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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