3/16/2015 Hafiz Zaheer Hussain

3/16/2015 Hafiz Zaheer Hussain Circuit Analysis-II Spring-2015 EE -1112 Instructor: Hafiz Zaheer Hussain Email: zaheer.hussain@ee.uol.edu.pk www.hafizzaheer.pbworks.com Department of Electrical Engineering The University of Lahore Week 3 3/16/2015 Hafiz Zaheer Hussain

Fundamentals of Electric Circuits by Alexander-Sadiku Chapter 9 Sinusoidal Steady-State Analysis 3/16/2015 Hafiz Zaheer Hussain

Content 9.1 Introduction 9.2 Sinusoids’ features 9.3 Phasors 9.4 Phasor relationships for circuit elements 9.5 Impedance and admittance 9.6 Kirchhoff’s laws in the frequency domain 9.7 Impedance combinations 3/16/2015 Hafiz Zaheer Hussain

9.5 Impedance and Admittance (1) The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I, measured in ohms Ω. V = I Z , Positive X is for L and negative X is for C. The admittance Y is the reciprocal of impedance, measured in siemens (S). 3/16/2015 Hafiz Zaheer Hussain

9.5 Impedance and Admittance (2) 4/19/2019 3/16/2015 Hafiz Zaheer Hussain 6 6

9.5 Impedance and Admittance (3) 4/19/2019 3/16/2015 Hafiz Zaheer Hussain 7 7

Impedances and admittances of passive elements 9.5 Impedance and Admittance (4) Impedances and admittances of passive elements Element Impedance Admittance R L C 3/16/2015 Hafiz Zaheer Hussain

9.5 Impedance and Admittance (5) 3/16/2015 Hafiz Zaheer Hussain

Is impedance a phasor ??? 9.5 Impedance and Admittance (6) No, it is not a phasor, because it does not represent a sinusoidal quantity. 3/16/2015 Hafiz Zaheer Hussain

9.5 Impedance and Admittance (7) After we know how to convert RLC components from time to phasor domain, we can transform a time domain circuit into a phasor/frequency domain circuit. Hence, we can apply the KCL laws and other theorems to directly set up phasor equations involving our target variable(s) for solving. 3/16/2015 Hafiz Zaheer Hussain

9.5 Impedance and Admittance (8)Example 9.9 3/16/2015 Hafiz Zaheer Hussain

9.5 Impedance and Admittance (9) Example 9.9 3/16/2015 Hafiz Zaheer Hussain

9.5 Impedance and Admittance (10) PP (9.9) Refer to Figure below, determine v(t) and i(t). Answers: i(t) = 1.118cos(10t – 26.56o) A; v(t) = 2.236cos(10t + 63.43o) V 3/16/2015 Hafiz Zaheer Hussain

Content 9.1 Introduction 9.2 Sinusoids’ features 9.3 Phasors 9.4 Phasor relationships for circuit elements 9.5 Impedance and admittance 9.6 Kirchhoff’s laws in the frequency domain 9.7 Impedance combinations 3/16/2015 Hafiz Zaheer Hussain

9.6 Kirchhoff’s laws in the frequency domain Both KVL and KCL are hold in the phasor domain or more commonly called frequency domain. Moreover, the variables to be handled are phasors, which are complex numbers. All the mathematical operations involved are now in complex domain. 3/16/2015 Hafiz Zaheer Hussain

Content 9.1 Introduction 9.2 Sinusoids’ features 9.3 Phasors 9.4 Phasor relationships for circuit elements 9.5 Impedance and admittance 9.6 Kirchhoff’s laws in the frequency domain 9.7 Impedance combinations 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (1) The following principles used for DC circuit analysis all apply to AC circuit. For example: voltage division current division circuit reduction impedance equivalence Y-Δ transformation 3/16/2015 Hafiz Zaheer Hussain

(N impedances in series) 9.7 Impedance combinations (2) (N impedances in series) 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 2 impedances in series 3/16/2015 Hafiz Zaheer Hussain

N Impedances in Parallel 9.7 Impedance combinations (2) N Impedances in Parallel 3/16/2015 Hafiz Zaheer Hussain

2 Impedances in parallel 9.7 Impedance combinations (2) 2 Impedances in parallel 3/16/2015 Hafiz Zaheer Hussain

Example 9.10 9.7 Impedance combinations (2) Find the input impedance of the circuit in Fig. 9.23. Assume that the circuit operations at  = 50 red/s. 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) Solution 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 3/16/2015 Hafiz Zaheer Hussain

Example 9.11 9.7 Impedance combinations (2) Determine v0(t) in the circuit 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) Solution 9.11 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) Let Z1 = Impedance of the 60-Ω resistor Z2 = Impedance of the parallel combination of the 10-mF capacitor and the 5-H inductor Then Z1 = 60 Ω and 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 3/16/2015 Hafiz Zaheer Hussain

Delta-Wye Wye-Delta Transformation 9.7 Impedance combinations (2) Delta-Wye Wye-Delta Transformation 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) The delta-wye and wye-delta transformation, that was applied to resistive circuits, are also valid for impedances. 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) Wye(Y)-Delta(Δ) a b c Za Zc Zb Z1 Z2 Z3 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) Summary 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) Example-9.12 Find current I in the circuit. 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) Solution 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 3/16/2015 Hafiz Zaheer Hussain

9.7 Impedance combinations (2) 3/16/2015 Hafiz Zaheer Hussain

CHAPTER 10 Chapter 10 will show that other circuit techniques—such as superposition, nodal analysis, mesh analysis, source transformation, the Thevenin theorem, and the Norton theorem are all applied to ac circuits in a manner similar to their application in dc circuits. 3/16/2015 Hafiz Zaheer Hussain

Summary 1. A sinusoid is a signal in the form of the sine or cosine function. It has the general form 3/16/2015 Hafiz Zaheer Hussain

Summary 3/16/2015 Hafiz Zaheer Hussain

3/16/2015 Hafiz Zaheer Hussain