The scariest thing you learn in Electrical Engineering | The Smith Chart

This video is sponsored by brilliant. I present to you Smith's graph. Oh, it's scary, but it's actually not that bad. So what is this? Why do we use it? Here's the story when it comes to low frequency signals in a cable like 50 or 60 hertz signals. come from our wall sockets or even audio signals that reach up to 20 kilohertz, which is the maximum frequency that humans can hear, the associated wavelengths are very long if a signal travels at the speed of light through a cable, even at 20 kilohertz, the wavelength comes out 15,000 meters and is probably much longer than the cable it goes through, but increase that frequency to 100 million Hertz, the frequency of radio waves, and you get three meters and this is much more comparable, maybe even shorter than the cable it will go through.

You will be traveling and when that happens you will get reflections inside the wire, like if I take a string and pluck it very slowly, the string moves in a very predictable way because the actual wavelength is much longer than the string itself, but the pulse that string is faster where the wavelength is comparable or shorter than the string and then you will get reflections and

thing

s will get more complicated, so in the world of circuits you might have some high frequency input, such time for radio, television, satellite communications, etc. through some

thing

called a transmission line, just a specialized cable that is often used for these high frequency signals until that signal reaches a certain load, maybe an antenna will be transmitted now the transmission line will have some impedance associated with it.

What is often used is 50 ohms. So it's really just a resistor and this is a fundamental property of the cable determined by the material properties and the physical dimensions and then the antenna will also have an associated impedance, probably both a real and imaginary component, which means it has something of resistance and some capacitance or inductance. capacitance and inductance are represented by an imaginary number and EES uses j instead of I because I is used for current, so what we have here is like a rope tied to a larger rope, both free to quote, move or change the voltage and current, but they have different properties, so what would happen if we pulse?

We send a wave down the first string and it continues until it reaches that junction. So at that point, some of the wave energy will be reflected back while some will be transmitted to In the antenna, you can see that visually here we have a smaller string attached to a larger string. A transmission line attached to the antenna sends a wave downward once it reaches the junction at the center arm. Some of the energy passes through while some is reflected. We generally don't like them. Thoughts: We want as much signal power as possible to reach the antenna so it can be transmitted and that's where the Smith

chart

comes in, telling us the parameters we need to know, such as how much voltage is reflected versus how much is reflected. transmit. here is a quick example with the numbers shown here.

The first thing to keep in mind is that as chaotic as it may seem, you're actually just looking at a bunch of circles. You have these that are completely inside the Smith

chart

and that have to do with the resistance that we have. I'll see in a second that these curves are also just circles, the part of them inside the Smith diagram and they have to do with reactants, the capacitive or inductive part of the charge represented by an imaginary value anyway, the first step with the Smith diagram is to take the load impedance and divide it by the transmission line impedance, then you take the real part of that and find that the value on the horizontal axis is hard to read, but 0.5 is fair here, in this circle that we are going to highlight again.

These circles are all of constant normalized resistance and all correspond to the real component; then for the imaginary part you will find that value here along the perimeter of the Smith graph, in our case a positive one can be found right here, the top part are all positive values, also known as inductive, if the value was negative, then we find that in the bottom half of the Smith chart we will highlight that associated circle of constant reactants again, those are always for the imaginary component, so the point of intersection of those two circles will tell us shows us how much of our wave will be reflected from the antenna and that is found by observing the distance that point is from the center of the Smith chart, taking the outer circle as the distance of the unit circle of one away, so in this case and you For You will usually have a small scale below your Smith chart, the distance of which is about 0.62, which means that the ratio between the voltage of the reflected wave and the voltage of the incoming or incident wave is 0.62, so so if the incoming wave had an amplitude of 10, the reflected wave will have an amplitude of 6.2, so the lower that ratio is or the closer this intersection is to the center, the better it means that less wave will be reflected and more will go to the antenna, so if now the antenna impedance was something like 45 plus J10 then, normalizing that and finding the associated circles, we would find an intersection point much closer to the origin, which means less reflection and that is due because our load impedance now more closely matches our 50 ohm transmission line, the actual parts being 45 versus 50 respectively. pretty close and then the imaginary values ​​are 10 versus 0.

Also closer than before, if the antenna also had an impedance of only 50 ohms, then the intersection would be at the very center of the Smith chart, at a distance of zero from the center means that there would be no reflected wave, which is exactly what we want, this would be like before, where we had ropes of different sizes, we only had one rope tied to an identical rope, now there will be no reflection because well, it's all the same. string, that's why we like matching impedances or strings of the same size because all the energy goes to our load and this is actually the real use of the Smith chart, when we have mismatched impedances that cause reflections, we can add things to the circuit which make the impedances more closely matched, allowing more power to reach what we want, the load and Smith chart is what helps tell us what we should add to minimize reflections, chunk matching is definitely more beyond this video, but that's some of the information on how the Smith works.

The graph works and why it is useful and for engineers looking to further expand their knowledge in all things mathematics, science and

engineering

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