Low Cost, Low Power, True RMS-to-DC Converter AD737 Data Sheet FEATURES FUNCTIONAL BLOCK DIAGRAM CC 8kΩ 8kΩ COM CF ABSOLUTE VALUE CIRCUIT VIN SQUARER DIVIDER OUTPUT CAV +VS POWER DOWN CAV BIAS SECTION –VS 00828-001 Computes True rms value Average rectified value Absolute value Provides 200 mV full-scale input range (larger inputs with input scaling) Direct interfacing with 3½ digit CMOS analog-to-digital converters (ADCs) High input impedance: 1012 Ω Low input bias current: 25 pA maximum High accuracy: ±0.2 mV ± 0.3% of reading RMS conversion with signal crest factors up to 5 Wide power supply range: ±2.5 V to ±16.5 V Low power: 25 μA (typical) standby current No external trims needed for specified accuracy The AD737 output is negative going; the AD736 is a positive output-going version of the same basic device Figure 1. GENERAL DESCRIPTION The AD737 is a low power, precision, monolithic, true rms-to-dc converter. It is laser trimmed to provide a maximum error of ±0.2 mV ± 0.3% of reading with sine wave inputs. Furthermore, it maintains high accuracy while measuring a wide range of input waveforms, including variable duty cycle pulses and triac (phase) controlled sine waves. The low cost and small physical size of the AD737 make it suitable for upgrading the performance of non-rms precision rectifiers in many applications. Compared to these circuits, the AD737 offers higher accuracy at equal or lower cost. The AD737 computes the rms value of both ac and dc input voltages, and is ac-coupled by adding an input capacitor. In this mode, the AD737 resolves input signal levels of 100 μV rms or less, despite variations in temperature or supply voltage. High accuracy is maintained for input waveforms with crest factors of 1 to 3 and crest factors at 2.5% or less with respect to full-scale input level. The AD737 has both high (1012 Ω) and low impedance input options. The high-Z FET input connects high source impedance input attenuators, and a low impedance (8 kΩ) input accepts rms voltages of up to 0.9 V while operating from the minimum power supply voltage of ±2.5 V. The two inputs can be used either single-ended or differentially. The AD737 achieves 1% of reading error bandwidth, exceeding 10 kHz for input amplitudes from 20 mV rms to 200 mV rms, while consuming only 0.72 mW. The AD737 is available in two performance grades. The AD737J and AD737K grades operate over the commercial temperature range of 0°C to 70°C. The AD737JR-5 is tested with supply voltages of ±2.5 V dc. The AD737A grade operates over the industrial temperature range of −40°C to +85°C. The AD737 is available in two low cost, 8lead packages: PDIP and SOIC_N. PRODUCT HIGHLIGHTS The AD737 has no output buffer amplifier, thereby significantly reducing dc offset errors occurring at the output and making the device highly compatible with high input impedance ADCs. 1. Requiring only 160 μA of power supply current, the AD737 is optimized for use in portable multimeters and other batterypowered applications. In power-down mode, the standby supply current in is typically 25 μA. 3. Rev. J 2. Computes the average rectified, absolute, or true rms value of a signal regardless of waveform. Only one external component, an averaging capacitor, is required for the AD737 to perform true rms measurement. The standby power consumption of 125 μW makes the AD737 suitable for battery-powered applications. Document Feedback 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 that may result from its use. Specifications subject to change without notice. No license is granted by implication or otherwise under any patent or patent rights of Analog Devices. Trademarks and registered trademarks are the property of their respective owners. One Technology Way, P.O. Box 9106, Norwood, MA 02062-9106, U.S.A. Tel: 781.329.4700 ©1988–2015 Analog Devices, Inc. All rights reserved. Technical Support www.analog.com AD737 Data Sheet TABLE OF CONTENTS Features .............................................................................................. 1 DC Error, Output Ripple, and Averaging Error .................... 14 Functional Block Diagram .............................................................. 1 AC Measurement Accuracy and Crest Factor ........................ 14 General Description ......................................................................... 1 Calculating Settling Time .......................................................... 14 Product Highlights ........................................................................... 1 Applications Information .............................................................. 15 Revision History ............................................................................... 3 RMS Measurement—Choosing an Optimum Value for CAV 15 Specifications..................................................................................... 4 Absolute Maximum Ratings............................................................ 7 Rapid Settling Times via the Average Responding Connection.................................................................................. 15 Thermal Resistance ...................................................................... 7 Selecting Practical Values for Capacitors ................................ 15 ESD Caution .................................................................................. 7 Scaling Input and Output Voltages .......................................... 15 Pin Configurations and Function Descriptions ........................... 8 Additional Information ............................................................. 