 18. Log Conformance Test Circuit LOG CONFORMANCE TESTING The log conformance of the MAT02 is tested using the circuit shown above. The circuit employs a dual transdiode logarithmic converter operating at a fixed ratio of collector currents that are swept over a 10:1 range. The output of each transdiode converter is the VBE of the transistor plus an error term which is the product of the collector current and rBE, the bulk emitter resistance. The difference of the VBE is amplified at a gain of ×100 by the AMP01 instrumentation amplifier. The differential emitter-base voltage (∆VBE) consists of a temperaturedependent dc level plus an ac error voltage which is the deviation from true log conformity as the collector currents vary. The output of the transdiode logarithmic converter comes from the idealized intrinsic transistor equation (for silicon): VBE kT I C In = where IS q (1) An error term must be added to this equation to allow for the bulk resistance (rBE) of the transistor. Error due to the op amp input current is limited by use of the OP15 BiFET-input op amp. The resulting AMP01 input is: kT (2) A ramp function which sweeps from 1 V to 10 V is converted by the op amps to a collector current ramp through each transistor. Because IC1 is made equal to 10 IC2, and assuming TA = 25°C, the previous equation becomes: ∆VBE = 59 mV + 0.9 IC1 rBE (∆rBE ~ 0) As viewed on an oscilloscope, the change in ∆VBE for a 10:1 change in IC is then displayed as shown below: k = Boltzmann’s Constant (1.38062 × 10-23 J/°K) q = Unit Electron Charge (1.60219 × 10-19 °C) T = Absolute Temperature, °K (= °C + 273.2) IS = Extrapolated Current for VBE→0 IC = Collector Current REV. C I C1 ∆VBE = q In I + IC1 rBE1 – IC2 rBE2 C2 –7– MAT02 With the oscilloscope ac coupled, the temperature dependent term becomes a dc offset and the trace represents the deviation from true log conformity. The bulk resistance can be calculated from the voltage deviation ∆VO and the change in collector current (9 mA): rBE ∆V O 1 × = 9 mA 100 by various offsetting techniques. Protective diodes across each base-to-emitter junction would normally be needed, but these diodes are built into the MAT02. External protection diodes are therefore not needed. For the circuit shown in Figure 19, the operational amplifiers make I1 = VX/R1, I2 = VY/R2, I3 = VZ/R3, and IO = VO/RO. The output voltage for this one-quadrant, log-antilog multiplier/divider is ideally: (3) This procedure finds rBE for Side A. Switching R1 and R2 will provide the rBE for Side B. Differential rBE is found by making R1 = R2. VO = R3RO V XV Y (VX, VY, VZ > 0) R1R2 V Z (4) If all the resistors (RO, R1, R2, R3) are made equal, then VO = VXVY/VZ. Resistor values of 50 kΩ to 100 kΩ are recommended assuming an input range of 0.1 V to +10 V. APPLICATIONS: NONLINEAR FUNCTIONS MULTIPLIER/DIVIDER CIRCUIT The excellent log conformity of the MAT02 over a very wide range of collector current makes it ideal for use in log-antilog circuits. Such nonlinear functions as multiplying, dividing, squaring, and square-rooting are accurately and easily implemented with a log-antilog circuit using two MAT02 pairs (see Figure 19). The transistor circuit accepts three input currents (I1, I2, and I3) and provides an output current IO according to IO = I1I2/I3. All four currents must be positive in the log-antilog circuit, but negative input voltages can be easily accommodated ERROR ANALYSIS The base-to-emitter voltage of the MAT02 in its forward active operation is: VBE = kT I C In + rBEIC, VCB ~ 0 IS q (5) The first term comes from the idealized intrinsic transistor equation previously discussed (see equation (1)). Figure 19. One-Quadrant Multiplier/Divider –8– REV. C MAT02 approximately 26 mV and the error due to an rBEIC term will be rBEIC/26 mV. Using an rBE of 0.4 Ω for the MAT02 and assuming a collector current range of up to 200 µA, then a peak error of 0.3% could be expected for an rBEIC error term when using the MAT02. Total error is dependent on the specific application configuration (multiply, divide, square, etc.) and