Which means that in the figures that we've shown here, we really have the one to one correlation between the lambda elements LoC and the short circuited, open circuited transmission line. We see that the large omega which is with beta L simplifies to 1. We get the feature that says beta is equal to 2 pi over lambda, with the length lambda over 8. Now in the particular case, and that's what we assumed already in these figures that the length is equal to lambda over 8. And similarly, we have the equivalence of a capacitor with an impedance of 1 divided by J omega C which is an open circuit. With a certain length which is shorter at the end. With j omega L is equivalent to a transmission line. Well, in fact, these equations show that we have an equivalence and the equivalence, the first equivalence is the equivalence of an inductor. Which again already is very familiar to us, because it looks like 1 over j omega C. And then we get this equation where the input impedance can be written in terms of the Z0 divided by J large omega. Now, in a similar way, we can calculate the input impedance of a transmission line, which is open at the end at the termination. And that looks already similar to the impedance of an inductor, so j omega L. So it's jZ0 tan beta l, which can also be written as j large omega times Z0. Which transforms the input impedance of the line section, which is shorter at the end to this equation. Now the short circuits means that the complex impedance at the end of the transmission line is equal to zero. The first special case that we're going to consider as a short circuit and the second one is an open termination. Now let us take a closer look at some specific cases and how we come to Richards transformation. Which in fact is and varying input impedance, since when varying the length L, we can change this impedance. That this input impedance it's given by this equation. When we look into this line section of length L and we try to determine the impedance, the input impedance then, we have shown in one of the previous web lectures. So we have a line with length L which is connected at the end to a loads with an impedance set L. Now, first let us go back to the terminated transmission line which we introduced in one of the previous web lectures already. And we're going to illustrate it using an example. We're going to apply that to shouldn't shun-stub matching, single and double stub matching. Now in particular, we go into discussing this web lecture, Richards transformation. So distributed elements to perform matching. Now in this web lecture, we will show that you can also use transmission line based elements. Now in the previous web lecture, we have used lambda elements, inductors and capacitors, LC components. In this web lecture, we're going to use distributed elements to perform impedance matching. The lecturers all have an academic and industrial background and are embedded in the Center for Wireless Technology Eindhoven (CWT/e) of Eindhoven University of Technology, The Netherlands. After finalizing the course a certificate can be obtained (5 ECTS), which can be used when you start a full MSc program at Eindhoven University of Technology. The course is supported by a book written by the team of lecturers, which will be made available to the students. Throughout the course you will work on the design challenge in which you will design a complete active phased array system, including antennas, beamformers and amplifiers. Next to this, we will provide you hands-on experience in a design-challenge in which you will learn how to design microwave circuits and antennas. The web lectures are supported by many on-line quizzes in which you can practice the background theory. We will provide you with the required theoretical foundation as well as hands-on experience using state-of-the-art design tools. Future applications, like millimeter-wave 5G/beyond-5G wireless communications or automotive radar, require experts that can co-design highly integrated antenna systems that include both antennas and microwave electronics. The course combines both passive and active microwave circuits as well as antenna systems. This unique Master-level course provides you with in-depth know-how of microwave engineering and antennas.
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