16 Typical Performance Characteristics ............................................. 9 AD737 Evaluation Board............................................................... 19 Theory of Operation ...................................................................... 13 Outline Dimensions ....................................................................... 21 Types of AC Measurement ........................................................ 13 Ordering Guide .......................................................................... 22 Rev. J | Page 2 of 24 Data Sheet AD737 REVISION HISTORY 10/15—Rev. I to Rev. J Changes to General Description Section ....................................... 1 Changes to Table 4 ............................................................................ 8 Updated Typical Performance Characteristics Section Format; Reordered Figures ............................................................................. 9 Changes to Figure 4 to Figure 6....................................................... 9 Change to Types of AC Measurement Section ...........................13 Changes to Figure 23 ......................................................................13 Changes to Figure 25 ......................................................................15 Added Additional Information Section .......................................16 Changes to Figure 27 to Figure 31 ................................................17 Change to Figure 38 ........................................................................20 6/12—Rev. H to Rev. I Removed CERDIP Package............................................... Universal Changes to Features, General Description, Product Highlights Sections and Figure 1 ........................................................................ 1 Changes to Table 1 ............................................................................ 3 Changes to Table 2 ............................................................................ 6 Deleted Figure 3, Renumbered Sequentially ................................. 7 Changes to Figure 5, Figure 7, and Figure 8 Captions ................. 8 Changes to Figure 12 Caption ......................................................... 9 Changes to Figure 19 Caption .......................................................10 Changes to Figure 23 ......................................................................12 Changes to Figure 26 ......................................................................14 Changes to Scaling the Output Voltage Section ..........................15 Changes to Figure 27 ......................................................................16 Deleted Table 7 ................................................................................19 Updated Outline Dimensions ........................................................20 Changes to Ordering Guide ...........................................................21 10/08—Rev. G to Rev. H Added Selectable Average or RMS Conversion Section and Figure 27 ...........................................................................................14 Updated Outline Dimensions ........................................................20 Changes to Ordering Guide ...........................................................22 12/06—Rev. F to Rev. G Changes to Specifications ................................................................. 3 Reorganized Typical Performance Characteristics ....................... 8 Changes to Figure 21 ......................................................................11 Reorganized Theory of Operation Section ..................................12 Reorganized Applications Section ................................................ 14 Added Scaling Input and Output Voltages Section .................... 14 Deleted Application Circuits Heading ......................................... 16 Changes to Figure 28 ...................................................................... 16 Added AD737 Evaluation Board Section .................................... 18 Updated Outline Dimensions........................................................ 20 hanges to Ordering Guide ............................................................. 21 1/05—Rev. E to Rev. F Updated Format ................................................................. Universal Added Functional Block Diagram .................................................. 1 Changes to General Description Section ....................................... 1 Changes to Pin Configurations and Function Descriptions Section ......................................................................... 6 Changes to Typical Performance Characteristics Section ........... 7 Changes to Table 4 .......................................................................... 11 Change to Figure 24 ........................................................................ 12 Change to Figure 27 ........................................................................ 15 Changes to Ordering Guide ........................................................... 18 6/03—Rev. D to Rev. E Added AD737JR-5 ............................................................. Universal Changes to Features .......................................................................... 1 Changes to General Description ..................................................... 1 Changes to Specifications ................................................................ 2 Changes to Absolute Maximum Ratings........................................ 