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Unformatted text preview: Sources of Phase Shift * Lab 3: Operational Amplifiers and FirstOrder Circuits ECE 209: Circuits and Electronics Laboratory Understanding why phase shift occurs is one of the most difficult aspects of learning to analyze circuits. In this document, the sources of phase shift for two simple firstorder filters are discussed. In both cases, the ultimate source is the lag between pressure and flow across the storage elements in the circuit. For example, when sinusoidal capacitor voltage is near zero, the rate of voltage change is very high, and so the current into the capacitor is at its peak (e.g., it is easiest to move a spring if it is relaxed). Resistive sources in the circuit turn that current into voltage, which results in two voltages in the same circuit with equal frequency and different phase. The tension between these two sources sets up different phase shifts at different frequencies. FirstOrder RC LowPass Filter The voltage divider shown below is a simple lowpass filter. R C v in v out 0 V i C ( t ) = C d v C ( t ) d t Z C ( s ) = 1 sC H ( s ) defines V out ( s ) V in ( s ) = 1 sC R + 1 sC = 1 sRC + 1  H ( jω )  = 1 radicalbig ( ωRC ) 2 + 1 ∠ H ( jω ) = arctan( ωRC ) 0 dB Magnitude ◦ − 45 ◦ − 90 ◦ Phase The magnitude response of the filter can be explained by likening the capacitor to an open circuit at low frequencies (i.e., impedance magnitude  1 / ( jωC )  is near infinity for ω ≈ 0) and a short circuit at high frequencies (  1 / ( jωC )  ≈ 0 when ω ≈ ∞ ). That is, • When the input is constant or has very slow changes, the capacitor acts like an open circuit. That is, it draws very little current. These slow frequencies are copied nearly perfectly onto the output....
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 Spring '08
 HALVERSON
 Phase Shift, Wave mechanics, Lowpass filter, Electrical impedance, Voltage drop

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