1. CIRCUITS and SYSTEMS – part II Prof. dr hab. Stanisław Osowski Electrical Engineering (B.Sc.) Projekt współfinansowany przez Unię Europejską w ramach Europejskiego Funduszu Społecznego. Publikacja dystrybuowana jest bezpłatnie

2. Lecture 13 Two-port networks

3. 3 Definition of 2-port 2-port network is a 4-terminal circuit structure of two terminals forming input and 2 terminals forming output port at following conditions satisfied

4. 4 2-port matrix description  Admittance form - (I1, I2) expressed as function of (U1, U2)  Impedance form - (U1, U2) expressed as function of (I1, I2)  Hybrid form - (U1, I2) expressed as function of (I1, U2)  Inverse hybrid form - (I1, U2) expressed as function of (U1, I2)  Chain form - (U1, I1) expressed as function of (U2, I2)  Inverse chain form - (U2, I2) expressed as function of (U1, I1).

5. 5 2-port matrix description (cont.) 1) Admittance desription 2) Impedance desription 3) Hybrid desription

6. 6 2-port matrix description (cont.) 4) Inverse hybrid desription 5) Chain desription

7. 7 Example Determine the matrix description of 2-port Solution: Chain description

8. 8 Transfer function and 2-port description Any transfer function can be expressed through the 2-port parameters. For example voltage transfer function chain matrix description admittance matrix description

9. 9 Input impedance Impedance in general form No load of the 2-port (Y o =0) Short circuit of output port (Z o =0)

10. 10 Example Determine the input impedance of the 2-port Chain matrix Voltage transfer function Input impedance

11. 11 Connections of 2-ports Series connection Chain connection

12. 12 Connections of 2-ports (cont.) Series-parallel connection Parallel connection

13. 13 Connections of 2-ports (cont.) Parallel-series connection

14. 14 Gyrator Loading gyrator by the impedance Z o the input impedance of the connection is inversely proportional to Z o.

15. 15 Gyrator loaded by capacitor Let us assume that Z o = 1/sC. In such case the input impedance of this connection represents the inductor.

16. 16 Negative impedance converters (NIC) Negative impedance converter (NIC) converts either the current or voltage with the negative sign. NIC with inversion of current (INIC) NIC with inversion of voltage (VNIC)

17. 17 NIC loaded by an impedance Input impedance of the connection Loading NIC by impedance Z o we implement the negative Z o. Observe that applying NIC we may introduce the instability to the circuit!