4 Changes to Ordering Guide ............................................................. 4 Added TPCs 16 through 19 ............................................................. 6 Changes to Figures 1 and 2 .............................................................. 8 Changes to Figure 8 ........................................................................ 11 Updated Outline Dimensions........................................................ 12 12/02—Rev. C to Rev. D Changes to Functional Block Diagram .......................................... 1 Changes to Pin Configuration......................................................... 4 Figure 1 Replaced .............................................................................. 8 Changes to Figure 2 .......................................................................... 8 Figure 5 Replaced ............................................................................ 10 Changes to Application Circuits Figures 4, 6–8 .......................... 10 Outline Dimensions Updated........................................................ 12 12/99—Rev. B to Rev. C Rev. J | Page 3 of 24 AD737 Data Sheet SPECIFICATIONS TA = 25°C, ±VS = ±5 V except as noted, CAV = 33 μF, CC = 10 μF, f = 1 kHz, sine wave input applied to Pin 2, unless otherwise specified. Specifications shown in boldface are tested on all production units at final electrical test. Results from these tests are used to calculate outgoing quality levels. Table 1. Parameter ACCURACY Total Error Test Conditions/ Comments Min EIN = 0 to 200 mV rms ±VS = ±2.5 V 0.2/0.3 ±VS = ±2.5 V, input to Pin 1 EIN = 200 mV to 1 V rms Over Temperature JN, JR, KR AN and AR AD737A, AD737J Typ Max −1.2 EIN = 200 mV rms, ±VS = ±2.5 V EIN = 200 mV rms, ±VS = ±2.5 V Min AD737K Typ Max 0.2/0.2 0.4/0.5 −1.2 ±2.0 0.007 0.007 0.014 0.014 Min AD737J-5 Typ Max Unit ±mV/±POR1 0.2/0.3 0.2/0.3 0.4/0.5 ±mV/±POR1 0.2/0.3 0.4/0.5 ±mV/±POR1 POR ±2.0 0.02 ±POR/°C ±POR/°C vs. Supply Voltage DC Reversal Error Nonlinearity2 Input to Pin 13 Total Error, External Trim ADDITIONAL CREST FACTOR ERROR4 For Crest Factors from 1 to 3 For Crest Factors from 3 to 5 INPUT CHARACTERISTICS High-Z Input (Pin 2) Signal Range Continuous RMS Level EIN = 200 mV rms, ±VS = ±2.5 V to ±5 V EIN = 200 mV rms, ±VS = ±5 V to ±16.5 V DC-coupled, VIN = 600 mV dc ±VS = ±2.5 V VIN = 200 mV dc EIN = 0 mV to 200 mV rms, at 100 mV rms AC coupled, EIN = 100 mV rms, after correction, ±VS = ±2.5 V EIN = 0 mV to 200 mV rms CAV = CF = 100 μF CAV = 22 μF, CF = 100 μF, ±VS = ±2.5 V, input to Pin 1 CAV = CF = 100 μF 0 −0.18 −0.3 0 −0.18 −0.3 0 −0.18 −0.3 %/V 0 0.06 0.1 0 0.06 0.1 0 0.06 0.1 %/V 1.3 2.5 1.3 2.5 1.7 0 0.25 0.35 0 0.25 0.1/0.2 0.7 0.7 0.1 0.1/0.2 % % 2.5 % 200 200 1 Rev. J | Page 4 of 24 POR ±mV/±POR 1.7 2.5 POR POR 0.02 0.1/0.2 2.5 0.35 ±VS = +2.5 V ±VS = +2.8 V/−3.2 V ±VS = ±5 V to ±16.5 V POR 200 1 mV rms mV rms V rms Data Sheet Parameter Peak Transient Input Input Resistance Input Bias Current Low-Z Input (Pin 1) Signal Range Continuous RMS Level Peak Transient Input Input Resistance Maximum Continuous Nondestructive Input Input Offset Voltage5 Over the Rated Operating Temperature Range vs. Supply OUTPUT CHARACTERISTICS Output Voltage Range Output Resistance FREQUENCY RESPONSE High-Z Input (Pin 2) 1% Additional Error 3 dB Bandwidth Low-Z Input (Pin 1) 1% Additional Error 3 dB Bandwidth AD737 Test Conditions/ Comments ±VS = +2.5 V input to Pin 1 ±VS = +2.8 V/−3.2 V ±VS = ±5 V ±VS = ±16.5 V Min AD737A, AD737J Typ Max Min ±0.9 AD737K Typ Max ±2.7 ±4.0 1012 1 ±VS = +2.5 V ±VS = +2.8 V/−3.2 V ±VS = ±5 V to ±16.5 V ±VS = +2.5 V ±VS = +2.8 V/−3.2 V ±VS = ±5 V ±VS = ±16.5 V AD737J-5 Typ Max ±0.9 ±2.7 ±VS = ±5 V Min ±0.6 ±4.0 1012 1 25 1012 1 25 25 300 300 1 300 1 ±1.7 6.4 ±1.7 ±3.8 ±11 8 All supply voltages AC-coupled 9.6 ±12 6.4 ±1.7 ±3.8 ±11 8 9.6 ±12 8 ±3 30 8 ±3 30 80 50 150 80 50 150 6.4 8 8 Unit V V V V Ω pA mV rms mV rms V rms 9.6 ±12 V V V V kΩ V p-p ±3 30 mV μV/°C VS = ±2.5 V to ±5 V VS = ±5 V to ±16.5 V No load, output is negative with respect to COM ±VS = +2.8 V/−3.2 V −1.6 −1.7 −1.6 −1.7 V6 ±VS = ±5 V −3.3 −3.4 −3.3 −3.4 ±VS = ±16.5 V ±VS = ±2.5 V, input to Pin 1 DC −4 −5 −4 −5 V6 V 6.4 8 9.6 6.4 8 80 9.6 −1.1 –0.9 6.4 8 μV/V μV/V V6 9.6 kΩ VIN = 1 mV rms VIN = 10 mV rms VIN = 100 mV rms VIN = 200 mV rms VIN = 1 mV rms VIN = 10 mV rms VIN = 100 mV rms VIN = 200 mV rms 1 6 37 33 5 55 170 190 1 6 37 33 5 55 170 190 1 6 37 33 5 55 170 190 kHz kHz kHz kHz kHz kHz kHz kHz VIN = 1 mV rms VIN = 10 mV rms VIN = 40 mV rms VIN = 100 mV rms VIN = 200 mV rms VIN = 1 mV rms VIN = 10 mV rms VIN = 100 mV rms VIN = 200 mV rms 1 6 1 6 90 90 5 55 350 460 90 90 5 55 350 460 1 6 25 90 90 5 55 350 460 kHz kHz kHz kHz kHz kHz kHz kHz kHz Rev. J | Page 5 of 24 AD737 Parameter POWER-DOWN MODE Disable Voltage Input Current, PD Enabled POWER SUPPLY Operating Voltage Range Current Data Sheet Test Conditions/ Comments Min AD737A, AD737J Typ Max 0 11 VPD = VS +2.8/ −3.2 No input Rated input Powered down Min AD737K Typ Max Min AD737J-5 Typ Max 0 11 ±5 ±16.5 120 170 25 160 210 40 +2.8/ −3.2 1 Unit V μA ±5 ±16.5 120 170 25 160 210 40 ±2.5 ±5 ±16.5 V 120 170 25 160 210 40 μA μA μA POR is % of reading. Nonlinearity is defined as the maximum deviation (in percent error) from a straight line connecting the readings at 0 V and at 200 mV rms. After fourth-order error correction using the equation y = −0.31009x4 − 0.21692x3 − 0.06939x2 + 0.99756x + 11.1 × 10−6 where y is the corrected result and x is the device output between 0.01 V and 0.3 V. 4 Crest factor error is specified as the additional error resulting from the specific crest factor, using a 200 mV rms signal as a reference. The crest factor is defined as VPEAK/V rms. 5 DC offset does not limit ac resolution. 