resonant circuits the resonance phenomenon and its characterization filter networks networks with...
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Resonant CircuitsThe resonance phenomenon and its characterization
Filter NetworksNetworks with frequency selective characteristics:low-pass, high-pass, band-pass
VARIABLE-FREQUENCY NETWORKPERFORMANCE
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RESONANT CIRCUITS
These are circuits with very special frequency characteristics…And resonance is a very important physical phenomenon
LCCL
110
when zero iscircuit each of reactance The
The frequency at which the circuit becomes purely resistive is calledthe resonance frequency
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circuit RLC Series
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circuit RLC Parallel
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Properties of resonant circuits
At resonance the impedance/admittance is minimal
Current through the serial circuit/voltage across the parallel circuit canbecome very large (if resistance is small)
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Given the similarities between series and parallel resonant circuits, we will focus on serial circuits
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EXAMPLE Determine the resonant frequency, the voltage across eachelement at resonance and the value of the quality factor
LC
10 sec/2000
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Resonance for the series circuit
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The Q factorCRR
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M
BW SmallQ High
dissipates
Stores as Efield
Stores as M field
Capacitor and inductor exchange storedenergy. When one is at maximum the other is at zero
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EXAMPLE The Tacoma Narrows Bridge Opened: July 1, 1940Collapsed: Nov 7, 1940
Likely cause: windvarying at frequencysimilar to bridgenatural frequency
2.020
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FILTER NETWORKS
Networks designed to have frequency selective behavior
COMMON FILTERS
Low-pass filterHigh-pass filter
Band-pass filter
Band-reject filter
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Simple low-pass filter
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Simple high-pass filter
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Simple band-pass filter
Band-pass
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Simple band-reject filter
011
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10 VV circuit open as actsinductor the at
filter pass-band
the in as determined are HILO ,
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)( jGvfor plot Bode the of sticcharacteri magnitude the Sketch
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sradFRC /2.0)1020)(1010( 63 20dB/dec- of asymptotefrequency High
0dB/dec of asymptotefrequency low
5rad/s :frequencyer Break/corn
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)( jGvfor plot Bode the of sticcharacteri magnitude the Sketch
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sradFRC /5.0)1020)(1025( 63
srad /21
at 0dB Crosses 20dB/dec.
20dB/dec- of asymptotefrequency High
0dB/dec of asymptotefrequency low
2rad/s :frequencyer Break/corn