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Sizing a speaker cab port


Mottlefeeder
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Following on from my thread about whether WinISD was giving me bad advice, 

I'm now trying to work out whether I need a port sized for full power, or something less that full power.

I downloaded a spectrum analyser and played a low C through it (lowest available fretted note). The analyser shows that the signal at ~30 Hz is about 12 dB below the signal at ~60 Hz, which is the same level as the signal at ~100-120Hz. 

For a port tuned to 60 Hz, my question is, if the voltage applied to the speaker is mainly two frequencies, and one transducer is reproducing those frequencies, the power must be split between those frequencies, so is it reasonable to design the port to take a maximum of half the amplifier power at 60 Hz, on the basis that the rest of the power will be at other frequencies?

David

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You are probably over-thinking this. What your amp will do is actually trace a complex waveform which tracks all the different harmonics added together. It will do this until it runs out of volts or sometimes the power supply in the amp will run out of current. If you are putting music in rather than a test signal then the notes decay over time and there will be gaps between the notes. Your amp will pump out its full power at all frequencies over its pass band if you put the right signal in.

You are back to where you were in the other thread. Your bass pickups aren't in the middle of the strings so won't give you as much fundamental as harmonics, you'll find all your fundamentals are down about 12dB or 1/16th of the power compared to the 2nd harmonic unless you are fretting higher up the neck just as I said last time, your own measurements confirm this. The advice to keep wind speeds below 18m/s are from people designing for hi-fi use It's nice if you can achieve that but sometimes you can't in a practical cab especially if you are trying to build something really compact. In practice this is not going to be a problem.

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2 hours ago, Phil Starr said:

You are probably over-thinking this. What your amp will do is actually trace a complex waveform which tracks all the different harmonics added together. It will do this until it runs out of volts or sometimes the power supply in the amp will run out of current. If you are putting music in rather than a test signal then the notes decay over time and there will be gaps between the notes. Your amp will pump out its full power at all frequencies over its pass band if you put the right signal in.

You are back to where you were in the other thread. Your bass pickups aren't in the middle of the strings so won't give you as much fundamental as harmonics, you'll find all your fundamentals are down about 12dB or 1/16th of the power compared to the 2nd harmonic unless you are fretting higher up the neck just as I said last time, your own measurements confirm this. The advice to keep wind speeds below 18m/s are from people designing for hi-fi use It's nice if you can achieve that but sometimes you can't in a practical cab especially if you are trying to build something really compact. In practice this is not going to be a problem.

Unfortunately it's my nature to analyse things to death, and I still cut wood to the wrong size ...

Taking your second paragraph first, I've taken on board that the harmonic mix will change as I move around the fretboard, but I chose the low C because it is the note most likely to overwhelm a port tuned to its harmonic. 

With regard to what the amp will deliver, I'm assuming that at some point I will turn up the amp and it will start to clip - 5 inch speakers are not as efficient as 10 inch speakers, so this is inevitable. Turning down slightly from that volume, the amp will be delivering its maximum voltage to the speaker, and the signal will initially have the lowest two harmonics predominating as each note decays.

Using that scenario, I'm questioning whether I can derate the power handling of the port, but you appear to be saying that a port overload for the initial fraction of the note can be ignored.  So, if the aim is to avoid chuffing, is chuffing a continuous overload of the port, or just overloading during the initial transient?

David

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Not quite, the point is actually really simple physics. The fundamental is the note produced when the string is vibrating as a whole. It's fixed at the bridge and nut (nodes) and the middle of the string is the bit that is moving furthest (antinode). The antinode for the fundamental on an open string is at the 12th fret and that is the only spot where you'll get full output of fundamental. The closer to the bridge you place the pickups the less fundamental you'll get.  The note is irrelevant if your bass is 34" scale the fundamental dominates only 17" into the string at fret 12. if your PUP is at 4" from the bridge it isn't going to get much fundamental.

https://www.physicsclassroom.com/class/waves/Lesson-4/Nodes-and-Anti-nodes

You've found that on your bass it is 12dB down and this is typical, in fact what I predicted. That means at the point where your amp is turned up loud not much of the power is going to be in the lowest frequencies which will cause over excursion. If you are running at 100W into the speakers it's unlikely that 10 of those watts are going to be fundamental unless you are using a lot of bass boost. If you are my feeling is that the speakers are going to be overwhelmed before you get a noticeable level of chuffing from the ports.