6 Value is measured with respect to COM. 2 3 Rev. J | Page 6 of 24 Data Sheet AD737 ABSOLUTE MAXIMUM RATINGS THERMAL RESISTANCE Table 2. Parameter Supply Voltage Internal Power Dissipation Input Voltage Pin 1 Pin 2 to Pin 8 Output Short-Circuit Duration Differential Input Voltage Storage Temperature Range Lead Temperature, Soldering (60 sec) ESD Rating Rating ±16.5 V 200 mW θJA is specified for the worst-case conditions, that is, a device soldered in a circuit board for surface-mount packages. ±12 V ±VS Indefinite +VS and −VS −65°C to +125°C 300°C 500 V Package Type 8-Lead PDIP (N-8) 8-Lead SOIC_N (R-8) Table 3. Thermal Resistance ESD CAUTION Stresses at or above those listed under Absolute Maximum Ratings may cause permanent damage to the product. This is a stress rating only; functional operation of the product at these or any other conditions above those indicated in the operational section of this specification is not implied. Operation beyond the maximum operating conditions for extended periods may affect product reliability. Rev. J | Page 7 of 24 θJA 165 155 Unit °C/W °C/W AD737 Data Sheet AD737 8 COM CC 1 7 +VS VIN 2 POWER DOWN 3 6 OUTPUT TOP VIEW –VS 4 (Not to Scale) 5 CAV POWER DOWN 3 00828-002 CC 1 VIN 2 –VS 4 8 COM AD737 7 +VS TOP VIEW (Not to Scale) 6 OUTPUT 5 CAV 00828-004 PIN CONFIGURATIONS AND FUNCTION DESCRIPTIONS Figure 3. PDIP Pin Configuration (N-8) Figure 2. SOIC_N Pin Configuration (R-8) Table 4. Pin Function Descriptions Pin No. 1 Mnemonic CC 2 3 VIN POWER DOWN 4 5 6 7 8 –VS CAV OUTPUT +VS COM Description Coupling Capacitor Connection for Indirect DC Coupling to Pin 2. In addition, CC is an alternative low impedance input access to an 8 kΩ voltage to current (V to I) resistor. RMS Input to FET. Disables the AD737. When Pin 3 is grounded or pulled low, the AD737 is enabled; when Pin 3 is pulled high, it changes to power saving mode. Negative Power Supply. Averaging Capacitor Connection. DC Output (Negative Going Polarity). Positive Power Supply. Common. Rev. J | Page 8 of 24 Data Sheet AD737 TYPICAL PERFORMANCE CHARACTERISTICS TA = 25°C, ±VS = ±5 V (except AD737J-5, where ±VS = ±2.5 V), CAV = 33 µF, CC = 10 µF, f = 1 kHz, sine wave input applied to Pin 2, unless otherwise specified. 10V 0.7 VIN = 200mV rms CAV = 100µF CF = 22µF 1V 100mV 1% ERROR 10mV –3dB 1mV 100µV 0.1 1 10 FREQUENCY (kHz) 100 00828-008 10% ERROR 0.5 0.3 0.1 0 –0.1 –0.3 –0.5 1000 00828-005 ADDITIONAL ERROR (% of Reading) INPUT/OUTPUT LEVEL (rms/|DC|) CAV = 22µF, C F = 4.7µF, C C = 22µF 0 6 8 10 SUPPLY VOLTAGE (±V) 12 14 16 14 16 16 10V DC COUPLED PEAK INPUT BEFORE CLIPPING (V) CAV = 22µF, C F = 4.7µF, C C = 22µF 1V 100mV 1% ERROR 10mV 10% ERROR 1mV 100µV 0.1 1 10 FREQUENCY (kHz) 100 12 10 PIN 1 8 PIN 2 6 4 2 00828-009 –3dB 14 0 1000 00828-006 INPUT/OUTPUT LEVEL (rms/|DC|) 4 Figure 7. Additional Error vs. Supply Voltage Figure 4. Frequency Response Driving Pin 1, Low-Z Input (DC Output Polarity is Negative Going) 0 4 2 6 8 10 SUPPLY VOLTAGE (±V) 12 Figure 8. Peak Input Level for 1% Saturation vs. Supply Voltage Figure 5. Frequency Response Driving Pin 2, High-Z Input (DC Output Polarity is Negative Going) 25 10V VS = ±2.5V, CAV = 22µF, C F = 4.7µF, C C = 22µF 1V SUPPLY CURRENT (µA) INPUT/OUTPUT LEVEL (rms/|DC|) 2 100mV 10mV 20 15 10 1 10 FREQUENCY (kHz) 100 5 1000 Figure 6. Frequency Response with ±2.5V Supplies when Driving Pin 1, Low-Z Input (DC Output Polarity is Negative Going) 00828-007 100µV 0.1 00828-020 1mV 0 2 4 6 8 10 12 14 DUAL SUPPLY VOLTAGE (±V) 16 18 Figure 9. Supply Current (Power-Down Mode) vs. Dual Supply Voltage Rev. J | Page 9 of 24 AD737 Data Sheet 10mV CAV = 10µF CAV = 33µF 4 3 2 1 CAV = 100µF CAV = 250µF 0 1 2 3 4 CREST FACTOR (VPEAK /V rms) 100µV 10µV 100 5 1k 10k –3dB FREQUENCY (Hz) 100k Figure 13. RMS Input Level vs. –3 dB Frequency; Negative DC Output Figure 10. Additional Error vs. Crest Factor 1.0 0.8 VIN = 200mV rms CAV = 100µF CF = 22µF 0.6 0.5 0.4 ERROR (% of Reading) 0.2 0 –0.2 0 –0.5 –1.0 –1.5 –0.4 –2.0 –0.8 –60 00828-011 –0.6 –40 –20 0 20 40 60 80 TEMPERATURE (°C) 100 120 CAV = 22µF, CC = 47µF, CF = 4.7µF –2.5 10mV 140 00828-014 ADDITIONAL ERROR (% of Reading) 1mV 00828-013 5 AC-COUPLED INPUT LEVEL (rms) 3ms BURST OF 1kHz = 3 CYCLES 200mV rms SIGNAL CC = 22µF CF = 100µF 00828-010 ADDITIONAL ERROR (% of Reading) 6 100mV INPUT LEVEL (rms) 1V 2V Figure 14. Error vs. RMS Input Level Using Circuit in Figure 29 Figure 11. Additional Error vs. Temperature 100 500 AVERAGING CAPACITOR (µF) VIN = 200mV rms CC = 47µF CF = 47µF 300 200 10 –0.5% 100 0 0 0.2 0.4 0.6 RMS INPUT LEVEL (V) 0.8 1.0 1 10 00828-015 –1% 00828-012 DC SUPPLY CURRENT (µA) 400 100 FREQUENCY (Hz) Figure 15. Value of Averaging Capacitor vs. Frequency for Specified Averaging Error Figure 12. DC Supply Current vs. RMS Input Level Rev. J | Page 10 of 24 1k Data Sheet AD737 10nA 1V –0.5% 1nA INPUT BIAS CURRENT 100mV 10mV 1 10 100 10pA 00828-016 100fA –55 1k 00828-019 1pA AC-COUPLED CAV = 10µF, CC = 47µF, CF = 47µF 1mV 100pA –35 45 65 25 5 TEMPERATURE (°C) –15 FREQUENCY (Hz) 10V 4.0 VS = ±2.5V, CAV = 22µF, CF = 4.7µF, CC = 22µF 3.5 1V INPUT LEVEL (rms) INPUT BIAS CURRENT (pA) 125 Figure 19. Input Bias Current vs. Temperature Figure 16. RMS Input Level vs. Frequency for Specified Averaging Error 3.0 2.5 2.0 100mV 0.5% 10mV 10% 1mV 1.5 0 2 4 6 8 10 SUPPLY VOLTAGE (±V) 12 14 100µV 0.1 16 10 FREQUENCY (kHz) 100 1000 5 ADDITIONAL ERROR (% of Reading) CC = 22µF CF = 0µF 100mV CAV = 10µF CAV = 100µF CAV = 33µF 00828-018 