10 22 Circuits and Analog Electronics Prof Li

10 级计算机科学 2＋2 Circuits and Analog Electronics 电路与模拟电子技术 Prof. Li Chen, School of Information Science and Technology, Sun Yat-sen University 中山大学信息科学与技术学院 陈立副教授 Email: chenli 55@mail. sysu. edu. cn

Circuits and Analog Electronics References： • W. H. Hayt, Jr. , J. E. Kemmerly and S. M. Durbin, Engineering Circuit Analysis, Mc. Graw-Hill, 2005, ISBN 978 -7 -121 -01667 -7. • R. L. Boylestad and L. Nashelsky, Electronic Devices and Circuit Theory, Pearson Education, 2007, ISBN 978 -7 -121 -04396 -3. • 高玉良, 电路与模拟电子技术, 高教出版社, 2004, ISBN 7 -04014536 -7.

Circuits and Analog Electronics Handouts available at: sist. sysu. edu. cn/~chenli References： • W. H. Hayt, Jr. , J. E. Kemmerly and S. M. Durbin, Engineering Circuit Analysis, Mc. Graw-Hill, 2005, ISBN 978 -7 -121 -01667 -7. • R. L. Boylestad and L. Nashelsky, Electronic Devices and Circuit Theory, Pearson Education, 2007, ISBN 978 -7 -121 -04396 -3. • 高玉良, 电路与模拟电子技术, 高教出版社, 2004, ISBN 7 -04 -014536 -7.

Teaching Schedule Weeks Chapters References 1, 2 Basis concepts and laws of electronics Hayt: Ch 1 2 5 3, 4 Basis analysis methods to circuits Hayt: Ch 3 4 Basis RL & RC circuits Hayt: Ch 6 Sinusoidal steady state analysis Hayt: Ch 7 5 6, 7, 8 9 Midterm 10 Diodes and diodes circuits Boylestad: Ch 1 2 11, 12, 13 Basic BJT amplifier circuits Boylestad: Ch 3 -6 14, 15, 16 Operational amplifier and Op Amp circuits Boylestad: Ch 11 17 Review

Circuits and Analog Electronics Ch 1 Basic Concepts and Laws of Electric Circuits 1. 1 Basic Concepts and Electric Circuits 1. 2 Basic Quantities 1. 3 Circuit Elements 1. 4 Kirchhoff's Current and Voltage Laws References: Hayt: Ch 1, 2, 5; Gao: Ch 1;

1. 1 Basic Concepts and Electric Circuits l Signal processing and transmission transmitter Antenna l Amplifiers Circuits Speaker Kinescope Electrical power conversion and transmission Power Supplies Transmission Loads

1. 1 Basic Concepts and Electric Circuits l Electrical power conversion and transmission

1. 1 Basic Concepts and Electric Circuits Concept of Abstraction Question: What is the current through the bulb? Solution: In order to calculate the current, we can replace the bulb with a resistor. R is the only subject of interest, which serves as an abstraction of the bulb.

1. 1 Basic Concepts and Electric Circuits Resistance: R = V/I, 1 =1 V/A, ohm; Conductance: G = 1/R = 1 A/V, siemens (S); 1 S = 1 A/V, i(t) = G × v(t); Instantaneous current and voltage at time t; • A resistor is a circuit element that transforms the electrical energy (e. g. electricity heat); • Commonly used devices that are modeled as resistors include incandescent, heaters, wires and etc; • A circuit consists of sources, resistors, capacitors, inductors and conductors; • Elements are lumped. • Conductors are perfect. Lumped circuit abstraction!

1. 1 Basic Concepts and Electric Circuits The AM Radio System Transmitter Receiver Understanding the AM radio requires knowledge of several concepts • Communications/signal processing (frequency domain analysis) • Electromagnetics (antennas, high-frequency circuits) • Power (batteries, power supplies) • Solid state (miniaturization, low-power electronics)

1. 1 Basic Concepts and Electric Circuits Example 1: The AM audio system Example 2: The telephone system

1. 1 Basic Concepts and Electric Circuits The AM Radio System l A signal is a quantity that may vary with time. * Voltage or current in a circuit * Sound (sinusoidal wave traveling through air) * Light or radio waves (electromagnetic energy traveling through free space) l The analysis and design of AM radios (and communication systems in general) is usually conducted in the frequency domain using Fourier analysis, which allows us to represent signals as combinations of sinusoids (sines and cosines).

