1. Fundamentals of Analog and Digital Design
ET-IDA-134
Lecture-1
Review: Fundamentals of Circuit Analysis
Ch-1 and Ch-2
(L1 to L6)
, v9
Prof. W. Adi
Source: Analog Devices, Digilent course material

2. Fundamentals of Analog and Digital Design
Recommended Textbook (MIT):
Agarwal, Anant, and Jeffrey H. Lang. Foundations of Analog and Digital Electronic Circuits. San Mateo, CA: Morgan Kaufmann Publishers, Elsevier, July ISBN: View e-book versionElsevier companion site: supplementary sections and examples
Lecture Material:
- Provided in the class. Source: Digilent/Analog Devices Course material
- Suplimentary advanced analog and digital design topics with laboratory
Laboratory:
- DIGILENT „Analog Discovery“ unit with lab‘s kit.

3. Laboratory Equipment: „Analog Discovery-1“
Capabilities of Analog Discovery unit:
• 2-Channel Oscilloscope
• 2-Channel Waveform Generator
• 16-Channel Logic Analyzer
• 16-Channel Digital Pattern Generator
• ±5VDC Power Supplies
• Spectrum Analyzer
• Network Analyzer
• Voltmeter
• Digital I/O
USB connected with user interface
The Analog Parts Kit contains a large selection of components perfect for creating a wide variety of useful circuits & devices. Featuring Analog Devices components, the kit includes transistors, resistors, capacitors, diodes, sensors, and variety of useful ICs including Op Amps, convertors, and regulators. Finally, the kit also comes with an assortment of lead wires, a solderless breadboard, and a screwdriver.

4. Laboratory Equipment: „Analog Discovery-2“
Capabilities of Analog Discovery unit:
Two-channel USB digital oscilloscope (1MΩ, ±25V, differential, 14-bit, 100MS/s, 30MHz+ bandwidth - with the Analog Discovery BNC Adapter Board)
Two-channel arbitrary function generator (±5V, 14-bit, 100MS/s, 12MHz+ bandwidth - with the Analog Discovery BNC Adapter Board)
Stereo audio amplifier to drive external headphones or speakers with replicated AWG signals
16-channel digital logic analyzer (3.3V CMOS and 1.8V or 5V tolerant, 100MS/s) 16-channel pattern generator (3.3V CMOS, 100MS/s) 16-channel virtual digital I/O including buttons, switches, and LEDs – perfect for logic training applications
Two input/output digital trigger signals for linking multiple instruments (3.3V CMOS)
Single channel voltmeter (AC, DC, ±25V)
Network analyzer – Bode, Nyquist, Nichols transfer diagrams of a circuit. Range: 1Hz to 10MHz
Spectrum Analyzer – power spectrum and spectral measurements (noise floor, SFDR, SNR, THD, etc.)
Digital Bus Analyzers (SPI, I²C, UART, Parallel)
Two programmable power supplies (0…+5V , 0…-5V). The maximum available output current and power depend on the Analog Discovery 2 powering choice:
500mW total when powered through USB. (Each supply can provide between 0mW and 500mW so long as the total does not exceed 500mW.)
2.1W max for each supply when powered by an auxiliary supply.
700mA maximum current for each supply.
The Analog Parts Kit contains a large selection of components perfect for creating a wide variety of useful circuits & devices. Featuring Analog Devices components, the kit includes transistors, resistors, capacitors, diodes, sensors, and variety of useful ICs including Op Amps, convertors, and regulators. Finally, the kit also comes with an assortment of lead wires, a solderless breadboard, and a screwdriver.

5. Lecture 1 Course Overview Basic Circuit Parameters
System modeling, analysis and design
Basic Circuit Parameters
Passive Sign Convention
Related educational materials:
Chapter 1.1

6. Pre-requisite and Co-requisite requirements
Pre-requisites (recommended)
Basic exposure to electricity and magnetism
Two semesters of Calculus
Co-requisites (recommended)
Differential equations
Pre- and Co-requisite requirements are rather weak
Quick introductions to necessary topics provided at the appropriate points on-demand during this course
Note that a series of background lectures is available to provide some useful material.

