Electrical Engineering 348: ELECTRONIC CIRCUITS I Dr. John Choma, Jr. Professor of Electrical Engineering University of Southern California Department of Electrical Engineering– Electrophysics University Park; Mail Code: 0271 Los Angeles, California [Office] [Fax] [Cell] Spring Semester 2001
EE 348 – Spring 2001J. Choma, Jr.Slide 2 EE 348: Lecture Supplement Notes SN1 Review of Basic Circuit Theory and Introduction To Fundamental Electronic System Concepts 01 January 2001
EE 348 – Spring 2001J. Choma, Jr.Slide 3 Outline Of Lecture Thévenin’s & Norton’s Theorems Basic Electronic System Concepts Steady State Sinusoidal Response Transient Response
EE 348 – Spring 2001J. Choma, Jr.Slide 4 Thevénin’s Theorem Concept Two Terminals Of Any Linear Network Can Be Replaced By Voltage Source In Series With An Impedance Thévenin Voltage Is “Open Circuit” Voltage At Terminals Of Interest Thévenin Impedance Is Output Impedance At Terminals Of Interest Linear Load Thévenin Concept Applies To Linear Or Nonlinear Load Voltage V L Is Zero If No Independent Sources Are Embedded In The Load
EE 348 – Spring 2001J. Choma, Jr.Slide 5 Thévenin Model Parameters Thévenin Voltage Zero Load Current V oc V th Thévenin Impedance “Ohmmeter” Calculation Thévenin Voltage Is Set To Zero By Nulling All Independent Sources In Linear Network Superposition
EE 348 – Spring 2001J. Choma, Jr.Slide 6 Thévenin Example Bipolar Emitter Follower Equivalent Circuit Load Is The Capacitor, C l Calculate: Thévenin Voltage Seen By Load Thévenin Impedance Seen By Load Transfer Function, V o (s)/V s (s) 3–dB Bandwidth
EE 348 – Spring 2001J. Choma, Jr.Slide 7 Thévenin Voltage And Impedance Thévenin Voltage Gain Thévenin Impedance
EE 348 – Spring 2001J. Choma, Jr.Slide 8 Thévenin Output Model Gain Resistance
EE 348 – Spring 2001J. Choma, Jr.Slide 9 Transfer Function (Gain) Gain At Zero Frequency Is A th Bandwidth Definition 3–dB Bandwidth (Radians/Sec)
EE 348 – Spring 2001J. Choma, Jr.Slide 10 Frequency and Phase Responses –45°
EE 348 – Spring 2001J. Choma, Jr.Slide 11 Input Impedance Very Large Zero Frequency Input Impedance Other Characteristics Left Half Plane Pole And Left Half Plane Zero Non-Zero High Frequency Impedance
EE 348 – Spring 2001J. Choma, Jr.Slide 12 Voltage Delivery To Load System Problem Voltage Generated By Some Linear Network Is To Be Supplied To A Fixed Load Impedance, Z l Because The Source Network Is Linear, Its Output Can Be Represented By A Thévenin Circuit (V s — Z s ) Assume Thévenin Source and Load Impedances are Fixed Load Voltage If |Z l | << |Z s |, Much Of The Source Voltage Is “Lost” In The Source Impedance If |Z l | = |Z s |, 50% Of The Source Voltage Is Lost, Resulting In A factor Of Two Attenuation Or 6 dB Gain Loss. Many Systems Are Intolerant Of Such A Loss
EE 348 – Spring 2001J. Choma, Jr.Slide 13 Insertion Of Voltage Buffer
EE 348 – Spring 2001J. Choma, Jr.Slide 14 Impact Of Voltage Buffer Practical Buffer Z out Very Small Z in Very Large A buf Near Unity Effect Of Ideal Buffer
EE 348 – Spring 2001J. Choma, Jr.Slide 15 Norton’s Theorem Concept Two Terminals Of Any Linear Network Can Be Replaced By A Current Source In Shunt With An Impedance Norton Current Is “Short Circuit” Current At Terminals Of Interest Norton Impedance Is Output Impedance At Terminals Of Interest And Is Identical To Thévenin Output Impedance Linear Load Norton Concept Applies To Linear Or Nonlinear Load Voltage V L Is Zero If No Independent Sources Are Embedded In The Load
EE 348 – Spring 2001J. Choma, Jr.Slide 16 Norton Model Parameters Norton Current Zero Load Voltage I sc I no Norton Impedance “Ohmmeter” Calculation Norton Current Is Set To Zero By Nulling All Independent Sources In Linear Network Superposition
EE 348 – Spring 2001J. Choma, Jr.Slide 17 Thévenin–Norton Relationship From Thévenin Model: From Norton Model: Thévenin–Norton Equivalence:
EE 348 – Spring 2001J. Choma, Jr.Slide 18 Current and Voltage Sources Ideal Voltage Source Ideal Current Source
EE 348 – Spring 2001J. Choma, Jr.Slide 19 Voltage Amplifier Ideal Properties Infinitely Large Input Impedance, Z in Zero Output Impedance, Z out Sufficiently Large Voltage Gain, A v, Independent Of Input Voltage, V I and Output Voltage V o Circuit Schematic Symbol
