Exp4- Step Response Analysis2.pdf

Exp4- Step Response Analysis2.pdf

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Step Response Analysis Purpose: Examine the behavior of under-damped, critically-damped and over-damped second- order circuits. Equipment Required: 1 - HP 54600B Oscilloscope 1 - HP 33120A Function Generator 1 - Protoboard 1 - Multimeter 1 - RCL meter (can be shared) 1 - 10-k Potentiometer 1 - 0.25-H Inductor 1 - 0.1- µ F capacitor Prelab: Read Sections 8-5 , 8-6 and 8-7 in the text * . 1. The characteristic equation A simplified model for an inductor, shown in Fig. 1, consists of an ideal inductor in series with a parasitic resistance R P . For all prelab calculations, use the inductor model in Fig. 1 and assume R P = 100 . a. For R = 10 k , L = 0.25 H, and C = 0.1 µ F, find the roots of the characteristic equation of the circuit in Fig. 2. b. Find the critical resistance R C that will result in two equal roots. Find an expression for v C (t) if v i (t) = 2u(t) V and R = R C . c. For R = 150 , find the roots of the characteristic equation of the circuit in Fig. 2. 2. CCA The procedure section of this lab exercise examines all three cases for an RLC circuit, overdamped (Case A), critically damped (Case B) and underdamped (Case C). This CCA exercise predicts the circuit response in these three states.
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Enter the circuit of Fig. 3 into a CCA program. In all cases, v i (t) is a square wave source with V pp = 2 V. Use the transient analysis method. The output is the circuit voltage across the capacitor, v C (t). R TH should be set to the output resistance of the function generator used in your laboratory. R P is 100 . Plot and print out the circuit response for two transitions of the source, one positive-going step and one negative-going step, for each “case” listed below. Case A: Set the value of R to 10 k . Case B: Compute the value of R required to critically damp the circuit of Fig. 3, from R C = R + R P + R TH . The resistance R in the circuit of Fig. 2 represents the total circuit resis-tance, including R P and R TH . To achieve the critically damped state for the CCA — and in the
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  • Winter '19
  • jihad daba
  • Derivative, Resistor, Inductor, RC circuit, Exponential decay

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