1. 1 Basic Concepts and Electric Circuits The AM Radio System Frequency is the rate at which a signal oscillates. Duration of the signal T, frequency of the signal f = 1/T. High Frequency Low Frequency

1. 1 Basic Concepts and Electric Circuits The AM Radio System Visible light is the electromagnetic energy with frequency between 380 THz (Terahertz) and 860 THz. l Our visual system perceives the frequency of the electromagnetic energy as color: is 460 THz, is 570 THz, and is 630 THz. l l red green blue An AM radio signal has a frequency of between 500 k. Hz and 1. 8 MHz. FM radio and TV uses different frequencies. l Mathematical analysis of signals in terms of frequency Most commonly encountered signals can be represented as a Fourier series or a Fourier transform. A Fourier series is a weighted sum of cosines and sines.

1. 1 Basic Concepts and Electric Circuits The AM Radio System Fourier Series: A Fourier series decomposes a periodic function (or signal) into the sum of a set of sines and cosines. Given function f(t) with angular frequency ω and period T, its Fourier series can be written as: f(t) = A 0 + A 1 msin(ωt + ψ1) + A 2 msin(2ωt + ψ2) + ··· =

1. 1 Basic Concepts and Electric Circuits Example: Given function during a period: t For the example : , k is even. , k is odd.

1. 1 Basic Concepts and Electric Circuits The AM Radio System Example-Fourier Series 1 st series + 3 rd series 1 st series (k = 1) 3 rd series (k = 3) • Signals can be represented in terms of their frequency components. • The AM transmitter and receiver are analyzed in terms of their effects on the frequency components signals.

1. 1 Basic Concepts and Electric Circuits The AM Radio System Transmitter Block Diagram Signal Source Modulator Power Amplifier Antenna Modulator The modulator converts the frequency of the input signal from the audio range (05 k. Hz) to the carrier frequency of the station (i. e. 605 k. Hz-615 k. Hz) 5 k. Hz freq Frequency domain representation of input 610 k. Hz Frequency domain representation of output freq

1. 1 Basic Concepts and Electric Circuits The AM Radio System Modulator: Time Domain Input Signal Output Signal

1. 1 Basic Concepts and Electric Circuits The AM Radio System Power Amplifier • A typical AM station broadcasts several k. W – Up to 50 k. W-Class I or Class II stations – Up to 5 k. W-Class III station – Up to 1 k. W-Class IV station • Typical modulator circuit can provide at most a few m. W • Power amplifier takes modulator output and increases its magnitude Antenna The antenna converts a current or a voltage signal to an electromagnetic signal which is radiated through the space.

1. 1 Basic Concepts and Electric Circuits The AM Radio System Receiver Block Diagram Antenna RF Amplifier IF Mixer Audio Amplifier Speaker IF Amplifier Envelope Detector

1. 1 Basic Concepts and Electric Circuits The AM Radio System Antenna • The antenna captures electromagnetic energy and converts it to a small voltage or current. • In the frequency domain, the antenna output is Undesired Signals 0 interferences Carrier Frequency of desired station Desired Signal interferences frequency

1. 1 Basic Concepts and Electric Circuits The AM Radio System RF (Radio Frequency) Amplifier • RF Amplifier amplifies small signals from the antenna to voltage levels appropriate for transistor circuits. • RF Amplifier also performs as a Bandpass filter for the signal – Bandpass filter attenuates the other components outside the frequency range that contains the desired station Undesired Signals 0 Desired Signal Carrier Frequency of desired station frequency

The AM Radio System IF (Intermediate Frequency) Mixer • The IF Mixer shifts input in the frequency domain from the carrier frequency to an intermediate frequency of 455 k. Hz Desired Signal Undesired Signals 0 frequency 455 k. Hz IF Amplifier • The IF amplifier bandpass filters the output of the IF mixer, eliminating all of the undesired signals. Desired Signal 0 455 k. Hz frequency

1. 1 Basic Concepts and Electric Circuits The AM Radio System Envelope Detector • Computes the envelope of its input signal Input Signal Output Signal

1. 1 Basic Concepts and Electric Circuits The AM Radio System Audio Amplifier • Amplifies signal from envelope detector • Provides power to drive the speaker Hierarchical System Models • Modelling at different levels of abstraction • Higher levels of the model describe overall function of the system • Lower levels of the model describe necessary details to implement the system • In the AM receiver, the input is the antenna voltage and the output is the sound energy produced by the speaker. • In EE, a system is an electrical and/or mechanical device, a process, or a mathematical model that relates one or more inputs to one or more outputs. Inputs System Outputs

1. 1 Basic Concepts and Electric Circuits The AM Radio System Top Level Model Input Signal AM Receiver Sound Second Level Model Antenna RF Amplifier IF Mixer IF Amplifier Power Supply Audio Amplifier Speaker Envelope Detector

1. 1 Basic Concepts and Electric Circuits The AM Radio System Low Level Model Envelope Detector. Half-wave Rectifier Low-pass Filter Circuit Level Model Envelope Detector Vin + - + R C - Vout