7. Course Goals
Introduction to modeling, analysis and design of electrical circuits
We will often use a systems-level approach:
Note that we may start thinking of the system strictly in terms of the equation(s) relating the input and output
It is entirely possible to lose track of the physics of the system, to the extent that it doesn’t matter whether the system is electrical, mechanical, fluidic, or thermal
It is very common (especially in thermal and fluid systems) to represent the system as an “equivalent” electrical system
Laboratory Objectives: Practical Introduction to analysis and design of electronic circuits

8. Modeling, analysis, and design – overview

9. Circuits I modeling approach
We will restrict our attention to lumped parameter models of linear, time-invariant systems
Governing equations will be linear, constant-coefficient, ordinary differential equations

10. Basic Circuit Parameters
Charge (q) is the basic quantity in circuit analysis
Units are Coulombs (C)  1 Coulomb  -6.241018 electrons
Current (i) is the rate of change of charge with time:
Units are Amperes (A) 

11. Basic Circuit Parameters – continued
Voltage (v) is the change in energy of a unit charge at two different points:
Units are Volts (V) 

12. Basic Circuit Parameters – continued
Power (P) is the time rate of change of energy:
Units are Watts (W)

13. Passive Circuit Elements
For a passive circuit element, the total energy delivered to the circuit element by the rest of the circuit is non-negative
The element can store energy, but it cannot create energy
Active circuit elements can supply energy to the circuit from external sources

14. Passive Sign Convention
We will assume the sign
of the current relative to
voltage for passive circuit
Elements
Positive current enters the
node at the higher voltage
Sign must be known for active circuit elements
Note on active elements:
We haven’t really talked about these, yet. However, if you’ve watched the background lectures, we can mention that:
You must know the voltage polarity on a voltage source (though you know nothing about current direction)
You must know the current direction for a current source (though you don’t know what the voltage polarity is)
More on this later!
!! You can assume (arbitrarily) either the voltage polarity or the current direction !!
!Negative results tells that the assumption has to be reversed!

15. Passive Sign Convention – Example 1
Provide the appropriate sign convention for the missing parameter on the passive elements represented by grey boxes.
Point out active elements. Voltage source and current source. Note that:
We will introduce these types of elements more formally later
The necessary signs are provided on these elements. We do not know:
Anything about the voltage across the current source
Anything about the current through the voltage source

16. Passive Sign Conventions – Hints
It is generally counter-productive to attempt to determine the “correct” voltage polarities and current directions before analyzing the circuit
Just arbitrarily choose either the assumed voltage polarity or current direction for each passive circuit element
This choice dictates the sign of the other parameter
Perform analysis using assumed signs
Negative signs mean that the assumption was incorrect

17. Passive Sign Convention – Example 2
Assign reference voltage and current directions for the passive elements represented by shaded boxes in the circuit below:

18. Passive Sign Convention – Example 3
Assign reference voltage and current directions for the passive elements represented by shaded boxes in the circuit below:
Do this problem at least two ways. (choose one set of reference directions, then erase and choose a different set.) Note that it doesn’t matter!

19. Passive Sign Convention – Example 4
For the circuit below, the sign convention shown is chosen
After analyzing the circuit, it is determined that I1 = -3mA, I2 = 3mA, V1 = -1.5V, and V2 = 2.5V. Re-draw the circuit showing the actual voltages and currents and their directions

20. Lecture 2 Review Passive Sign Convention Power Generation, Absorption
Power Sources
Resistance
Related educational materials:
Chapter 1.1, 1.2, 1.3

21. Passive sign convention – review
For passive circuit elements, we assume that the current enters the node with the higher voltage potential
Your analyses will not be reliable unless you do this correctly
Examples:
Note that a series of background lectures is available to provide some useful material.

