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1 Guide to Individual Circuit System Design Method Cards Neil E. Cotter, Member, IEEE, and Cynthia Furse, Fellow, IEEE Abstract—This guide contains notes on individual Circuit System Design Method (CSDM) Cards. Index Terms— Linear circuit, system design method, cards, Thevenin equivalent I INTRODUCTION T HE deck of Circuit System Design Method (CSDM) cards described individually here, allows users to design complete circuits by taking a systems-design perspective shown on one side of the cards and flipping the cards over to see an exact circuit design. The theory and use of the cards is described in detail in [1]. Here, detailed notes on each card are presented. It is suggested that users view the Catalog of Circuit System Design Method Cards [2] side-by-side with this card guide. The layout of the comments in this guide and in the catalog is the same, starting on the next page. II GLOBAL FEATURES OF CARDS The CSDM cards are organized in suits. Table I lists the symbols for the suits, how many cards are in that suit, and their word descriptions. TABLE I CSDM CARD SUITS Symbol Suit Measurement Wire Component Amplifier Gate # of Cards 4 8 8 15 12 Description Meters for v and i values Wires, including reference Power sources and resistors Blocks with voltage gains Nonlinear blocks Each card includes the logo for the Electrical and Computer Engineering Department at the University of Utah in the upper left-hand corner. In the lower left-hand corner on the circuit side is a picture of the main circuit component or components. The circuit side of each card has a Thevenin equivalent of that card and all preceding circuits in a gray strip on the right edge of the card. The system side of each card has a yellow background and yellow in the suit and card number box in the upper right-hand corner. Note that the yellow disappears on some black and white copiers. N. E. Cotter is with the Electrical and Computer Engineering Dept., University of Utah, Salt Lake City, UT 84112 USA (phone 801-581-8566, email: [email protected]). C. Furse is with the Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, UT 84112-9206 USA and also with LiveWire Test Labs, Inc., Salt Lake City, UT 84117 USA (e-mail: [email protected]). The system side of each card has a gray buffer zone around the outside in which special wire symbols for input or output resistance are indicated. 2 1 . 5 . Voltmeter v1 unlabeled (Right Angle Wire) Transparent card Used to indicate arbitrary voltage drop v1 Transparent card Used to connect card output to another card's 2nd input. Can be rotated or flipped as needed. Red and black strings attached to card to represent probes 2 . 6 . Voltmeter v2 unlabeled (Right Angle Wire) Transparent card Used to indicate node voltage v2 Transparent card Used to indicate node voltage v2 Can be rotated or flipped as needed. 3 . 7 . Voltmeter v3 unlabeled (Verticle Wire) Transparent card Used to indicate arbitrary voltage drop v3 Transparent card Used to extend 2nd input connection to lower row. 4 . 8 . Ammeter i1 unlabeled (Horizontal Wire with Vertical Extension) Transparent card Used to indicate current i1 Transparent card Used to indicate node voltage v2 When printed in color, yellow path breaks circuit so current shows as flowing through meter. 3 1 System 1 Circuit Reference Reference Printed on cardstock. Printed on cardstock. Starting card for many systems. Creates initial voltage of zero. Reference (sometimes mistakenly called ground) in circuit. 2 System 2 Circuit Reference Reference Printed on cardstock. Printed on cardstock. Starting card for many systems. Creates initial voltage of zero. Reference connection (open triangle). Shows that Thevenin equivalent of reference is 0V and 0Ω. Pictures connector for common terminal of power supply. 3 System 3 Circuit Wire Wire Printed on cardstock. Printed on cardstock. Passes signal (and Thevenin equivalent) unchanged to next block. Included for completeness, it might be used to represent a forward-biased ideal diode. Can be used for connections in place of transparent wire card. Shows Thevenin equivalent notation, since Thevenin equivalent is unchanged by extending system by wire. 4 System 4 Circuit Open Open Printed on cardstock. Printed on cardstock. Interrupts signal output, causing input to next block to float. Can represent open-circuit diode. Since floating input is undefined, user must determine what voltage will be found at the subsequent input using circuit analysis methods. Problematic when used in system view, as output voltage can only be found by circuit analysis. Interrupts signal output, causing input to next block to float. Can represent open-circuit diode. Since floating input is undefined, user must determine what voltage will be found at the subsequent input using circuit analysis methods. 