a FEATURES Simple: Basic Function is W = XY + Z Complete: Minimal External Components Required Very Fast: Settles to 0.1% of FS in 20 ns DC-Coupled Voltage Output Simplifies Use High Differential Input Impedance X, Y and Z Inputs Low Multiplier Noise: 50 nV/√Hz APPLICATIONS Very Fast Multiplication, Division, Squaring Wideband Modulation and Demodulation Phase Detection and Measurement Sinusoidal Frequency Doubling Video Gain Control and Keying Voltage Controlled Amplifiers and Filters 250 MHz, Voltage Output 4-Quadrant Multiplier AD835 FUNCTIONAL BLOCK DIAGRAM X1 X = X1 –X2 AD835 X2 XY ∑ XY + Z +1 W OUTPUT Y1 Y2 Y = Y1 –Y2 Z INPUT PRODUCT DESCRIPTION PRODUCT HIGHLIGHTS The AD835 is a complete four-quadrant voltage output analog multiplier fabricated on an advanced dielectrically isolated complementary bipolar process. It generates the linear product of its X and Y voltage inputs, with a –3 dB output bandwidth of 250 MHz (a small signal rise time of 1 ns). Full-scale (–1 V to +1 V) rise/fall times are 2.5 ns (with the standard RL of 150 Ω) and the settling time to 0.1% under the same conditions is typically 20 ns. 1. The AD835 is the first monolithic 250 MHz four quadrant voltage output multiplier. Its differential multiplication inputs (X, Y) and its summing input (Z) are at high impedance. The low impedance output voltage (W) can provide up to ± 2.5 V and drive loads as low as 25 Ω. Normal operation is from ± 5 V supplies. Though providing state-of-the-art speed, the AD835 is simple to use and versatile. For example, as well as permitting the addition of a signal at the output, the Z input provides the means to operate the AD835 with voltage gains up to about ×10. In this capacity, the very low product noise of this multiplier (50 nV√Hz) makes it much more useful than earlier products. 2. Minimal external components are required to apply the AD835 to a variety of signal processing applications. 3. High input impedances (100 kΩi2 pF) make signal source loading negligible. 4. High output current capability allows low impedance loads to be driven. 5. State of the art noise levels achieved through careful device optimization and the use of a special low noise bandgap voltage reference. 6. Designed to be easy to use and cost effective in applications which formerly required the use of hybrid or board level solutions. The AD835 is available in an 8-pin plastic mini-DIP package (N) and an 8-pin SOIC (R) and is specified to operate over the –40°C to +85°C industrial temperature range. REV. A 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. © Analog Devices, Inc., 1994 One Technology Way, P.O. Box 9106, Norwood. MA 02062-9106, U.S.A. Tel: 617/329-4700 Fax: 617/326-8703 AD835–SPECIFICATIONS (TA = +258C, VS = 65 V, RL = 150 V, CL ≤ 5 pF unless otherwise noted) Model AD835AN/AR TRANSFER FUNCTION Parameter INPUT CHARACTERISTICS (X, Y) Differential Voltage Range Differential Clipping Level Low Frequency Nonlinearity vs. Temperature Common-Mode Voltage Range Offset Voltage vs. Temperature CMRR Bias Current vs. Temperature Offset Bias Current Differential Resistance Single-Sided Capacitance Feedthrough, X Feedthrough, Y DYNAMIC CHARACTERISTICS –3 dB Small-Signal Bandwidth –0.1 dB Gain Flatness Frequency Slew Rate Differential Gain Error, X Differential Phase Error, X Differential Gain Error, Y Differential Phase Error, Y Harmonic Distortion Settling Time, X or Y SUMMING INPUT (Z) Gain –3 dB