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FOWLER CHAPTER 13LECTURE 13 RCL CIRCUITS
IMPEDANCE (Z): COMBINED OPPOSITION TO RESISTANCE AND REACTANCE. MEASURED IN OHMS.
CHAPTER 13 COMBINED RESISTANCE, INDUCTANCE AND CAPACITANCE(RCL) CIRCUITS
ALL 3 RCL COMPOENTS ARE IN SERIES
ELI THE ICEMAN
FOR INDUCTORS: VOLTAGE LEADS CURRENT
FOR CAPACITORS: CURRENT LEADS VOLTAGE
FOR SERIES RCL CIRCUIT CURRENT IS THE SAME IN EACH COMPOENTVOLTAGE IS ALWAYS OUT OF PHASE IN EACH COMPOENT.
ANOTHER WAY TO REPRESENT COMPLEX WAVEFORMS IS BY THE USE OF VECTORS
SERIES RCL CIRCUITS1. CURRENT IN RCL CIRCUITS. CURRENT FLOW IN ALL PARTS OF THIS CIRCUIT ARE THE SAME AND IN PHASE.
CLRT IIII
RIVR
LL XIV
CC XIV
RV
I0
0
0
I
I
90LV
90CV
2. VOLTAGE IN RCL CIRCUITS
R
C
LSV
fCXC 28.6
1
fLX L 28.6
FOR INDUCTORS: VOLTAGE LEADS CURRENT
FOR CAPACITORS: CURRENT LEADS VOLTAGE
THESE V/I PHASE DIAGRAMS ARE DIFFICULT TO FOLLOW, LETS LOOK AT THIS IN ANOTHER LIGHT.
3.265106028.6
1
28.6
1
5.7206028.628.6
FHzfCX
mHHzfLX
XANDXFINDFIRST
ZTOTALFIND
C
L
CL
THINK IN TERMS OF VECTORS OR PHASORS.
8.257
3.2655.7
X
X
XXX CL
8.257
R
L
C
33
mH20
F10
3.265
33
5.7
XZ
RLX
CX
33 R
Z
X
R33
Hz
V
VS
60
115
8.257
mAAV
Z
VILAWSOHMUSING
IIIISINCE
Z
Z
EXAMPLEOURFOR
XXRXRZ
ORXRZ
ST
LCRT
CL
44044.0260
115'
260
8.25733 22
2222
222
VARIV TR 52.143344.0
VAXIV LTL 3.35.744.
VAXIV CTC 73.1163.26544.
RIV TR LTL XIV CTC XIV
CLRT VVVV FIND VT, SINCE
NONE OF THE VOLTAGES ARE IN PHASE. MUST BE ADDED AS VECTORS.
R
L
C
33
mH20
F10
Hz
V
VS
60
115
Z
X
R 33
8.257
USE PYTHAGOREAN THEOREM TO FIND THE INPEDANCE Z OF THIS CIRCUIT
8.257
3.2655.7
X
X
XXX CL
VVL 3.3 52.14RV
73.116CV
VV
VVV
VVV CL
43.113
73.1163.3
TV
52.14RV 52.14RV
TVV
43.113SV
VV
V
V
VVVV
VVV
T
T
T
CLRT
TRT
115
996,12225
43.11352.14 22
22
22
MUST USE PHASORS TO FINE VT FOR THIS SERIES CIRCUIT
PARALLEL RCL CIRCUITS
VOLTAGE ACROSS ANY PARALLEL CIRCUIT ELEMENT WILL BE THE SAME AND IN PHASE. SO;
CLRS VVVV
Hz
V
VS
60
115
R L C33 mH20 F10
90BYVLAGSI LL90BYVLEADSI CC
CLRT IIIFORSOLVEIFINDTO ,,,
FIRSTXANDXFIND CL
3.265106028.6
1
28.6
1
5.7206028.628.6
FHzfCX
mHHzfLX
C
L
AV
R
VIR 5.3
33
115
AV
X
VI
LL 3.15
5.7
115
AV
X
VI
CC 43.0
3.265
115
LAWSOHMUSINGIIIFIND CLR ',,
AIC 43.0AIR 5.3
AIL 3.15
TI
AI
AAI
IIII
III
T
T
LCRT
LC
3.15
9.145.3 22
22
5.73.15
115
A
V
I
VZ
T
S
AI 9.14TI
AI 9.14
TO FIND THE TOTAL IMPEDANCE FOR THIS CIRCUIT USING OHM’S LAW
FIND IT, AGAIN SINCE IR,IL, IC ARE ALL OUT OF PHASEMUST USE VECTORS TO FIND A SOLUTION.