4 1 Circuit 1 System Voltage Source Voltage Source Battery or power supply. Requires reference on some card to its left. May be used after any card to increase voltage by vs. Adds a constant value to system voltage. Does not change Thevenin resistance. 2 Circuit 2 System Voltage Source Voltage Source Battery or power supply. Requires reference on some card to its left. May be used after any card to increase voltage by vs. Adds a constant value to system voltage. Leaves Thevenin resistance unchanged. 3 Circuit Resistor Adds constant value to Thevenin resistance. Leaves Thevenin voltage unchanged. 4 Circuit Resistor: variable (Thermistor) Adds variable value to Thevenin resistance. Leaves Thevenin voltage unchanged. Thermistor is temperature sensitive. Example thermistor datasheet: RL0503-5820-97-MS plot shows ln(R/R25°C) 3 System Resistor Leaves system voltage unchanged. Changes Thevenin resistance. 4 System Resistor: variable Leaves system voltage unchanged. Changes Thevenin resistance by variable amount that may affect gain in later block. 5 5 System 5 Circuit Resistor: variable Resistor: variable (Photocell) Leaves system voltage unchanged. Changes Thevenin resistance by variable amount that may affect gain in later block. Adds variable value to Thevenin resistance. Leaves Thevenin voltage unchanged. Photocell is light sensitive. Example photocell datasheet: PDV-P9008 Advanced Photonics Typical response of photocell is straight line with negative slope on log R vs log illumination plot. 6 System 6 Circuit Resistor: variable Resistor: variable Leaves system voltage unchanged. Changes Thevenin resistance by variable amount that may affect gain in later block. Adds variable value to Thevenin resistance. Rheostant (Potentiometer with only two connections) 7 System 7 Circuit Potentiometer Potentiometer Yields sum of two system voltages multiplied by gains. Sum of gains = 1. Gains ≤ 1. Changes Thevenin resistance to parallel combination of resistances on either side of wiper. Thevenin resistance can vary from 0 to Rpot/2 (if input Output is wiper of potentiometer. Inputs are at two ends of potentiometer. Thevenin resistances are zero. May be used (with references and voltage source) to make a second voltage reference. 8 System 8 Circuit Resistor: parallel Resistor: parallel Gives gain ≤ 1 for system voltage. Changes Thevenin resistance to lower value than before. Represents effects of adding a load to a system. Adds load on circuit (from output to reference). May be used with series resistance card to form voltagedivider. Changes Thevenin resistance to parallel of this R and previous Thevenin resistance. 6 1 Circuit 1 System Voltage Reference Voltage Reference Voltage is determined by V-divider formula. Thevenin resistance is parallel combination of resistances on either side of potentiometer wiper. Output voltage stays constant if next block has high input resistance. Outputs a fixed fraction of a supply voltage, VCC, as system 2 Circuit voltage. Thevenin resistance varies with the system voltage produced. Output voltage is stable if next block has high input resistance. Useful when creating voltage reference for one input of comparator. 2 System V-Divider V-Divider Voltage is determined by V-divider formula. Thevenin resistance is parallel combination of bottom resistor and top resistor plus previous block's Thevenin resistance. Produces fixed gain if previous block has low output resistance and next block has high input resistance. Since resistor tolerances imply variations in resistor values, the gain may vary accordingly. Outputs a fixed fraction (gain ≤ 1) of input voltage. Gain depends on resistor values in block and Thevenin resistance of previous block. Output voltage is stable if next block has high input resistance. Useful when creating voltage reference for one input of comparator. 3 Circuit 3 System Thevenin Equivalent Thevenin Equivalent Equivalent of any number of system blocks. User specifies voltage source value and Thevenin resistance value. Can represent any linear circuit. Representing all the circuitry (i.e., cards) preceding another card may be conceptually useful. For example, using the two Thevenin equivalent cards as inputs to the Op-Amp card reveals a universal formula for linear op-amp circuits. Used to represent an entire system or subsystem. User specifies the output system voltage. Useful for collapsing many blocks (i.e., cards) into one. May be used to represent part of a system if the user runs out of cards. 4 Circuit 4 System Thevenin Equivalent Thevenin Equivalent Equivalent of any number of system blocks. User specifies voltage source value and Thevenin resistance value. Can represent any linear circuit. Representing all the circuitry (i.e., cards) preceding another card may be conceptually useful. For example, using the two Thevenin equivalent cards as inputs to the Op-Amp card reveals a universal formula for linear op-amp circuits. Used to represent an entire system or subsystem. User specifies the output system voltage. Useful for collapsing many blocks (i.e., cards) into one. May be used to represent part of a system if the user runs out of cards. 