Small-Signal Bandwidth Differential Input Resistance Single Sided Capacitance Maximum Gain Bias Current OUTPUT CHARACTERISTICS Voltage Swing vs. Temperature Voltage Noise Spectral Density Offset Voltage vs. Temperature2 Short Circuit Current Scale Factor Error vs. Temperature Linearity (Relative Error)3 vs. Temperature POWER SUPPLIES Supply Voltage For Specified Performance Quiescent Supply Current vs. Temperature PSRR at Output vs. Vp PSRR at Output vs. Vn Conditions VCM = 0 X = ± 1 V, Y = 1 V Y = ± 1 V, X = 1 V TMIN to TMAX1 X = ± 1 V, Y = 1 V Y = ± 1 V, X = 1 V W = ( X1 – X 2)(Y1 – Y 2) Min Typ 61.2 ±1 ± 1.4 0.3 0.1 –2.5 TMIN to TMAX1 f ≤ 100 kHz; ± 1 V p-p U ±3 +Z Max Unit 0.5 0.3 V V % FS % FS 0.7 0.5 +3 620 ± 25 70 10 TMIN to TMAX1 20 27 2 100 2 X = ± 1 V, Y = 0 V Y = ± 1 V, X = 0 V –46 –60 150 W = –2.5 V to +2.5 V f = 3.58 MHz f = 3.58 MHz f = 3.58 MHz f = 3.58 MHz X or Y = 10 dBm, 2nd and 3rd Harmonic Fund = 10 MHz Fund = 50 MHz To 0.1%, W = 2 V p-p From Z to W, f ≤ 10 MHz 0.990 X, Y to W, Z Shorted to W, f = 1 kHz ± 2.2 ± 2.0 TMIN to TMAX1 X = Y = 0, f < 10 MHz 250 15 1000 0.3 0.2 0.1 0.1 MHz MHz V/µs % Degrees % Degrees –70 –40 20 dB dB ns 0.995 250 60 2 50 50 MHz kΩ pF dB µA ± 2.5 50 ± 25 TMIN to TMAX1 75 ±5 TMIN to TMAX1 ± 0.5 TMIN to TMAX1 ± 4.5 TMIN to TMAX1 +4.5 V to +5.5 V –4.5 V to –5.5 V % FS % FS V mV mV dB µA µA µA kΩ pF dB dB ±5 16 68 ±9 61.0 ± 1.25 V V nV/√Hz mV mV mA % FS % FS % FS % FS ± 5.5 25 26 0.5 0.5 V mA mA %/V %/V 675 ± 10 NOTES 1 TMIN = –40°C, TMAX = +85°C. 2 Normalized to zero at +25°C. 3 Linearity is defined as residual error after compensating for input offset, output voltage offset and scale factor errors. All min and max specifications are guaranteed. Specifications in boldface are tested on all production units at final electrical test. Specifications subject to change without notice. –2– REV. A AD835 ABSOLUTE MAXIMUM RATINGS 1 PIN CONNECTIONS 8-Pin Plastic DIP (N) 8-Pin Plastic SOIC (R) Supply Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .± 6 V Internal Power Dissipation2 . . . . . . . . . . . . . . . . . . . . 300 mW Operating Temperature Range . . . . . . . . . . . . . –40°C to +85C Storage Temperature Range . . . . . . . . . . . . –65°C to +150°C Lead Temperature, Soldering 60 sec . . . . . . . . . . . . . . +300°C ESD Rating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1500 V Y1 NOTES 1 Stresses above those listed under “Absolute Maximum Ratings” may cause permanent damage to the device. This is a stress rating only and functional operation of the device at these or any other conditions above those indicated in the operational sections of this specification is not implied. Exposure to absolute maximum ratings for extended periods may affect device reliability. 2 Thermal Characteristics: 8-Pin Plastic DIP (N): θJC = 35°C/W; θJA = 90°C/W 8-Pin Plastic SOIC (R): θJC = 45°C/W; θJA = 115°C/W. 1 8 X1 Y2 2 AD835 7 X2 VN 3 TOP VIEW (Not to Scale) 6 VP Z 4 5 W ORDERING GUIDE Model Temperature Range Package Options* AD835AN AD835AR –40°C to +85°C –40°C to +85°C N-8 R-8 *N = Plastic DIP; R = Small Outline IC Plastic Package (SOIC). Typical Performance Characteristics Wfm FCC COMPOSITE 0.16 0.19 0.20 0.0 MIN = 0.00 MAX = 0.20 p-p/MAX = 0.20 –0.2 DIFFERENTIAL PHASE – Degrees –0.4 0.3 1ST 2ND 3RD 4TH 5TH 6TH 0.00 0.02 0.02 0.03 0.03 0.06 0.2 90 –2 0 PHASE –4 –90 –6 –180 –8 0.0 MIN = 0.00 MAX = 0.06 p-p = 0.06 –0.1 –0.2 1ST 2ND 3RD 4TH 5TH –10 1M 6TH