22. Subscript notation can denote voltage polarity
Voltage polarity is sometimes indicated by subscript notation
The order of the subscripts indicates the polarity
The first subscript indicates assumed higher-voltage node
The second subscript is the assumed lower-voltage node

23. “Ground” Voltages are often represented as relative to “ground”:
Ground (symbol: ) is a reference voltage; often 0V
Voltages relative to ground generally not called a voltage difference; they are a difference relative to zero volts
Voltages relative to ground often represented with a single subscript

24. Power Generation and Dissipation
Circuit elements can either dissipate or generate power
Power is dissipated (or absorbed) if current enters the positive voltage node
Power is generated (or supplied) if current enters the negative voltage node

25. Power Generation and Dissipation
Power = voltage  current (p= vi)
Power is absorbed if the power is positive (voltage and current are consistent with the passive sign convention)
Power is generated if the power is negative (voltage and current not consistent with the passive sign convention)

26. Examples Determine the power absorbed by the circuit element below.
The circuit element absorbs 10W. Determine the current in the element.

27. Power Supplies Power supplies provide a source of electrical power
Conceptual types of power supplies (models of physical supplies):
Voltage, current sources
Independent, dependent sources
Ideal and non-ideal sources

28. Independent voltage sources
Common symbols:
Independent voltage sources maintain specified voltage, regardless of the current

29. Independent voltage sources – continued
Voltage-current characteristic for constant voltage source:

30. Independent current sources
Common symbol:
Independent current sources maintain specified current, regardless of the voltage

31. Independent current sources – continued
Voltage-current characteristic for constant current source:

32. Ideal power sources – limitations
Ideal sources can provide infinite power
Voltage sources provide specified voltage, regardless of the current  current can be infinite  power can be infinite
Current sources provide specified current, regardless of the voltage  voltage can be infinite  power can be infinite
These models can be unrealistic
We will examine more realistic power source models later

33. Dependent Power Supplies
Some active circuit elements can be modeled as dependent power sources
The current or voltage delivered by the source is controlled by a current or voltage somewhere else in the circuit
Four possible combinations
Voltage controlled voltage source (VCVS)
Current controlled voltage source (CCVS)
Voltage controlled current source (VCCS)
Current controlled current source (CCCS)

34. Dependent Power Supplies – continued
Examples:

35. Resistors Circuit symbol: R is the resistance
Units are ohms ()
Voltage-current relation (Ohm’s Law):

36. Resistors – continued Notes: Resistors can only dissipate energy
The voltage-current relation is algebraic

37. Resistor Power Dissipation
Ohm’s Law:
Power:
Combining:

38. Example
Determine the power (generated or absorbed) by the resistor below:

39. Conservation of energy
In an electrical circuit, the power generated is the same as the power absorbed
Slightly more mathematically,
Recall that power absorbed is positive and power generated is negative

40. Conservation of power – example
Determine the power (absorbed or generated) by the voltage source VS

41. Lecture 3 Review: Kirchoff’s Current Law Kirchoff’s Voltage Law
Ohm’s Law, Power, Power Conservation
Kirchoff’s Current Law
Kirchoff’s Voltage Law
Related educational materials:
Chapter 1.4

42. Review: Ohm’s Law Ohm’s Law Voltage-current characteristic
of ideal resistor:

43. Review: Power
Power:
Power is positive if i, v agree with passive sign convention (power absorbed)
Power is negative if i, v contrary to passive sign convention (power generated)

44. Review: Conservation of energy
Power conservation:
In an electrical circuit, the power generated is the same as the power absorbed.
Power absorbed is positive and power generated is negative

45. Two new laws today: Kirchoff’s Current Law Kirchoff’s Voltage Law
These will be defined in terms of nodes and loops

46. Basic Definition – Node
A Node is a point of connection between two or more circuit elements
Nodes can be “spread out” by perfect conductors

47. Basic Definition – Loop
A Loop is any closed path through the circuit which encounters no node more than once

48. Kirchoff’s Current Law (KCL)
The algebraic sum of all currents entering (or leaving) a node is zero
Equivalently: The sum of the currents entering a node equals the sum of the currents leaving a node
Mathematically:
We can’t accumulate
charge at a node

49. Kirchoff’s Current Law – continued
When applying KCL, the current directions (entering or leaving a node) are based on the assumed directions of the currents
Also need to decide whether currents entering the node are positive or negative; this dictates the sign of the currents leaving the node
As long all assumptions are consistent, the final result will reflect the actual current directions in the circuit