7 5 System 5 Circuit Op-Amp Op-Amp Generic negative feedback amplifier circuit. Positive gain for first system input voltage. Negative gain for second system input voltage. Sums the positive and negative gain signals. Gain G can be any positive value. Positive and negative gains are linked. High input resistance for + input, intermediate input resistance for – input. Low output resistance. Universal formula for negative-feedback linear op-amp circuits in terms of Thevenin equivalent at + input and Thevenin equivalent at – input. Gain is determined by ratio of feedback resistance and Thevenin resistance of circuit at – input. Thevenin resistance at + input plays no role in output. Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. 6 System 6 Circuit Op-Amp Buffer (V-Follower) Op-Amp Buffer (V-Follower) Leaves system voltage unchanged but changes Thevenin resistance at output to zero. Used to decouple circuit with intermediate output resistance so output of previous block is not loaded down. Gain of unity circuit, Output voltage follows input voltage. Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. LM324A datasheet 7 System 7 Circuit Voltage Reference Op-Amp Buffer (V-Follower) Leaves system voltage unchanged but changes Thevenin resistance at output to zero. Used to decouple circuit with intermediate output resistance so output of previous block is not loaded down. High input resistance avoids loading down previous stage. Low Thevenin equivalent output resistance. Gain of unity circuit, Output voltage follows input voltage. Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. LM324A datasheet 8 System 8 Circuit Op-Amp Non-Inverting Amp Op-Amp Non-Inverting Amp Multiplies system input voltage by positive gain ≥ 1. High input resistance avoids loading down previous stage. Low Thevenin equivalent output resistance. Gain is determined by ratio of feedback resistor, Rf, and series resistor, Rs. Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. LM324A datasheet 8 9 Circuit 9 System Op-Amp Inverting Amp Op-Amp Inverting Amp Gain is determined by ratio of feedback resistor, Rf, and series Multiplies system input voltage by negative gain, –G. Gain can be any negative value. Intermediate input resistance; gain depends on Thevenin equivalent resistance of previous block. resistor, Rs. Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. LM324A datasheet 10 Circuit Op-Amp Non-Inverting Summer Gain G is determined by ratio of feedback resistor, Rf, and series resistor, Rs. Gains G1 and G2 are determined by Ra and Rb. Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. LM324A datasheet 11 Circuit 10 System Op-Amp Non-Inverting Summer Computes weighted sum of two system input voltages. Gains are all positive. Net gains for two inputs sum to value between 1 and ∞. Intermediate input resistances; gains depends on Thevenin equivalent resistances of previous blocks. 11 System Op-Amp (Inv) Summing Amp Op-Amp (Inv) Summing Amp Gains G1 and G2 are determined by ratio of feedback resistor, Computes negative weighted sum of two system input voltages. Gains may be any negative values between 0 and -∞. Net gains for two inputs sum to value between 1 and ∞. Intermediate input resistances; gains depends on Thevenin equivalent resistances of previous blocks. Rf to series resistors, Rs1 and Rs2. Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. LM324A datasheet 12 Circuit 12 System Op-Amp Differential Amp Op-Amp Differential Amp Gains G1 and G2 should be matched. Amplifies the difference between two system input voltages. A small error is added to output if ratios of resistor values in circuit not quite identical. The error is usually neglected. The gain, G2, is often large. Typically used to amplify small signals. Buffers usually used in input blocks to eliminate loading effects on small signals driving low input resistance of difference amplifier. Input resistance is approximately Rs + Rf but is not constant, owing to changing voltages at + and – inputs of op-amp. Output voltage is limited to range of power supply voltages. LM324 IC output can drive 20 mA minimum. The gain may have any positive value. 9 13 System 13 Circuit Op-Amp Difference Amp Op-Amp Difference Amp Computes difference of two system input voltages after multiplying each input by gain. Gains G1 and G2 may be any positive values. Intermediate input resistance on both inputs. Same circuit as difference amplifier if Ra = Rs and Rb = Rf. 14 System Output voltage is limited to range of power supply voltages, V+ and V–. LM324 IC output can drive 20 mA minimum. LM324A datasheet 14 Circuit Op-Amp Level-Shifter Op-Amp Level-Shifter This side of card is on inside of double card. Shows definitions of terms used in gain calculations to achieve desired shifting of high and low voltages to different values of high and low voltages. Outside of double card formed by putting cards back-to-back with tape on one edge so cards can be opened up like book. Specialized difference amplifier with power supply replacing 2nd input voltage. Gain stated by different formula to allow gains to be written as simple ratios of resistances. Circuit maps one range of voltages into another so that circuits with, e.g., different power supply voltages, can be connected to each other. 