Direct Current and Alternating Current Circuits: An Introduction, Summaries of Computer Science

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PHYSICS

LECTURE NOTES

PHYS 395

ELECTRONICS

© cD.M. Gingrich

University of Alberta

Department of Physics

Preface

Electronics is one of the fastest expanding fields in research, application development and commercialization. Substantial growth in the field has occured due to World War II, the invention of the transistor, the space program, and now, the computer industry. The research grants are high, jobs are available and there is much money to be made in areas related to electronics. With the beginning of the “information superhighway” and computerized video coming to your home, it is hard to imagine that electronics will not continue to expand in the future. Electronics is everywhere in our lives. It is difficult for the practicing engineer to stay informed of the most recent developments in electronics. What is taught in this course could well be out of date by the time you actually go to use it. However the physical concepts of circuit behavour will be largely applicable to any future development. The approach to electronics taken in this course will be a mixture of physical concepts and design principles. The course will thus appear more qualitative and wordy compared to other physics courses. Nevertheless, it is hoped that this course will become a useful tool for your future physics laboratories and research. We can not begin to scratch the surface of the field of electronics in a one term course. Rather than cover a few topics in detail you will be exposed to most of the concepts and areas of design. The knowledge you gain will hopefully allow you to communicate with design engineers and technicians to enable them to design and build the electronics you require. You should also be equipped to pursue any area of electronics that may interest you in the future. This will include reading more detailed texts, the component data sheets and manuals. As well as, understanding the popular literature, including manuals for your stereo, computer, etc.. But above all I hope you find electronics interesting and enjoyable.