the required dynamic range. An obvious way to reduce ICrBE error is to reduce the maximum collector current, but then op amp offsets and leakage currents become a limiting factor at low input levels. A design range of no greater than 10 µA to 1 mA is generally recommended for most nonlinear function circuits. Figure 20. Compensation of Bulk Resistance Error Extrinsic resistive terms and the early effect cause departure from the ideal logarithmic relationship. For small VCB, all of these effects can be lumped together as a total effective bulk resistance rBE. The rBEIC term causes departure from the desired logarithmic relationship. The rBE term for the MAT02 is less than 0.5 Ω and ∆rBE between the two sides is negligible. Returning to the multiplier/divider circuit of Figure 1 and using Equation (4): VBE1A + VBE2A – VBE2B –VBE1B + (I1 + I2 – IO – I3) rBE = 0 If the transistor pairs are held to the same temperature, then: kT II kT I S1AI S2A In 1 2 = In + (I1 + I2 – IO – I3) rBE I 3IO q I S1B I S2B q (6) If all the terms on the right-hand side were zero, then we would have In (I1 I2/I3 IO) equal to zero which would lead directly to the desired result: IO = I1I 2 , where I1, I2, I3, IO > 0 I3 (7) Note that this relationship is temperature independent. The right-hand side of Equation (6) is near zero and the output current IO will be approximately I1 I2/I3. To estimate error, define ø as the right-hand side terms of Equation (6): ø = In I S1AI S2A q + (I + I2 – IO – I3) rBE I S1B I S2B kT 1 (8) For the MAT02, In (ISA/ISB) and ICrBE are very small. For small ø, εØ ~ 1 + ø and therefore: I1I 2 =1+ø I 3IO A powerful technique for reducing error due to ICrBE is shown in Figure 20. A small voltage equal to ICrBE is applied to the transistor base. For this circuit: VB = In more complex circuits, such as the circuit in Figure 19, it may be inconvenient to apply a compensation voltage to each individual base. A better approach is to sum all compensation to the bases of Q1. The “A” side needs a base voltage of (VO/RO + VZ/R3) rBE and the “B” side needs a base voltage of (VX/R1+VY/ R2) rBE. Linearity of better than ± 0.1% is readily achievable with this compensation technique. Operational amplifier offsets are another source of error. In Figure 20, the input offset voltage and input bias current will cause an error in collector current of (VOS/R1) + IB. A low offset op amp, such as the OP07 with less than 75 µV of VOS and IB of less than ± 3 nA, is recommended. The OP22/OP32, a programmable micropower op amp, should be considered if low power consumption or single-supply operation is needed. The value of frequency-compensating capacitor (CO) is dependent on the op amp frequency response and peak collector current. Typical values for CO range from 30 pF to 300 pF. . . . FOUR-QUADRANT MULTIPLIER A simplified schematic for a four-quadrant log/antilog multiplier is shown in Figure 21. As with the previously discussed onequadrant multiplier, the circuit makes IO = I1 I2/I3. The two input currents, I1 and I2, are each offset in the positive direction. This positive offset is then subtracted out at the output stage. Assuming ideal op amps, the currents are: REV. C I1 = VX VR V V + ,I = Y + R R1 R2 2 R1 R2 I1I2 (1 – ø) I3 The In (ISA/ISB) terms in ø cause a fixed gain error of less than ± 0.6% from each pair when using the MAT02, and this gain error is easily trimmed out by varying RO. The ICrBE terms are more troublesome because they vary with signal levels and are multiplied by absolute temperature. At 25°C, kT/q is (10) The error from rBEIC is cancelled if RC/R2 is made equal to rBE/ R1. Since the MAT02 bulk resistance is approximately 0.39 Ω, an RC of 3.9 Ω and R2 of 10 R1 will give good error cancellation. (9) IO ~ RC r BE V and ICrBE = V R2 1 R1 1 (11) IO = V X VY V R V O V + + + ,I = R R1 R1 R2 RO 3 R2 From IO = I1 I2/I3, the output voltage will be: VO = –9– RO R2 V XV Y 2 VR R1 (12) MAT02 Collector-current range is the key design decision. The inherently low rBE of the MAT02 allows the use of a relatively high