DG DP (NTSC) FIELD = 1 LINE = 18 0.00 0.01 –0.00 0.3 Wfm 0.00 10M 100M FREQUENCY – Hz FCC COMPOSITE –0.01 –0.20 MIN = –0.02 MAX = 0.01 p-p/MAX = 0.03 0.2 0.1 X, Y CH = OdBm RL = 150Ω CL ≤ 5pF 0.0 0 –0.1 1ST 2ND 3RD 4TH 5TH 6TH 0.00 0.03 0.04 0.07 0.10 0.16 MAGNITUDE – dB –0.2 –0.3 0.20 0.10 MIN = 0.00 MAX = 0.16 p-p = 0.16 –0.10 –0.2 –0.3 –0.4 –0.6 300k 1ST 2ND 3RD 4TH 5TH 6TH 1M 10M 100M FREQUENCY – Hz Figure 4. Gain Flatness to 0.1 dB Figure 2. Typical Composite Output Differential Gain & Phase, NTSC for Y Channel; f = 3.58 MHz, RL = 150 Ω REV. A –0.1 –0.5 0.00 –0.20 1G Figure 3. Gain & Phase vs. Frequency of X, Y, Z Inputs Figure 1. Typical Composite Output Differential Gain & Phase, NTSC for X Channel; f = 3.58 MHz, RL = 150 Ω DIFFERENTIAL GAIN – % 180 GAIN 0 0.1 –0.3 DIFFERENTIAL PHASE – Degrees 2 –3– 1G PHASE – Degrees X, Y, Z CH = 0dBm RL = 150Ω CL ≤ 5pF 0.2 MAGNITUDE – dB DIFFERENTIAL GAIN – % DG DP (NTSC) FIELD = 1 LINE = 18 0.00 0.06 0.11 0.4 AD835 X, Y CH = 5dBm RL = 150Ω CL < 5pF 0 –20 20 Y FEEDTHROUGH –30 40 –40 60 CMRR – dB MAGNITUDE – dB –10 X FEEDTHROUGH –50 80 X FEEDTHROUGH –60 Y FEEDTHROUGH 1M 10M 100M FREQUENCY – Hz 1G 1M Figure 5. X and Y Feedthrough vs. Frequency 10M 100M FREQUENCY – Hz 1G Figure 8. CMRR vs. Frequency for X or Y Channel, RL = 150 Ω, CL ≤ 5 pF 0dBm ON SUPPLY X, Y = 1V –10 PSRR – dB 0.200V GND PSRR ON V+ –20 –30 –40 PSRR ON V– –50 –0.200V –60 100mV 10ns 300k 1M 10M 100M FREQUENCY – Hz 1G Figure 9. PSRR vs. Frequency for V+ and V– Supply Figure 6. Small Signal Pulse Response at W Output, RL = 150 Ω, CL ≤ 5 pF, X Channel = ± 0.2 V, Y Channel = ± 1.0 V 10MHz 1V GND 10dB/DIV –1V 30MHz 20MHz 500mV 10ns Figure 10. Harmonic Distortion at 10 MHz; 10 dBm Input to X or Y Channels, RL = 150 Ω, CL = ≤ 5 pF Figure 7. Large Signal Pulse Response at W Output, RL = 150 Ω, CL ≤ 5 pF, X Channel = ± 1.0 V, Y Channel = ± 1.0 V –4– REV. A AD835 15 OUTPUT OFFSET DRIFT WILL TYPICALLY BE WITHIN SHADED AREA 10 VOS OUTPUT DRIFT – mV 50MHz 10dB/DIV 100MHz 150MHz 5 0 –5 –10 OUTPUT VOS DRIFT, NORMALIZED TO 0 AT 25°C –15 –55 –35 –15 5 25 45 65 85 105 125 TEMPERATURE – °C Figure 11. Harmonic Distortion at 50 MHz, 10 dBm Input to X or Y Channel, RL = 150 Ω, CL ≤ 5 pF Figure 14. VOS Output Drift vs. Temperature 35 3RD ORDER INTERCEPT – dBm 200MHz 10dB/DIV X CH = 6dBm Y CH = 10dBm RL = 100Ω 30 100MHz 300MHz 25 20 15 10 5 0 0 20 40 60 80 100 120 140 160 RF FREQUENCY INPUT X CHANNEL – MHz 180 200 Figure 15. Fixed LO on Y Channel vs. RF Frequency Input to X Channel Figure 12. Harmonic Distortion at 100 MHz, 10 dBm Input to X or Y Channel, RL = 150 Ω, CL ≤ 5 pF 35 X CH = 6dBm Y CH = 10dBm RL = 100Ω 3RD ORDER INTERCEPT – dBm 30 +2.5V GND –2.5V 25 20 15 10 5 1V 10ns 0 0 Figure 13. Maximum Output Voltage Swing, RL = 50 Ω, CL ≤ 5 pF REV. A 20 40 60 80 100 120 140 160 LO FREQUENCY ON Y CH – MHz 180 200 Figure 16. Fixed IF vs. LO Frequency on Y Channel –5– AD835 PRODUCT DESCRIPTION Simplified representations of this sort, where all signals are presumed to be expressed in volts, are used throughout this data sheet, to avoid the needless use of less-intuitive subscripted variables (such as VX1). We can view all variables as being normalized to 1 V. For example, the input X can either be stated as being in the range –1 V to +1 V, or simply –1 to +1. The latter representation will be found to facilitate the development of new functions using the AD835. The explicit inclusion of the denominator, U, is