INTERSIL FEATURES e Accuracy of +0.5% (A version) Full +10V [/O voltage range 1 MHz bandwidth Uses standard +15V supplies Built in op amp provides level shifting, division and square root functions. ICL8013 Four Quadrant Analog Multiplier GENERAL DESCRIPTION The 1CL8013 is a four quadrant analog multiplier whose output is proportional to the algebraic product of two input signals. Feedback around an internal op-amp provides tevel shifting and can be used to generate division and square root functions. A simple arrangement of potentiometers may be used to trim gain accuracy, offset voltage and feedthrough performance. The high accuracy, wide bandwidth, and increased versatility of the |CL8013 makes it ideal for all multiplier applications in control and instrumentation systems. Applications include RMS measuring equipment, frequency doublers, balanced modulators and demodulators, function generators, and systems process controls. BLOCK DIAGRAM (MULTIPLIER) 2in Xin VOLTAGE TO CURRENT [| BALANCED op CONVERTER AND VARIABLE GAIN AMP. OUTPUT Xos. SIGNAL COMPRESSION }+1 AMPLIFIER [es Yino-4 VOLTAGE TO CURRENT CONVERTER Yoso- | Zin ORDERING INFORMATION PIN CONFIGURATION TEMPERATURE | MULTIPLICATION | ORDER PART TYPE RANGE ERROR NUMBER ICLBO13AM] 55C to +125C) 5% (CL8013AM TZ ICL8013BM] -55C to +125C +1% ICL8013BM TZ ICL8013CM] -55C to +125C| +2% \ MAX {CL8013CM TZ ICL8O13AC} 0C to +70C +.5% ICL8013AC TZ ICL8013BC} 0C to +70C +1% ICL8013BC TZ ICL8013CC| 0C to +70C +2% ICL8013CC TZ ICL8013C/D]_0C to +70C +2% TYP ICL8013C/D TOP VIEW {outline dwg TO-100} 5-176ICL8013 ABSOLUTE MAXIMUM RATINGS Supply Voitage ................ Power Dissipation (Note 1) enna seeeeeeseees TBV 500 mW input Voltages (X, Y, Z, Xo, Yo, Zo)... .. es. keene Lead Temperature (soldering, 10 sec) Storage Temperature Range NOTE 1: Derate at 6.8 mW/C for operation at ambient temperature above 75C. INIERSIL -65C to +150C 300C Stresses above those listed under Absolute Maximum Ratings may cause permanent damage to the device. These are stress ratings only, and functional operation of the device at these or any other conditions above those indicated in the operational sections of the specifications is not implied. Exposure to absolute maximum rating conditions for extended periods may affect device reliability. ELECTRICAL CHARACTERISTICS (Unless otherwise specified Ta = 25C, Vsupp = +15V, Gain and Offset Potentiometers Externally Trimmed) ICL8013A ICL8013B 1CL8013C : PARAMETER CONDITIONS MIN | TYP | MAX MIN {| TYP | MAX | MIN { TYP | MAX UNITS xy XY. XY Multiplier Function 10 10 10 Multiplication Error -10<xX<10 5 1.0 2.0 | 2.0 |% Full Scale -10< <10 . 10Z 10Z 102, Divider Function x x x Division Error X=-10 0.3 0.3 0.3 % Full Scale =-1 15 16 1.5 % Full Scale Feedthrough X=O0Y =20Vp_p f= 50Hz 50 100 200* | 200 mVp-p Y =0X = 20Vp-p f = 50Hz 50 100 150 | 150 MVp-p Nonlinearity X Input X = 20Vp-p +0.5 +0.5 +0.8 % Y = +10Vdc Y Input Y = 20Vp-p +0.2 +0.2 +0.3 % X = 10Vdc Frequency Response Smal Signal Bandwidth (-3dB) 1.0 1.0 1.0 MHz Full Power Bandwidth 750 750 750 kHz Slew Rate 45 45 45 V/ps 1% Amplitude Error 75 76 75 kHz 1% Vector Error 5 kHz (0.5 Phase Shift) Settling Time Vin = +10V 1 1 1 BS (to 2% of Final Value) ' Overload Recovery 1 1 1 us {to +2% of Final Value) : Output Noise 5 Hz to 10 kHz 0.6 0.6 0.6 mV rms 5 Hz to 5 MHz 3 3 3 mV rms Input Resistance X Input 10 10 10 MO Y Input 6 6 6 MQ Z Input 36 36 36 KO Input Bias Current ~ X or input 2 5 7.6 10 BA Z Input 25 25 25 BA Power Supply Variation Multiplication Error 0.2 0.2 0.2 %/%o Output Offset 50 75 100 mvV/V Scale Factor 0.1 0.1 01 %/% Quiescent Current : . 