• 1 Direct Current Circuits
  • 1.1 Basic Concepts
    • 1.1.1 Current
    • 1.1.2 Potential Difference
    • 1.1.3 Resistance and Ohm’s Law
  • 1.2 The Schematic Diagram
    • 1.2.1 Electromotive Force (EMF)
    • 1.2.2 Ground
  • 1.3 Kirchoff’s Laws
    • 1.3.1 Series and Parallel Combinations of Resistors
    • 1.3.2 Voltage Divider
    • 1.3.3 Current Divider
    • 1.3.4 Branch Current Method
    • 1.3.5 Loop Current Method
  • 1.4 Equivalent Circuits
    • 1.4.1 Thevenin’s and Norton’s Theorems
    • 1.4.2 Determination of Thevenin and Norton Circuit Elements
  • 1.5 Problems
• 2 Alternating Current Circuits - 2.1 AC Circuit Elements - 2.1.1 Capacitance - 2.1.2 Inductance - 2.2 Circuit Equations - 2.2.1 RC Circuit - 2.2.2 RL Circuit - 2.2.3 LC Circuit - 2.2.4 RCL Circuit - 2.3 Sinusoidal Sources and Complex Impedance - 2.3.1 Resistive Impedance - 2.3.2 Capacitive Impedance - 2.3.3 Inductive Impedance - 2.3.4 Combined Impedances - 2.4 Resonance and the Transfer Function - 2.5 Four-Terminal Networks
  • CONTENTS
    • 2.6 Single-Term Approximations of H
    • 2.7 Problems
  • 3 Filter Circuits
    • 3.1 Filters and Amplifiers
    • 3.2 Log-Log Plots and Decibels
    • 3.3 Passive RC Filters
      • 3.3.1 Low-Pass Filter
      • 3.3.2 Approximate Integrater
      • 3.3.3 High-Pass Filter
      • 3.3.4 Approximate Differentiator
    • 3.4 Complex Frequencies and the s-Plane
      • 3.4.1 Poles and Zeros of H
    • 3.5 Sequential RC Filters
    • 3.6 Passive RCL Filters
      • 3.6.1 Series RCL Circuit
    • 3.7 Amplifier Model
      • 3.7.1 One-, Two- and Three-Pole Amplifier Models
      • 3.7.2 Amplifier with Negative Feedback
    • 3.8 Problems
  • 4 Diode Circuits
    • 4.1 Energy Levels
    • 4.2 The PN Junction and the Diode Effect
      • 4.2.1 Current in the Diode
      • 4.2.2 The PN Diode as a Circuit Element
      • 4.2.3 The Zener Diode
      • 4.2.4 Light-Emitting Diodes
      • 4.2.5 Light-Sensitive Diodes
    • 4.3 Circuit Applications of Ordinary Diodes
      • 4.3.1 Power Supplies
      • 4.3.2 Rectification
      • 4.3.3 Power Supply Filtering
      • 4.3.4 Split Power Supply
      • 4.3.5 Voltage Multiplier
      • 4.3.6 Clamping
      • 4.3.7 Clipping
      • 4.3.8 Diode Gate
      • 4.3.9 Diode Protection
    • 4.4 Problems
• 5 Transistor Circuits - 5.1 Bipolar Junction Transistors - 5.1.1 Transistor Operation (NPN) - 5.1.2 Basic Circuit Configurations
  • CONTENTS - 5.1.3 Small-Signal Models - 5.1.4 Ideal and Perfect Bipolar Transistor Models - 5.1.5 Transconductance Model
    • 5.2 The Common Emitter Amplifier
      • 5.2.1 DC Biasing
      • 5.2.2 Approximate AC Model
      • 5.2.3 The Basic CE Amplifier
      • 5.2.4 CE Amplifier with Emitter Resistor
    • 5.3 The Common Collector Amplifier
    • 5.4 The Common Base Amplifier
    • 5.5 The Junction Field Effect Transistor (JFET)
      • 5.5.1 Principles of Operation
      • 5.5.2 Small-Signal AC Model
    • 5.6 JFET Common Source Amplifier
    • 5.7 JFET Common Drain Amplifier
    • 5.8 The Insulated-Gate Field Effect Transistor
    • 5.9 Power MOSFET Circuits
    • 5.10 Multiple Transistor Circuits
      • 5.10.1 Coupling Between Single Transistor Stages
      • 5.10.2 Darlington and Sziklai Connections
    • 5.11 Problems
• 6 Operational Amplifiers - 6.1 Open-Loop Amplifiers - 6.2 Ideal Amplifier Approximation - 6.2.1 Non-inverting Amplifiers - 6.2.2 Inverting Amplifiers - 6.2.3 Mathematical Operations - 6.2.4 Active Filters - 6.2.5 General Feedback Elements - 6.2.6 Differential Amplifiers - 6.3 Analysis Using Finite Open-Loop Gain - 6.3.1 Output Impedance - 6.3.2 Input Impedance - 6.3.3 Voltage and Current Offsets - 6.3.4 Current Limiting and Slew Rate - 6.4 Problems
• 7 Digital Circuits - 7.1 Number Systems - 7.1.1 Binary, Octal and Hexadecimal Numbers - 7.1.2 Number Representation - 7.2 Boolean Algebra - 7.3 Logic Gates - 7.4 Combinational Logic
  • CONTENTS - 7.4.1 Combinational Logic Design Using Truth Tables - 7.4.2 The AND-OR Gate - 7.4.3 Exclusive-OR Gate - 7.4.4 Timing Diagrams - 7.4.5 Signal Race - 7.4.6 Half and Full Adders
    • 7.5 Multiplexers and Decoders
    • 7.6 Schmitt Trigger
    • 7.7 The Data Bus
    • 7.8 Two-State Storage Elements
    • 7.9 Latches and Un-Clocked Flip-Flops
      • 7.9.1 Latches
      • 7.9.2 RS and RS Flip-Flops
    • 7.10 Clocked Flip-Flops
      • 7.10.1 Clocked RS Flip-Flop
      • 7.10.2 D Flip-Flop
      • 7.10.3 JK Flip-Flop
    • 7.11 Dynamically Clocked Flip-Flops
      • 7.11.1 Master/Slave or Pulse Triggering
      • 7.11.2 Edge Triggering
    • 7.12 One-Shots
    • 7.13 Registers
      • 7.13.1 Data Registers
      • 7.13.2 Shift Registers
      • 7.13.3 Counters
      • 7.13.4 Divide-by-N Counters
    • 7.14 Problems
• 8 Data Acquisition and Process Control - 8.1 Transducers - 8.2 Signal Conditioning Circuits - 8.2.1 De-bouncing the Mechanical Switch - 8.2.2 Op Amps for Gain, Offset and Function Modification - 8.2.3 Sample-and-Hold Amplifiers - 8.2.4 Gated Charge-to-Voltage Amplifier - 8.2.5 Comparator - 8.3 Oscillators - 8.3.1 Application to Interval Timers - 8.4 Digital-to-Analog Conversion - 8.4.1 Current Summing and IC Devices - 8.4.2 DAC Limitations - 8.5 Analog-to-Digital Conversion - 8.5.1 Parallel-Encoding ADC (flash ADC) - 8.5.2 Successive-Approximation ADC - 8.5.3 Dual-Slope ADC
• CONTENTS
  • 8.6 Time-to-Digital Conversion
  • 8.7 Problems
• 9 Computers and Device Interconnection
  • 9.1 Elements of the Microcomputer
    • 9.1.1 Microprocessor and Microcomputer
    • 9.1.2 Functional Elements of the Computer
    • 9.1.3 Mechanical Arrangement
    • 9.1.4 Addressing Devices on the Bus
    • 9.1.5 Control of the Bus
    • 9.1.6 Clock Lines
    • 9.1.7 Random Access Memory
    • 9.1.8 Read-Only Memory
    • 9.1.9 I/O Ports
    • 9.1.10 Interrupts
  • 9.2 8-, 16-, or 32-Bit Busses

