2 Port Network analysis2 Port Network analysisN k h d il d fi i f Not necessary to know the detailed configuration of the network elements.

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Terminal, portTerminal, port

A pair of terminal at which a signal (current or lta e) ma enter r lea e is called a rtvoltage) may enter or leave is called a port

A network having only one pair of such i l i ll d kterminals is called one port network

No connections can be made to any other node internal to the network

One port network can be modeled by p ythevenin or norton equivalent

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One port networkOne port network--2 terminals2 terminals

For example, the determination of Thevenin'sand Norton's equivalents pertain to one-ports and Norton s equivalents pertain to one-ports, since there is one pair of terminals through which we look into the network

Thevenin or Norton equivalent is sufficient for determining the voltages and currents in g gany 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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2 port network2 port network——4 terminals4 terminals

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

entry. An amplifier, for example, has a pair of

input terminals (the input port) and a pair of output terminals (the output port).

There are four variables of interest in a two-port; the current and voltage at the input port and the current and voltage at the output g pport.

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The response of a two-port network is st died b sin arameter matrices that studied by using parameter matrices that express the interdependence of these four variables variables.

The actual configuration of elements is of no i i d l h l i hi interest in order to analyze the relationship between any external connections at the input

d and output ports.

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Need to studyNeed to study 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.

The attractive feature of two-port theory is p ythat the network is viewed simply as a black box described by certain parameter matrices. y p

We can concentrate on the four variables (currents and voltages at the two ports) and (currents and voltages at the two ports) and any external connections to the two-port.

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Conditions to be metConditions to be met

Th k i h bl k b i d The network in the black box is assumed to consist of linear components, linear dependent

) sources), no independent sources. No stored energy in the network

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The standard convention is to choose both the c rrents I and 1 enterin the siti e the currents I I and 12 entering the positive voltage reference terminals at the input and output ports to introduce symmetry in the output ports to introduce symmetry in the analysis of two-ports.

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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4 types of TWO PORT NW4 types of TWO PORT NW

Open-circuit impedance (Z) parameters. (I1, I2) Hybrid (H) parameters. (I1, V2) Short-circuit admittance (Y) parameters. (V1, V2) Transmission (ABCD)parameters. (V2, I2)Transmission (ABCD)parameters. (V2, I2)

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4 choices of independent variable 4 choices of independent variable

Open-circuit impedance parametersTh I d 1 l d h The current II and 12 are selected as the independent variables,

and the voltages V2 and VI are then expressed as functions of II and 12 .

The parameters that appear in the resulting equations are called open circuit impedance, q p por z parameters.

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ONE PORTONE PORT

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2 PORT NW2 PORT NW

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Z parameter modelZ parameter model

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EXAMPLE EXAMPLE EXAMPLE EXAMPLE

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Reciprocal networksReciprocal networks

Reciprocal networks. A network is said to be reci r cal if the lta e a earin at rt 2 be reciprocal if the voltage appearing at port 2 due to a current applied at port 1 is the same as the voltage appearing at port 1 when the as the voltage appearing at port 1 when the same current is applied to port 2. E h i l d l i Exchanging voltage and current results in an equivalent definition of reciprocity.

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Symmetrical networksSymmetrical networks

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 physically symmetrical.

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EXAMPLE 2EXAMPLE 2

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Example Example -- Terminated Two Port NetworkTerminated Two Port Network

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Equations Equations Equations Equations

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Driving point impedanceDriving point impedanceDriving point impedanceDriving point impedance

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EXAMPLEEXAMPLE——DO YOURSELFDO YOURSELF

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System Analysis Using Z ParametersSystem Analysis Using Z Parameters

For Analysis, it is customary to connect a 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 input port and a load impedance to the output port.

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Hybrid parametersHybrid parameters

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Example1 Example1

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Relationship of h and z parametersRelationship of h and z parameters

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ShortShort--circuit Admittance Parameters of a circuit Admittance Parameters of a TTTwoTwo--portport

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Y parameter modelY parameter model

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Transmission parametersTransmission parametersTransmission parametersTransmission parameters

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Cascaded two port Cascaded two port nwnwpp

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