3.5 6.0 3.5 6.0 3.5 6.0 mA THE FOLLOWING SPECIFICATIONS APPLY OVER THE OPERATING TEMPERATURE RANGES . Multiplication -10< X < 10, 15 2 3 % Full Scale Error -10<<10 Average Temperature Coefficient of Accuracy 0.06 0.06 0.06 %/C Output Offset 0.2 0.2 0.2 mv/C Scale Factor 0.04 0.04 0.04 %/C Input Bias Current X or Y Input 5 5 10 pA Z Input 25 25 35 BA Input Voltage (X, Y, or 2) +10 +10 +10 v Output Voltage Swing RL 2 2k +10 +10 +10 v Ci < 1000 pF . *Dice only 5-177CIRCUIT DESCRIPTION The fundamental element of the ICL8013 multiplier is the bipolar differential amplifier of Figure 1. i 2le v- Figure 1: Differential Amplifier The small signal differentiai voltage: gain of this circuit is given by y Your _ Rt VIN le Substituti Kt ul o_o stituting fe = gle R le Ri Vour=Vin =Vine ve fe kT input voltage Vin and the emitter current le. In the simple transconductance multiplier of Figure 2, a current source comprising Q3, Di, and Ry is used. If Vy is large compared with the drop across Di, then Vv = 2le and oe Ip Ry Vout = Re ivy e wy) OUT kTRy x Y. vt AL RL Vout! Vout = K (Wx Vy) | of Vx _ aR y~ Vout = irAy (Vx Vy) Figure 2: Transconductance Multiplier There are several difficulties with this simple moduiator: 1: Vy must be positive and greater than Vp 2: Some portion of the signal at Vx will appear at the output unless te = 0. Vx must be a small signal for the differential pair to be linear. : The output voltage is not centered around ground. 3: The output voltage is thus proportional to the product of the. The first problem relates to the method of converting the Vy voltage to a current to vary the gain of the Vx differential pair. A better method, Figure 3, uses another differential pair but with considerable emitter degeneration. In this circuit the differential input voltage appears across the common emitter resistor, producing a current which adds or subtracts from the quiescent current in either collector. This type of voltage to current converter handies signals from 0 volts to +10 voits with excellent linearity. Figure 3: Voltage to Current Converter The second problem is called feedthrough; i.e. the product of zero and some finite input signal does not produce zerd output voltage. The circuit whose operation is illustrated by Figures 4A, B, and C overcomes this problem and forms the heart of many multiplier circuits in use today. This circuit is basically two matched differential pairs with cross coupled collectors. Consider the case shown in 4A of exactly equal current sources biasing the two pairs. With a small positive signal at Vin, the collector current of Qi and Qs will increase but the collector currents of Qe and Qs will decrease by the same amount. Since the collectors are cross coupled the current through the load resistors remains unchanged and independent of the Vin input voltage. vt te| RL AVouT = 0 o Wate - a | [wate +3 Figure 4A; Input Signal with Balanced Current Sources AVout = OV 5-178yt ___|_ == Pe + Qa oF Qe p-1 G3 VIN Re Yin AAA v- le] fle Figure 4B: No input Signal with Unbalanced Current Sources : 4 Vout = OV v- in Figure 4B, notice that with Vin = Oany variation in the ratio Figure 5: Typical Four Quadrant Multiplier-Modulator of biasing current sources will produce a common mode voltage across the load resistors. The differential output Figure 3 showed a current source formed by retying on the voitage will remain zero. In Figure 4C we apply a differential matching characteristics of a diode and the emitter base input voltage with unbalanced current sources. If lE1 is twice junction of a transistor. Extension of this idea toa differential lez, the gain of differential pair Q1 and Qe is twice the gain of circuit is shown in Fig. 6A. In a differential pair, the input pair Q3 and Q4. Therefore, the change in cross coupled voltage splits the biasing current in a logarithmic ratio. (The collector currents wiil be unequal and a differential output usual assumption of linearity is useful only for small signais.) o voltage will result. By replacing the separate biasing current Since the input to the differential pair in Figure 6A is the sources with the voltage to current converter of Figure 3 we have a balanced multiplier circuit capable of four quadrant operation (Figure 5). xelo| \o ~X) lo vt 3)- g!