Resonant CircuitsThe resonance phenomenon and its characterization

Filter NetworksNetworks with frequency selective characteristics:low-pass, high-pass, band-pass

VARIABLE-FREQUENCY NETWORKPERFORMANCE

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

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

EXAMPLE Determine the resonant frequency, the voltage across eachelement at resonance and the value of the quality factor

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10 sec/2000

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Capacitor and inductor exchange storedenergy. When one is at maximum the other is at zero

EXAMPLE The Tacoma Narrows Bridge Opened: July 1, 1940Collapsed: Nov 7, 1940

Likely cause: windvarying at frequencysimilar to bridgenatural frequency

2.020

FILTER NETWORKS

Networks designed to have frequency selective behavior

COMMON FILTERS

Low-pass filterHigh-pass filter

Band-pass filter

Band-reject filter

Simple low-pass filter

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R

CjV

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1

11

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1

0

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1

2

tan)(

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v

v

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GM

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frequencypower half

1

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BW

Simple high-pass filter

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CjR

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V

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1

0

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1

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tan2

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frequencypower half

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LO

Simple band-pass filter

Band-pass

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R

V

VGv

11

0

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LCRC

RCM

11

LCM 0)()0( MM

2

4/)/( 20

2

LRLRLO

LC

10

2

4/)/( 20

2

LRLRHI

L

RBW LOHI

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1)( HILO MM

Simple band-reject filter

011

000

CLj

LC

10 VV circuit open as actscapacitor the 0at

10 VV circuit open as actsinductor the at

filter pass-band

the in as determined are HILO ,

)( jGvfor plot Bode the of sticcharacteri magnitude the Sketch

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0dB/dec of asymptotefrequency low

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)( jGvfor plot Bode the of sticcharacteri magnitude the Sketch

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at 0dB Crosses 20dB/dec.

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0dB/dec of asymptotefrequency low

2rad/s :frequencyer Break/corn