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Unformatted text preview: Boise State University Department of Electrical and Computer Engineering ECE 212L – Circuit Analysis and Design Lab Experiment #2: Sinusoidal Steady State and Resonant Circuits 1 Objectives The objectives of this laboratory experiment are: • To investigate the sinusoidal steady-state response of a resonant circuit in the phasor domain. • To compare the timebase and the Lissajous methods for measuring the phase shift between two sinusoidal waveforms. 2 Theory Electric circuits containing components like capacitors and inductors can introduce a phase shift between an exciting (input) sine waveform and a measured (output) sine waveform. This phase shift may be an important parameter to be measured in certain applications. This experiment investigates the timebase and Lissajous methods for measuring such a phase shift between two sine waveforms. 2.1 Timebase Method 2 D 1 D v 2 1 v Figure 1: Timebase Method for Measuring the Phase Difference Between Two Sine Waveforms Figure 1 shows two sinusoidal waveforms, v 1 ( t ) = V m 1 cos ωt = √ 2 V 1 cos ωt (1) v 2 ( t ) = V m 2 cos( ωt + ϕ ) = √ 2 V 2 cos( ωt + ϕ ) (2) 1 where v 1 ( t ) is the reference waveform with peak magnitude V m 1 (and rms magnitude V 1 ), and v 2 ( t ) is a secondary waveform with peak magnitude V m 2 (or rms magnitude V 2 ) and shifted by an angle ϕ with respect to the first waveform. The secondary waveform v 2 ( t ) is said to be lagging the reference waveform v 1 ( t ) if it peaks later in time as shown in the above figure. In this case, the angle ϕ in Equation (2) is negative ( − 180 o < ϕ < o ). The waveform v 2 ( t ) is said to be lead- ing the reference waveform v 1 ( t ) if it peaks earlier in time with a positive phase ϕ (0 o < ϕ < 180 o )....
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This document was uploaded on 11/01/2011 for the course ECE 212 at Boise State.
- Fall '08