- Ash 3 Vout = 2RAL 3 Figure 6A: Current Gain Cell + vt Vin 7 q ate | fue Figure 4C: Input Signal with Unbalanced Current Sources, Vin Ditferential Output Voltage eS 8 This circuit of Fig. 5 still has the problem that the input voltage Vin must be small to keep the differential amplifier in the linear region. To be able to handle large signals, we need a an amplitude compression circuit. Figure 6B: Voltage Gain with Signal Compression 5-179difference in voltage across the two diodes, which in turn is proportional to the log of the ratio of drive currents, it follows that the ratio of diode currents and the ratio of collector currents are linearly related and independent of amplitude. If we combine this circuit with the voltage to current converter of Fig. 3, we have Fig: 68. The output of the differential amplifier is now proportional to the input voltage over a large dynamic range, thereby improving linearity while minimizing drift and noise factors. The complete schematic is shown in Figure 7. The differential pair Q3 and Q4 form a voltage to current converter whose output is compressed in collector diodes Qi and Qe. These diodes drive the balanced cross-coupled differential amplifier Q7/Qg Q14/Q15. The gain of these amplifiers is modulated by the voltage to current converter Qg and Qiao. Transistors Qs, Qe, Q11, and Qi2 are constant current sources which bias the voltage to current converter. The output amplifier comprises transistors Q16 through Qe7. R2 gm ze Sem R27 Na Zin t mect = j Q21 : . [ Q@1 a pe hee fo tras Ras R9 { Yin } Ry Qs R13 at Cats aa Ln RB SR? [common }- fou: oth < g R30 R31 s Q22 026 t R24 2 R28 Q18 023 tar | }| (area) ih | Figure 7: |CL8013 Schernatic MULTIPLICATION In the standard multiplier connection, the Z terminal is connected to the op amp output. All of the modulator output current thus flows through the feedback resistor R27 and produces a proportional output voltage. _xeY Eout = to x MODULATOR oo Figure 8A: Multiplier Block Diagram 3 oY Zin OUTPUT = 75 XIN o__-_ ICL8013 4 Yin r - 5k Oo 7| 10) 9 75k Xos Yos Zos Figure 8B: Actual Circuit Connection MULTIPLIER Trimming Procedure 1. Set Xin = Yin = OV and adjust Zos for zero Output. 2. Apply a +10V low frequency (<100Hz) sweep (sine or triangle) to Yin with Xin = OV, and adjust Xos for minimum output. . 3 Apply the sweep signal of Step 2 to Xin with Yin = OV and - adjust Yos for minimum Output. 4. Readjust Zos as in.Step 1, if necessary. 5. With Xin = 10.0V DC and the sweep signal of Step 2 applied to Yin, adjust the Gain potentiometer for Output = Vin. This is easily accomplished with a differential scope plug-in (A + B) by inverting one signal and adjusting Gain control for (Output ~ Yin) = Zero. DIVISION If the Z terminal is used as an input, and the output of the op- amp connected to the Y input, the device functions as a divider. Since the input to the op-amp is at virtual ground, and requires negligible bias current, the overall feedback forces the modulator output current to equal the current produced by Z. Therefore ip = XeY = 2 = 102 = 10Z Since Y = Eout, Eout X 5-180Note that when connected as a divider, the Xinput must bea negative voitage to maintain overall negative feedback. MODULATOR Figure 9A: Division Block Diagram Xas Yos Zos Figure 9B: Actual Circuit Connection DIVIDER Trimming Procedure 1. Set trimming potentiometers at mid-scale by adjusting voltage on pins 7, 9 and 10 (Xos, Yos, Zos) for zero volts. With Zin = OV, trim Zos to hold