collector current. For input scaling of ± 10 V full-scale and using a 10 V reference, we have a collector-current range for I1 and I2 of: –10 10 10 10 R + R ≤ IC ≤ R + R 1 1 2 2 MULTIFUNCTION CONVERTER The multifunction converter circuit provides an accurate means of squaring, square rooting, and of raising ratios to arbitrary powers. The excellent log conformity of the MAT02 allows a wide range of exponents. The general transfer function is: (13) V Z VO = VY V X Practical values for R1 and R2 would range from 50 kΩ to 100 kΩ. Choosing an R1 of 82 kΩ and R2 of 62 kΩ provides a collector-current range of approximately 39 µA to 283 µA. An RO of 108 kΩ will then make the output scale factor 1/10 and VO = VXVY/10. The output, as well as both inputs, are scaled for ± 10 V full scale. V Z VO = 10 10 (I1 + I2 – I3 – IO) rBE + ρVO = 0 m (16) As with the multiplier/divider circuits, assume that the transistor pairs have excellent matching and are at the same temperature. The In ISA/ISB will then be zero. In the circuit of Figure 22, the voltage drops across the base-emitter junctions of Q1 provide: The currents are known from the previous discussion, and the relationship needed is simply: r BE V RO O (15) VX, VY, and VZ are input voltages and the exponent “m” has a practical range of approximately 0.2 to 5. Inputs VX and VY are often taken from a fixed reference voltage. With a REF01 providing a precision +10 V to both VX and VY, the transfer function would simplify to: Linear error for this circuit is substantially improved by the small correction voltage applied to the base of Q1 as shown in Figure 21. Assuming an equal bulk emitter resistance for each MAT02 transistor, then the error is nulled if: VO = m (14) The output voltage is attenuated by a factor of rBE/RO and applied to the base of Q1 to cancel the summation of voltage drops due to rBEIC terms. This will make In (I1 I2/I3 IO) more nearly zero which will thereby make IO = I1 I2/I3 a more accurate relationship. Linearity of better than 0.1% is readily achievable with this circuit if the MAT02 pairs are carefully kept at the same temperature. RB kT I V = In Z RB + KR A A q IX (17) IZ is VZ/R1 and IX is VX/R1. Similarly, the relationship for Q2 is: RB kT I VA = In O IY q RB + (1 – K )RA (18) IO is VO/RO and IY is VY/R1. These equations for Q1 and Q2 can then be combined. RB + KR A I I In Z = In O I I RB + (1 – K )RA X Y (19) Figure 21. Four-Quadrant Multiplier –10– REV. C MAT02 Substituting in the voltage relationships and simplifying leads to: m V Z RO VO = R V Y V , where X 1 (20) Accuracy is limited at the higher input levels by bulk emitter resistance, but this is much lower for the MAT02 than for other transistor pairs. Accuracy at the lower signal levels primarily depends on the op amp offsets. Accuracies of better than 1% are readily achievable with this circuit configuration and can be better than ± 0.1% over a limited operating range. FAST LOGARITHMIC AMPLIFIER RB + KR A m = R + 1– K R ) A B ( The factor “K” is a potentiometer position and varies from zero to 1.0, so “m” ranges from RB/(RA + RB) to (RB + RA)/RB. Practical values are 125 Ω for RB and 500 Ω for RA; these values will provide an adjustment range of 0.2 to 5.0. A value of 100 kΩ is recommended for the R1 resistors assuming a fullscale input range of 10 V. As with the one-quadrant multiplier/ divider circuit previously discussed, the VX, VY, and VZ inputs must all be positive. The op amps should have the lowest possible input offsets. The OP07 is recommended for most applications, although such programmable micropower op amps as the OP22 or OP32 offer advantages in low-power or single-supply circuits. The micropower op amps also have very low input bias-current drift, an important advantage in log/antilog circuits. External offset nulling may be needed, particularly for applications requiring a wide dynamic range. Frequency compensating capacitors, on the order of 50 pF, may be required for A2 and A3. Amplifier A1 is likely to need a larger capacitor, typically 0.0047 µF, to assure