## Topic outline

• ### Topic 2, Smith chart and impedance matching

Impedance matching is a fundamental and very typical task in microwave engineering. It is important for several reasons: 1) maximum power is not delivered to the load if there is mismatching between the load and the transmission line (especially problematic in limited-power application such as mobile phones), 2) standing wave may cause the electrical breakdown and/or heating in high-power applications (e.g., base stations, broadcasting and radar systems), 3) some components (e.g., transmitters) may become unstable and start oscillating because of reflecting waves, 4) amplitude and phase errors in mismatched power division networks, for instance, in antenna arrays. The basic idea in impedance matching is to place an impedance matching circuit between the load impedance and the transmission line. The basic tool for designing impedance matching circuits is the Smith chart. Learning to think with the help of Smith chart improves intuition of the transmission lines theory and impedance matching problems. In this topic, we will first recap the Smith chart and then learn to design matching circuits based on 1) quarter-wave transformer, 2) lumped elements (L section) and 3) single-stub. A glance to impedance bandwidth issues and multi-resonant matching techniques will be taken.

The dedicated intended learning outcomes of Topic 2 are:

• The student can design impedance matching circuits using the Smith chart and a simulator tool (AWRDE).
• The student is able to explain the design principles and bandwidth issues related to impedance matching.

In this topic one should command the following subjects of the course book:

• The terminated mismatched load impedance (Chapter 2.3)
• The Smith chart (Chapter 2.4)
• The quarter-wave transformer (Chapter 2.5 and Chapter 5.4)
• Matching with lumped elements (Chapter 5.1)
• Single-stub tuning (Chapter 5.2)
• The Bode-Fano criterion (Chapter 5.9)

You will need the AWRDE simulation softwave in this topic. You can access the software through remote connection to Maarintie 8 computers via https://vdi.aalto.fi.

• ### Example videos

• Example: Match the load impedance ZL=20+j 40 Ω with a lumped-element circuit to Z0=50 Ω at 1.5 GHz frequency.

In addition to the courcebook chapter 5.1, this example may be helpful when solving Problem 1 of Topic 2.

Duration is 17 minutes.

• In this video, the basic use (i.e., from scratch) of AWRDE is shown. The example is related to an earlier video on lumped-element matching circuits design).

You can access the software through a remote connection to Maarintie 8 computers via https://vdi.aalto.fi.

• In this video, microstrip line based matching circuit design is shown.

Unfortunately, the "TX Line..." calculator window is not visible on the screen.
• ### Exercise problems

• Read this file carefully before completing the exercise problems