AIR 5.3 AIR 5.3
CAPACITIVE CURRENT
RESISTIVE CURRENT
INDUCTIVE CURRENT
COMBINED INDUCTIVEAND CAPACITIVE CURRENT
FOR A CIRCUIT WITH CAPACITANCE
FOR A CIRCUIT WITH INDUCTANCE
RESONANCE P.347
RESONANT OCCURS WHEN CL XX
CAN OCCUR IN SERIES OR PARALLEL CIRCUITS WITH RCL OR LC COMPOENTS.FOR ANY VALVE OF L AND C THERE IS ONLY ONE FREQUENCY WHERE,
CL XX THIS IS CALLED THE RESONANT FREQUENCY:
LCfR
28.6
1
DO EX. 13-11 p.348
Rf
PARALLEL RESONANT CIRCUITS P.348
SERIES RESONANT CIRCUITS F.13-26AT RESONANT
CLCL VVALSOXX
CLCL IIALSOXX
For resonance to occur in any circuit it must have at least one inductor and one capacitor.
Resonance is the result of oscillations in a circuit as stored energy is passed from the inductor to the capacitor.
Resonance occurs when XL = XC
At resonance the impedance of the circuit is equal to the resistance value as Z = R.
At low frequencies the circuit is capacitive as XC > XL.
At low frequencies the circuit is inductive as XL > XC.
The high value of current at resonance produces very high values of voltage across the inductor and capacitor.
Series resonance circuits are useful for constructing highly frequency selective filters. However, its high current and very high component voltage values can cause damage to the circuit.
Resonant Circuits
Resonance occurs when XL equals XC.
There is only one resonant frequency for each LC combination.
However, an infinite number of LC combinations have the same fr .
Rea
ctan
ce
frFrequency
XL2
XL1
XC3
XC1XC2
XL3
PARALLEL RESONANT TANK CIRCUIT
THIS CIRCUIT WOULD PRODUCE A SINE WAVE FOREVER IF L AND CWERE IDEAL COMPOENTS.
WITH REAL WORLD L AND C THE WAVEFORM WILL DAMP OUT WITH TIME. YOU MUST FEED ENERGYINTO THE TANK CIRCUIT TO KEEP THE SINE WAVEPROPOGATING.
Bandwidth, (BW) is the range of frequencies over which at least half of the maximum power and current is provided
BANDWIDTH : RANGE OF f OF A CIRCUIT WHICH PROVIDES 70.7% OR MORE OF THE MAX. RESPONSE.
RESPONSE CURVE FOR LC CIRCUITARE PLOTS OF EITHER VOLTAGE, CURRENT OR INPEDANCE vs. FREQUENCY ABOVE AND BELOW RESONANCE
SERIES LC CIRCUIT
The selectivity of a circuit is dependent upon the amount of resistance in the circuit. The variations on a series resonant circuit are drawn below. The smaller the resistance, the higher the "Q" for given values of L and C. The parallel resonant circuit is more commonly used in electronics, but the algebra necessary to characterize the resonance is much more involved.
Series ResonanceThe resonance of a series RLC circuit occurs when the inductive and capacitive reactance are equal in magnitude but cancel each other because they are 180 degrees apart in phase. The sharp minimum in impedance which occurs is useful in tuning applications. The sharpness of the minimum depends on the value of R and is characterized by the "Q" of the circuit.
LX
CX
0 CL XX
An example of the application of resonant circuits is the selection of AM radio stations by the radio receiver. The selectivity of the tuning must be high enough to discriminate strongly against stations above and below in carrier frequency.
FILTERS: USE RC, RL, LC, AND RCL CIRCUITS TO FILTER ONE GROUP OF FREQUENCIESFROM ANOTHER GROUP OF FREQUENCIES.4 CLASSES OF FILTERS 1.LOW PASS 2.HIGH PASS 3.BAND PASS 4.BAND-REJECT 0R BAND STOP,
YOU TUBE: Passive RC low pass filters
YOU TUBE: Passive RC high pass filters
http://www.youtube.com/watch?v=OBM5T5_kgdI
http://www.youtube.com/watch?v=4CcIFycCnxU
LOW PASS FILTER
THE HIGH PASS FILTER
BAND PASS FILTER