1. 1 EKT 441 MICROWAVE COMMUNICATIONS CHAPTER 1: TRANSMISSION LINE THEORY (PART III)

2. 2 Impedance Matching Quarter-Wave Transformer Single/double stub Tuner Lumped element tuner Multi-section transformer TRANSMISSION LINE THEORY PART II

3. 3 LUMPED ELEMENTS MATCHING (L NETWORKS) Figure 10: L-section matching networks. (a) Network for z L inside the 1+jx circle. (b) Network for z L outside the 1+jx circle.

4. 4 LUMPED ELEMENTS MATCHING (L NETWORKS) Figure 11: Effect of adding a Parallel L

5. 5 LUMPED ELEMENTS MATCHING (L NETWORKS) Figure 12: Effect of adding a Series L

6. 6 LUMPED ELEMENTS MATCHING (L NETWORKS) Figure 13: Effect of adding a parallel C

7. 7 LUMPED ELEMENTS MATCHING (L NETWORKS) Figure 14: Effect of adding a Series C

8. 8 EXAMPLE 1.11 Given the circuit below, visualize using Smith Chart the changes from R L till Z in

9. 9 SOLUTION TO EXAMPLE 1.11 In this question, it is given that; Since we are adding a resistor with a shunt capacitor, we need to work in admittance form. Changing R L to g A (normalized form of G A );

10. 10 SOLUTION TO EXAMPLE 1.11 Normalizing B CL to get b CL, B CL need to be multiplied with Z 0 The capacitance value is given as C L = 1.91 pF. The value of b CL is calculated so that the imaginary part of the impedance (R L + jB L ) can be determined

11. 11 SOLUTION TO EXAMPLE 1.11 The amount of movement from the series inductance can be calculated as follow: Thus, the total admittance from (G + jB CL ) is given as y B = 1.6 + j1.2. Since the next element is a inductance connected serially, we need to work in impedance again. Converting;

12. 12 SOLUTION TO EXAMPLE 1.11 To add the capacitance value of shunt C, the impedance must first be converted back to admittance; Then calculating the effect of the shunt C;

13. 13 SOLUTION TO EXAMPLE 1.11 The last element in the circuit is the serially connected L with a value 3.98nH, we need to once again convert to impedance before adding the value of x L to determine the z in value Then calculating the effect of the shunt C;

14. 14 SOLUTION TO EXAMPLE 1.11 (Cont’d)

15. 15 MULTISECTION TRANSFORMER This transformer consist of N equal-length (commensurate) sections of transmission lines. Figure 12: Partial reflection coefficients for a multisection matching transformer

16. 16 MULTISECTION TRANSFORMER Partial reflection coefficients can be defined at each junction, as follow: [36] [37] [38]