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)
- FileThe Smith chart FilePDF document
- FileThe Smith chart (jpg) FileImage (JPEG)
Interactive lectures take place on Thursday 27 January and 3 February at 9
Preliminary tasks
Example videos
- FileVideo on lumped-element matching circuit design File33.6MB Video file (MP4) Uploaded 20/01/22, 18:54
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.
- FileVideo on AWR and microstrip lines based matching circuit FileVideo file (MP4)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
- FileExercise problems of Topic 2 FilePDF document