![reflection coefficient smith chart reflection coefficient smith chart](https://slidetodoc.com/presentation_image_h/02df5a0ca1af11536d72762dec0b1f71/image-5.jpg)
This is what the return loss would look like on a polar plot. If there is a little loss in the line, which increases as we increase frequency, the S11 will appear to spiral into the center as it rotates around in the clockwise direction. On a polar plot, S11 should start on the far-right edge of the circle, where the magnitude is 1 and the angle with the real axis is close to 0 degrees.Īs we increase frequency, the phase increases in a negative direction and S11 moves along the unit circle in the clockwise direction. This means the phase of S11 will be negative and it get larger, and more negative as we increase frequency.Īt the lowest frequency, the phase difference going in and coming out will be very small. The phase going in, now, has advanced ahead in the time it took the sine wave to travel through the transmission line. The phase coming out now is not the same was the phase going in, now.
![reflection coefficient smith chart reflection coefficient smith chart](https://media.cheggcdn.com/media/8a5/8a5e8361-5d16-47d0-a0ab-49de188ba63f/phpkIFZcR.png)
The signal travels to the end of the line, sees the open, reflects, with no phase shift, and makes its way back out of the line into the port. We send a signal into the front of the line. Since the line is lossless, whatever we send in, should come back out, so the magnitude of S11 should always be 1.
![reflection coefficient smith chart reflection coefficient smith chart](https://i.ytimg.com/vi/-elW1W0cr0k/maxresdefault.jpg)
Let’s take as an initial example, the return loss from a uniform, lossless, 50 Ohm transmission line, open at the far end. When we take the ratio of the sine wave reflected to the sine wave incident, we end up with two numbers, the ratio of the amplitudes of the two waves and the difference between the reflected wave’s phase minus the incident wave’s phase: Since we are describing sine waves of signals entering and leaving a DUT, we have to keep track of the frequency, the amplitude and the phase of each wave. This means there is valuable information about the impedance structure of a DUT buried in S11. The ONLY thing that can cause a reflection is an impedance change. The ONLY way a signal going into port 1 can come back out port 1 is due to a reflection, somewhere in the DUT. We call this the reflection coefficient and also, for historical reasons, the return loss. It is the ratio of the reflected wave to the incident wave. When there is only one port, the only S-parameter term is S11. We label each specific S-parameter term based on the port number of the going in port and the coming out port. Regardless, their properties and the information we extract from them, are the same. S-parameters can come from measurements or simulations. Establishing the incident signal, which is the same as Vref, and the reflected signal from a DUT. Figure 1 illustrates this idea of an incident and reflected sine wave signal from a DUT.įigure 1. The DUT can be anything, even a discrete component like a resistor or capacitor, or an extended structure like a transmission line, traces on a board or an entire channel. For now, we will consider only one port connected to the interconnect, or device under test (DUT). Let’s Start with ReflectionsĮach S-parameter is really the ratio of the sine wave voltage signal coming out of the end of an interconnect, relative to the sine wave voltage signal going in. But there are some valuable insights a Smith Chart can illuminate. It’s an important tool for RF applications.
![reflection coefficient smith chart reflection coefficient smith chart](https://i.pinimg.com/736x/67/44/16/674416402e1458f5d644b09a51d42722.jpg)
Upon clicking, a point is "selected" and r and z will be populated with their correct values (and a change event is fired).Ĭlicking the element again un-selects/unlocks the point.Every RF engineer learns about the Smith Chart their first day studying S-parameters. R and z will both be null when the element is "unlocked", meaning the cursor will follow the mouse around the element. In the example above, the smith-chart element's z value will be, corresponding to the r-value of. R and z are automatically kept in sync (i.e., each is the correct value corresponding to the other on the Smith chart), and either can be set to change the selected point on the chart.