1. 2 Basic Quantities Units • Standard SI Prefixes – 10 -12 pico (p) – 10 -9 nano (n) – 10 -6 micro ( ) – 10 -3 milli (m) – 103 kilo (k) – 106 mega (M) – 109 giga (G) – 1012 tera (T) • Electric charge (q) – in Coulombs (C) • Current (I) – in Amperes (A) • Voltage (V) – in Volts (V) • Energy (W) – in Joules (J) • Power (P) – in Watts (W) l

1. 2 Basic Quantities Current • A mount of electric charges flowing through the surface per unit time. Constant current • Time rate of change of charge Time varying current (1 A = 1 C/s) Unit • Notation: Current flow represents the flow of positive charge • Alternating versus direct current (AC vs DC) i(t) t t AC Time – varying current DC Steady current

1. 2 Basic Quantities Current Positive versus negative current -2 A 2 A or Positive charge of 2 C/s moving Negative charge of -2 C/s moving or Negative charge of -2 C/s moving Positive charge of 2 C/s moving P 1. 1, In the wire electrons moving left to right to create a current of 1 m. A. Determine I 1 and I 2. Ans: I 1 = -1 m. A; I 2 = +1 m. A. Current is always associated with arrows (directions)

1. 2 Basic Quantities Voltage(Potential) • Energy per unit charge. • It is an electrical force drives an electric current. Voltage Units: 1 V = 1 J/C Positive versus negative voltage + Two “Do Not (DN)” – 2 V -2 V – + +/- of current (I) DN tell the actual direction of particle’s movement. +/- of voltage (V) DN tell the actual polarity of a certain point.

1. 2 Basic Quantities Voltage (Potential) Example a a、b, which point’s potential is higher？ b a Vab = ? b a b +Q from point b to point a get energy ，Point a is Positive? or negative ?

1. 2 Basic Quantities Voltage (Potential) Example c c´ b d I d´ a

1. 2 Basic Quantities Voltage (Potential) Example Va=? K Open I K Close I

1. 2 Basic Quantities Example I I

1. 2 Basic Quantities Power • One joules of energy is expanded per second. P = W/t • Rate of change of energy i(t) + v(t) – p(t) = v(t) i(t) v(t) is defined as the voltage with positive reference at the same terminal that the current i(t) is entering. • Used to determine the electrical power is being absorbed or supplied – if P is positive (+), power is absorbed – if P is negative (–), power is supplied

1. 2 Basic Quantities Power Example + 2 A Power is supplied. external element. -5 V – delivered power to + 2 A Power is absorbed. Power delivered to 5 V – Note : + 2 A – +5 V -5 V – + -2 A Power absorbed.

1. 2 Basic Quantities Power • Power absorbed by a resistor:

1. 2 Basic Quantities Power P 1. 5 Find the power absorbed by each element in the circuit. - + 5 I 1 - + + 1 + I 2 - - 3 - + 2 + I 3 + 4 + - Supply energy : element 1、3、4. Absorb energy : element 2、5 -

1. 2 Basic Quantities Open Circuit R= R 0 I=0, V=E , P=0 E Short Circuit R=0 R 0 R＝ 0 E

1. 2 Basic Quantities Loaded Circuit I R 0 E R

1. 3 Circuit Elements Key Words: Resistors, Capacitors, Inductors, voltage source, current source

1. 3 Circuit Elements • Passive elements (cannot generate energy) – e. g. , resistors, capacitors, inductors, etc. • Active elements (capable of generating energy) – batteries, generators, etc. • Important active elements – Independent voltage source – Independent current source – Dependent voltage source • voltage dependent and current dependent – Dependent current source • voltage dependent and current dependent

1. 3 Circuit Elements Resistors l Dissipation Elements v=i. R l v-i relationship P=vi=Ri 2=v 2/R >0 ， i v l l Resistors connected in series: – Equivalent Resistance is found by Req= R 1 + R 2 + R 3 + … Resistors connected in parallel 1/Req=1/R 1 + 1/R 2 + 1/R 3 + … R 1 R 2 R 3

1. 3 Circuit Elements Capacitors • Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator). • Charge on the two conductors creates an electric field that stores energy. • The voltage difference between the two conductors is proportional to the charge: q = C v • The proportionality constant C is called capacitance. • Units of Farads (F) - C/V 1 F=106 F, 1 F=106 PF • 1 F= one coulomb of charge of each conductor causes a voltage of one volt across the device.