1mV 10ms 100ms 1s SETTLING TIME 10s 100s 3 CYCLES OF 1kHz 200mV rms VS = ±2.5V CC = 22µF CF = 100µF 4 CAV = 10µF CAV = 22µF CAV = 33µF 3 CAV = 100µF 2 CAV = 220µF 1 0 00828-022 1V 100µV 1ms 1 Figure 20. Error Contours Driving Pin 1 Figure 17. Input Bias Current vs. Supply Voltage 10mV –3dB 1% 00828-017 1.0 INPUT LEVEL (rms) 105 85 00828-021 INPUT LEVEL (rms) –1% 1 2 3 CREST FACTOR 4 5 Figure 21. Additional Error vs. Crest Factor for Various Values of CAV Figure 18. RMS Input Level vs. Settling Time for Three Values of CAV Rev. J | Page 11 of 24 AD737 Data Sheet 1.0 0 –0.5 –1.0 –1.5 –2.0 00828-023 ERROR (% of Reading) 0.5 CAV = 22µF, VS = ±2.5V CC = 47µF, CF = 4.7µF –2.5 10mV 100mV INPUT LEVEL (rms) 1V 2V Figure 22. Error vs. RMS Input Level Driving Pin 1 Rev. J | Page 12 of 24 Data Sheet AD737 THEORY OF OPERATION external averaging capacitor, CF. In the rms circuit, this additional filtering stage reduces any output ripple that was not removed by the averaging capacitor. The AD737 has four functional subsections: an input amplifier, a full-wave rectifier, an rms core, and a bias section (see Figure 23). The FET input amplifier allows a high impedance, buffered input at Pin 2 or a low impedance, wide dynamic range input at Pin 1. The high impedance input, with its low input bias current, is ideal for use with high impedance input attenuators. The input signal can be either dc-coupled or ac-coupled to the input amplifier. Unlike other rms converters, the AD737 permits both direct and indirect ac coupling of the inputs. AC coupling is provided by placing a series capacitor between the input signal and Pin 2 (or Pin 1) for direct coupling and between Pin 1 and ground (while driving Pin 2) for indirect coupling. Finally, the bias subsection permits a power-down function. This reduces the idle current of the AD737 from 160 µA to 30 µA. This feature is selected by connecting Pin 3 to Pin 7 (+VS). TYPES OF AC MEASUREMENT The AD737 measures ac signals either by operating as an average responding converter or by operating as a true rms-to-dc converter. As its name implies, an average responding converter computes the average absolute value of an ac (or ac and dc) voltage or current by full-wave rectifying and low-pass filtering the input signal; this approximates the average. The resulting output, a dc average level, is then scaled by adding (or reducing) gain; this scale factor converts the dc average reading to an rms equivalent value for the waveform being measured. For example, the average absolute value of a sine wave voltage is 0.636 times that of VPEAK; the corresponding rms value is 0.707 times VPEAK. Therefore, for sine wave voltages, the required scale factor is 1.11 (0.707 divided by 0.636). AC CC = 10µF + DC OPTIONAL RETURN PATH CURRENT MODE ABSOLUTE VALUE CC 8 1 8kΩ COM VIN VIN + 8kΩ 2 7 +VS CF 10µF (OPTIONAL LPF) FET OP AMP IB < 10pA POWER 3 DOWN BIAS SECTION Mathematically, the rms value of a voltage is defined (using a simplified equation) as 6 OUTPUT V rms = Avg (V 2 ) RMS TRANSLINEAR CORE –VS 4 5 CAV CA 33µF + +VS POSITIVE SUPPLY 00828-024 0.1µF COMMON 0.1µF NEGATIVE SUPPLY In contrast to measuring the average value, true rms measurement is a universal language among waveforms, allowing the magnitudes of all types of voltage (or current) waveforms to be compared to one another and to dc. RMS is a direct measure of the power or heating value of an ac voltage compared to that of a dc voltage; an ac signal of 1 V rms produces the same amount of heat in a resistor as a 1 V dc signal. –VS Figure 23. AD737 True RMS Circuit (Test Circuit) The output of the input amplifier drives a full-wave precision rectifier, which, in turn, drives the rms core. It is the core that provides the essential rms operations of squaring, averaging, and square rooting, using an external averaging capacitor, CAV. This involves squaring the signal, taking the average, and then obtaining the square root. True rms converters are smart rectifiers; they provide an accurate rms reading regardless of the type of waveform being measured. However, average responding converters can exhibit very high errors when their input signals deviate from their pre-calibrated waveform; the magnitude of the error depends on the type of waveform being measured. As an example, if an average responding converter is calibrated to measure the rms value of sine wave voltages and then is used to measure either symmetrical square waves or dc voltages, the converter has a computational error 11% (of reading) higher than the true rms value (see Table 5). The transfer function for the AD737 is Without CAV, the rectified input signal passes through the core unprocessed, as is done with the average responding connection (see Figure 25). In the average responding mode, averaging is carried out by an RC post filter consisting of an 8 kΩ internal scale factor resistor connected between Pin 6 and Pin 8 and an Rev. J | Page 13 of 24 VOUT = − Avg (VIN 2 ) AD737 Data Sheet DC ERROR, OUTPUT RIPPLE, AND AVERAGING ERROR AC MEASUREMENT ACCURACY AND CREST FACTOR Figure 24 shows the typical output waveform of the AD737 with a sine wave input voltage applied. As with all real-world devices, the ideal output of VOUT = VIN is never exactly achieved; instead, the output contains both a dc and an ac error component. The crest factor of the input waveform is often overlooked when determining the accuracy of an ac measurement. Crest factor is defined as the ratio of the peak signal amplitude to the rms amplitude (crest factor = VPEAK/V rms). Many common waveforms, such as sine and triangle waves, have