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EE40 Lecture 12 - Second Order Circuits

EE40 Lecture 12 - Second Order Circuits - EE40 Lecture 12...

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EE40 Lecture 12 Second Order Circuits Neel Shah 7/20/11
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Class Homework 4 is up, due 7/26 Midterm 2 is 7/27 2 cheat sheets, same rules as before We’ll start a little earlier, say 12.05 pm Final Projects Parts list due Friday Any rejections: come see me Syllabus updated Friday is active filtering, Monday is transformers and complex power handling
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A Note on Shortcuts Last day I presented an alternative method to finding the magnitude of a complex fraction This only works if the numerator is Purely real Purely imaginary
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First Order Circuit Summary Low Pass Filter Canonical form DC magnitude response Short inductors, open capacitors, solve for V SS HF magnitude rolloff -20 dB/decade DC phase = 0° HF phase = -90° Corner frequency ω c = 1/τ Magnitude plot: -3 dB pt Phase plot: -45° pt High Pass Filter Canonical form DC magnitude rolloff +20 dB/decade HF magnitude response Open inductors, short capacitors, solve for V SS DC phase = 90° HF phase = 0° Corner frequency ω c = 1/τ Magnitude plot: -3 dB pt Phase plot: 45° pt
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A Two-Stage RC Filter Ladder + - R 1 R 2 1/jωC 1 V in V out = ?? 1/jωC 2 Brute force impedance analysis
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A Two-Stage RC Filter Ladder + - R 1 R 2 1/jωC 1 V in V out = ?? 1/jωC 2 It would be nice if we could just say… …but we can’t. Why?
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Second Order Filtering If we had a system like… Then we could get a second order filter… 1/(1+jωτ 1 ) x(t) X(s) y(t) Y(s) 1/(1+jωτ 2 )
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Second Order Filtering We can’t achieve this with RC because of input
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