14 System 14 Circuit Op-Amp Level-Shifter Op-Amp Level-Shifter Outside of double card formed by putting cards back-to-back with tape on one edge so cards can be opened up like book. Shifts high and low input voltages to different high and low voltages. Used for converting op-amp or comparator output levels to logic input levels, for example. This side of car is on inside of double card. Shows how to calculate ratio of resistors to achieve desired shifting of high and low voltages to different values of of high and low voltages. 15 System 15 Circuit Op-Amp Level-Shifter Op-Amp Level-Shifter Second copy of level-shifter, but lacks instruction cards and is a single card. See detailed description of level shifter on cards 14. Second copy of level-shifter, but lacks instruction cards and is a single card. See detailed description of level shifter on cards 14. 10 1 Circuit 1 System Comparator Comparator LM324 Op-Amp used as comparator. One of four op-amps on chip. Power supplies for op-amp may be VCC = 5V or 15V Acts like switch. Output voltage is high if first system input voltage is higher than second system input voltage. Otherwise, output voltage is low. High and low output voltages are close to ±power supply voltages. Comparator has high input resistance and low output resistance. Voltage Reference + Comparator = Comparator with V-Ref and -VCC = 0V or –15V. User's choice. Input voltage must not exceed power supply voltage. 2 Circuit Comparator with V-Ref LM324 Op-Amp used as comparator. One of four op-amps on chip. Power supplies for op-amp may be VCC = 5V or 15V and -VCC = 0V or –15V. User's choice. Input voltage must not exceed power supply voltage. 3 Circuit 2 System Comparator with V-Ref Acts like switch. Output voltage is high if first system input voltage is higher than vref voltage. Otherwise, output voltage is low. High and low output voltages are close to ±power supply voltages. Comparator has high input resistance and low output resistance. 3 System Diode: forward-biased Diode: forward-biased Acts like fixed voltage drop. Diode is forward-biased if input voltage on left is greater than 1.5V and output side provides path for current to reference, e.g., by parallel resistor. If no current flows in diode, output voltage floats. Act likes negative voltage source, dropping system output voltage by 0.7V. Diode voltage drop may vary, depending on current in diode. 4 Circuit 4 System Diode: reverse-biased Diode: reverse-biased Acts like open circuit. Output voltage floats. Subsequent block's input Thevenin equivalent will determine output voltage of this block. Typically, output voltage will be 0V (from reference). Acts like open circuit. Card included for completeness and may be useful for analyzing output voltage as function of whether diode is carrying current or not. 11 5 System 5 Circuit LED: forward-biased LED: forward-biased Use system side only if following LED with another block. Otherwise, use formula for LED current on circuit side. LED current is proportional to Thevenin voltage – 1.5V where 1.5V is approximate voltage drop for LED. LED current is the quantity of interest, since LED brightness is proportional to current. Gain formulas, included for completeness, may generally be ignored. LED modeled as 1.5 V drop. Thevenin equivalent model on card not needed unless card is followed by another system block. 6 System 6 Circuit LED: reverse-biased LED: reverse-biased Block is equivalent to wire. Block leaves system output voltage unchanged. LED acts like open circuit, and circuit becomes equivalent to wire. 7 System 7 Circuit LED: bicolor LED: bicolor Use system side only if following LED with another block. Otherwise, use formula for LED current on circuit side. LED current is proportional to Thevenin voltage – 1.5V where 1.5V is approximate voltage drop for LED. LED current is the quantity of interest, since LED brightness is proportional to current. Gain formulas, included for completeness, may generally be ignored. Back-to-back LED's modeled as ±1.5 V drops. Thevenin equivalent model on card not needed unless card is followed by another system block. 8 System 8 Circuit XOR Gate XOR Gate Output is logical eXclusive-OR function of inputs. Inputs are 0 = 0V or 1 = 5V. Same voltage levels for output. Designed for 74HC86 chip with 5V supply. One of four XOR gates from one IC. Tie one input high to make NOT gate. XOR logic gate. Inputs can be directly from other logic gates. Inputs must be 0-1V for logic 0, 4-5V for logic 1. Use Op-Amp Level Shifter to shift comparator output from 0 to 15 V or -15 to 15V to e.g., 0.5 for logic 0, and 4.5 V for logic 1. 