I’m considering designing a transmission line. Everything I read says that the length of the line is to be ¼ the length of the “target” frequency. The internet says that this will create a 90˚ phase shift which will cancel out waves coming from the back of the driver.
This makes no sense to me. I reason that, if the transmission line has an open end, nothing is going to bounce back to cancel out any waves coming from the back of the driver. Furthermore, if the waves coming out of the open end of the transmission line are shifted 90˚ relative to the waves coming from the front of the driver, this would only boost the target frequency by 1.41X. It would seem the sensible thing to do for an open-ended transmission line would be to make the line ½ of the target wavelength. That way the wave would come out of the port in phase with the wave coming off the front of the driver.
The PDF and the graph I made uses an example of a driver vibrating at 60Hz with a 1.43m (1/4 wavelength), open-ended TL.
It does make sense to me that a closed-ended TL would be ¼ the wavelength of the target frequency. The wave from the back of the driver would travel down the line and bounce back, traveling ½ of its wavelength. It would hit the back of the driver in phase with the wave coming out of the front of the driver – doubling its amplitude.
Yet everything I read on the internet says to make an open-ended TL ¼ the wavelength of the target frequency.
Can anyone figure out what I’m missing here?
This makes no sense to me. I reason that, if the transmission line has an open end, nothing is going to bounce back to cancel out any waves coming from the back of the driver. Furthermore, if the waves coming out of the open end of the transmission line are shifted 90˚ relative to the waves coming from the front of the driver, this would only boost the target frequency by 1.41X. It would seem the sensible thing to do for an open-ended transmission line would be to make the line ½ of the target wavelength. That way the wave would come out of the port in phase with the wave coming off the front of the driver.
The PDF and the graph I made uses an example of a driver vibrating at 60Hz with a 1.43m (1/4 wavelength), open-ended TL.
It does make sense to me that a closed-ended TL would be ¼ the wavelength of the target frequency. The wave from the back of the driver would travel down the line and bounce back, traveling ½ of its wavelength. It would hit the back of the driver in phase with the wave coming out of the front of the driver – doubling its amplitude.
Yet everything I read on the internet says to make an open-ended TL ¼ the wavelength of the target frequency.
Can anyone figure out what I’m missing here?
Both but 1/4 wave being more common for low frequency.
Its a port that is really long to make it simple.
60 to 80 Hz pretty high for any port So 60 Hz starts getting close to when 1/2 wavelength tends to be used.
Actual useful woofer around 20 to 40 Hz 1/4 wave rule of thumb for low frequency.
Would be in HornResp regardless so you can see resonance and deal with more realistic correction factors/offset absorption etc etc
Plenty of tutorials now on Youtube but when limited examples around Audio Judgement gave a reasonable explanation to start
Its a port that is really long to make it simple.
60 to 80 Hz pretty high for any port So 60 Hz starts getting close to when 1/2 wavelength tends to be used.
Actual useful woofer around 20 to 40 Hz 1/4 wave rule of thumb for low frequency.
Would be in HornResp regardless so you can see resonance and deal with more realistic correction factors/offset absorption etc etc
Plenty of tutorials now on Youtube but when limited examples around Audio Judgement gave a reasonable explanation to start
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Your vector math is fine, but delay/phase only plays a bit-part in quarterwave resonance speakers. I'll try to draw a picture -- wavelengths 1.2 - 6X line-length will add constructive interference; 1.33 and 4X by 90° 3dB (as you show); and 2X in-phase 6dB. (Same mathematical considerations are quite important for open-baffle wall-bounce and OB-U open-box wrap-around sound.)
TL/QW is discussed all over diyaudio and (it seems) all the time. The key paper is MJK:
http://quarter-wave.com/TLs/TL_Anatomy.pdf
My 2-cents on tapered TL:
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The main idea of a TL is that a sudden impedance shift occurs when the wave exits the end of the pipe, and a reverse wave gets reflected back to the driver.
When that reflected backwave reaches the driver, it is now 180 degrees out of phase with the driver (2 way trip, each direction taking up 90 degrees of the wave) and this counteractive force greatly reduces driver excursion at Fb.
Analogy: Picture a ball hanging at the end of a spring, and you are holding the top end of the spring and moving your hand up and down.