50. KCL – Example 1
Write KCL at the node below:

51. KCL – Example 2
Use KCL to determine the current i

52. Kirchoff’s Voltage Law (KVL)
The algebraic sum of all voltage differences around any closed loop is zero
Equivalently: The sum of the voltage rises around a closed loop is equal to the sum of the voltage drops around the loop
Mathematically:
If we traverse a loop, we end up
at the same voltage we started with

53. Kirchoff’s Voltage Law – continued
Voltage polarities are based on assumed polarities
If assumptions are consistent, the final results will reflect the actual polarities
To ensure consistency, I recommend:
Indicate assumed polarities on circuit diagram
Indicate loop and direction we are traversing loop
Follow the loop and sum the voltage differences:
If encounter a “+” first, treat the difference as positive
If encounter a “-” first, treat the difference as negative

54. KVL – Example
Apply KVL to the three loops in the circuit below. Use the provided assumed voltage polarities

55. Circuit analysis – applying KVL and KCL
In circuit analysis, we generally need to determine voltages and/or currents in one or more elements
We can determine voltages, currents in all elements by:
Writing a voltage-current relation for each element (Ohm’s law, for resistors)
Applying KVL around all but one loop in the circuit
Applying KCL at all but one node in the circuit

56. Circuit Analysis – Example 1
For the circuit below, determine the power absorbed by each resistor and the power generated by the source. Use conservation of energy to check your results.

57. Example 1 – continued

58. Circuit Analysis – Example 2
For the circuit below, write equations to determine the current through the 2 resistor

59. Example 2 – Alternate approach

60. Circuit Analysis
The above circuit analysis approach (defining all “N” unknown circuit parameters and writing N equations in N unknowns) is called the exhaustive method
We are often interested in some subset of the possible circuit parameters
We can often write and solve fewer equations in order to determine the desired parameters

61. Circuit analysis – Example 3
For the circuit below, determine:
(a) The current through the 2 resistor
(b) The current through the 1 resistor
(c) The power (absorbed or generated) by the source

62. Circuit Analysis Example 3 – continued

63. Lecture 4 Review: Circuit analysis examples
KVL, KCL
Circuit analysis examples
Series, parallel circuit elements
Related educational materials:
Chapter 1.4, 1.5

64. Review: KVL & KCL
KVL: algebraic sum of all voltage differences around any closed loop is zero
KCL: algebraic sum of all currents entering a node is zero

65. Review: Circuit analysis
General circuit analysis approach:
Assign element voltages, currents according to passive sign convention
Apply KVL, KCL, and voltage-current relations as necessary to solve for desired circuit parameters
The general idea is to write as many equations as you have unknowns, and solve for the desired unknowns

66. Circuit analysis – example 1
For the circuit below, determine: vAC, vX, vDE, RX, and the power absorbed by the 2 resistor

67. Example 1 – continued

68. Circuit analysis – example 2
Determine the voltages across both resistors.

69. Example 2 – continued

70. Circuit analysis – example 3
We have a “dead” battery, which only provides 2V
Second battery used to “charge” the dead battery – what is the current to the dead battery?

71. Non-ideal voltage source models
Add a “source resistance” in series with an ideal voltage source
We will define the term series formally later

72. Non-ideal current source models
Add a “source resistance” in parallel with an ideal current source
We will define the term parallel formally later

73. Example 3 – revisited Our battery charging example can now make sense
Include internal (source resistances) in our model

74. Ideal sources can provide infinite power
Connect a “load” to an ideal voltage source:

75. Non-ideal sources limit power delivery
“Loaded” non-ideal voltage source

76. Non-ideal sources limit power delivery
“Loaded” non-ideal current source

77. When are ideal source models “good enough”?
Ideal and non-ideal voltage sources are the “same” if RLoad >> RS
Ideal and non-ideal current sources are the “same” if RLoad << RS

78. Series and parallel circuit elements
Circuit elements are in series if all elements carry the same current
KCL at node “a” provides i1 = i2

79. Series and parallel circuit elements
Circuit elements are in parallel if all elements have the same voltage difference
KVL provides v1 = v2

