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Lecture 19 High Pass Filters, 2 nd Order Filters, Active Filters, Resonances. Series Resonance. For resonance the reactance of the inductor and the capacitor cancel:. Series Resonance. Quality factor Q S. Series Resonance. Series Resonance. Series Resonant Band-Pass Filter.
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Lecture 19High Pass Filters, 2nd Order Filters, Active Filters, Resonances
Series Resonance For resonance the reactance of the inductor and the capacitor cancel:
Series Resonance Quality factor QS
Series Resonant Band-Pass Filter For QS>>1
Parallel Resonance At resonance ZP is purely resistive:
Parallel Resonance Quality factor QP
Parallel Resonance Vout for constant current, varying the frequency
Second Order High-Pass Filter At low frequency the capacitor is an open circuit At high frequency the capacitor is a short and the inductor is open
Second Order Band-Pass Filter At low frequency the capacitor is an open circuit At high frequency the inductor is an open circuit
Second Order Band-Reject Filter At low frequency the capacitor is an open circuit At high frequency the inductor is an open circuit
Exercise 6.20 Design a filter with QS=1 that passes frequency components lower than 5 kHz and rejects components higher than 5 kHz. Chose L=5 mH
Exercise 6.21 Design a filter that passes frequency components between fL=45 kHz and fH=55 kHz. Chose L=1 mH
Active Filters • Ideally, an active filter circuit should: • Contain few components • 2. Have a transfer function that is insensitive to component tolerances
3. Place modest demands on the op amp’s gain–bandwidth product, output impedance, slew rate, and other specifications 4. Be easily adjusted 5. Require a small spread of component values 6. Allow a wide range of useful transfer functions to be realized
First-Order Low-Pass Filter A low-pass filter with a dc gain of -Rf/Ri
First-Order High-Pass Filter A high-pass filter with a high frequency gain of -Rf/Ri
Butterworth Transfer Function Butterworth filters are characterized by having a particularly flat pass-band.
Sallen–Key Circuits Non-inverting amplifier with a gain of K
K Values for Low-Pass and High-Pass Butterworth Filters of Various Orders
Low-Pass Active Filter Design Design a fourth-order low-pass Butterworth filter having a frequency cut-off of 100 Hz
Low-Pass Active Filter Design From the table a fourth order filter requires K values of 1.152 and 2.235. The DC gain is (1.152)(2.235) = 2.575
Magnetic fields (B flux density, H magnetic field intensity, magnetic permeability ) Right hand rule Forces on charges and current carrying wires moving in a magnetic field Faraday’s Law Lenz’s Law Ampere’s Law Review for Next Lecture!