stability. The circuit of Figure 23 is a modification of a standard logarithmic amplifier configuration. Running the MAT02 at 2.5 mA per side (full-scale) allows a fast response with wide dynamic range. The circuit has a 7 decade current range, a 5 decade voltage range, and is capable of 2.5 µs settling time to 1% with a 1 V to 10 V step. The output follows the equation: VO = (21) The output is inverted with respect to the input, and is nominally –1 V/decade using the component values indicated. LOW-NOISE 31000 AMPLIFIER The MAT02 noise voltage is exceptionally low, only 1 nV/√Hz at 10 Hz when operated over a collector-current range of 1 mA to 4 mA. A single-ended ×1000 amplifier that takes advantage of this low MAT02 noise level is shown in Figure 24. In addition to low noise, the amplifier has very low drift and high CMRR. An OP32 programmable low-power op amp is used for the second stage to obtain good speed with minimal power consumption. Small-signal bandwidth is 1 MHz, slew rate is 2.4 V/µs, and total supply current is approximately 2.8 mA. Figure 22. Multifunction Converter REV. C R3 + R2 kT V REF In R2 V IN q –11– MAT02 Frequency compensation is very easy with this circuit; just vary the set-resistor RS for the desired frequency response. Gain-bandwidth of the OP32 varies directly with the supply current. A set resistor of 549 kΩ was found to provide the best step response for this circuit. The resultant supply current is found from: RSET = (V +) – (V –) – (2V BE ), I I SET SY =15 I SET (22) The ISET, using ± 15 V supplies and an RSET of 549 kΩ, is approximately 52 µA which will result in supply current of 784 µA. Dynamic range of this amplifier is excellent; the OP32 has an output voltage swing of ± 14 V with a ± 15 V supply. 000000000 Transistors Q2 and Q3 form a 2 mA current source (0.65 V/ 330 Ω ~ 2 mA). Each collector of Q1 operates at 1 mA. The OP32 inputs are 3 V below the positive supply voltage (RLIC ~ 3 V). The OP32’s low input offset current, typically less than 1 nA, and low offset voltage of 1 mV cause negligible error when referred to the amplifier input. Input stage gain is gmRL, which is approximately 100 when operating at IC of 1 mA with RL of 3 kΩ. Since the OP32 has a minimum open-loop gain of 500,000, total open-loop gain for the composite amplifier is over 50 million. Even at closed-loop gain of 1000, the gain error due to finite open-loop gain will be negligible. The OP32 features excellent symmetry of slew-rate and very linear gain. Signal distortion is minimal. Input characteristics are outstanding. The MAT02F has offset voltage of less than 150 µV at 25°C and a maximum offset drift of 1 µV/°C. Nulling the offset will further reduce offset drift. This can be accomplished by slightly unbalancing the collector load resistors. This adjustment will reduce the drift to less than 0.1 µV/°C. Input bias current is relatively low due to the high current gain of the MAT02. The minimum β of 400 at 1 mA for the MAT02F implies an input bias current of approximately 2.5 µA. This circuit should be used with signals having relatively low source impedance. A high source impedance will degrade offset and noise performance. This circuit configuration provides exceptionally low input noise voltage and low drift. Noise can be reduced even further by raising the collector currents from 1 mA to 3 mA, but power consumption is then increased. OUTLINE DIMENSION Dimensions shown in inches and (mm). 6-Lead Metal Can (TO-78) REFERENCE PLANE Figure 23. Fast Logarithmic Amplifier 0.185 (4.70) 0.165 (4.19) 0.750 (19.05) 0.500 (12.70) 0.250 (6.35) MIN 0.100 (2.54) BSC 0.160 (4.06) 0.110 (2.79) 0.050 (1.27) MAX 0.335 (8.51) 0.305 (7.75) 5 0.200 (5.08) BSC 0.045 (1.14) 0.010 (0.25) 6 0.045 (1.14) 0.027 (0.69) 2 0.019 (0.48) 0.016 (0.41) 0.040 (1.02) MAX 3 0.100 (2.54) BSC 0.021 (0.53) 0.016 (0.41) 1 0.034 (0.86) 0.027 (0.69) 45° BSC BASE & SEATING PLANE Figure 24. Low-Noise, Single-Ended X1000 Amplifier –12– REV. C PRINTED IN U.S.A. 0.370 (9.40) 0.335 (8.51) 4

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