74HC86 output can drive 20 mA, sufficient for LED. TC74HC86AP datasheet 12 9 Circuit 9 System NAND Gate NAND Gate NAND logic gate. Inputs can be directly from other logic gates. Inputs must be 0-1V for logic 0, 4-5V for logic 1. Use Op-Amp Level Shifter to shift comparator output from 0 to 15 V or -15 to 15V to e.g., 0.5 for logic 0, and 4.5 V for logic 1. 74HC00 output can drive 20 mA, sufficient for LED. TC74HC00AP datasheet Output is logical Not-AND or NAND function of inputs. Inputs are 0 = 0V or 1 = 5V. Same voltage levels for output. Designed for 74HC00 chip with 5V supply. First of four NAND gates from one IC. Tie inputs together to make NOT gate. Use De Morgan's theorem to make OR gate from three NAND gates. 10 Circuit 10 System NAND Gate NAND Gate NAND logic gate. Inputs can be directly from other logic gates. Inputs must be 0-1V for logic 0, 4-5V for logic 1. Use Op-Amp Level Shifter to shift comparator output from 0 to 15 V or -15 to 15V to e.g., 0.5 for logic 0, and 4.5 V for logic 1. 74HC00 output can drive 20 mA, sufficient for LED. TC74HC00AP datasheet Output is logical Not-AND or NAND function of inputs. Inputs are 0 = 0V or 1 = 5V. Same voltage levels for output. Designed for 74HC00 chip with 5V supply. Second of four NAND gates from one IC. Tie inputs together to make NOT gate. Use De Morgan's theorem to make OR gate from three NAND gates. 11 Circuit 11 System NAND Gate NAND Gate NAND logic gate. Inputs can be directly from other logic gates. Inputs must be 0-1V for logic 0, 4-5V for logic 1. Use Op-Amp Level Shifter to shift comparator output from 0 to 15 V or -15 to 15V to e.g., 0.5 for logic 0, and 4.5 V for logic 1. 74HC00 output can drive 20 mA, sufficient for LED. TC74HC00AP datasheet Output is logical Not-AND or NAND function of inputs. Inputs are 0 = 0V or 1 = 5V. Same voltage levels for output. Designed for 74HC00 chip with 5V supply. Third of four NAND gates from one IC. Tie inputs together to make NOT gate. Use De Morgan's theorem to make OR gate from three NAND gates. 12 Circuit 12 System NAND Gate NAND Gate NAND logic gate. Inputs can be directly from other logic gates. Inputs must be 0-1V for logic 0, 4-5V for logic 1. Use Op-Amp Level Shifter to shift comparator output from 0 to 15 V or -15 to 15V to e.g., 0.5 for logic 0, and 4.5 V for logic 1. 74HC00 output can drive 20 mA, sufficient for LED. TC74HC00AP datasheet Output is logical Not-AND or NAND function of inputs. Inputs are 0 = 0V or 1 = 5V. Same voltage levels for output. Designed for 74HC00 chip with 5V supply. Third of four NAND gates from one IC. Tie inputs together to make NOT gate. Use De Morgan's theorem to make OR gate from three NAND gates. 13 REFERENCES [1] [2] N. E. Cotter and C. Furse. (2014, July 30) Instructions for Using Circuit System Design Method Cards [Online]. Available: http://www.atm.com N. E. Cotter and C. Furse. (2014, July 30) Catalog of Circuit System Design Method Cards [Online]. Available: http://www.atm.com Neil E. Cotter (M’84) earned an M.S. degree in mathematics and a Ph.D. in electrical engineering from Stanford University, Palo Alto, CA, in 1986. He is currently Associate Professor (Lecturer) in the Electrical and Computer Engineering Department at the University of Utah in Salt Lake City, Utah, where he has worked since 1999. He previously worked as a Design Engineer on speech recognition algorithms at Fonix, Inc. and on control systems at Geneva Steel Corp. Prior to that, he published papers on artificial neural networks as an Assistant Professor at the University of Utah. Dr. Cotter was awarded a millennium medal by IEEE in 2000. Cynthia Furse (M’87–SM’99–F’08) received the Ph.D. degree from the University of Utah, Salt Lake City, in 1994. She is the Associate Vice President for Research at the University of Utah and Professor in the Electrical and Computer Engineering Department. Her research focuses on imbedded antennas and sensors in complex environments, such as telemetry systems in the human body, and sensors for location of faults on aging aircraft wiring. She has directed the Utah “Smart Wiring” program, sponsored by NAVAIR and USAF, since 1998. She is Chief Scientist for LiveWire Test Labs, Inc., a spin off company commercializing devices to locate intermittent faults on live wires. She teaches electromagnetics, wireless communication, computational electro- magnetics, microwave engineering, and antenna design. Dr. Furse was the Professor of the Year in the College of Engineering, Utah State University for the year 2000, Faculty Employee of the Year 2002, a National Science Foundation Computational and Information Sciences and Engineering Graduate Fellow, IEEE Microwave Theory and Techniques Graduate Fellow, and President’s Scholar at the University of Utah. She also received the Distinguished Young Alumni Award from the Department of Electrical and Computer Engineering, University of Utah and the College of Engineering Distinguished Engineering Educator Award.