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UNIT- IV
Magnetically Coupled Circuits
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Topics:
Self inductance. Mutual inductance
Dot rule
Coefficient of coupling
Analysis of multi-winding coupled circuits
Series, Parallel connection of coupled inductors
Single tuned and double tuned coupled circuits.
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Mutual & Self Inductance
Mutual Inductance
Mutual Inductance of Coaxial
Solenoids
Self Inductance
Inductie !eactance " Impedance
Inductance # $nit %engt& of a Coaxial Cable
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Mutual Inductance
If ' coils are placed near eac& ot&er (in t&e same plane),
a c&anging current in one coil will induce an *M+ in t&e ot&er
coil
+rom +aradays law, t&e *M+E2induced in coil ', is
proportional to t&e rate of c&ange of t&e magnetic flux passing
t&roug& it
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Mutual Inductance %et - be t&e magnetic flux in eac& loop of coil ', created
by t&e current in coil . If coil ' containsN
2turns, t&e is t&e total fluxin coil '
t&eMutual Inductance
from +aradays %aw
&is relates t&e c&ange in current in coil to t&e *M+ induced in
coil '
-,'B
-,'' BN
-
'
-,'
-,'
I
NMDefine
B
=
dt
dNBut B -,'
''
=
dt
dIM
dt
dI
N
MN
dt
dI
N
M
dt
dand
N
IM
B
B
,'
'
.'''
'
,'
'
,'
,'
,'
==
=
=
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Mutual Inductance
&e mutual inductance of coil ' wit& respect to coil is aconstant and depends upon t&e geometry of t&e two coils
&e reerse situation can also ta/e place w&en a c&ange in
current in coil ' induces an *M+ into coil
&e mutual inductancesM1,2= M2,1so that
t&e SI $nits for mutual inductance is
t&e 0enry (0)
0 1 23s#A 1 43s
dt
dIM '
',-- =
dt
dIM
dt
dIM
'
'
=
=
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Mutual Inductance of a CoaxialSolenoid
A long t&in solenoid of lengt&l, radius
r1,
containsN
1turns
Coil ' is wrapped around coil , wit& a radius r2, containsN2
turns
The mutual inductance of the coils is
l
N
nwhererlnnM ==
'
-'-5
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Self Inductance &e concept of inductance applies also to a single isolated coil
ofN turns
6&en a c&anging current passes t&roug& a coil (solenoid), a
c&anging magnetic flux is produced in t&e coil. &is in turn,
induces an *M+ in t&e same coil.
&is *M+ opposes t&e c&ange in flux (%en7s %aw)
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Self Inductance
&e magnetic flux 89passing t&roug& :-turns of t&e coil isproportional to t&e currentIinn t&e coil. &is proportionality
is now called self inductance
&e induced *M+E, due to t&e self-inductance of t&e coil is
(from +aradays %aw);
Self Inductance is also measured in 0enrys
INL B
=
dt
dIL
dt
IL
B
B
=
=
dt
dIL
dt
dN B =
=
lANLthen
l
ANIABSince
'5
5
=
==
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Inductance
The inductance, L, is dependent on the geometryand the presence of a core made out of ferro-magnetic material
The symbol for inductance is:
Every electronic component, such as a resistor, ora ire, has some amount of inductance called!parasitic inductance", hich is usuallyunanted#
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Inductive $eactance
%arge inductance tends to oppose alternatingcurrent# The greater the inductance, the less &Ccurrent that can pass 'ie: it impedes the (o of&C current similar to ho resistance impedes the(o of )C current*
The opposition to &C current is called inductivereactance (XL)
The term impedanceis used to represent thevector magnitude of resistance and inductivereactance
''
LXRZ +=
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Inductance +nit %ength of a CoaxialCable
Conductors in a coaxial cable are thin hollotubes# There is nomagnetic eld ithin the inner
conductor# The magnetic eld ithin the thinconductor tubes can be ignored# The conductorscarry e.ual currents in opposite directions
The inductance per unit length is:
=
'
-5 ln
' r
r
l
L
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Tuned &mpliers
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/re.uency selectivity of resonant circuits allos a radio to be
tuned to one of a set of transmitting stations# Tuning is usually underta0en by varying the capacitance of an
ad1ustable capacitor#
$esonant circuits are also important for tuning and fortransmitting signals#
Tuned ampliers
To amplify the selective range of fre.uencies , the resistive load ,$c is replaced by a tuned circuit#
The tuned circuit is capable of amplifying a signal over a narroband of fre.uencies centered at fr#
Tuned Circuits
R
LZ
Lf
r
r
=
= '
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Types Of tuned amplifiers
Single tuned amplier
one parallel tuned circuit is used as a load %imitation:Smaller 2andidth , smaller gain bandidth product,
does not provide (atten response#
)ouble tuned amplier
It provides high gain, high selectivity and re.uired bandidth# sed in I/ in radio and T3 receivers# It gives greater 4db bandidth having steep sides and (at top # 2ut
alignment of double tuned amplier is di5cult
Stagger tuned amplier
To single tuned amplier are connected in cascaded form# $esonant fre.uency are displaced#To have better (at , ideband charcteristics ith a very sharp
re1ective, narro band characteristics#
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Single tuned amplier
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)ouble tuned amplier
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Stagger tuned amplier
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Synchronously tuned amplifer
To obtain a high over all gain , several identical stages of tunedampliers can be used in cascade#
&ll ampliers stages are assumed to be identical and to be tunedto the same fre.uency 6#
7 factor:
$atio of reactance to resistance#
Measure of e5ciency ith hich inductor can store the energy#
nloaded 7 of tuned circuit
$atio of stored energy to dissipated energy in a reactor orresonator#
%oaded 7
It is determined by ho tightly the resonator is coupled to itsterminations#
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Instability of tuned circuits:
Transistor are used at the fre.uencies nearer to their unity gain28 to amplify narro band of high fre.uencies#
&t this $/ fre.uencies , inter capacitance beteen base andcollector becomes dominant#
Some feedbac0 signal manages to reach the input from output ,so circuit becomes unstable and generating the oscillation and
can stop or0ing as amplier#
Stabili9ation techni.ues:
# ;a9eltine neutrali9ation
# $ice neutrali9ation
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Than0 ?ou