also less helpful, as in the case of the AD835, if it is not an electrical input variable. The AD835 is a four-quadrant, voltage output, analog multiplier fabricated on an advanced, dielectrically isolated, complementary bipolar process. In its basic mode, it provides the linear product of its X and Y voltage inputs. In this mode, the –3 dB output voltage bandwidth is 250 MHz (a small signal rise time of 1 ns). Full-scale (–1 V to +1 V) rise/fall times are 2.5 ns (with the standard RL of 150 Ω) and the settling time to 0.1% under the same conditions is typically 20 ns. As in earlier multipliers from Analog Devices, a unique summing feature is provided at the Z-input. As well as providing independent ground references for inputs and output, and enhanced versatility, this feature allows the AD835 to operate with voltage gain. Its X-, Y- and Z-input voltages are all nominally ± 1 V FS, with overrange of at least 20%. The inputs are fully differential and at high impedance (100 kΩi2 pF) and provide a 70 dB CMRR (f ≤ 1 MHz). Scaling Adjustment The basic value of U in Equation 1 is nominally 1.05 V. Figure 18, which shows the basic multiplier connections, also shows how the effective value of U can be adjusted to have any lower voltage (usually 1 V) through the use of a resistive-divider between W (Pin 5) and Z (Pin 4). Using the general resistor values shown, we can rewrite Equation 1 as The low impedance output is capable of driving loads as small as 25 Ω. The peak output can be as large as ± 2.2 V minimum for RL = 150 Ω, or ± 2.0 V minimum into RL = 50 Ω. The AD835 has much lower noise than the AD534 or AD734, making it attractive in low level signal-processing applications, for example, as a wideband gain-control element or modulator. W = In this way, we can modify the effective value of U to The multiplier is based on a classic form, having a translinear core, supported by three (X, Y, Z) linearized voltage-to-current converters, and the load driving output amplifier. The scaling voltage (the denominator U, in the equations below) is provided by a bandgap reference of novel design, optimized for ultralow noise. Figure 17 shows the functional block diagram. U ' = (1 – k)U (5) without altering the scaling of the Z' input. (This is to be expected, since the only “ground reference” for the output is through the Z' input.) Thus, to set U' to 1 V, remembering that the basic value of U is 1.05 V, we need to choose R1 to have a nominal value of 20 times R2. The values shown here allow U to be adjusted through the nominal range 0.95 V to 1.05 V, that is, R2 provides a 5% gain adjustment. In general terms, the AD835 provides the function (X 1 – X 2)(Y 1 – Y 2) +Z U (3) (where Z' is distinguished from the signal Z at Pin 4). It follows that XY W = + Z' (4) (1 – k)U Basic Theory W = XY + kW + (1 – k)Z ' U (1) where the variables W, U, X, Y and Z are all voltages. Connected as a simple multiplier, with X = X1 – X2, Y = Y1 – Y2 and Z = 0, and with a scale factor adjustment (see below) which sets U = 1 V, the output can be expressed as +5V +5V FB 4.7µF TANTALUM (2) W = XY 0.01µF CERAMIC X X1 X = X1 –X2 AD835 ∑ XY + Z +1 7 6 5 X1X1 X2 VP W Y1 Y2 VN Z 1 2 3 4 W OUTPUT Y Y1 Y2 R1 = (1–k) R 2kΩ AD835 X2 XY W 8 R2 = kR 200Ω 4.7µF TANTALUM Y = Y1 –Y2 0.01µF CERAMIC FB Z1 Z INPUT –5V Figure 17. Functional Block Diagram Figure 18. Multiplier Connections Note that in many applications, the exact gain of the