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