EE 348 – Spring 2001J. Choma, Jr.Slide 20 Transconductor Ideal Properties Infinitely Large Input Impedance, Z in Infinitely Large Output Impedance, Z out Sufficiently Large Transconductance, G m, Independent Of Input Voltage, V I and Output Voltage V o Circuit Schematic Symbol
EE 348 – Spring 2001J. Choma, Jr.Slide 21 Current Amplifier Ideal Properties Zero Input Impedance, Z in Infinitely Large Output Impedance, Z out Sufficiently Large Current Gain, A i, Independent Of Input Voltage, V I and Output Voltage V o Circuit Schematic Symbol
EE 348 – Spring 2001J. Choma, Jr.Slide 22 Transresistance Amplifier Ideal Properties Zero Input Impedance, Z in Zero Output Impedance, Z out Sufficiently Large transresistance, R m, Independent Of Input Voltage, V I and Output Voltage V o Circuit Schematic Symbol
EE 348 – Spring 2001J. Choma, Jr.Slide 23 Max Voltage & Current Transfer Voltage Transfer Current Transfer M aximum Voltage Transfer Requires Very Small Z th Maximum Current Transfer Requires Very Large Z th
EE 348 – Spring 2001J. Choma, Jr.Slide 24 Power Dissipated In The Load Sinusoidal Steady State Load Power
EE 348 – Spring 2001J. Choma, Jr.Slide 25 Maximum Power Transfer Condition: Max Power:
EE 348 – Spring 2001J. Choma, Jr.Slide 26 Example–50 Transmission Line Parameters Antenna RMS Voltage Signal Is 10 V Transmission Line Coupling To RF Stage Behaves Electrically As A 50 Ohm Resistance Power To RF Input Port Maximized When RF Input Impedance Is 50 Ohms dBm Value:
EE 348 – Spring 2001J. Choma, Jr.Slide 27 Second Order Lowpass Filter Lowpass Filter Unity Gain Structure (Gain At Zero Frequency Is One) Ideal Transconductors KVL (Solve For V o /V s )
EE 348 – Spring 2001J. Choma, Jr.Slide 28 Filter Transfer Function Generalization: Parameters DC Gain = H(0) = 1 Undamped Resonant Frequency = o = (g m1 g m2 /C 1 C 2 ) 1/2 Damping Factor = = (g m2 C 1 / 4g m1 C 2 ) 1/2
EE 348 – Spring 2001J. Choma, Jr.Slide 29 Lowpass 2 nd Order Function Poles At s = –p 1 & s = –p 2 Undamped Frequency: Damping Factor: P 1 & P 2 Real Results In >1 (Overdamping) Or = 1 (Critical Damping) P 1 & P 2 Complex Requires P 1 & P 2 Conjugate Pairs, Whence < 1 (Underdamping)
EE 348 – Spring 2001J. Choma, Jr.Slide 30 Lowpass – Critical Damping Critical Damping = 1 p 1 = p 2 Frequency Response Bandwidth Constraint Bandwidth | H(0)| |H(j )| in dB -3 dB B Slope = –40 db/dec
EE 348 – Spring 2001J. Choma, Jr.Slide 31 Lowpass – Overdamping Overdamping > 1 p 1 < p 2 Poles Are Real Numbers Dominant Pole System Implies p 1 << p 2 Dominant Pole Bandwidth Transfer Function Approximation Bandwidth Approximation Gain-Bandwidth Product
EE 348 – Spring 2001J. Choma, Jr.Slide 32 Lowpass Frequency Response 3-dB Down
EE 348 – Spring 2001J. Choma, Jr.Slide 33 Lowpass Phase Response
EE 348 – Spring 2001J. Choma, Jr.Slide 34 Lowpass Step Response Input Is Unit Step [X(s) = 1/s] Overdamped ( > 1) Critical Damping ( = 1 o = p 1 = p 2 )
EE 348 – Spring 2001J. Choma, Jr.Slide 35 Real Pole Step Response Plots 95% Line
EE 348 – Spring 2001J. Choma, Jr.Slide 36 Lowpass – Underdamping Overdamping < 1 p 1 = p 2 * = o e j Circuit Bandwidth Proportional To o Equal To o For = Frequency Response Peaking |H(j )| Not Monotone Decreasing Frequency Function If < Non-Zero Frequency Associated With Maximal |H(j )|
EE 348 – Spring 2001J. Choma, Jr.Slide 37 Underdamped Frequency Response 3-dB Line
EE 348 – Spring 2001J. Choma, Jr.Slide 38 Underdamped Phase Response
EE 348 – Spring 2001J. Choma, Jr.Slide 39 Delay Response Steady State Sinusoidal Response If Phase Angle Is Linear With Frequency Constant Time Shift, Independent Of Signal Frequency No Phase Angle Is Ever Perfectly Linear Over Entire Passband Envelope Delay
EE 348 – Spring 2001J. Choma, Jr.Slide 40 Underdamped Delay Response
EE 348 – Spring 2001J. Choma, Jr.Slide 41 Underdamped Step Analysis Input Is Unit Step [X(s) = 1/s] Underdamped ( < 1) Characteristics Damped Oscillations Oscillation For Zero Damping ( = 0) Undamped Frequency Is Oscillatory Frequency For Zero Damping
EE 348 – Spring 2001J. Choma, Jr.Slide 42 Underdamped Step Response