7. AC ANALYSIS CIRCUITS by Ulaby & Maharbiz All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Overview All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Linear Circuits at ac Objective: To determine the steady state response of a linear circuit to ac signals  Sinusoidal input is common in electronic circuits  Any time-varying periodic signal can be represented by a series of sinusoids (Fourier Series)  Time-domain solution method can be cumbersome All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Sinusoidal Signals Useful relations All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phase Lead/Lag All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phasor Domain 1. The phasor-analysis technique transforms equations from the time domain to the phasor domain. 2. Integro-differential equations get converted into linear equations with no sinusoidal functions. 3. After solving for the desired variable--such as a particular voltage or current-- in the phasor domain, conversion back to the time domain provides the same solution that would have been obtained had the original integro-differential equations been solved entirely in the time domain. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phasor Domain Phasor counterpart of All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Time and Phasor Domain It is much easier to deal with exponentials in the phasor domain than sinusoidal relations in the time domain. You just need to track magnitude/phase, knowing that everything is at frequency  All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phasor Relation for Resistors Time DomainFrequency Domain Current through a resistor Time domain Phasor Domain All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phasor Relation for Inductors Time Domain Current through inductor in time domain Time domain Phasor Domain All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phasor Relation for Capacitors Time Domain Voltage across capacitor in time domain is Time domain Phasor Domain All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Summary of R, L, C All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

ac Phasor Analysis General Procedure Using this procedure, we can apply our techniques from dc analysis All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Example 7-4: RL Circuit Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Example 7-4: RL Circuit cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Impedance and Admittance R = resistance = Re(Z) Impedance is voltage/current X = reactance = Im(Z) Resistor Inductor Capacitor G = conductance = Re(Y) Admittance is current/voltage B = susceptance = Im(Y) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Impedance Transformation All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Voltage & Current Division All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Example 7-5: Input Impedance (cont.) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Example 7-8: Thévenin Circuit All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Linear Circuit Properties Thévenin/Norton and Source Transformation Also Valid All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phasor Diagrams All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Phase-Shift Circuits All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Example 7-10: Cascaded Phase Shifter Choose R such that output is ahead of input Solution leads to: All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Node 1Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

(cont.) Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

(cont.) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Example 7-13: Mesh Analysis by Inspection All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Power Supply Circuit All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Ideal Transformer All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Half-Wave Rectifier All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Full-Wave Rectifier Current flow during first half of cycle Current flow during second half of cycle All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Smoothing RC Filter All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Complete Power Supply All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

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Example 7-19: Multisim Measurement of Phase Shift All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

Example 7-19 (cont.) Using Transient Analysis All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

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Summary All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press