EE203-SUNYBuffalo-03-Chapter09-01

EE203-SUNYBuffalo-03-Chapter09-01 - SMALL for Big Things...

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Unformatted text preview: SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Sinusoidal voltage source EE 203 Circuit Analysis 2 Lecture 03 Chapter 9.1 The Sinusoidal Source Kwang W. Oh, Ph.D., Assistant Professor SMALL (Nanobio Sensors & MicroActuators Learning Lab) Department of Electrical Engineering University at Buffalo, The State University of New York 215E Bonner Hall, SUNY-Buffalo, Buffalo, NY 14260-1920 Tel: (716) 645-3115 Ext. 1149, Fax: (716) 645-3656 [email protected], http://www.SMALL.Buffalo.edu the frequency = 1/ period the number of cycles per second Hertz (Hz) ω (Omega) = the angular frequency of the sinusoidal function 2π rad = 360 º ±1 bounds the cosine function the phase angle EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 1/11 Sinusoidal Voltage = Alternative Voltage (AC) EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 2/11 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Sinusoidal voltage source Vm cos(ωt + φ ) Vm cos ωt = Vm cos (0) rms value rms (root-mean-square) value of a periodic function = square root of the mean value of the squared function =0 = Vm ∴t = −φ ω = 2 Vm 2 cos(0 º) = cos(0/2 π rad)= 1 cos(90 º) = cos(1/2 π rad)= 0 cos(180 º) = cos(2/2 π rad)= -1 cos(270 º) = cos(3/2 π rad)= 0 cos(360 º) = cos(4/2 π rad)= 1 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 3/11 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 4/11 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.1 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Example 9.2 Lecture 03 | Chapter 09 | 1/7 | 5/11 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 6/11 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.3 Example 9.4 Trigonometric identity EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 7/11 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 8/11 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Sinusoidal Response: RL EE 203 Circuit Analysis 2 Lecture 03 Chapter 9.2 The Sinusoidal Response Consider Consider the sinusoidal voltage source Kwang W. Oh, Ph.D., Assistant Professor SMALL (Nanobio Sensors & MicroActuators Learning Lab) Department of Electrical Engineering University at Buffalo, The State University of New York 215E Bonner Hall, SUNY-Buffalo, Buffalo, NY 14260-1920 Tel: (716) 645-3115 Ext. 1149, Fax: (716) 645-3656 [email protected], http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 9/11 SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Sinusoidal Response: RL Transient component Transient dies out in a finite amount of time time Steady-state component The steady-state response is a sinusoid sinusoid We will study a technique for calculating the stead-state response directly, thus avoiding the problem of solving the differential equation 9.3 The Phasor The frequency of the response signal is the same as the source signal In general, the maximum amplitude of the response is different than the source The maximum amplitude of the response The maximum amplitude of the source The phase angle differs from the source by some constant amount For this circuit the voltage phase is φ and the current is (φ − θ ) EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] = arctan( ) Lecture 03 | Chapter 09 | 1/7 | 11/11 Vm : the amplitude of the sinusoid ω : the angular frequency in radians per second φ : the phase angle Assume the initial current i = 0 for t < 0 KVL KVL Find the mathematical expression for the current i(t) for t > 0 Solving this differential equation yields EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 03 | Chapter 09 | 1/7 | 10/11 ...
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