dr. gyurcsek istván - főmenü - vilivili.pmmf.hu/~gyurcsek/pub1ea/5.40l-res.pdf · dr. gyurcsek...
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1 [email protected] 2018.03.23.
DR. GYURCSEK ISTVN
Resonance Circuits
Sources and additional materials (recommended)
Dr. Gyurcsek Dr. Elmer: Theories in Electric Circuits, GlobeEdit, 2016, ISBN:978-3-330-71341-3
Ch. Alexander, M. Sadiku: Fundamentals of Electric Circuits, 6th Ed., McGraw Hill NY 2016, ISBN: 978-0078028229
Simonyi K.: Villamossgtan. AK Budapest 1983, ISBN:9630534134
Dr. Selmeczi K. Schnller A.: Villamossgtan 1. MK Budapest 2002, TK szm: 49203/I
Dr. Selmeczi K. Schnller A.: Villamossgtan 2. TK Budapest 2002, ISBN:9631026043
Zombory L.: Elektromgneses terek. MK Budapest 2006, (www.electro.uni-miskolc.hu)
http://www.electronics-tutorials.ws/accircuits
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.html
https://en.wikipedia.org/wiki/RLC_circuit#Damping
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Progress in Content
Series Resonance Circuits
Parallel Resonance Circuits
Free Resonance
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Series Resonance Circuit
= =1
=1
=
1
2
William Thomson
(Lord Kelvin - 1824-1907)
= 0 = + 1
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Series RLC Circuit at Resonance 1
= + = + = 2 +
1
2
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Series RLC Circuit at Resonance 2
=
=
+
=
2 + 1
2
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Phase Angle of a Series Resonance Circuit
= 1
( 0 !)
= +
= 2 + 1
2
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Q-factor and Wave Impedance of a Series Resonance Circuit
2
= 2
1 2 2
1 2 2
=
=
=1
=
=
=
1
=
1
=
1
=
1
=0
0 =
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Bandwidth of a Series Resonance Circuit
=1
= ; = =
2
2 = 2
= 2 + 2 = 2
=
=
=
2+
2
2
+1
= +
2+
2
2
+1
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BW and Q-factor of Series Resonance Circuit
=
2+
2
2
+1
= +
2+
2
2
+1
=
=
BW = =1
2
=
+ = 2 2
=1
=
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Voltage Resonance
= = =
= = =
=
1
=
= =
Series resonance voltage resonance
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Progress in Content
Series Resonance Circuits
Parallel Resonance Circuits
Free Resonance
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Parallel Resonance Circuit
Lord William Thomson Kelvin(1824-1907)
= =1
=1
=
1
2
, =1
= 2 + 2
, =1
, =1
2
, = 2
=1
+
1
+
= +
= 0
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Impedance in Parallel Resonance Circuit
Inductive Capacitive
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Susceptance in Parallel Resonance Circuit
= + = + = 2 +
1
2
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Current in a Parallel Resonance Circuit
=
=
=
=
2
=
= 2
= + +
= 2 +
2
= 2 + 0 2 =
V/R
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Bandwidth & Selectivity (Q-factor) of a Parallel Resonance Circuit
2.
=2 2
=
=
1
=1
=0
=
=
BW = =1
2
=
=
=
2+
2
2
+1
= +
2+
2
2
+1
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Current Resonance
=
=
=
= =
=
= =
= =
Parallel resonance current resonance
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Progress in Content
Series Resonance Circuits
Parallel Resonance Circuits
Free Resonance
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Free resonance (LC, RLC)
undamped (free oscillation)
underdamped (slowly dampening osc.)
critical damping (no oscillation)
overdamped (no oscillation)
= 0 sin (: )
=1
2 2, =
1
2 2
1
2 2 =
1
2 2
=
= 0
= 02 2, 0 =
1
, =
2
= 0
< 0 = 0 > 0
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Resonance Frequency using Impure Components
IN PRACTICE coil and capacitor contains some resistance.
Series RLC pure / impure components no affect the resonance frequency
Parallel RLC with impure components affect the resonance frequency
=1
2
2
= 02 2, 0
2 =1
, =
2
= 0
=
0 +
2
0
= 0 2
20 +
2
2= 0
2 02
42= 0 1
1
42 1
0, 0 0
+
2
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Application Tesla Coil
Air-core resonant transformer (N. Tesla 1891) high-voltage, high frequency
Transmission of electrical energy without wires
Spark gap radio transmitters for wireless telegraphy until the 1920s (Titanic 1912)
Today: transistor / thyristor instead of spark gap
Primer and seconder circuits tuned for same resonance freq
0 = 0 =
1
2
2 =1
2
2 =
=
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Questions