of 28
7/30/2019 Chapter 2 Passive Network
1/28
PASSIVE CIRCUITS
PREPARED BY:
HARDIKPRAJAPATI 1
7/30/2019 Chapter 2 Passive Network
2/28
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
7/30/2019 Chapter 2 Passive Network
3/28
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
7/30/2019 Chapter 2 Passive Network
4/28
Virtually all communications equipment
contains tuned circuits made up ofinductors and capacitors that resonate at
specific frequencies.
Hardik PrajapatiElectronics & Communication Dept.4
7/30/2019 Chapter 2 Passive Network
5/28
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 ().
Hardik PrajapatiElectronics & Communication Dept.5
7/30/2019 Chapter 2 Passive Network
6/28
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
Hardik PrajapatiElectronics & Communication Dept.6
7/30/2019 Chapter 2 Passive Network
7/28
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.
Hardik PrajapatiElectronics & Communication Dept.7
7/30/2019 Chapter 2 Passive Network
8/28
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
Hardik PrajapatiElectronics & Communication Dept.8
7/30/2019 Chapter 2 Passive Network
9/28
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.
Hardik PrajapatiElectronics & Communication Dept.9
7/30/2019 Chapter 2 Passive Network
10/28
Hardik PrajapatiElectronics & Communication Dept.10
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.
7/30/2019 Chapter 2 Passive Network
11/28
Hardik PrajapatiElectronics & Communication Dept.11
C1
L1
R1
GEN
7/30/2019 Chapter 2 Passive Network
12/28
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.
Hardik PrajapatiElectronics & Communication Dept.12
7/30/2019 Chapter 2 Passive Network
13/28
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.
Hardik PrajapatiElectronics & Communication Dept.13
7/30/2019 Chapter 2 Passive Network
14/28
Hardik PrajapatiElectronics & Communication Dept.14
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
7/30/2019 Chapter 2 Passive Network
15/28
Hardik PrajapatiElectronics & Communication Dept.15
CL
R
V
7/30/2019 Chapter 2 Passive Network
16/28
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.
Hardik PrajapatiElectronics & Communication Dept.16
7/30/2019 Chapter 2 Passive Network
17/28
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
Hardik PrajapatiElectronics & Communication Dept.17
7/30/2019 Chapter 2 Passive Network
18/28
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
Hardik PrajapatiElectronics & Communication Dept.18
7/30/2019 Chapter 2 Passive Network
19/28
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.
Hardik PrajapatiElectronics & Communication Dept.19
7/30/2019 Chapter 2 Passive Network
20/28
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.
Hardik PrajapatiElectronics & Communication Dept.20
7/30/2019 Chapter 2 Passive Network
21/28
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.
Hardik PrajapatiElectronics & Communication Dept.21
7/30/2019 Chapter 2 Passive Network
22/28
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.
Hardik PrajapatiElectronics & Communication Dept.22
7/30/2019 Chapter 2 Passive Network
23/28
Mutual inductive coupling forms the basis
of high frequency transformers.
Hardik PrajapatiElectronics & Communication Dept.23
I R0 Cp
Lp LsCs RL
IZ1
rp Lp-
M
Ls-M rs
Z2M
High frequency transformer
Equivalent circuit
7/30/2019 Chapter 2 Passive Network
24/28
Hardik PrajapatiElectronics & Communication Dept.24
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
7/30/2019 Chapter 2 Passive Network
25/28
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.
Hardik PrajapatiElectronics & Communication Dept.25
7/30/2019 Chapter 2 Passive Network
26/28
Hardik PrajapatiElectronics & Communication Dept.26
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
7/30/2019 Chapter 2 Passive Network
27/28
It is the ratio of load voltage Vs (IZT) to
input voltage Vp (IZIN).
VTF = ZT /ZIN
= Z2ZMZp(Zs+Z2)-ZM
2
Hardik PrajapatiElectronics & Communication Dept.27
7/30/2019 Chapter 2 Passive Network
28/28
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.
Hardik PrajapatiElectronics & Communication Dept.28