relatively low crest factors (≥2). Other waveforms, such as low duty cycle pulse trains and SCR waveforms, have high crest factors. These types of waveforms require a long averaging time constant to average out the long time periods between pulses. Figure 10 shows the additional error vs. the crest factor of the AD737 for various values of CAV. EO IDEAL EO DC ERROR = EO – EO (IDEAL) TIME 00828-026 AVERAGE EO = EO DOUBLE-FREQUENCY RIPPLE CALCULATING SETTLING TIME Figure 24. Output Waveform for Sine Wave Input Voltage As shown, the dc error is the difference between the average of the output signal (when all the ripple in the output has been removed by external filtering) and the ideal dc output. The dc error component is, therefore, set solely by the value of the averaging capacitor used—no amount of post filtering (using a very large postfiltering capacitor, CF) allows the output voltage to equal its ideal value. The ac error component, an output ripple, can be easily removed using a large enough CF. In most cases, the combined magnitudes of the dc and ac error components must be considered when selecting appropriate values for CAV and CF capacitors. This combined error, representing the maximum uncertainty of the measurement, is termed the averaging error and is equal to the peak value of the output ripple plus the dc error. As the input frequency increases, both error components decrease rapidly. If the input frequency doubles, the dc error and ripple reduce to one-quarter and one-half of their original values, respectively, and rapidly become insignificant. Figure 18 can be used to closely approximate the time required for the AD737 to settle when its input level is reduced in amplitude. The net time required for the rms converter to settle is the difference between two times extracted from the graph: the initial time minus the final settling time. As an example, consider the following conditions: a 33 μF averaging capacitor, an initial rms input level of 100 mV, and a final (reduced) input level of 1 mV. From Figure 18, the initial settling time (where the 100 mV line intersects the 33 μF line) is approximately 80 ms. The settling time corresponding to the new or final input level of 1 mV is approximately 8 seconds. Therefore, the net time for the circuit to settle to its new value is 8 seconds minus 80 ms, which is 7.92 seconds. Note that, because of the inherent smoothness of the decay characteristic of a capacitor/diode combination, this is the total settling time to the final value (not the settling time to 1%, 0.1%, and so on, of the final value). Also, this graph provides the worst-case settling time because the AD737 settles very quickly with increasing input levels. Table 5. Error Introduced by an Average Responding Circuit When Measuring Common Waveforms Type of Waveform 1 V Peak Amplitude Undistorted Sine Wave Symmetrical Square Wave Undistorted Triangle Wave Gaussian Noise (98% of Peaks <1 V) Rectangular Pulse Train SCR Waveforms 50% Duty Cycle 25% Duty Cycle Crest Factor (VPEAK/V rms) 1.414 1.00 1.73 3 2 10 True RMS Value (V) 0.707 1.00 0.577 0.333 0.5 0.1 Reading of an Average Responding Circuit Calibrated to an RMS Sine Wave Value (V) 0.707 1.11 0.555 0.295 0.278 0.011 Error (%) 0 11.0 −3.8 −11.4 −44 −89 2 4.7 0.495 0.212 0.354 0.150 −28 −30 Rev. J | Page 14 of 24 Data Sheet AD737 APPLICATIONS INFORMATION Because the external averaging capacitor, CAV, holds the rectified input signal during rms computation, its value directly affects the accuracy of the rms measurement, especially at low frequencies. Furthermore, because the averaging capacitor is connected across a diode in the rms core, the averaging time constant (τAV) increases exponentially as the input signal decreases. It follows that decreasing the input signal decreases errors due to nonideal averaging but increases the settling time approaching the decreased rms-computed dc value. Thus, diminishing input values allow the circuit to perform better (due to increased averaging) while increasing the waiting time between measurements. A trade-off must be made between computational accuracy and settling time when selecting CAV. RAPID SETTLING TIMES VIA THE AVERAGE RESPONDING CONNECTION Because the average responding connection shown in Figure 25 does not use an averaging capacitor, its settling time does not vary with input signal level; it is determined solely by the RC time constant of CF and the internal 8 kΩ output scaling resistor. CC 8kΩ AD737 1 8 VIN 2 INPUT AMPLIFIER POWER 3 DOWN 8kΩ BIAS SECTION + 6 CF 33µF +VS 0.1µF NEGATIVE SUPPLY –VS 00828-025 0.1µF COMMON +VS 3 OUT 4 –V S CAV 7 +2.5V 6 VOUTDC 5 33µF 33µF NTR4501NT1 rms AVG ASSUMED TO BE A LOGIC SOURCE –2.5V Figure 26. CMOS Switch is Used to Select RMS or Average Responding Modes SELECTING PRACTICAL VALUES FOR CAPACITORS Table 6 provides practical values of CAV and CF for several common applications. The input coupling capacitor, CC, in conjunction with the 8 kΩ internal input scaling resistor, determines the −3 dB low frequency roll-off. This frequency, FL, is equal to FL = 1 2π × 8000 × C C ( in Farads ) (1) Note that, at FL, the amplitude error is approximately −30% (−3 dB) of reading. To reduce this error to 0.5% of reading, choose a value of CC that sets FL at one-tenth of the lowest frequency to be measured. The AD737 is an extremely flexible device. With minimal external circuitry, it can be powered with single- or dualpolarity power supplies, and input and output voltages are independently scalable to accommodate nonmatching input/output devices. This section describes a few such applications. 