2-port networks final

8/10/2019 2-Port Networks Final

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BITS PilaniPilani Campus ANU GUPTA, BITS PILANI

EEE / INSTR C272

2-port network analysis


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BITS PilaniPilani Campus

2 Port Network analysisNot necessary to know the detailed configuration of the network elements.

5/1/2013Anu Gupta BITS PILANI


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Network analysis is the process of finding the voltages

across, and the currents through, every component in

the network

Network analysis

BITS Pilani, Pilani Campus


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Component-- device with two or more terminals into which, or

out of which, charge may flow.

Node--A point at which terminals of more than two components

Other Definitions


.

considered to be a node for the purpose of analysis.

Branch--The component(s) joining two nodes

Mesh--A group of branches within a network joined so as to form

a complete loop


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Port--Two terminals where the current into one is identical to the current out of

the other

Circuit--A current from one terminal of a generator, through load component(s)

and back into the other terminal.

Definitions


A circuit is, in this sense, a one-port network and is a trivial case to analyse. If

there is any connection to any other circuits then a non-trivial network has

been formed and at least two ports must exist.

Often, "circuit" and "network" are used interchangeably, but many analysts

reserve "network" to mean an idealised model consisting of ideal

components.[


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A pair of terminal at which a signal (current or voltage) may

enter or leave is called a port

A network having only one pair of such terminals is called

Terminal, port


No connections can be made to any other node internal to

the network

One port network can be modeled by thevenin or norton

equivalent



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A large number of networks of practical interest and importance have two ports of

entry.

The two-port network model is used in circuit analysis techniques to isolate portions of

larger circuits.

" "

Need for 2 Port N/ W analysis


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matrix of numbers.

This allows the response of the network to signals applied to the ports to be calculated

easily, without solving for all the internal voltages and currents in the network.

Any linear circuit with four terminals can be transformed into a two-port network

provided that it does not contain an independent source and satisfies the port

conditions.


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We can develop an electrical equivalent of an unknown circuit

A complex circuit can be broken up in its sub circuits whose

electrical equivalents can be developed by using 2-port

Usefulness of 2 port N/W analysis


.

together appropriately to do analysis of complete system

An electrical equivalent of active devices like BJT, MOSFET

can be developed using 2-port theory, which can be used for

analysis and synthesis of systems using these electrical

equivalents


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For example, the determination of Thevenins and Nortons

equivalents pertain to one-ports, since there is one pair of

terminals through which we look into the network

One port network2 terminals


Thevenin or Norton equivalent is sufficient for determining the

voltages and currents in any branch or circuit connected

externally to the one-port.

A network with n ports of entry is called an n-port.



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The one-port is a black box with a

single pair of input/output terminals,

referred to as aport.

One Port

Vs

Is


vo tage s app e at t e term na s

and a current flows in the direction

shown.

The admittance seen at the port is

called thedriving point admittance


Is x (s)


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The response of a two-port network is studied by using

parameter matrices that express the interdependence of

these four variables.


The actual configuration of elements is of no interest in

order to analyze the relationship between any externalconnections at the input and output ports.



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The common occurrence of two-ports in modeling electronic

devices, electronic circuits, and communication networks and

systems makes it important to study them in some detail.

-

Need to study


viewed simply as a black box described by certain parameter

matrices.

We can concentrate on the four variables (currents and voltages

at the two ports) and any external connections to the two-port.



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The network in the black box is assumed to consist of

linear components,

Conditions to be met


linear dependent sources),

no independent sources.

No stored energy in the network



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The standard convention is to choose both the currents I I

and 12 entering the positive voltage reference terminals

at the input and output ports to introduce symmetry in

Convention


e ana ys s o wo-por s.

It is possible to express any two of the four variables, V1, II,V2 , and 12 as linear functions of the other two variables.



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Symmetrical networks. A network is symmetrical if its input

impedance is equal to its output impedance.

Most often, but not necessarily, symmetrical networks are also

Properties of 2 port network


physically symmetrical.

Sometimes also ant metrical networks are of interest. These are

networks where the input and output impedances are the

duals of each other.


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Common types are -

Open-circuit impedance (Z) parameters. (I1, I2)

Types of two port N/W


. ,

Short-circuit admittance (Y) parameters. (V1, V2)

Transmission (ABCD)parameters. (V2, I2)



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Open-circuit impedance parameters

The current II and 12 are selected as the independent variables,

choices of independentvariable


2 I I

12 .

The parameters that appear in the resulting equations are called

open circuit impedance, orz parameters.



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2 port N/W

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956



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5/1/2013 Anu Gupta BITS PILANI


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Z parameter model



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EXAMPLE 2




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Example - Terminated TwoPort Network




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Equations




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Driving point impedance




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For analysis, it is customary to connect a signal source

with a series impedance to the input port and a load

impedance to the output port.

System Analysis Using ZParameters




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Model of reciprocal N/W



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Example



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Hybrid parameters




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Example1




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Relationship of h and zparameters




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Short-circuit AdmittanceParameters of a Two-port




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Y parameter model




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Transmission parameters




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When the design of a two-port leads to a rather complex

structure, it is advisable to break the design down into

simpler two-ports and interconnect them

Interconnection Of Two-portNetworks


Two commonly used interconnections

parallel connection of two-ports

cascaded connection of two-ports.


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The parallel connection of two-ports requires that the

voltages VI and V 2 of each two port are, respectively,

equal to the voltages VI and V 2 of the other two-ports.

Parallel Connection of Two-Ports


In addition, an important condition must be observed: the

parallel connection must not alter any of the original

networks.


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Example



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the y parameter matrix of the parallel connection is the sum of

the y parameter matrices of the individual two-ports.

The result for the parallel connection of two two-ports is readily

extended to cover the general case of n two-ports in parallel:


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Cascaded two port nw




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the ABCD parameter matrix of the cascaded connection of

two two-ports is the product

of the ABCD parameter matrices of the individual two-ports.

BITS Pil i Pil i C

2-port networks final

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