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Unformatted text preview: e often used since the
exponential function e is used extensively for circuit analysis and circuit problem
solution EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 04  Chapter 09  2/7  13/17 EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 04  Chapter 09  2/7  14/17 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 The Phasor and Its Transforms Frequency Domain and Time Domain The phasor and its transforms find such use in circuit analysis.
Reduces the tasks, time, and effort to find maximum amplitudes and phase angles
for steadystate sinusoidal responses. Since the transient solutions dies out, the steadystate must also
satisfy the differential equation that defines the circuits behavior.
In linear circuits, having a sinusoidal source, the steadystate
response has the same frequency.
The form of the steadystate response has the form of
where A is the maximum amplitude of the response signal and β is
the
the phase angle.
The solution to the circuit analysis in this form is in the domain of
complex
complex numbers (the frequency domain).
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 04  Chapter 09  2/7  15/17 Representation
Representation of
as a phasor rotating counterclockwise
and its projection on the real axis as a function of time
Frequency (or ComplexNumber) Domain Time Domain Im t = t
1
t = t0 =0 t = t2
φ 0 t1 t2 t3 Re
t = t3 Rotation at ω
radians per sec
EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 04  Chapter 09  2/7  16/17 SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.5 •20 cos(300) •20 sin(300) •40 cos(600) •40 sin(600) •Sqrt (37.322+24.642) •arctan (24.64/37.32) EE 203 Circuit Analysis 2  Spring 2008  Prof. Kwang W. Oh  EE@SUNYBuffalo Lecture 04  Chapter 09  2/7  17/17...
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