1. EMLAB 1 16. Two-port networks

2. EMLAB 2 In cases of very complex circuits, observe the terminal voltage and current variations, from which simple equivalent circuit can be constructed.

3. EMLAB 3 + - a b a b Single port network 1.To find B, measure voltage with i=0. (open circuit voltage) 2.To find A, measure the variation of v with i changing. (impedance) 1.To find D, measure current with v=0. (short circuit current) 2.To find C, measure the variation of i with v changing. (admittance) Thevenin’s and Norton’s theorem S V V R S I I R

4. EMLAB 4 Two port network Admittance parameters The network contains NO independent sources Admittance parameter

5. EMLAB 5 The computation of the parameters follows directly from the definition Measurement of Y-parameters + - - + - 

6. EMLAB 6 Example 16.1 Find the admittance parameters for the network Next we show one use of this model

7. EMLAB 7 An application of the admittance parameters The model plus the conditions at the ports are sufficient to determine the other variables. Determine the current through the 4 Ohm resistor

8. EMLAB 8 16.2 Impedance parameters + - + - +-+- +-+-

9. EMLAB 9 Find the Z parameters Write the loop equations rearranging Example 16.2

10. EMLAB 10 Use the Z parameters to find the current through the 4 Ohm resistor Output port constraint Input port constraint

11. EMLAB 11 16.3 hybrid parameter - + - + -  +-+- - + + - 

12. EMLAB 12 Find the hybrid parameters for this circuit Non-inverting amplifier Equivalent linear circuit Example 16.3

13. EMLAB 13 - + + - 16.4 Transmission parameter

14. EMLAB 14 - + + - + - + - + - Cascade of networks

15. EMLAB 15 Determine the transmission parameters Example 16.4

16. EMLAB 16 Cascade of networks

17. EMLAB 17 Interconnections permit the description of complex systems in terms of simpler components or subsystems The basic interconnections to be considered are: parallel, series and cascade PARALLEL: Voltages are the same. Current of interconnection is the sum of currents CASCADE: Output of first subsystem acts as input for the second The rules used to derive models for interconnection assume that each subsystem behaves in the same manner before and after the interconnection 16.6 Interconnection of two ports SERIES: Currents are the same. Voltage of interconnection is the sum of voltages

18. EMLAB 18 Find the Y parameters for the network Example 16.5

19. EMLAB 19 Given the demand at the receiving end, determine the conditions on the sending end Transmission parameters are best suited for this application In the next slide we show how to determine the transmission parameters for the line. Here we assume them known and use them for analysis Power factor angle Example 16.8

20. EMLAB 20 Determining the transmission parameters for the line