- #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
- Start date
Click For Summary
Discussion Overview
The discussion focuses on determining the resonant frequencies of two coaxial cylinders, specifically the cavity between them. Participants explore theoretical aspects and practical considerations related to resonant frequencies in this configuration.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant inquires about a formula for the resonant frequencies of two coaxial cylinders with specified dimensions.
- Another participant suggests that resonant frequency is influenced by the length of the cylinder and describes the relationship for closed and open-ended cylinders.
- A different participant clarifies that their interest lies in the cavity between two coaxial cylinders, indicating they have a formula for a single cylinder but not for the coaxial arrangement.
- A subsequent reply raises questions about the configuration, including the type of connector, the impedance of the connecting cable, and whether one end of the coaxial assembly is open or shorted.
- This reply also provides a formula for the impedance of the coaxial tube assembly and discusses the implications of impedance mismatch and transit time in relation to resonant frequencies.
- Additionally, a participant shares a link to a resource on quarter wave lines, suggesting further reading on the topic.
Areas of Agreement / Disagreement
Participants express differing views on the specifics of the coaxial cylinder configuration and its impact on resonant frequencies. The discussion remains unresolved regarding the exact formula for the coaxial setup.
Contextual Notes
Participants reference assumptions about the configuration of the coaxial cylinders, including the type of connector and the nature of the ends (open or shorted), which may affect the analysis. There is also mention of impedance considerations that could influence the resonant frequency calculations.
- #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
Attachments
Last edited:
Similar threads
- · Replies 12 ·
- · Replies 10 ·
- · Replies 26 ·
Graduate
Question about Helmholtz resonance
- · Replies 14 ·
- · Replies 21 ·
- · Replies 12 ·
- · Replies 4 ·
- · Replies 40 ·
- · Replies 14 ·