At the exact frequency of resonance, your ball is always moving the opposite direction of your hand. The end of the spring pulls very hard on your hand, so it takes very little motion to keep the ball moving. The ball’s amplitude is much larger than the amplitude of your hand.
At this frequency, the line exit is producing almost all of the output, and the driver’s excursion is minimized.
That is why a TL can produce a lot more output at Fb than a sealed box.
In the above model, the Red curve is the driver output, the brown curve is the port output, and the black curve is the total output.
The TL’s behavior is almost identical to a bass reflex at its own Fb tuning frequency. It’s just that you’re using a pipe instead of a Helmholtz resonator.
And the transmission line has additional resonances at 3X, 5X, 7X Fb and so on for all odd numbers. In the design pictured above, the driver is placed about 1/3 the way down the line and that cancels the 3X resonance.
The Quarter Wave website discusses all of this in great detail.
When that reflected backwave reaches the driver, it is now 180 degrees out of phase with the driver (2 way trip, each direction taking up 90 degrees of the wave) and this counteractive force greatly reduces driver excursion at Fb.
Analogy: Picture a ball hanging at the end of a spring, and you are holding the top end of the spring and moving your hand up and down.
At the exact frequency of resonance, your ball is always moving the opposite direction of your hand. The end of the spring pulls very hard on your hand, so it takes very little motion to keep the ball moving. The ball’s amplitude is much larger than the amplitude of your hand.
At this frequency, the line exit is producing almost all of the output, and the driver’s excursion is minimized.
That is why a TL can produce a lot more output at Fb than a sealed box.
In the above model, the Red curve is the driver output, the brown curve is the port output, and the black curve is the total output.
The TL’s behavior is almost identical to a bass reflex at its own Fb tuning frequency. It’s just that you’re using a pipe instead of a Helmholtz resonator.
And the transmission line has additional resonances at 3X, 5X, 7X Fb and so on for all odd numbers. In the design pictured above, the driver is placed about 1/3 the way down the line and that cancels the 3X resonance.
The Quarter Wave website discusses all of this in great detail.
Could you give a straight TL example, instead of hyp-exp, thanks. (Impedance please.) I would like to understand the resonance farther away from the tuning point, in relation to force-cancellation by reflection. Specifically, said "return force" at wavelength = 1.5X 1X 0.75X 0.67X effective quarterwave line-length*4 (eyeball approx. 22hz 33hz 44hz 50hz), phase offset 120° 180° 240° 270° from backwave, respectively.
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An open end of a transmission line is a sudden drop of impedance, which creates an inverted reflection. A closed end is a sudden rise of impedance which creates a positive reflection.
Beyond that, at resonance the closed end impedance better matches the mechanical impedance (~compression) of a speaker cone, that is much smaller than the wave, similar to what happen in compression horn drivers. So at resonance, the open-end inversion plus 1/4 there and 1/4 back returns the wave in phase (1/4+1/2+1/4=1), and you could say is reflected in phase again to repeat the trip again and again, ie resonance. Note that the kinetic wave is out of phase because it is traveling in the opposite direction, but the pressure/potential wave is in phase.
Radio antennas operate much the same way. They are driven at the current peak and voltage min (low Z) and the tips of the antenna are voltage peaks and current ~zero (high Z).
Beyond that, at resonance the closed end impedance better matches the mechanical impedance (~compression) of a speaker cone, that is much smaller than the wave, similar to what happen in compression horn drivers. So at resonance, the open-end inversion plus 1/4 there and 1/4 back returns the wave in phase (1/4+1/2+1/4=1), and you could say is reflected in phase again to repeat the trip again and again, ie resonance. Note that the kinetic wave is out of phase because it is traveling in the opposite direction, but the pressure/potential wave is in phase.
Radio antennas operate much the same way. They are driven at the current peak and voltage min (low Z) and the tips of the antenna are voltage peaks and current ~zero (high Z).
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I like this explanation. So wavelength = 3X 1.5X 1X 0.75X 0.67X 0.6X quarterwave (11hz 22hz 33hz 44hz 50hz 55hz) after reflection phase-offset with backwave (degrees) 240 300 0 60 90 120 i.e. constructive range. Whereas wavelength = 2X quarterwave (66hz) after reflection 180° antiphase with backwave. By the numbers... though the phase-changed sum vectors spin 'round-and-round.
