1. 1. A two-port network is an electrical network circuit or device with two pairs of terminals to connect to external circuits. Two terminals constitute a port if the currents applied to them satisfy the essential requirement known as the port condition.The electric current entering one terminal must equal the current emerging from the other terminal on the same port. INTRODUCTION
2. 2. A terminal is the point at which a conductor from an electrical component, device or network comes to an end and provides a point of connection to external circuits. All electric cell have two terminals. The first is the positive terminal and the second is the negative terminal. The positive terminal looks like a metal cap and the negative terminal looks like a metal disc. The current flows from the positive terminal, and out through the negative terminal, the current flow (positive (+) to negative (-) flow). TERMINAL
3. 3. A port is a pair of terminals connecting an electrical network or circuit to an external circuit, a point of entry or exit for electrical energy. A port consists of two nodes (terminals) connected to an outside circuit, that meets the port. The currents flowing into the two nodes must be equal and opposite. PORT Network N has a port connecting it to an external circuit. The port meets the port condition because the current I entering one terminal of the port is equal to the current exiting
4. 4. ONE PORT NETWORK A port is combination of two terminals on the same side of network. Thus a terminal pair is nothing but a port as shown in fig . A network having only one terminal pair or port is called one port network. One port network can be represented as below. R 1I 1V + - + - 1I 1V
5. 5. NETWORK FUNCTION FOR ONE PORT NETWORK Voltage and current for the one port linear network as shown in fig. As there is one port , voltage and current measured at same port. thus for one port network only driving function can be defined as below. Hear V is applied voltage. DRIVING POINT IMPEDANCE FUNCTION. The ratio of laplace transform of voltage and current measured at port under zero initial condition is called driving point impedance function It is denoted by Z(s) Z(s)=V(s)/I(s)
6. 6. DRIVING POINT ADMITTANCE FUNCTION It is the ratio of laplace transform of current and voltage measured at port under zero initial condition is called driving point admittance function. It denoted by Y(s) Y(s)=I(s)/V(s) ,E H n S V 1V 1I + -
7. 7. N-port Network To represent multi-port networks we use: - Z (impedance) parameters - Y (admittance) parameters - h (hybrid) parameters - ABCD parameters - S (scattering) parameters Not easily measurable at high frequency Measurable at high frequency Multiport Networks 8 + + + + + 1I 2I 3I mI NI 1V 2V 3V mV NV - - - - -
8. 8. Two Port Networks Generalities: The standard configuration of a two port: The Network Input Port Output Port + _ _ + V1 V2 I1 I2
9. 9. A two-port network requires two terminal pairs (total 4 terminals). Amongst the two voltages and two currents shown,generally two can be independently specified (externally). input output By convention, regard Port 1 as the input and Port 2 as the input (and use the polarity labels shown). We consider circuits with no internal independent sources.
10. 10. Network Equations: V1 = z11I1 + z12I2 V2 = z21I1 + z22I2 I1 = y11V1 + y12V2 I2 = y21V1 + y22V2 V1 = AV2 - BI2 I1 = CV2 - DI2 V2 = b11V1 - b12I1 I2 = b21V1 b22I1 V1 = h11I1 + h12V2 I2 = h21I1 + h22V2 I1 = g11V1 + g12I2 V2 = g21V1 + g22I2 Impedance Z parameters Admittance Y parameters Transmission A, B, C, D parameters Hybrid H parameters
11. 11. Summary A two-port network has an input port and an output port, each with each port involving a single current and a single voltage. If the two-port network is linear and does not contain any independent sources, it may be possible to characterize up to 6 different sets of matrix relationships. We discussed four: admittance [y], impedance [z],hybrid [h], and transmission [T]. If the parameters exist, they can be calculated or measured individually by short-circuiting or open
12. 12. Network functions for Two-Port Network Consider a two port network with voltages and currents at ports 1-1 and 2-2 as V1(t), I1(t) and V2(t), I2(t) respectively as shown in figure .
13. 13. Network functions for Two-Port Network are as follows: 1. Driving point functions: Driving point impedance functions Driving point admittance functions 2. Transfer Functions: Voltage transfer functions Current transfer functions Transfer impedance functions Transfer admittance functions
14. 14. Driving point functions: Driving point impedance functions The ratio of Laplace transform of voltage and current at port 1-1 or 2-2 is defined as driving point impedance function. Thus there are two driving point impedance functions. At port 1-1 denoted as Z11(s) Z11(s)= V1(s) I1(s) At port 2-2 denoted as Z22(s) Z22(s)= V2(s) I2(s)
15. 15. Driving point functions: Driving point admittance functions The ratio of Laplace transform of current and voltage at port 1-1 or 2-2 is defined as driving point admittance function. Thus there are two driving point admittance functions. At port 1-1 denoted as Y11(s) Y11(s)= I1(s) V1(s) At port 2-2 denoted as Y11(s) Y22(s)= I2(s) V2(s)
16. 16. Transfer Functions: Voltage Transfer Function: It is defined as the ratio of Laplace transform of voltage at one port and voltage at another port. It is denoted as G(s). G12(s) = V1(s) and G21(s) = V2(s) V2(s) V1(s) Current Transfer Function: It is defined as the ratio of Laplace transform of current at one port and current at another port. It is denoted as A(s). A12(s) = I1(s) and A21(s) = I2(s) I2(s) I1(s)
17. 17. Transfer Functions: Transfer Impedance Function: It is defined as the ratio of Laplace transform of voltage at one port and current at another port. Z12(s) = V1(s) and Z21(s) = V2(s) I2(s) I1(s) Transfer Admittance Function: It is defined as the ratio of Laplace transform of current at one port and voltage at another port. Y12(s) = I1(s) and Y21(s) = I2(s) V2(s) V1(s)
18. 18. References;- U.A PATEL BY MAHAJAN PUBLICATION TATA MCGRAW HILL.