Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

Introduction

The Lattice Network in Network Analysis is a symmetrical and balanced with four arms as shown in the given Fig. (a). The arms consisting impedance ZA are called series arms of the lattice network. The arms consisting impedance ZB are called shunt or diagonal arms. The lattice network can be rearranged in the bridge structure as shown in the given Fig. (b) which is very suitable for the analysis of the lattice network.

Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

As lattice network is a symmetrical network, let us derive expressions for the characteristic impedance (Z0) and propagation constant (γ). It is very convenient to use bridge structure of the lattice network for the calculation of propagation constant.

Characteristic Impedance (Z0)

Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Consider the Fig. (b) 

Consider closed path 1-2-2′-1′-1, applying KVL, we get
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Consider closed path 1-2′-2-1′-1, applying KVL, we get
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
From equation (1),
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
From equation (2),
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Equating equations (3) and (4),
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

But by the property of symmetrical network, the input impedance of the network terminated in its characteristic impedance is equal to Z0.
Let
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Putting value of E/Is in above equation,
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
(B) In terms of open and short circuit impedances
For the calculation of open and short circuit impedances arranging bridge structure of the lattice network as shown in the given Fig. (a) and (b).

Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Consider Fig. (a),
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)Consider Fig. (b),

Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Multiplying equations (6) and (7) , we can write,
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Propagation Constant (γ)

For any symmetrical network, propagation constant can be expressed as,
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Consider equations for current IR given by equation (3) and (4) derived
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
But we know that E = Is . Z0
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Impedances ZA and ZB in terms of characteristic impedance (Z0) and propagation constant (γ)

Consider equation,
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Similarly,
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Hence lattice network with impedances expressed in terms of characteristic impedance and propagation constant is as shown in the given Figure.

Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)

After detail analysis of some of the important symmetrical networks now consider analysis of typical asymmetrical networks.

The document Lattice Network | Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
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