Chapter 1

Direct Current Circuits

These lectures follow the traditional review of direct current circuits, with emphasis on two- terminal networks and equivalent circuits. The idea is to bring you up to speed for what is to come. The course will get less quantitative as we go along. In fact, you will probably find the course gets easier as we go.

1.1 Basic Concepts

Direct current (DC) circuit analysis deals with constant currents and voltages, while al- ternating current (AC) circuit analysis deals with time-varying voltage and current signals whose time average values are zero. Circuits with time-average values of non-zero are also important and will be mentioned briefly in the section on filters. The DC circuit compo- nents considered in this course are the constant voltage source, constant current source, and resistor. Electronics also deals with charge Q, electric E and magnetic B fields, as well as, potential V. We will not be concerned with a detailed description of these quantities but will use approximation methods when dealing with them. Hence electronics can be considered as a more practical approach to these subjects. For the details look at your classical physics and quantum mechanics courses.

1.1.1 Current

The fundamental quantity in electronics is charge and at its basic level is due to the charge properties of the fundamental particles of matter. For all intensive purposes it is the electron (or lack of electrons) that matter. The role of the proton charge is negligible. The aggregate motion of charges is called current I

I =

dq dt

where dq is the amount of positive charge crossing a specified surface in a time dt. Be aware that the charges in motion are actually negative electrons. Thus the electrons move in the opposite direction to the current flow. The SI unit for current is the ampere (A). For most electronic circuits the ampere is a rather large unit so the mA unit is more common.

CHAPTER 1. DIRECT CURRENT CIRCUITS 8

V

(a)

I

(b)

R

(c)

Figure 1.1: Common circuit elements encountered in DC circuits: a) ideal voltage source, b) ideal current source and c) resistor.

1.2.1 Electromotive Force (EMF)

Charge can flow in a material under the influence of an external electric field. Eventually the internal field due to the repositioned charge cancels the external electric field resulting in zero current flow. To maintain a potential drop (and flow of charge) requires an external energy source, ie. EMF (battery, power supply, signal generator, etc.). We will deal with two types of EMFs: The ideal voltage source is able to maintain a constant voltage regardless of the current it must put out (I → ∞ is possible). The ideal current source is able to maintain a constant current regardless of the voltage needed (V → ∞ is possible). Because a battery cannot produce an infinite amount of current, a model for the behavior of a battery is to put an internal resistance in series with an ideal voltage source (zero resistance). Real-life EMFs can always be approximated with ideal EMFs and appropriate combinations of other circuit elements.

1.2.2 Ground

A voltage must always be measured relative to some reference point. It is proper to speak of the voltage across an electrical component but we often speak of voltage at a point. It is then assumed that the reference voltage point is ground. Under strict definition, ground is the body of the earth. It is an infinite electrical sink. It can accept or supply any reasonable amount of charge without changing its electrical characteristics. It is common, but not always necessary, to connect some part of the circuit to earth or ground, which is taken, for convenience and by convention, to be at zero volts. Frequently, a common (or reference) connection of the metal chassis of the instrument suffices. Sometimes there is a common reference voltage that is not at 0 V. Figure 1.2 show some common ways of depicting grounds on a circuit diagram. When neither a ground nor any other voltage reference is shown explicitly on a schematic diagram, it is useful for purposes of discussion to adopt the convention that the bottom line on a circuit is at zero potential.

CHAPTER 1. DIRECT CURRENT CIRCUITS 9

(a) (b) (c)

Figure 1.2: Some grounding circuit diagram symbols: a) earth ground, b) chassis ground and c) common.

