Resonant Ckts

8/8/2019 Resonant Ckts

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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

Resonant Ckts

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