chapter 2 passive network

7/30/2019 Chapter 2 Passive Network

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PASSIVE CIRCUITS

PREPARED BY:

HARDIKPRAJAPATI 1


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Series tuned circuit Parallel tuned circuit

Self capacitance of a coil

Skin effect Mutual inductance

High frequency transformer

Tapped inductor

Capacitive tap

Low frequency transformer

Hardik Prajapati Electronics & Communication 2


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A circuit designed by using passivecomponents is called a passive circuit.

Resistor, capacitor and inductor are called

passive elements, because they can notproduce energy.

The elements which generates or

produces electrical energy are calledactive elements, like battery, generator,

transistor, operational amplifier etc.

Hardik PrajapatiElectronics & Communication Dept.3


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Virtually all communications equipment

contains tuned circuits made up ofinductors and capacitors that resonate at

specific frequencies.



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All tuned circuits and many filters are made up of

inductive and capacitive elements.

Opposition to alternating-current flow offered bycoils and capacitors is known as reactance.

Reactance is expressed in ohms ().



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Reactive Components: Capacitors A capacitor used in an ac circuit charges and

discharges.

Capacitors tend to oppose voltage changes

across them. Opposition to alternating current offered by a

capacitor is known as capacitive reactance (Xc).

Capacitive reactance (Xc) is inversely proportionalto the value of capacitance (C) and

operatingfrequency (f).

Xc= 1/2fC



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Reactive Components: Inductors An inductor, also called a coil orchoke, is a

winding of multiple turns of wire. When a current is passed through a coil, a

magnetic field is produced around the coil. If the applied voltage and current are varying, thiscauses a voltage to be self-induced into the coilwinding.

This process has the effect of opposing current

changes in the coil. This effect is known asinductance.



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Opposition to alternating current offered by

inductors is continuous and constant and is known

as inductive reactance (XL).

Inductive reactance (XL) is directly proportional tofrequency and inductance.

XL =2fL



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Ideal Series resonant circuit contains no

resistance. It contains only inductance and

capacitance that are in series with each other

and with the source voltage. At Resonance ( XL = XC ); therefore, XL - XC = 0. The

resultant reactance is equal to 0. Impedance ( Z ) is

minimum.

Since Z is minimum, current is maximum for a givenvoltage. Maximum current flow causes maximum

voltage drops across individual reactances.



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Series tuned circuit, any electrical circuitcontaining both inductive and capacitiveelements. If these elements are connectedin series, the circuit presents low

impedance to ac at the resonant frequencyand high impedance to current of otherfrequencies.

In a Parallel tuned circuit, the impedance

is high at the resonant frequency, low atothers.


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C1

L1

R1

GEN


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Series resonance occurs when the

reactive part of the impedance is zero or

the phase angle is zero.

At resonance XL=Xc, so resonance

frequency ,

f = 1/2 LC

By adjustment of L or C circuit can bebrought into resonance with applied

frequency, which is called tuning.



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The Q-Factor (quality factor) is defined asratio of inductive resonance to resistance intuned circuits.

Qs = soL/r = 1/soCr

Q is a measure of the 'sharpness' of theresponse of the tuned circuit to the resonantfrequency.

Thus, a circuit with a high Q will exhibit a

higher amplitude at the resonant frequency,but will decay more quickly as the frequencymoves away from the resonant frequency.



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The relation between impedance and q

can be expressed as,Zs = r(1+jyQs)

The reactive response is the ratio of

current (V/Zs) at any given frequency to

the current at resonance (V/r).

Ar= r/Zs= 1/1+jyQs

In decibel,ArdB = 20 log 1/ 1+(yQ)

2


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CL

R

V


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At resonance, a parallel tuned circuit appears to

have infinite resistance

draw no current from the source

have infinite impedance act as an open circuit.



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Parallel resonance occurs when reactive

part of the impedance is zero.

The Q-factor can be expressed as,

Q = 0L/r = 1/0Cr

The relative response is given by, V/V0Ar= 1/1+jyQ



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Parallel impedance can be expressed as,

Zp= ZLZc/ZL+ZcBy comparing with series impedance

equations,Zp = L/C = RD

r(1+jQs) (1+jQs)

Where RD is dynamic impedance



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Skin effect isthe tendency of electrons flowingin a conductor to flow near and on the outer

surface.

The self induced emf is greatest at the centre ofthe conductor and becomes less towards outer

surface.

This leads in the current density being least at

the centre and increasing towards outercircumference.



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The self induced emf is greatest at thecentre of the conductor and becomes lesstowards outer surface.

This leads in the current density beingleast at the centre and increasing towardsouter circumference.

Skin effect isthe tendency of electronsflowing in a conductor to flow near and onthe outer surface of the conductor.



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Reaction between physically isolatedinductive circuits can occur as a result ofcommon magnetic flux linkage.

For current I1 in inductance L1,magnetically coupled to inductance L2, theinduced emf in L2 is given by,

E2 = +/- jMI1The sign depends on physical position of

coil.



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If the two coils are connected in series than thetotal series and parallel inductance can be givenas,

Ls

= L1+L

2+/-2M

Lp = L1L2-M2/ L1+L2+2M, respectively.

M should be determined by measurement onlyby,

M =k L1L2where k is coefficient of coupling.



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Mutual inductive coupling forms the basis

of high frequency transformers.


I R0 Cp

Lp LsCs RL

IZ1

rp Lp-

M

Ls-M rs

Z2M

High frequency transformer

Equivalent circuit


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At primary the impedance Z1 is

Z1 = RL/1+j

CSRLAt secondary the impedance Z2 is

Z2 = Ro/1+jCPRoThe transfer impedance ZT is the ratio of

output voltage Vs to input current I.

By analyzing,

IS = I Z1Zm/(Zp+Z1)(Zs+Z2)- Zm2

The secondary voltage is ISZ2 soZT = Z1Z2Zm /(Zp+Z1)(Zs+Z2)- Zm

2


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When the primary and secondary are

tuned separately to the same resonant

frequency transformer is called

Synchronously Tuned Transformer.

Due to mutual coupling of secondary and

primary, each circuit will detune another,

which may result in two peaks in overallfrequency response curve.



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The shape of the

response curvedepends on k QpQs.

For kQ=1, transformer

is said to be critically

coupled, for kQ1 it is called over

coupled.

kQ=0.5

kQ=1

kQ=2

f/fo

I ZT I

dB


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It is the ratio of load voltage Vs (IZT) to

input voltage Vp (IZIN).

VTF = ZT /ZIN

= Z2ZMZp(Zs+Z2)-ZM

2



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In tapped circuit load is connected to a

tapping point on the inductor which results

in mutual inductive coupling between two

sections of a coil.The tapped inductor is used to reduce the

damping effect of a load on the Q factor.


chapter 2 passive network

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