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Unformatted text preview: tory response with a frequency called natural frequency n 0 2 . 76 EE1002 Introduction to Circuits and Systems Steady‐state sinusoidal analysis Time‐dependent signal sources Ideal voltage and current sources can also be time‐varying. v (t ) i(t ) One of the most important classes of time‐dependent signals is that of periodic signals, which satisfies the equation: x(t ) x(t nT ),
n 1,2,3,... where T is the time period of x(t ). A
T 2T 3T 4T A
T 2T 3T 4T A
T 2T T 2T 3T 4T 3T 4T A A 77 EE1002 Introduction to Circuits and Systems Sinusoidal Currents and Voltages A general sinusoidal voltage is given by v(t ) Vm cos(t ) , where Vm is the peak value of the voltage, and is the phase angle. sin(t )
cos(t ) T T
2 T t
t The frequency of the periodic signal is the number of cycles completed in one second. f 1 T The units of frequency are hertz (Hz). Angular frequency (radians per second) 2 2 f , as one period in time corresponds to T 2 radian. Sinusoidal functions can be represented by both the cosine and the sine forms, which are inter changeable as sin( z ) cos( z 900 ) and cos( z ) sin( z 900 ) . Hence, even though a bunch of sinusoidal...
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This document was uploaded on 01/20/2014.
- Winter '14