Chapter 8 – Methods of Analysis

Lecture 11

by Moeen Ghiyas

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CHAPTER 8

Bridge Networks

Y – Δ (T – π) and Δ to Y (π – T) Conversions

A configuration that has a multitude of applications

DC meters & AC meters

Rectifying circuits (for converting a varying signal to one of a

steady nature such as dc)

Wheatstone bridge (smoke detector ) and other applications

A bridge network may appear in one of the three forms

The network of Fig (c) is also called a symmetrical lattice

network if R2 = R3 and R1 = R4.

Figure (c) is an excellent example of how a planar network

can be made to appear non-planar

Solution by Mesh Analysis (Format Approach)

Solution by Nodal Analysis (Format Approach)

Can we replace R5 with a short circuit here?

Can we replace R5 with a short circuit?

Since V5 = 0V, yes! From nodal analysis we

can insert a short in place of the bridge arm

without affecting the network behaviour

Lets determine VR4 and VR3 to confirm validity

of short ie VR4 must equal VR3

As before VR4 and VR3 = 2.667 V

Can we replace same R5 with a open circuit?

From mesh analysis we know I5 = 0A, therefore yes! we can have

an open circuit in place of the bridge arm without affecting the

network behaviour (Certainly I = V/R = 0/(∞ ) = 0 A)

Lets determine VR4 and VR3 to confirm validity of open circuit ie VR4

must equal VR3

The bridge network is said to be balanced when the

condition of I = 0 A or V = 0 V exists

Lets derive relationship for bridge network meeting condition

I = 0 and V = 0

If V = 0 (short cct b/w node a and b),

then V1 = V2

or I1R1 = I2R2

Two circuit configurations not falling into series or parallel

configuration and making it difficult to solve without the mesh or

nodal analysis are Y and Δ or (T and π).

Under these conditions, it may be necessary to convert the

circuit from one form to another to solve for any unknown qtys

Note that the pi (π) is actually an inverted delta (Δ)

Conversion will normally help to solve a

network by using simple techniques

With terminals a, b, and c held fast, if the

wye (Y) configuration were desired instead

of the inverted delta (Δ) configuration, all

that would be necessary is a direct

application of the equations, which we will

derive now

If the two circuits are to be equivalent, the

total resistance between any two terminals

must be the same

If the two circuits are to be equivalent, the total

resistance between any two terminals must be

the same

Consider terminals a-c in the Δ -Y configurations

of Fig

If the resistance is to be the same between terminals a-c, then

To convert the

Δ (RA, RB,

RC) to Y (R1,

R2, R3)

Note that each resistor of

the Y is equal to the

product of the resistors in

the two closest branches of

the Δ divided by the sum of

the resistors in the Δ.

Note that the value of

each resistor of the Δ is

equal to the sum of the

possible product

combinations of the

resistances of the Y

divided by the resistance

of the Y farthest from the

resistor to be determined

what would occur if all the values of a Δ or Y

were the same. If RA = RB = RC

The Y and the Δ will often appear as shown in Fig. They are then

referred to as a tee (T) and a pi (π) network, respectively

Example – Find the total resistance of the network

Bridge Networks

Y – Δ (T – π) and Δ to Y (π – T) Conversions

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