5 CAV POSITIVE SUPPLY 1MΩ SCALING INPUT AND OUTPUT VOLTAGES VOUT OUTPUT RMS CORE –VS 4 7 +VS 2 V IN VINRMS COM 8 AD737 In addition, if the input voltage has more than 100 mV of dc offset, the ac coupling network at Pin 2 is required in addition to Capacitor CC. COM FULL-WAVE RECTIFIER 1 C C 00828-039 RMS MEASUREMENT—CHOOSING AN OPTIMUM VALUE FOR CAV Figure 25. AD737 Average Responding Circuit Selectable Average or RMS Conversion For some applications, it is desirable to be able to select between rms-value-to-dc conversion and average-value-to-dc conversion. If CAV is disconnected from the root-mean core, the AD737 fullwave rectifier is a highly accurate absolute value circuit. A CMOS switch whose gate is controlled by a logic level selects between average and rms values. Extending or Scaling the Input Range For low supply voltage applications, the maximum peak voltage to the device is extended by simply applying the input voltage to Pin 1 across the internal 8 kΩ input resistor. The AD737 input circuit functions quasi-differentially, with a high impedance FET input at Pin 2 (noninverting) and a low impedance input at Pin 1 (inverting, see Figure 25). The internal 8 kΩ resistor behaves as a voltage-to-current converter connected to the summing node of a feedback loop around the input amplifier. Because the feedback loop acts to servo the summing node voltage to match the voltage at Pin 2, the maximum peak input voltage increases until the internal circuit runs out of headroom, approximately double for a symmetrical dual supply. Rev. J | Page 15 of 24 AD737 Data Sheet Battery Operation All the level-shifting for battery operation is provided by the 3½ digit converter, shown in Figure 27. Alternatively, an external op amp adds flexibility by accommodating nonzero common-mode voltages and providing output scaling and offset to zero. When an external operational amplifier is used, the output polarity is positive going. Figure 28 shows an op amp used in a single-supply application. Note that the combined input resistor value (R1 + R2 + 8 kΩ) matches that of the R5 feedback resistor. In this instance, the magnitudes of the output dc voltage and the rms of the ac input are equal. R3 and R4 provide current to offset the output to 0 V. Scaling the Output Voltage The output voltage can be scaled to the input rms voltage. For example, assume that the AD737 is retrofitted to an existing application using an averaging responding circuit (full-wave rectifier). The power supply is 12 V, the input voltage is 10 V ac, and the desired output is 6 V dc. For convenience, use the same combined input resistance as shown in Figure 28. Calculate the rms input current as I INMAG = 10 V = 125 µA = I OUTMAG 69.8 kΩ + 2.5 kΩ + 8 kΩ R5 = 6V = 48.1 kΩ 125 μA (3) Select the closest-value standard 1% resistor, 47.5 kΩ. Because the supply is 12 V, the common-mode voltage at the R7/R8 divider is 6 V, and the combined resistor value (R3 + R4) is equal to the feedback resistor, or 47.5 kΩ. R2 is used to calibrate the transfer function (gain), and R4 sets the output voltage to zero with no input voltage. Perform calibration as follows: 1. 2. 3. With no ac input applied, adjust R4 for 0 V. Apply a known input to the input. Adjust the R2 trimmer until the input and output match. The op amp selected for any single-supply application must be a rail-to-rail type, for example an AD8541, as shown in Figure 28. For higher voltages, a higher voltage part, such as an OP196, can be used. When calibrating to 0 V, the specified voltage above ground for the operational amplifier must be taken into account. Adjust R4 slightly higher as appropriate. ADDITIONAL INFORMATION (2) For additional information about rms-to-dc conversions, see the AN-268 Application Note or download the Analog Devices, Inc., RMS to DC Conversion Application Guide. Next, using the IOUTMAG value from Equation 2, calculate the new feedback resistor value (R5) required for 6 V output using Table 6. AD737 Capacitor Selection Application General-Purpose RMS Computation RMS Input Level 0 V to 1 V 0 mV to 200 mV General-Purpose Average Responding 0 V to 1 V 0 mV to 200 mV SCR Waveform Measurement 0 mV to 200 mV 0 mV to 100 mV Audio Applications Speech Music 1 0 mV to 200 mV 0 mV to 100 mV Low Frequency Cutoff (−3 dB) 20 Hz 200 Hz 20 Hz 200 Hz 20 Hz 200 Hz 20 Hz 200 Hz 50 Hz 60 Hz 50 Hz 60 Hz Maximum Crest Factor 5 5 5 5 300 Hz 20 Hz 5 5 5 5 CAV (µF) 150 15 33 3.3 None None None None 100 82 50 47 CF(µF) 10 1 10 1 33 3.3 33 3.3 33 27 33 27 Settling Time 1 to 1% 360 ms 36 ms 360 ms 36 ms 1.2 sec 120 ms 1.2 sec 120 ms 1.2 sec 1.0 sec 1.2 sec 1.0 sec 3 10 1.5 100 0.5 68 18 ms 2.4 sec Settling time is specified over the stated rms input level with the input signal increasing from zero. Settling times are greater for decreasing amplitude input signals. Rev. J | Page 16 of 24 Data Sheet AD737 20kΩ 1µF +VS + AD589 1PRV 0.01µF VIN + CC 10µF CC 200mV 8kΩ 1.23V COM AD737 1 200kΩ 8 50kΩ 1N4148 9MΩ FULL-WAVE RECTIFIER VIN 2V 2 900kΩ 20V 90kΩ 47kΩ 1W POWER DOWN –VS 10kΩ REF LOW +V 7 COMMON OUTPUT BIAS SECTION 3 REF HIGH +VS 8kΩ INPUT AMPLIFIER 1N4148 200V 31/2 DIGIT ICL7136 TYPE CONVERTER 1MΩ 0.1µF 1µF 9V ANALOG CAV RMS CORE 4 + LOW 6 HIGH 5 + + –VS 33µF 00828-027 SWITCH CLOSED ACTIVATES POWER-DOWN MODE. AD737 DRAWS JUST 40µA IN THIS MODE Figure 27. 