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Induction Course (Radio)

( )( 2Rs/Xs1RsRp +=

( )( )( )

( ) 2

2

2

1

1

1

1

1

Rp/XpXpXs

,Xs/RsXsXp,Xp/Rp

RpRs

+=

+=   

  

 

+=

Fig. 1 Series to Parallel Conversion

 After the conversion we find that the mast impedance has a resistance in parallel with areactance which could be either capacitive or inductive. This reactance can beneutralised with the help of a reactance of same magnitude but opposite in phase.These two reactance’s which are equal but opposite in polarity resonate and offer pureresistance. Further this resistance Rp can be matched to the feeder line with the help of any network. The advantage of this method is that whenever the mast is capacitive wecan neutralise with a parallel inductive reactance. This reactance in addition tomatching, also provide a static leaks for the lightning. This will eliminate the separateprovision of static leaks. Besides the coils being sturdy will be a more appropriatesolution for lightning protection.

The third method employed is shunting the mast impedance with a high Q coilirrespective of whether the mast is inductive or capacitive. This will alter the netimpedance offered by the antenna and can be manipulated to the desired value byvarying the inductive reactance. In effect the coil impedance alters the mast impedance.This method is used to bring down the higher value of mast impedance to a manageablelevel for designing suitable network. This method is often known as Pre-Tuning.

Design of ‘L’ ‘Pi’ & ‘T’ Networks

‘L’ Networks

L networks consists of two elements of reactance. It could be inductance andcapacitance in any combination L-C, L-L, C-L, C-C. The network can be in the shape of ‘L’ or inverted ‘L’ depending on impedance at the input and at output. If inductivereactance comes in series arm it is a lagging network and when it is capacitive it isleading.

STI(T) Publication 152 004/IC(Radio)/2004

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 Antenna Tuning Unit 

i. Phase lag (Rin > RL)

Fig. 2

ii. Phase lag (RL > Rin)

Fig. 3

iii. Phase lead (Rin > RL)

Fig. 4

iv. Phase lead (RL > Rin)

Fig. 5

‘L’ networks are simple to implement and component losses are less. Phase angle φ

introduced is equal toL

inRRCos . Therefore phase control is not possible with this

network.

STI(T) Publication 153 004/IC(Radio)/2004

R in R LXL

XC

R in R LXL

XC

R in R LXL

XC

R in R LXL

XC

 Lin

 L

inC 

 Lin L L

 R R

 R R X  

 R R R X  

−=

−= )(

in L

in LC 

in Lin L

 R R

 R

 R X  

 R R R X  

−=

−= )(

)( Lin LC 

 Lin

 L

in L

 R R R X  

 R R

 R R X  

−=

−=

)(in LinC 

in L

in

 L L

 R R R X  

 R R

 R R X  

−=

−=

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Induction Course (Radio)

Pi Networks

PI Networks can be designed in number of ways like

♦ By assuming phase shift

♦ By assuming the Q factor 

♦ By splitting the network as two “L” networks

By assuming Phase shift

♦ Find the ratio n = R1/R2

♦  Assume the phase angle β from 0° to 180°

R1Xc R2

XB

X A

Fig. 6 Pi Network

Then

a =β

β−

sinnCosn

b =β

−Sin.n

1

c =β

β−

Sin.n

Cos.n1

Then X A = R2/a XB = R2/b XC = R2/c

In the above case for all phase angles the XB shall be positive and hence inductive , X A

shall be negative and hence capacitive. Where as XC could be positve/negativedepending on phase angle selected. For   some values of phase angle Pi networkbecomes L network.

By Assuming XB

STI(T) Publication 154 004/IC(Radio)/2004

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 Antenna Tuning Unit 

For Stability XB2 ≤ R1 . R2

Then , 

21 R/R

)XX(X

)XX(X

B AC

CB A=

+

+

X A = -2

211

1

B

B

XR.RR

X.R

−−+

XC = -2

212

2

B

B

XR.RR

X.R

−−+

 

Pi networks are flexible and can be designed for any phase shift. They can act as very

good fitters to suppress harmonics.

T Network

In some typical cases where “L” network is not possible it may be necessary to design“T” networks. This can be designed as follows.

X1 X2

X3R 1 R 2

Fig. 7 T Network

T Network between R1 and R2 is possibile only if X32≥ R1R2

X1 = R1 c, X2 = R1 a , X3 =R1 b

Where a = β

β−

sinn

Cosn

b = -βSin.n

1

c =β

β−

Sin.n

Cos.n1

STI(T) Publication 155 004/IC(Radio)/2004

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Induction Course (Radio)

β = Phase shift and n = R1/R2

 

Some times it is possible to design “T” networks with the load reactance as the X2 arm of the above network. Therefore there will be only two components in the matchingnetworks , means it is an “L” network. ‘T’ network can precisely control phase shifts and

can tune wide range of impedances.

STI(T) Publication 156 004/IC(Radio)/2004