Impedance Matching by YEASIN NEWAJ

In this presentation, you will learn how to do impedance matching in a smith chart.

1. Impedance Matching (Microwave Engineering) Presented by YEASIN NEWAJ Bsc . in Electrical and Electronic Engineering

2. Impedance Matching Matching indicates terminating the transmission line in its characteristic impedance (Z ). Then reflections will be eliminated on the transmission line to the left of the matching network (for the load). This procedure is sometimes referred to as tuning. An impedance matching network is used between two dissimilar impedances in order to ensure maximum power transfer between them. We typically want to match an arbitrary load Z L to a transmission line Z .

3. Impedance Matching Importance of Impedance Matching Maximum power is delivered when the load is matched to the line (assuming the generator is matched), and ensures minimum power loss in the feed line is. Impedance matching sensitive receiver components (antenna, low noise amplifier, etc.) may improve the signal-to-noise ratio of the system. Impedance matching in a power distribution network (such as an antenna array feed network)may reduce amplitude and phase errors. Important factors for Impedance Matching: Complexity - simpler matching network is usually cheaper, smaller, more reliable, and less lossy. Bandwidth – In many applications it is desirable to match a load over a band of frequencies. Although in this course we will consider matching at single frequency. Implementation – Advantages of different matching methods, e.g. stub matching, waveguide matching, quarter wavelength transformer. Adjustability - may require adjustment to match a variable load impedance.

4. 4 /28 Impedance Matching I. Matching with lumped elements (L Networks): L section uses two reactive elements to match an arbitrary load impedance to a TL; There are two possible configurations; is inside the 1+jX circle on the SC is outside the 1+jX circle on the SC Type 1 Type 2

5. 5 /28 Impedance Matching is inside the 1+jX circle on the SC is outside the 1+jX circle on the SC

6. 6 /28 High pass vs Low pass L-Section networks

7. 7 /28 Comments on the use of lumped elements: Actual lumped element capacitors and inductors can be used up to several GHz. However, there is a large range of frequencies and circuit sizes where lumped elements cannot be realized. This is considered to be the major limitation of the L-Section matching network. Impedance Matching

8. 8 /28 Impedance Matching Frequency response of a real lumped inductor :

9. 9 /28 Frequency response of a real lumped capacitor : Impedance Matching

10. 10 /28 Realization of inductors and capacitors from TL sections A small section of high impedance line is equivalent to a series inductance: Impedance Matching

11. 11 /28 Realization of inductors and capacitors from TL sections A small section of low impedance line is equivalent to a shunt capacitance: Impedance Matching

12. 12 /28 The effect of adding reactive elements Impedance Matching

13. 13 /28 The effect of adding reactive elements Impedance Matching

14. 14 /28 Unit resistance / conductance circles Impedance Matching

15. 15 /28 4-Step Design procedure for L-Sections Impedance Matching

16. 16 /28 Example: Design an L section matching network to match a load Z L =(100-j50) W to a 50 W line at 1.0 GHz. is inside the 1+jX circle Impedance Matching

17. 1. 2 1 . 2 2 . 3. 4. 3. 4. Impedance Matching

18. 18 /28 Impedance Matching

19. 19 /28 Impedance Matching

20. 20 /28 II . Single Stub matching In single stub tuning, the two adjustable parameters are the distance d from the load to the stub position , and the length of the stub l. Impedance Matching

21. 21 /28 The basic idea is to select d so that and to find the length of the stub l such that hence Impedance Matching

22. 22 /28 Example: Design two single-stub shunt tuning networks to match Impedance Matching to a 50W line. Solution: - There are two approaches to solve such a problem; using Smith Chart and using analytical expressions of TL. - Solution with Smith Chart is more intuitive, and easier than solving the problem analytically.

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24. 26 /28 Impedance Matching

25. 27 /28 Impedance Matching d 1 =(0.416-0.15) l =0.266 l d 2 =(0.416-0.35) l =0.066 l Find the length d of the TL;

26. 28 /28 Impedance Matching l 1 =0.067 l l 2 =0.339 l

27. 29 /28 II . Double- Stub matching In double-stub tuning, the two adjustable parameters are the lengths of the stubs, l 1 and l 2 . Note that the distance between the two stubs d is usually set to a fixed value l /8 or 3 l /8. Impedance Matching

28. 30 /28 The operation of this tuner: i. For a perfect match point must be located on the circle. Impedance Matching

29. 31 /28 The operation of this tuner: ii. point must lie on the rotated circle circle is rotated towards load by the distance d. Forbidden Region Impedance Matching

30. 32 /28 Design of a double-stub matching network It is assumed that in the double-stub matching network seen below, the lengths of the TLs are l 1 = λ /8 and l 3 =l 2 =3 λ /8. Find the lengths of the short circuited stubs that match the load impedance Z L =(50+j50) Ω to a 50 Ω input impedance. The chracteristic line impedance for all components is Z =50 Ω Impedance Matching

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32. 34 /28 Forbidden Region The difference between Y D and Y C is: Therefore the length of first stub is l S1 = 0.074 λ . The difference between Y B and Y A is: Therefore the length of second stub is l S2 = 0.051 λ . MAKE SURE THAT Y D IS NOT INSIDE THE FORBIDDEN REGION

33. Thank You