# Transmission Lines and Impedance Matching: what is considered electrically 'short'?

by satchmo05
Tags: considered, electrically, hort, impedance, lines, matching, transmission
 P: 114 Hey all, Between two devices, I will need to have a coaxial line (with SMA connections on either end) connecting them. The operating frequency of the signal I am propagating is approximately 125 MHz. With this said, the wavelength (assuming ideal) is 2.4 meters. I have heard from numerous sources that if electrically 'long,' it is greater than 0.25λ, which is any length larger than 0.6 meters. Any transmission line length smaller than 0.6 meters is considered "electrically short." My question is in regards to impedance matching: if my transmission line is "electrically short," do I need to worry about impedance matching? Obviously, everything would be happy if I matched at the load, but I'm interested to know if I can skip a step. My thought is that since I'm at such a high frequency, attenuation and loss effects will be near negligible. Thoughts? Thanks for your help! - Satchmo05
 P: 2,380 More info please. If the input and output impedances are the same then the length of the line is not significant. Of course they should match the impedance of the line that connects them unless the line is considerably shorter than a wavelength. Like 0.1λ. - Why do you equate high frequency to negligible attenuation?
 P: 114 I guess what I should've asked is when do I not have to worry about impedance matching, in terms of transmission line length? When less than 0.25 lambda? When electrically small (< 0.1 lambda)? My reasoning there was more of a length issue: attenuation constants, line capacitance, line impedance, etc. are all measured in meters. If my coax line is less than 0.1 lambda < 0.24 m, then minimal attenuation can be expected.
P: 3,797

## Transmission Lines and Impedance Matching: what is considered electrically 'short'?

 Quote by satchmo05 Hey all, Between two devices, I will need to have a coaxial line (with SMA connections on either end) connecting them. The operating frequency of the signal I am propagating is approximately 125 MHz. With this said, the wavelength (assuming ideal) is 2.4 meters. First, assume the $\epsilon_r=4\;$ velocity is about half of speed of light which is 1.5EE8 m/s. At 125MHz, λ= 1.2m, what you have is free air velocity. I have heard from numerous sources that if electrically 'long,' it is greater than 0.25λ, which is any length larger than 0.6 meters. Any transmission line length smaller than 0.6 meters is considered "electrically short." The is not correct at all. A short to the source is only refer to an open end coax 0.25λ long from the source. Any length longer or shorter will not be a short anymore. My question is in regards to impedance matching: if my transmission line is "electrically short," do I need to worry about impedance matching? Obviously, everything would be happy if I matched at the load, but I'm interested to know if I can skip a step. My thought is that since I'm at such a high frequency, attenuation and loss effects will be near negligible. Thoughts? Thanks for your help! - Satchmo05
Transmission line matching has to is a lot more complicated. The easiest way is to plot the source and load impedance onto the Smith Chart, then you need to design a network using either tx line or other elements to connect the two points, then you match the circuit. If you need the transmission line in between, then you plot the two points, then draw the circle from the load with center at the center of the graph. Find the length and add element to move to the source point. It is a lot more complicated. Very few cases you can just use a section of coax and get perfect match.
 P: 1,762 You also need to remember that the wavelength in free space is not the same as the wavelength in coax. You need to look up the propagation velocity for the coax you're using and divide your wavelength by that percentage. You do have to worry about impedance matching even with short transmission lines. RF engineers match impedances between stages even though the electrical length is essentially zero. When the impedances are not matched, some of the energy is reflected from the load reducing the power out. Also that reflected energy can cause the final stage to heat up and even go into oscillation. A quarter wavelength transmission line can be your worst case. If you have a quarter wavelength attached to your source and forget to connect a load, the open at the end of the transmission line will appear to be a short at the last stage and may destroy the transistor. If you can give us the complex impedances of your source and load, we can help you match them.

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