1.3 Kirchoff ’s Laws

The conservation of energy and conservation of charge when applied to electrical circuits are known as Kirchoff’s laws. Conservation of energy – zero algebraic sum of the voltage drops Vi around a closed circuit loop (imaginary loop) ∑

i

Vi = 0. (1.5)

Conservation of charge – zero algebraic sum of the currents Ik flowing into a point (total charge in, equals total charge out) ∑

k

Ik = 0. (1.6)

When applying these laws to solve for circuit unknowns we will find the following defini- tions useful:

• an element is an impedance (resistance) or EMF (ideal voltage source or ideal current source),
• a node is a point where three or more current-carrying elements are connected,
• a branch is one element or several in series connecting two adjacent nodes, and
• an interior loop is a circuit loop not subdivided by a branch.

Using these definitions we can apply Kirchoff’s laws to a circuit to solve for the unknown quantities. The general procedure is:

1. define the currents and voltages on a diagram,
2. apply Kirchoff’s laws to loops and nodes,
3. write down a set of linear algebraic equations, and
4. solve for the unknowns.

But before we look at general circuits lets consider how simple resistors add.

CHAPTER 1. DIRECT CURRENT CIRCUITS 11

Vout =

R 2

R 1 + R 2

Vin. (1.12)

Example: Determine an expression for the voltage V 2 on the voltage divider in figure 1.4.

V V

• R

R2 R

Figure 1.4: Example voltage divider.

We take the bottom line in figure 1.4 to be at ground and define the current flowing between V 2 and ground to be I. Ohm’s law gives

V 2 = IR 23 , where R 23 =

R 2 R 3

R 2 + R 3

Applying Kirchoff ’s voltage law for the input source gives

V = IR, where R = R 1 + R 23. (1.14) Combining the above two results and solving for V 2 leads to

V 2 =

R 23

R

V =

R 2 R 3 R 2 +R 3 R 1 + (^) RR 22 +RR^33

V (1.15)

R 2 R 3

R 1 R 2 + R 2 R 3 + R 3 R 1

V. (1.16)

1.3.3 Current Divider

Consider the current divider shown in figure 1.3b. The source current is divided between the two resistors and is given by Iin = I 1 + I 2 = V /R 1 + V /R 2. The voltage at the output is V = IoutR 2. The output current from the current divider is thus

Iout =

R 1

R 1 + R 2

Iin. (1.17)

Example: Determine an expression for the current I 3 through the resistor R 3 in the circuit shown in figure 1.5. The current I is divided amongst the three resistors and hence we use our expres- sion for resistors in parallel

CHAPTER 1. DIRECT CURRENT CIRCUITS 12

I R1 R2 R3 I

Figure 1.5: Example current divider.

V = R 123 I =

R 1 R 2 R 3

R 1 R 2 + R 2 R 3 + R 3 R 1

I. (1.18)

where V is the common voltage across the three parallel resistors. The current through R 3 is thus

I 3 =

V

R 3

R 1 R 2

R 1 R 2 + R 2 R 3 + R 3 R 1

I. (1.19)

Now lets consider some general approaches to solving for unknowns in circuits.

1.3.4 Branch Current Method

Use both of Kirchoff’s laws. But be aware that an arbitrary application of Kirchoff ’s two equations will not always yield an independent set of equations. But the following approach will probably work.

1. Label the current in each branch (do not worry about the direction of the actual current).
2. Use only interior loops and all but one node.
3. Solve the system of algebraic equations.

1.3.5 Loop Current Method

This method is also referred to as the mesh loop method. The independent current variables are taken to be the circulating current in each of the interior loops.

1. Label interior loop currents on a diagram.
2. Obtain expressions for the voltage changes around each interior loop.
3. Solve the system of algebraic equations.

Depending on the problem, it may ultimately be necessary to algebraically sum two loop currents in order to obtain the needed interior branch current for the final answer.

CHAPTER 1. DIRECT CURRENT CIRCUITS 14

Moreover, if we number the individual currents through each resistor using the same scheme as we have for each component (current through R 1 is I 1 , R 2 has I 2 , etc.) and identify I 0 as the current out of the battery, then

I 0 = Ia = 0. 267 A (1.27)

I 1 = Ia − Ib = 0. 127 A (1.28)

I 2 = Ib = 0. 140 A (1.29)

I 3 = Ia − Ic = 0. 154 A (1.30)

I 4 = Ic = 0. 113 A (1.31)

I 5 = Ib − Ic = 0. 027 A. (1.32) These are the same currents that would be found using only Kirchoff’s equations; however, here we had to handle only three simultaneous equations instead of six.

