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ECE CHAPTER5

# ECE CHAPTER5 - The response of a network has two parts the...

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- The response of a network has two parts: the forced response and the natural response. - In most circuits, the natural response decays rapidly to zero. - The forced response for sinusoidal sources persists indefinitely and, therefore, is called the steady-state response Sinusoidal Currents and Voltages - Given by: v(t) = V m cos( ϖ t + θ ) - V m : the peak value of the voltage - ϖ : the angular frequency (radians per second) - θ : phase angle - ϖ T = 2 π - T : period (time it takes for one cycle to be completed) - Frequency (number of cycles completed in one second): f = 1/T -Units: hertz (Hz) or inverse seconds (s -1 ) - sin(z) = cos(z - 90 ° ) - Root-mean-square (rms) value of the periodic voltage v(t) is defined by: - V rms = sqrt(1/T (intr 0 => T) v 2 (t)dt) - P avg = V 2 rms /R - The rms value is also called the effective value - I rms = sqrt(1/T (intr 0 => T) i 2 (t)dt) - P avg = I 2 rms R - V rms = V m / sqrt(2) Phasors - Phasors: vectors that represent currents and voltages in the complex-number plane - For a sinusoidal voltage of the form: v 1 (t) = V 1 cos( ϖ t + θ 1 ) - we define the phasor as

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ECE CHAPTER5 - The response of a network has two parts the...

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