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Straight-sided version of the same system, adjusted for a 40Hz resonance.
Frequency response of driver and port and total output, with box dimensions on the right:
Impedance:
Displacement of woofer cone:
Velocity of port output. Driver parameters on right side:
Thank you everyone who helped to answer my questions.
I think the root cause of my confusion was my belief that when a wave reached the end of the TL all energy would be released out into the world. I work in the Radio Frequency world and find it easy to understand electrons bouncing back from an open-ended TL, or wrapping around to the ground of a shorted TL. But I never imagined a wave of air molecules packed together causing a vacuum behind them – which travels backwards – when they reach the open end of the TL. I still can’t quite picture it. I wonder if it’s somehow related to Bernoulli’s Principle?
If I just accept that this happens, everything makes more sense. All the vector math and graphs make sense. I appreciate Perrymarshall’s analogy of a bouncing weight on the end of a spring. I intend to look through the Martin J. King paper as I find time.
Thank you everyone!🙏
I think the root cause of my confusion was my belief that when a wave reached the end of the TL all energy would be released out into the world. I work in the Radio Frequency world and find it easy to understand electrons bouncing back from an open-ended TL, or wrapping around to the ground of a shorted TL. But I never imagined a wave of air molecules packed together causing a vacuum behind them – which travels backwards – when they reach the open end of the TL. I still can’t quite picture it. I wonder if it’s somehow related to Bernoulli’s Principle?
If I just accept that this happens, everything makes more sense. All the vector math and graphs make sense. I appreciate Perrymarshall’s analogy of a bouncing weight on the end of a spring. I intend to look through the Martin J. King paper as I find time.
Thank you everyone!🙏
As an RF engineer, you'll likely recognize the concept of a purposeful impedance mismatch, similar to what occurs in an RF antenna cable.
In the case of an acoustic transmission line, the boundary conditions dictate that when the air velocity at the line's exit increases abruptly due to a drop in pressure, conservation of energy must still hold. This results in the generation of a backward-traveling wave that complements the forward-traveling wave. This behavior is analogous to the reflection of electromagnetic waves at an impedance discontinuity in RF systems.
I've always felt that "impedance matching" is a super useful concept in many dimensions of life, not just electricity and sound.
In the case of an acoustic transmission line, the boundary conditions dictate that when the air velocity at the line's exit increases abruptly due to a drop in pressure, conservation of energy must still hold. This results in the generation of a backward-traveling wave that complements the forward-traveling wave. This behavior is analogous to the reflection of electromagnetic waves at an impedance discontinuity in RF systems.
I've always felt that "impedance matching" is a super useful concept in many dimensions of life, not just electricity and sound.
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Just my own very poorly informed opinion, but the use of “transmission line” has probably caused more confusion and “spirited discussion” than clarification.
Martin King’s work dating back almost 20yrs (?) now should be required reading on the general subject of the continuum of quarter wave action - as opposed the assumptions of Helmholtz resonance based designs.
Martin King’s work dating back almost 20yrs (?) now should be required reading on the general subject of the continuum of quarter wave action - as opposed the assumptions of Helmholtz resonance based designs.
I'm a retired enterprise architect and that was my view. At first I wanted to make the impedance go to zero, then I realized their is good reason to have impedance in an organization and it should match. Dysfunctional organizations have mismatching impedance.
Yes ! 😆
Human Impedance ZH = Human Admittance HA / Human Reluctance HR
ZH = HA/HR
Easy...
No ?
Ah. It's a non-linear, Chaos Theory related law... Too bad... 😊😉
T
Yes. It’s all over the place in marketing where the rule is, “Enter the conversation inside the customer’s head.” When you do that, your ads get clicked on and people buy your stuff and share your social media posts. Which is eminently measurable.
“Like” means “impedance matched.”
Help desk forms make the association one of high impedance. Remove the form and the impedance is the same for the help desk and the employee with a computer problem. Then computers get fixed faster.
Check-out lines are high impedance. Any time you have to wait is high impedance. Staff Meetings are a total mismatch of impedance.
Check-out lines are high impedance. Any time you have to wait is high impedance. Staff Meetings are a total mismatch of impedance.
Indeed… more accurately called quarter-wave designs. The term TL has grown to be used as an equivalent term.
dave