multiplier may not be very important; in which case, this network may be omitted entirely, or R2 fixed at 100 Ω. –6– REV. A AD835 APPLICATIONS The AD835 is both easy to use and versatile. The capability for adding another signal to the output at the Z input is frequently valuable. Three applications of this feature are presented here: a wideband voltage controlled amplifier, an amplitude modulator and a frequency doubler. Of course, the AD835 may also be used as a square law detector (with its X- and Y-inputs connected in parallel) in which mode it is useful at input frequencies to well over 250 MHz, since that is the bandwidth limitation only of the output amplifier. 12dB (VG = 1V) 6dB (VG = 0.5V) 0dB (VG = 0.25V) Multiplier Connections Figure 18 shows the basic connections for multiplication. The inputs will often be single sided, in which case the X2 and Y2 inputs will normally be grounded. Note that by assigning Pins 7 and 2 to these (inverting) inputs, respectively, an extra measure of isolation between inputs and output is provided. The X and Y inputs may, of course, be reversed to achieve some desired overall sign with inputs of a particular polarity, or they may be driven fully differentially. 10k 100k START 10 000.000Hz 1M 10M 100M STOP 100 000 000.000Hz Figure 20. AC Response of VCA An Amplitude Modulator Figure 21 shows a simple modulator. The carrier is applied both to the Y-input and the Z-input, while the modulating signal is applied to the X-input. For zero modulation, there is no product term, so the carrier input is simply replicated at unity gain by the voltage follower action from the Z-input. At X = 1 V, the RF output is doubled, while for X = –1 V, it is fully suppressed. That is, an X-input of approximately ± 1 V (actually ± U, or about 1.05 V) corresponds to a modulation index of 100%. Carrier and modulation frequencies can be up to 300 MHz, somewhat beyond the nominal –3 dB bandwidth. Power supply decoupling and careful board layout are always important in applying wideband circuits. The decoupling recommendations shown in Figure 18 should be followed closely. In remaining figures in this data sheet, these power supply decoupling components have been omitted for clarity, but should be used wherever optimal performance with high speed inputs is required. However, they may be omitted if the full high frequency capabilities of AD835 are not being exploited. A Wideband Voltage Controlled Amplifier Figure 19 shows the AD835 configured to provide a gain of nominally 0 to 12 dB. (In fact, the control range extends from well under –12 dB to about +14 dB.) R1 and R2 set the gain to be nominally ×4. The attendant bandwidth reduction that comes with this increased gain can be partially offset by the addition of the peaking capacitor C1. Although this circuit shows the use of dual supplies, the AD835 can operate from a single 9 V supply with slight revision. Of course, a suppressed carrier modulator can be implemented by omitting the feedforward to the Z-input, grounding that pin instead. +5V MODULATION INPUT 8 7 6 5 X1X1 X2 VP W Y1 Y2 VN Z 1 2 3 4 MODULATED CARRIER OUTPUT AD835 +5V VG (GAIN CONTROL) VOLTAGE OUTPUT 8 X1X1 7 X2 6 VP W Y1 Y2 VN Z 1 2 3 4 –5V C1 33pF Figure 21. Simple Amplitude Modulator Using the AD835 Squaring and Frequency Doubling R2 301Ω Amplitude domain squaring of an input signal, E, is achieved simply by connecting the X- and Y-inputs in parallel to produce