3½ Digit DVM Circuit INPUT INPUT SCALE FACTOR ADJ R1 R2 C1 69.8kΩ 5kΩ 0.47µF 1% 1 CF 0.47µF COM 8 NC CC 5V 2 VIN +VS 7 C2 0.01µF R4 5kΩ R5 80.6kΩ 5V AD737 3 POWER DOWN R3 78.7kΩ OUTPUT ZERO ADJUST 0.01µF 1 OUTPUT 6 2 7 AD8541AR 4 CAV 5 –VS 6 OUTPUT 5 3 4 C3 0.01µF 5V + C4 2.2µF CAV 33µF R7 100kΩ 2.5V C5 + 1µF 00828-028 R8 100kΩ NC = NO CONNECT Figure 28. Battery-Powered Operation for 200 mV Maximum RMS Full-Scale Input CC 10µF + 100Ω SCALE FACTOR ADJUST CC VIN 8kΩ COM AD737 1 FULL-WAVE RECTIFIER 2 INPUT AMPLIFIER 8 8kΩ 7 200Ω +VS CF 10µF + OUTPUT BIAS SECTION 6 –VS 4 VOUT CAV RMS CORE 5 + CAV 33µF Figure 29. External Scale Factor Trim Rev. J | Page 17 of 24 00828-029 POWER 3 DOWN AD737 Data Sheet 13 CC 10µF CC + 8kΩ COM VIN FULL-WAVE RECTIFIER 2 INPUT AMPLIFIER 14 1kΩ 3500PPM/°C 12 * AD737 1 Q1 8kΩ PRECISION RESISTOR CORP TYPE PT/ST 60.4Ω 8 NC SCALE FACTOR TRIM 7 +VS 2kΩ 31.6kΩ OUTPUT POWER 3 DOWN BIAS SECTION 2 6 AD711 –VS CAV RMS CORE 4 3 * 10 Q2 11 CAV IREF R1** 9 00828-030 NC = NO CONNECT *Q1, Q2 PART OF RCA CA3046 OR SIMILAR NPN TRANSISTOR ARRAY. 4.3V **R1 + R CAL IN Ω = 10,000 × 0dB INPUT LEVEL IN V Figure 30. dB Output Connection OFFSET ADJUST 500kΩ 1MΩ CC 8kΩ 2 1kΩ AD737 1 VIN –VS FULL-WAVE RECTIFIER INPUT AMPLIFIER POWER DOWN COM 499Ω 8 7 +VS 6 3 1kΩ SCALE FACTOR ADJUST VOUT Figure 31. DC-Coupled Offset Voltage and Scale Factor Trims Rev. J | Page 18 of 24 00828-031 +VS dB OUTPUT 100mV/dB 5 + RCAL** 6 Data Sheet AD737 AD737 EVALUATION BOARD 00828-033 An evaluation board, the AD737-EVALZ, is available for experiments or for becoming familiar with rms-to-dc converters. Figure 32 is a photograph of the board; Figure 34 to Figure 37 show the signal and power plane copper patterns. The board is designed for multipurpose applications and can be used for the AD736 as well. Although not shipped with the board, an optional socket that accepts the 8lead surface-mount package is available from Enplas Corp. 00828-038 Figure 34. AD737 Evaluation Board—Component-Side Copper 00828-032 00828-034 Figure 32. AD737 Evaluation Board Figure 35. AD737 Evaluation Board—Secondary-Side Copper Figure 36. AD737 Evaluation Board—Internal Power Plane 00828-036 As described in the Applications Information section, the AD737 can be connected in a variety of ways. As shipped, the board is configured for dual supplies with the high impedance input connected and the power-down feature disabled. Jumpers are provided for connecting the input to the low impedance input (Pin 1) and for dc connections to either input. The schematic with movable jumpers is shown in Figure 38. The jumper positions in black are default connections; the dotted-outline jumpers are optional connections. The board is tested prior to shipment and requires only a power supply connection and a precision meter to perform measurements. 00828-035 Figure 33. AD737 Evaluation Board—Component-Side Silkscreen Figure 37. AD737 Evaluation Board—Internal Ground Plane Rev. J | Page 19 of 24 AD737 Data Sheet –VS GND1 GND2 GND3 GND4 +VS C1 10µF 25V + W1 DC COUP LO-Z W4 LO-Z IN + C2 10µF 25V +VS –VS W3 AC COUP R3 0Ω + CC J1 CIN 0.1µF DUT P2 HI-Z SEL HI-Z AD737 1 IN COM CC 8 2 V IN GND 7 +VS 3 POWER DOWN OUTPUT 6 W2 R1 1MΩ +VS 4 –VS J3 PD FILT NORM –VS SEL PIN3 CAV R4 0Ω +VS C6 0.1µF 5 CAV VOUT J2 CF1 CAV 33 µF 16V + C4 0.1µF CF2 Figure 38. AD737 Evaluation Board Schematic Rev. J | Page 20 of 24 00828-037 VIN Data Sheet AD737 OUTLINE DIMENSIONS 5.00 (0.1968) 4.80 (0.1890) 1 5 6.20 (0.2441) 5.80 (0.2284) 4 1.27 (0.0500) BSC 0.25 (0.0098) 0.10 (0.0040) 1.75 (0.0688) 1.35 (0.0532) 0.51 (0.0201) 0.31 (0.0122) COPLANARITY 0.10 SEATING PLANE 0.50 (0.0196) 0.25 (0.0099) 45° 8° 0° 0.25 (0.0098) 0.17 (0.0067) 1.27 (0.0500) 0.40 (0.0157) COMPLIANT TO JEDEC STANDARDS MS-012-AA CONTROLLING DIMENSIONS ARE IN MILLIMETERS; INCH DIMENSIONS (IN PARENTHESES) ARE ROUNDED-OFF MILLIMETER EQUIVALENTS FOR REFERENCE ONLY AND ARE NOT APPROPRIATE FOR USE IN DESIGN. 012407-A 8 4.00 (0.1574) 3.80 (0.1497) Figure 39. 8-Lead Standard Small Outline Package [SOIC_N] Narrow Body (R-8) Dimensions shown in millimeters and (inches) 0.400 (10.16) 0.365 (9.27) 0.355 (9.02) 8 5 1 4 0.280 (7.11) 0.250 (6.35) 0.240 (6.10) 0.100 (2.54) BSC 0.060 (1.52) MAX 0.210 (5.33) MAX 0.015 (0.38) MIN 0.150 (3.81) 0.130 (3.30) 0.115 (2.92) SEATING PLANE 0.022 (0.56) 0.018 (0.46) 0.014 (0.36) 0.325 (8.26) 0.310 (7.87) 0.300 (7.62) 0.195 (4.95) 0.130 (3.30) 0.115 (2.92) 0.015 (0.38) GAUGE PLANE 0.005 (0.13) MIN 0.014 (0.36) 0.010 (0.25) 0.008 (0.20) 0.430 (10.92) MAX COMPLIANT TO JEDEC STANDARDS MS-001 CONTROLLING DIMENSIONS ARE IN INCHES; MILLIMETER DIMENSIONS (IN PARENTHESES) ARE ROUNDED-OFF INCH EQUIVALENTS FOR REFERENCE ONLY AND ARE NOT APPROPRIATE FOR USE IN DESIGN. CORNER LEADS MAY BE CONFIGURED AS WHOLE OR HALF LEADS. Figure 40. 8-Lead Plastic Dual-In-Line Package [PDIP] (N-8) Dimensions shown in inches and (millimeters) Rev. J | Page 21 of 24 070606-A 0.070 (1.78) 0.060 (1.52) 0.045 (1.14) AD737 Data Sheet ORDERING GUIDE Model 1 AD737ANZ AD737ARZ AD737JNZ AD737JRZ AD737JRZ-R7 AD737JRZ-RL AD737JRZ-5 AD737JRZ-5-R7 AD737JRZ-5-RL AD737KR-REEL AD737KR-REEL7 AD737KRZ-RL AD737KRZ-R7 AD737-EVALZ 1 Temperature Range −40°C to +85°C −40°C to +85°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C 0°C to 70°C Package Description 8-Lead Plastic Dual In-Line Package [PDIP] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Plastic Dual In-Line Package [PDIP] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] 8-Lead Standard Small Outline Package [SOIC_N] Evaluation Board Z = RoHS Compliant Part. Rev. J | Page 22 of 24 Package Option N-8 R-8 N-8 R-8 R-8 R-8 R-8 R-8 R-8 R-8 R-8 R-8 R-8 Data Sheet AD737 NOTES Rev. J | Page 23 of 24 AD737 Data Sheet NOTES ©1988–2015 Analog Devices, Inc. All rights reserved. Trademarks and registered trademarks are the property of their respective owners. D00828-0-10/15(J) Rev. J | Page 24 of 24