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Integrate esign termination

- Hey, everybody. Thanks for tuning in. I'm Zach Peterson, I'm a technical consultant with Altium, and today we're gonna continue talking about a topic that we started on a little bit ago, and we're gonna wrap it up today. And this topic is input impedance, and specifically how it relates to termination in transmission lines into the circuits. So, this was inspired by a viewer question that was sent into our Q and A, and I wanted to look at this one specifically because it is an interesting question and it is something that comes up when you're working in RFPCDs. So let's go ahead and dig into it and get started. (upbeat music) Okay, so before we get started, I wanna look at a question that was sent in by one of our viewers, Mohammed Ahmad. "Hi, Sir, your video tutorials are really nice and helpful. Please answer the following questions." And he goes into a question about microstrip transmission lines and using a PI matching filter along the line. Now, this is typical in RF interconnects, and specifically what he's doing here in this image is he has what looks like a feed line for a Bluetooth antenna. And this BLE line is being matched with a... looks like a PI filter going along this loop here, and then we've got a capacitor here, looks like for AC coupling going into the antenna feed line. So this is all in the coplanar arrangement. The question says, "Normally the footprints of the lump components such as capacitors, inductors, or resistors, are more thicker than the trace width. For example, in the below circuit." And here he's saying he has to control the impedance of this particular coplanar waveguide trace. So, what this question is actually asking is, "How do you maintain control impedance on a transmission line or a coplanar waveguide in this case, when you have to put some components along the transmission line for purposes like impedance matching or filtering?" This is a case where in this particular question, we're looking at a PI matching filter, but you might also come across this in AC coupling caps. So, such as on like a PCIe trace. That's what we're gonna look at today. So to answer this question, we need to look back at the concept of input impedance. The question here is, we have a discontinuity along the transmission line, and we wanna know how does this discontinuity, in this case in the form of some component, affect the input impedance. So, if we go back to the input impedance equation, we have Z in equals a characteristic impedance, and then this multiplied by this big fraction. So here we have the load impedance, again the characteristic impedance. Here we have the hyperbolic tangent function, and inside the hyperbolic tangent function, we have an important quantity. We have our propagation constant and then the length of this section. Here we just kind of swap ZL and...