an output of E2/U. The input may have either polarity, but the output in this case will always be positive. The output polarity may be reversed by interchanging either the X or Y inputs. Figure 19. Voltage Controlled 50 MHz Amplifier Using the AD835 When the input is a sine wave E sin ωt, a signal squarer behaves as a frequency doubler, since The ac response of this amplifier for gains of 0 dB (VG = 0.25 V), 6 dB (VG = 0.5 V) and 12 dB (VG = 1 V) is shown in Figure 20. In this application, the resistor values have been slightly adjusted to reflect the nominal value of U = 1.05 V. The overall sign of the gain may be controlled by the sign of VG. REV. A –5V R1 97.6Ω AD835 VIN (SIGNAL) CARRIER OUTPUT 5 ( E sin ωt )2 = E 2 (1 – cos 2 ωt ) (6) U 2U While useful, Equation 6 shows a dc term at the output which will vary strongly with the amplitude of the input, E. –7– AD835 Figure 22 shows a frequency doubler which overcomes this limitation and provides a relatively constant output over a moderately wide frequency range, determined by the time-constant C1 and R1. The voltage applied to the X- and Y-inputs are exactly in quadrature at a frequency f = 1/2 πC1R1 and their amplitudes are equal. At higher frequencies, the X-input becomes smaller while the Y-input increases in amplitude; the opposite happens at lower frequencies. The result is a double frequency output, centered on ground, whose amplitude of 1 V for a 1 V input varies by only 0.5% over a frequency range of ± 10%. Because there is no “squared” dc component at the output, sudden changes in the input amplitude do not cause a “bounce” in the dc level. VG OUTLINE DIMENSIONS Dimensions shown in inches and (mm). 8 0.280 (7.11) 0.240 (6.10) 1 4 0.325 (8.25) 0.300 (7.62) 0.430 (10.92) 0.348 (8.84) 0.060 (1.52) 0.015 (0.38) 0.210 (5.33) MAX C1 8 7 6 5 X1X1 X2 VP W Y1 Y2 VN Z 1 2 3 4 –5V 0.100 (2.54) BSC 0.022 (0.558) 0.014 (0.356) R2 97.6Ω AD835 0.130 (3.30) MIN 0.160 (4.06) 0.115 (2.93) VOLTAGE OUTPUT R1 5 PIN 1 +5V 0.070 (1.77) 0.045 (1.15) SEATING PLANE 0.1574 (4.00) 0.1497 (3.80) PIN 1 This circuit is based on the identity ( 7) 0.2440 (6.20) 0.2284 (5.80) 4 1 0.1968 (5.00) 0.1890 (4.80) At ωO = 1/C1R1, the X input leads the input signal by 45° (and is attenuated by √2, while the Y input lags the input signal by 45°, and is also attenuated by √2. Since the X and Y inputs are 90° out of phase, the response of the circuit will be W = 0.015 (0.381) 0.008 (0.204) 5 8 1 sin 2θ 2 0.195 (4.95) 0.115 (2.93) 8-Pin Plastic SOIC (R Package) R3 301Ω Figure 22. Broadband “Zero-Bounce” Frequency Doubler cos θ sin θ = C1903a–3–12/94 8-Pin Plastic DIP (N Package) 0.0196 (0.50) x 45 ° 0.0099 (0.25) 0.102 (2.59) 0.094 (2.39) 0.0098 (0.25) 0.0040 (0.10) 0.0500 (1.27) BSC 0.0192 (0.49) 0.0138 (0.35) 0.0098 (0.25) 0.0075 (0.19) 8° 0° 0.0500 (1.27) 0.0160 (0.41) 1 E E E2 (sin ωt – 45° ) (sin ωt + 45° ) = (sin 2ωt ) (8) 2U U 2 2 PRINTED IN U.S.A. which has no dc component, R2 and R3 are included to restore the output to 1 V for an input amplitude of 1 V (the same gain adjustment as mentioned earlier). Because the voltage across the capacitor, C1, decreases with frequency, while that across the resistor, R1, increases, the amplitude of the output varies only slightly with frequency. In fact, it is only 0.5% below its full value (at its center frequency ωΟ = 1/C1R1) at 90% and 110% of this frequency. –8– REV. A

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