Skettering parameters, or S-parameters for short, can be used to describe the electrical behavior of devices or networks. They are often measured with a device called vector network analyzer or VNA, and are often used in electronics or microwave engineering. In this video, we want to give you a short introduction about what are these parameters and how we can extract them from an electronics circuit. In electrical engineering, we often think of components or circuits as so-called two-board devices or two-board networks. This means that two pairs of connections are combined into one port. S-parameters are used to describe the input output relationship of these ports. These relationships are represented by forwarded and reflected power waves and not in discrete voltages and currents. But why is that the case? To describe this, let's take a simple example. A voltage source is connected to one side of a wire, and the resistor is connected to the other side. Let's assume the wire has a length of 1 meter, and the voltage source gives an AC voltage with a frequency of 200 Mhz. If we would be able to measure the voltage at any point at the cable, we would see that it shows a sinusoidal distribution over it. One meter and 200 Mhz are, of course, not randomly chosen. At this frequency, the wavelength in a cable is exactly 1 meter. So, exactly one period of the voltage signal fits into the cable. So we can no longer assume that the wire has the same voltage and current at all points. This means that the voltages and currents in the high frequency domain behave more like waves running back and forth. These waves can now be reflected at points where impedance changes happen. So, we will get superposition of waves running back and forth. The ratio of these waves at the ports results in our scattering parameters or S parameters. The term scattering refers exactly to the fact that these waves are scattered when an impedance change happens, just like light gets scattered in optical systems. As already mentioned, we can now relate these wave quantities to each other. For a two-part device, we have four possibilities for this. Let us focus on one port. We have a wave that runs into this port, which is called forwarded wave. A part of this wave will now be reflected in the device and the test and runs back. This wave is called reflected wave. We can now relate the forwarded wave to the reflected wave. This gives us one of our S parameters. If this port is called port 1, the obtained S parameter is called S11 or reflection coefficient. A part of the wave will travel through the device and exit port 2. We can relate this wave with the forwarded wave of port 1 and get another S parameter. It is called S21 or transmission coefficient. We have now two of our four S parameters for this device. The other two are rather simple. We just switch port 1 and port 2 and we'll get our remaining S parameters S22 and S12. If we have a device with more than two ports, the measurement is more or less the same. The only difference is how we handle the unused ports. They have to be terminated with the system's impedance, which is 50 ohm in the most cases. In this picture, we can see an example of a three port device and how the measurement of S31 would look like. We do now know what S parameters are but how do we measure them? Measure the forwarded and reflected waves with an oscilloscope sounds like a very hard and time-consuming task. But luckily, there is a device which do this work for us. It is called vector network analyzer or VNA for short. Depending on the number of ports, they can measure all necessary S parameters at once. I will not go into detail about how VNAs work in this video. The work on basis of the Superheterodine principle, which is also used in radio receivers, spectrum analyzers and EMI receivers. Our colleague Co has made a few videos about this principle so we're free to watch them if you're interested in it. I would like to highlight only one possible measurement method for VNAs in this video. They are often used to measure impedances of components. If you have a two port device like a capacitor or an inductor, there are two possibilities to connect them between the ports of a VNA. The two circuits are called serial through connection and shunt through connection. With both methods, we will get a set of S parameters. Passive devices are normally symmetric, which means that S11 and S22 as well as S21 and S12 are the same. So it makes no difference in which direction you measure the component. From these S parameters, we are now able to calculate the impedance of the device. We focus on the transmission coefficient or S21. As you can see, we can easily obtain the impedance with these simple equations. The system impedance is again 50 ohm. But which method do you use now for which components? The serial through method is more suitable for large impedances, so you would use it for components like inductors. The shunt through method works better for smaller impedances like capacitors. The reason for that, we will discuss in another video. This video should briefly show what scattering parameters are and make it understandable how to extract them from different components. We have also shown one possible application for these parameters. Keep in mind that there are much more use cases for them. I'm Kristoff with the Institute of Electronics and the Institute of Microwave and Photonic Engineering. We hope you've learned something today, but anyway, thanks for watching.