Two-Port Network Parameters MAHATMA GANDHI INSTITUTE OF TECHNICAL EDUCATION AND RESEARCH CENTER, NAVSARI. Two-Port Network Parameters Group-12 PREPARED BY: EN.NO: Hafeji Mulla Ajmal 130330111011 Anklesaria Mazdad 130330111019 Prajapati Kunj 130330111036 Shaikh Mahmad uhaid 130330111042

INTRODUCTION A two-port network (a kind of four-terminal network or quadripole) is an electrical network (circuit) or device with two pairs of terminals to connect to external circuits.  The electric current entering one terminal must equal the current emerging from the other terminal on the same port.

INTRODUCTION In a two-port network, often port 1 is considered the input port and port 2 is considered the output port. The two-port network model is used in mathematical circuit analysis techniques to isolate portions of larger circuits. Any linear circuit with four terminals can be regarded as a two-port network provided that it does not contain an independent source and satisfies the port conditions. Examples of circuits analyzed as two-ports are filters, matching networks, transmission lines, transformers.

INTRODUCTION The common models that are used are referred to as z-parameters, y-parameters, h-parameters, g-parameters, and ABCD-parameters, each described individually below.  They are usually expressed in matrix notation, and they establish relations between the variables. voltage across port 1 current into port 1 voltage across port 2 current into port 2.

General properties Reciprocal networks: A network is said to 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 same current is applied to port 2. A network that consists entirely of linear passive components (that is, resistors, capacitors and inductors) is always reciprocal. Symmetrical networks: A network is symmetrical if its input impedance is equal to its output impedance. These are networks where the input and output impedances are the duals of each other

Impedance parameters (z-parameters) where Impedance parameters (z-parameters) Figure 2: z-equivalent two port showing independent variables I1 and I2

Impedance parameters (z-parameters) For reciprocal networks Z12=Z21 . For symmetrical networks Z11=Z22.

Examples 1 Determine the impedance parameters from the circuit in Fig. In frequency domain

Example 2 Find the Z parameters. Write the loop equations rearranging

Admittance parameters (y-parameters)  Y-equivalent two port showing independent variables V1 and V2. where

Admittance parameters (y-parameters) For reciprocal networks Y12=Y21 . For symmetrical networks Y11=Y22. 

Examples Find y parameters from the figure. 5Ω 15Ω 20Ω + V1 _ V2 I1 I2

V2 = 0 5Ω 20Ω + V1 _ I1 I2 Ia

ii) V1 = 0 5Ω 15Ω + V2 _ I1 I2 Ix C In matrix form;

Hybrid parameters (h-parameters) V1=h11I1 +h12V2 I2=h21I1 + h22V2

ABCD-parameters The ABCD-parameters are known variously as chain, cascade, or transmission line parameters. For reciprocal networks AD-BC=1 . For symmetrical networks A=D . Here A and D are purely real while B and C are purely imaginary.

Where The input voltage/current matrix vector can be directly replaced with the matrix equation of the preceding cascaded stage to form a combined A’B’C’D’ matrix.

The terminology of representing the ABCD parameters as a matrix of elements designated a11 etc. as adopted by some authors and the inverse A’B’C’D’ parameters as a matrix of elements designated b11 etc.

Conversion Table

COMBINATIONS OF TWO-PORT NETWORKS Series-series connection Parallel-parallel connection Series-parallel connection Parallel-series connection Cascade connection

SERIES-SERIES CONNECTION When two-ports are connected in a series-series configuration as shown in figure, the best choice of two-port parameter is the z-parameters.

PARALLEL-PARALLEL CONNECTION The best choice of two-port parameter is the y- parameters. The y-parameters of the combined network are found by matrix addition of the two individual y-parameter matrices

SERIES-PARALLEL CONNECTION Two two-port networks with input ports connected in series and output ports connected in parallel. The best choice of two-port parameter is the h-parameters. 

PARALLEL-SERIES CONNECTION Two two-port networks with input ports connected in parallel and output ports connected in series. The best choice of two-port parameter is the g-parameters. 

CASCADE CONNECTION Two two-port networks with the first's output port connected to the second's input port.  The best choice of two-port parameter is the ABCD-parameters. 

References http://en.wikipedia.org/wiki/Two-port_network www.ece.mcmaster.ca/~junchen/ch16_twoportnetworks.ppt portal.unimap.edu.my:7778/portal/.../portal30/.../Chapter_6_-_Two-Port..