1. 3 Circuit Elements Capacitors l store energy in an electric field l v-i relationship The rest of the circuit i(t) v. C(t+) = v. C(t-) l Energy stored l Capacitors connected in series: – Equivalent capacitance is found by 1/Ceq=1/C 1 + 1/C 2 + 1/C 3 + … l Capacitors connected in parallel Ceq= C 1 + C 2 + C 3 + … series parallel + v(t) -

1. 3 Circuit Elements Capacitors P 1. 7 For (1) : circuit i(t) + 0. 2 F v(t) - 1 A i(t) 2 s t 1 A 1 s v(t) 5 V 1 s (1) 2 s t

1. 3 Circuit Elements Capacitors P 1. 7 i(t) circuit + 0. 2 F v(t) For (2) : 1 A i(t) 2 s t 1 A For (1)、(2) : 1 s w (t) 2. 5 J 1 s 2 s (2) t

1. 3 Circuit Elements Inductors store energy in a magnetic field that is created by electric passing through it. l i(t) v-i relationship circuit l l l L v(t) - i. L(t+) = i. L(t-) l + Energy stored: Inductors connected in series: Leq= L 1 + L 2 + L 3 + … Inductors connected in parallel: 1/Leq=1/L 1 + 1/L 2 + 1/L 3 + …

1. 3 Circuit Elements Independent voltage source RS＝ 0 Ideal v VS VS + i practical

1. 3 Circuit Elements Independent current source Ideal v RS ＝ ∞ I IS practical i

1. 3 Circuit Elements Voltage source connected in series: Voltage source connected in parallel:

1. 3 Circuit Elements Voltage controlled (dependent) voltage source (VCVS) + + _ _ Current controlled (dependent) voltage source (CCVS) + _ Q: What are the units for and r?

1. 3 Circuit Elements Voltage controlled (dependent) current source (VCCS) + _ Current controlled (dependent) current source (CCCS) Q: What are the units for and g?

1. 3 Circuit Elements Independent source Can provide power to the circuit; Excitation to circuit ; Output is not controlled by external. dependent source Can provide power to the circuit; No excitation to circuit; Output is controlled by external.

1. 3 Circuit Elements Review • So far, we have talked about two kinds of circuit elements: – Sources (independent and dependent) • active, can provide power to the circuit. – Resistors • passive, can only dissipate power. The energy supplied by the active elements is equivalent to the energy absorbed by the passive elements!

1. 4 Kirchhoff's Current and Voltage Laws Key Words: Nodes, Branches, Loops, KCL, KVL

1. 4 Kirchhoff's Current and Voltage Laws Nodes, Branches, Loops, mesh Node: point where two or more elements are joined (e. g. , big node 1) Branch: Component connected between two nodes (e. g. , component R 4) Loop: A closed path that never goes twice over a node (e. g. , the blue line) The red path is NOT a loop Mesh: A loop that does not contain any other loops in it.

1. 4 Kirchhoff's Current and Voltage Laws Nodes, Branches, Loops, mesh P 1. 8 • • A circuit containing three nodes and five branches. Node 1 is redrawn to look like two nodes; it is still one nodes.

1. 4 Kirchhoff's Current and Voltage Laws KCL • sum of all currents entering a node is zero • sum of currents entering node is equal to sum of currents leaving node KCL Mathematically i 1(t) i 5(t) i 2(t) i 4(t) i 3(t)

1. 4 Kirchhoff's Current and Voltage Laws KCL • sum of all currents entering a node is zero • sum of currents entering node is equal to sum of currents leaving node P 1. 9

1. 4 Kirchhoff's Current and Voltage Laws KCL P 1. 10 KCL-Christmas Lights Is 120 V + - 50* 1 W Bulbs • Find currents through each light bulb: IB = 1 W/120 V = 8. 3 m. A • Apply KCL to the top node: IS - 50 IB = 0 • Solve for IS: IS = 50 IB = 417 m. A

1. 4 Kirchhoff's Current and Voltage Laws KCL P 1. 11 We can make supernodes by aggregting node.

1. 4 Kirchhoff's Current and Voltage Laws KCL In case of parallel : Current divider + I I 1 N V - G 1 I 2 G 2

1. 4 Kirchhoff's Current and Voltage Laws KVL l sum of voltages around any loop in a circuit is zero. KVL Mathematically • A voltage encountered + to - is positive. • A voltage encountered - to + is negative.

1. 4 Kirchhoff's Current and Voltage Laws KVL l KVL is a conservation of energy principle A positive charge gains electrical energy as it moves to a point with higher voltage and releases electrical energy if it moves to a point with lower voltage If the charge comes back to the same Initial point the net energy gain Must be zero.

1. 4 Kirchhoff's Current and Voltage Laws KVL P 1. 13 Determine the voltages Vae and Vec. 4 + 6 + Vec = 0

1. 4 Kirchhoff's Current and Voltage Laws KVL Voltage divider + + R 1 N + V R 2 - V 1 V 2 - Important voltage Divider equations

1. 4 Kirchhoff's Current and Voltage Laws KVL P 1. 14 Voltage divider Example: Vs = 9 V, R 1 = 90 kΩ, R 2 = 30 kΩ Volume control?