- #1
DRossman2
- 2
- 0
Does anyone know of a formula for determining the various resonant frequencies of 2 coaxial cylinders with radius a and b and height h? Thanks.
Resonant Frequencies of Coaxial Cylinders
- Thread starter DRossman2
- Start date
In summary, the conversation discusses determining the resonant frequencies of 2 coaxial cylinders with different radii and heights. It is mentioned that the resonant frequency is determined by the length of the cylinder, with closed end cylinders having a wavelength of four times the length and open end cylinders having a wavelength of double the length. The formula for the resonant frequency of a single cylinder is provided, but there is a question about finding the resonant frequency of the cavity between the two cylinders. Additional information is given regarding the impedance of the connecting cable and the ends of the coaxial tube assembly. A formula for determining the impedance of the coaxial tube is provided, as well as information on the lowest resonant frequency and impedance mismatch. A website
- #2
nooma
- 45
- 0
well the resonant frequency is basically determined by the length of the tube (cyclinder). In closed end cyclinders the resonant frequency has a wave length of four times the length of the cylinder. In order to get it resonating required a wave of enough amplitude (energy) to make it resonate.
Similarly the resonant wave length in an open ended cylinder is double the length of the cyclinder
Similarly the resonant wave length in an open ended cylinder is double the length of the cyclinder
- #3
DRossman2
- 2
- 0
I appreciate that, but my question pertains to two cylinders, on inside the other. I need to find the resonant frequency of the cavity between them. I have the formula for a single cylinder, but can not find one for the coaxial set.
- #4
Bob S
- 4,662
- 7
First, I assume you have a connector on one end. What kind of connector, and what is the impedance of the connecting cable? 50 ohms? 75 ohms
Second, is the other end of the coaxial tube assembly open or shorted?
third, the impedance of the coaxial tube assembly is
Z = [377/(2 pi)] Ln(b/a) where b is the radius of the larger cylinder.
Fourth, the one-way transit time is h/c where c= 3 x 108 meters per sec. h is the full wave wavelength. The full wave frequency is c/h. The lowest resonant frequency is the 1/4 wave frequency, c/4h. If one end is open, the other looks like a short. If one end is shorted, the other end should have an impedance Z2/(short resistance). A quarter wave line is an impedance transformer. If the Z of the coaxial tube is not the same as the impedance of the cable, then you have an impedance mismatch. See attached thumbnail for a 0 to 100 MHz frequency sweep of a 10-ns long coaxial 50 ohm line. The 10-ns line looks open at the 1/4 and 3/4 wavelength frequencies (25 and 75 MHz), and shorted at the 1/2 and 1/1 (50 and 100 MHz) wavelength frequencies
[Edit] Here is a website for quarter wave lines referred by Berkman
http://www.microwaves101.com/encyclopedia/quarterwave.cfm
Second, is the other end of the coaxial tube assembly open or shorted?
third, the impedance of the coaxial tube assembly is
Z = [377/(2 pi)] Ln(b/a) where b is the radius of the larger cylinder.
Fourth, the one-way transit time is h/c where c= 3 x 108 meters per sec. h is the full wave wavelength. The full wave frequency is c/h. The lowest resonant frequency is the 1/4 wave frequency, c/4h. If one end is open, the other looks like a short. If one end is shorted, the other end should have an impedance Z2/(short resistance). A quarter wave line is an impedance transformer. If the Z of the coaxial tube is not the same as the impedance of the cable, then you have an impedance mismatch. See attached thumbnail for a 0 to 100 MHz frequency sweep of a 10-ns long coaxial 50 ohm line. The 10-ns line looks open at the 1/4 and 3/4 wavelength frequencies (25 and 75 MHz), and shorted at the 1/2 and 1/1 (50 and 100 MHz) wavelength frequencies
[Edit] Here is a website for quarter wave lines referred by Berkman
http://www.microwaves101.com/encyclopedia/quarterwave.cfm
Attachments
Last edited:
1. What are resonant frequencies of coaxial cylinders?
The resonant frequencies of coaxial cylinders are the frequencies at which the cylinders vibrate with maximum amplitude when excited by an external force. These frequencies are determined by the physical dimensions and material properties of the cylinders.
2. How do you calculate the resonant frequencies of coaxial cylinders?
The resonant frequencies of coaxial cylinders can be calculated using the formula: fn = (n/2π)√(c/με) where n is the mode number, c is the speed of light, μ is the permeability of the medium between the cylinders, and ε is the permittivity of the medium between the cylinders.
3. What is the significance of resonant frequencies of coaxial cylinders?
The resonant frequencies of coaxial cylinders are important in the design of antennas, transmission lines, and other high frequency devices. These frequencies can also be used to determine the dielectric properties of the medium between the cylinders.
4. How do the dimensions of coaxial cylinders affect the resonant frequencies?
The resonant frequencies of coaxial cylinders are directly proportional to the dimensions of the cylinders. As the dimensions of the cylinders increase, the resonant frequencies also increase. This relationship is described by the equation in question 2.
5. Can the resonant frequencies of coaxial cylinders be adjusted?
Yes, the resonant frequencies of coaxial cylinders can be adjusted by changing the physical dimensions of the cylinders or by changing the dielectric properties of the medium between the cylinders. This can be done by using different materials or by inserting a material with a different dielectric constant between the cylinders.
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