80. Circuit reduction
In some cases, series and parallel combinations of circuit elements can be combined into a single “equivalent” element
This process reduces the overall number of unknowns in the circuit, thus simplifying the circuit analysis
Fewer elements  fewer related voltages, currents
The process is called circuit reduction

81. Lecture 5 Review: Circuit reduction Related educational materials:
Series, parallel circuit elements
Circuit reduction
Related educational materials:
Chapter 2.1, 2.2, 2.3

82. Review: series and parallel circuit elements
Elements in series if they have the same current
Elements in parallel have the same voltage

83. Circuit reduction
Some circuit problems can be simplified by combining elements to reduce the number of elements
Reducing the number of elements reduces the number of unknowns and thus the number of equations which must be written to determine these unknowns

84. Series circuit elements – example 1
Apply KCL at any node  all elements have the same current
All of the above circuit elements are in series

85. Series element circuit reduction – example 1
KVL around the loop:
-V1 + i·R1 + V2 + i·R2 + i·R3 – V3 + i·R4 = 0
(-V1 + V2– V3) + i(R1 + R2 + R3 + R4) = 0

86. Series circuit reduction
Notes:
Voltage sources in series add directly to form an equivalent voltage source
Resistances in series add directly to form an equivalent resistance

87. Series circuit reduction – Example 2
Determine the power delivered by the 20V source

88. Voltage Division
Series combination of N resistors:

89. Voltage Divider Formula
Ratio of VK to the total voltage is the same as the ratio of RK to the total series resistance

90. Voltage Dividers – special case
Voltage source in series with two resistors:

91. Voltage division – example 1
Determine the power dissipated by the 2 resistor

92. Voltage division – example 2
Determine the voltage V1 in the circuit below.

93. Parallel circuit elements – example 1
Apply KVL around any loop  all elements have the same voltage
All of the above circuit elements are in parallel

94. Parallel element circuit reduction – example 1
KCL at upper node:

95. Parallel circuit reduction
Notes:
Current sources in parallel add directly to form an equivalent current source
Definition: Conductance is the inverse of resistance
Units are siemens or mhos (abbreviated S or )
Conductances in parallel add directly to form an equivalent conductance

96. Parallel element circuit example 1 – revisted

97. Parallel circuit reduction – Example 2
Determine the power delivered by the 2A source

98. Current Division
Parallel combination of N resistors:

99. Current Divider Formula
Ratio of iK to the total current is the same as the ratio of GK to the total parallel conductance

100. Current Divider – special case
Current source in parallel with two resistors

101. Current division – example 1
Determine the current in the 2 resistor

102. Current division – example 2
Determine the value of R which makes i = 2mA

103. Circuit Reduction
Series and parallel combinations of circuit elements can be combined into a “equivalent” elements
The resulting simplified circuit can often be analyzed more easily than the original circuit

104. Circuit Reduction – example 1
Determine the current in the 2 resistor. (Note: we wrote the governing equations for this example in lecture 3.)

105. Lecture 6 Review: Circuit reduction examples Practical application
Temperature measurement
Related educational materials:
Chapter 2.3

106. Review: series resistors and voltage division
Equivalent resistance: Voltage divider formula:

107. Review: parallel resistance and current division
Equivalent resistance: Current divider formula:

108. Checking parallel resistance results
The equivalent resistance of a parallel combination of resistors is less than the smallest resistance in the combination
Resistance decreases as resistors are added in parallel
Range of equivalent resistance:
Rmin is the lowest resistance; N is the number of resistors

109. Examples: Non-ideal “loaded” power sources
Loaded voltage source:
Loaded current source:

110. Circuit Reduction
Series and parallel combinations of circuit elements can be combined into a “equivalent” elements
The resulting simplified circuit can often be analyzed more easily than the original circuit

111. Circuit reduction – example 1
Determine the equivalent resistance of the circuit below

112. Circuit reduction – example 2
Determine Vout in the circuit below.

113. Circuit reduction – example 3
In the circuit below, find i1, VS, and VO.

114. Example 3 – continued

115. Example 3 – continued

116. Circuit reduction – example 4
In the circuit below, determine
(a) the equivalent resistance seem by the source,
(b) the currents i1 and i2

117. Example 4 – continued