the Output constant, as Xin is varied from -10V through -1V. . With Zin = OV and Xin =-10.0V adjust Yos for zero Output voltage. . With Zin = Xin (and/or Zin = Xin) adjust Xos for minimum worst-case variation of Output, as XIN is varied from 10V to -1V. . Repeat Steps 2 and 3 if Step 4 required a large initial adjustment. . With Zin = Xin (and/or Zin = Xin) adjust the gain control until the output is the closest average around +10.0V (-10V for Zin = XiN) aS Xin is varied from -10V to -3V. 2. SQUARING The squaring function is achieved by simply multiplying with the two inputs tied together. The squaring circuit may also be used as the basis for a frequency doubler since cos? w = 1/2 (cos 2w +. 1). Figure 10A: Squarer Block Diagram jourpur - x IcLs013 >; oon 7; 10) 9 Xos Yos Zos Figure 10B: Actual Circuit Connection SQUARE ROOT Tying the X and Y inputs together and using overall feedback from the Op Amp results in the square root function. The output of the modulator is again forced to equal the current produced by the Z input. lo = XeY = (- Eout) = 10Z Eout =- VV 10Z The output is a negative voltage which maintains overall negative feedback. A diode in series with the Op Amp output prevents the latchup that would otherwise occur for negative input voltages. MODULATOR |ic = rH Figure 11A: Square Root Block Diagram seems Xcs Yos Zos 7,10] 9 (N4148 (TO we OUTPUT = = / T0Z Zin ICL8013 Figure 118: Actual Circuit Connection SQUARE ROOT Trimming Procedure 1. Connect the ICL8013 in the Divider configuration. 2. Adjust Zos, Yos, Xos, and Gain using Steps 1 through 6 of Divider Trimming Procedure. Convert to the Square Root configuration by connecting Xin to the Output and inserting a diode between Pin 4and the Output node. . With Zin = OV adjust Zos for zero Output voltage. 3. 6-181VARIABLE GAIN AMPLIFIER Most applications for the ICL8013 are straight forward variations of the simple arithmetic functions described above. Although the circuit description frequently disguises the fact, it has already. been shown that the frequency doubler is nothing more than a squaring circuit. Similarly the variable gain amplifier is nothing more than a multiplier, with the input signal applied at the X input and the control voltage applied at the Y input. z output = 3 Wy neur o] cians _ 1 GAIN CONTROL voLTace o* 4 10) 9 Xos Yos Zos 7.5k Figure 12: Variable Gain Amplifier TYPICAL APPLICATIONS MULTIPLICATION Zin Ls output = 2 XIN o7 6 (CL8013 4 o 4 Yin Sk Jl 7} 10) 9 GAIN 75k Xos Yos Zos DIVISION Xos Yos Zos Xino$ 10Z ZNO CTO 10) 5 1 Yin POTENTIOMETERS FOR TRIMMING OFFSET AND FEEDTHROUGH meee Yoso> 2 20k Zosoe o 20k va SQUARE ROOT Xos Yos Zos Xin (0 TO + 10v) ina148._| QutpUT = - /40Z 2N FT im _ GAIN TYPICAL PERFORMANCE CURVES AMPLITUDE AND PHASE AS A FUNCTION OF FREQUENCY EES) a 30% AMPLITUDE (dB) (DEG PHA NONLINEARITY (% OF FULL SCALE) tk = 10k = 100k 1M FREQUENCY (Hz) 10M NONLINEARITY AS A FUNCTION OF FREQUENCY 10k FREQUENCY (Hz) FEEDTHROUGH AS A FUNCTION OF FREQUENCY FEEDTHROUGH (dB) 100k FREQUENCY (Hz) 100k tk 10k 1M 10M DEFINITION OF TERMS Multiplication/Division Error: This is the basic accuracy specification. It includes terms due to linearity, gain, and offset errors, and is expressed as a percentage of the full scale output. Feedthrough: With either input at zero, the output of an ideal multiplier should be zero regardless of the signal applied to 5-182 the other input. The output seen in a non-ideal multiplier is known as the feedthrough. Nonlinearity: The maximum deviation from the best straight line constructed through the output data, expressed as a percentage of full scale. One input is held constant and the other swept through its nominal range. The nonlinearity is the component of the total multiplication/division error which cannot be trimmed out.