Example: Use the loop current method to determine the voltage developed across the terminals AB in the circuit shown in figure 1.7.

V

V

B

A

R R

R R

Figure 1.7: Example circuit for analysis using the loop current method.

Consider the clockwise current loop IA through the two resistors and the two potentials. Similarly consider the clockwise current IB around the other internal loop consisting of the three resistors and V 2. Kirchoff ’s law gives

V 1 − IA(2R) + IB R − V 2 = 0 loop A. (1.33)

V 2 − IB (3R) + IAR = 0 loop B. (1.34) Solving the above two equations for the unknown loop currents IA and IB gives

CHAPTER 1. DIRECT CURRENT CIRCUITS 15

V 1 − V 2 = 2 RIA − RIB (1.35)

V 2 = −RIA + 3RIB , (1.36)

( V 1 − V 2 V 2

)

( 2 R −R −R 3 R

) ( IA IB

) ≡ R

( IA IB

) , (1.37)

R−^1 =

R

( 3 / 5 1 / 5 1 / 5 2 / 5

) , (1.38)

IA =

R

[ 3

(V 1 − V 2 ) +

V 2

]

R

V 1 −

V 2

) (1.39)

IB =

R

[ 1 5

(V 1 − V 2 ) +

V 2

]

R

( 1 5

V 1 +

V 2

)

. (1.40)

The voltage across AB is given simply by

VAB = IB R (1.41)

(V 1 + V 2 ). (1.42)

1.4 Equivalent Circuits

Equivalent circuits is often the hardest concept and most numerically intensive in the course. Learning them well could make a difference on your midterm exam. Look in several books until you find the explanation you understand best. Since Ohm’s law and Kirchoff’s equations are linear, we can replace any DC circuit by a simplified circuit. Just like a combination of resistors and Ohm’s law could give an equivalent resistor, a combination of circuit elements and Kirchoff’s laws can give an equivalent circuit. Two possibilities are shown in figure 1.8.

1.4.1 Thevenin’s and Norton’s Theorems

A Thevenin equivalent circuit contains an equivalent voltage source VTh in series with an equivalent resistor RTh. A Norton equivalent circuit contains an equivalent current source IN in parallel with an equivalent resistor RN.

1.4.2 Determination of Thevenin and Norton Circuit Elements

One approach to determine the equivalent circuits is:

1. Thevenin – calculate the open-circuit voltage VAB = VTh.

CHAPTER 1. DIRECT CURRENT CIRCUITS 17

• The evaluation of VTh is performed using Kirchoff’s laws:

0 = 25 − (100 + 80)I 1 (1.50)

0 = 25 − (90 + 110)I 2 (1.51)

0 = 100I 1 + VTh − 90 I 2 (1.52)

The result is VTh = − 2 .64 V. The minus sign means only that the arbitrary choice of polarity was incorrect.

A B

A B

B

A

VTh

RTh

R 5

Figure 1.9: Thevenin’s theorem applied to the Wheatstone bridge circuit.

• The voltage source is shorted out and RTh is calculated (figure 1.9):

RTh =

Note that when the source is shorted out, the resistors that were in series (R 1 and R 3 ; R 2 and R 4 ) become parallel combinations.

• The network is assembled in series as shown in figure 1.9 and the current through R 5 is calculated.

CHAPTER 1. DIRECT CURRENT CIRCUITS 18

I 5 =

VTh RTh + R 5

= − 0. 027 A (1.54)

Note that the numerical value of the current is the same as that in the preceding calculations, but the sign is opposite. This is simply due to the incorrect choice of polarity of VTh for this calculation. In fact, the current flow is in the same direction in both examples, as would be expected.

Example: Find the Thevenin equivalent components VTh and RTh for the circuit in figure 1.10.

V

V

R

R

R

B

A

Figure 1.10: Example circuit for analysis using a Thevenin equivalent circuit.

Shorting the V ’s to find RT h gives two resistors in parallel, which are in series with a third resistor:

RTh = R +

RR

R + R

R. (1.55)

The open circuit voltage gives VT h. For the open circuit no current flows from the node joining the two resistors to A. A is thus at -V relative to this node. Around the interior loop Vloop = V 2 (cf. voltage divider). Therefore VAB = Vloop − V = −

V