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

All rights reserved. Do not copy or distribute 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

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

Phasor Domain 1. The phasor-analysis technique transforms equations 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.

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

All rights reserved. Do not copy or distribute 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 w.

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

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

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

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

ac Phasor Analysis General Procedure 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

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.

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

Impedance and Admittance Impedance is voltage/current Admittance is current/voltage R = resistance = Re(Z) G = conductance = Re(Y) X = reactance = Im(Z) B = susceptance = Im(Y) Resistor Inductor Capacitor 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 Impedance Transformation

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 Cont.

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 Example 7-8: Thévenin Circuit

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

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

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

All rights reserved. Do not copy or distribute 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 1200 ahead of input Solution leads to:

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

Cont. (cont.) 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

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

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

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

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

Complete Power Supply 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

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