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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.