- #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
- Context: Graduate
- Thread starter DRossman2
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SUMMARY
The resonant frequencies of coaxial cylinders can be determined using specific formulas that account for the dimensions and configuration of the cylinders. The impedance of the coaxial tube assembly is calculated using the formula Z = [377/(2 pi)] Ln(b/a), where 'b' is the radius of the larger cylinder. The lowest resonant frequency is identified as the 1/4 wave frequency, calculated as c/4h, where 'c' is the speed of light and 'h' is the height of the cylinder. Understanding the impedance matching between the coaxial tube and the connecting cable is crucial for accurate resonance analysis.
PREREQUISITES- Understanding of coaxial cable impedance, specifically 50 ohms and 75 ohms.
- Knowledge of wave propagation in cylindrical structures.
- Familiarity with the concept of resonant frequencies and wavelength calculations.
- Basic principles of transmission lines and impedance transformation.
- Research the calculation of resonant frequencies in coaxial structures.
- Learn about impedance matching techniques in RF applications.
- Study the effects of open and shorted ends on resonant frequencies in transmission lines.
- Explore the use of quarter wave transformers in RF design.
Engineers, physicists, and students involved in RF design, acoustics, or any field requiring an understanding of resonant frequencies in coaxial systems.
- #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
- 8
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
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