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Chapter 4 Resonant circuits
4.1 Series resonant circuits
steady state response, Q factor, half power frequencies, input
impedance,4.2 Parallel resonant circuits
steady state response, input impedance, loaded Q, external Q
4.3 Transformer-coupled circuits
equivalent resonator circuit
4.4 Transmission line resonant circuits
short-circuited /2 and /4 lines, open-circuited /2 and /4 lines
4.5 Microwave resonators
rectangular cavity, circular cylindrical cavity, dielectric resonator
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Discussion
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3. Ex.4.1 A series LS circuit passes signals from 9MHz to 11MHz, and is connected to acommunication system with Zin=50, find L and C
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4.2 Parallel resonant circuits
Basics1. Duality with series resonator: VI, RG, LC, CL.
2. Steady state response
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3. Input impedance near resonance
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3. Resonator relations
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4. Ex. 4.2 A parallel resonator with R=10k, L=10uH, C=10pF and its load RL=100, find w0,
Qu, QL.
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4.3 Transformer-coupled circuitsBasics
1. Equivalent circuit
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Discussion
1. Ex. 4.3 A tightly coupled transformer circuit, find equivalent resonator circuit, w0, Q
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2. Ex. 4.4 A double-tuned transformer-coupled circuit, find equivalent circuit, (a) w0 and Zin as
R1, C1 removed, (b) I0/Is with R1,C1
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2./2 short-circuited line series resonator
3./4 short-circuited line parallel resonator
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4. Open-circuited line
5./2 open-circuited line parallel resonator
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6./4 open -circuited line series resonator
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Discussion1. Ex. 4.5 A coaxial /2 short-circuited line has inner conductor radius a=0.455mm, outer
conductor radius b=1.499mm, find its Q at 5GHz for air dielectric and Teflon dielectric
(r=2.08, tan=0.0004).
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2. Ex. 4.6 A 50 microstrip/2 short-circuited line has Teflon substrate (r=2.08, tan
=0.0004) with thickness h=0.159cm, t=0.159m, find its Q and length at 2GHz
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4.5 Microwave resonatorsBasics
1. Rectangular cavities dimension a, b, c
2. Circular cylindrical cavities
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3. Dielectric resonator (DR): high , low tan, low temperature coefficient,
TE01 mode
Discussion
1. Ex. 4.7 A rectangular cavity made of WR-90 resonates at 9.379GHz in TE101 mode, find itslength and Q
2. Ex. 4.8 A rectangular cavity with a=1.6cm, b=0.71cm, c=1.56cm is filled with Teflon, find
TE101 mode frequency and Q
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3. Ex 4.9 A cylindrical cavity is operated at 5GHz in TE011 mode, find its Q and height.
4. DR selection in the operation with microstrip line
5. Ex. 5.10 DRr=36, substrate r=9.9, t=0.25mm, find the
dimension of DR at 35GHz
Homework #3 (due 2 weeks): 5,7,12,15,18