You've run WinISD, the plots you need to consider are the excursion plots and the maximum power plots which tell you whether the speakers are coping or not. That is a concern, but with little drivers like yours I wouldn't worry about chuffing. Experienced builders are telling you a single 68mm bit of pipe (outside diameter of course) is going to be enough and that is good advice IMO. I've got 12" drivers here with a pair of ports this size running at 300W at gigs and I've never noticed problems with port noises at gigs. i'm probably getting some problems with compression due to port resistance but again in practice I haven't noticed.

Speaker design is like squeezing a balloon, you squeeze one problem and another pops up. You can't really achieve perfection don't let that be the enemy of building something good.

Edited by Phil Starr
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1 hour ago, Phil Starr said:

Not quite, the point is actually really simple physics. The fundamental is the note produced when the string is vibrating as a whole. It's fixed at the bridge and nut (nodes) and the middle of the string is the bit that is moving furthest (antinode). The antinode for the fundamental on an open string is at the 12th fret and that is the only spot where you'll get full output of fundamental. The closer to the bridge you place the pickups the less fundamental you'll get.  The note is irrelevant if your bass is 34" scale the fundamental dominates only 17" into the string at fret 12. if your PUP is at 4" from the bridge it isn't going to get much fundamental.

https://www.physicsclassroom.com/class/waves/Lesson-4/Nodes-and-Anti-nodes

You've found that on your bass it is 12dB down and this is typical, in fact what I predicted. That means at the point where your amp is turned up loud not much of the power is going to be in the lowest frequencies which will cause over excursion. If you are running at 100W into the speakers it's unlikely that 10 of those watts are going to be fundamental unless you are using a lot of bass boost. If you are my feeling is that the speakers are going to be overwhelmed before you get a noticeable level of chuffing from the ports.

You've run WinISD, the plots you need to consider are the excursion plots and the maximum power plots which tell you whether the speakers are coping or not. That is a concern, but with little drivers like yours I wouldn't worry about chuffing. Experienced builders are telling you a single 68mm bit of pipe (outside diameter of course) is going to be enough and that is good advice IMO. I've got 12" drivers here with a pair of ports this size running at 300W at gigs and I've never noticed problems with port noises at gigs. i'm probably getting some problems with compression due to port resistance but again in practice I haven't noticed.

Speaker design is like squeezing a balloon, you squeeze one problem and another pops up. You can't really achieve perfection don't let that be the enemy of building something good.

I get the impression that we are running on similar but slightly different lines of thought, so I'm not getting the answers I was hoping for. Having said that, I'm grateful for the explanations you have provided. They have filled in a lot of gaps for me.

With my bass, the fundamental is 12 dB down, and since there will also be a 60 Hz 18 dB/octave HPF in the pre-amp, I agree that the fundamental is not an issue in my design.

The speakers are rated at 80 watts each, and in a cab of the appropriate volume (11.4 l), are capable of taking 100 W at any frequency above 57 Hz.

The excursion plots show that with the HPF in circuit, the speakers are below Xmax at all frequencies at 100 W.

The proposed cab is tuned to 64 Hz, which seems to give the best compromise of size, smooth roll-of and bass extension, but a port capable of handling 100 W at 64 Hz makes the cab bigger than I want, so reducing the port power-handling capacity is a compromise I'm investigating.

As I posted earlier, the spectral analysis of my lowest bass notes shows equal volumes at 60 Hz and 120 Hz, so I was hoping someone could comment on whether it was reasonable to assume that a low 100 W note could be regarded as for example 45 W at 60 Hz, 45 W at 120 Hz, and 10 W for everything else. That would give me the 'science' I need to reduce the size of the port and still be confident that it would do what I wanted. Am I oversimplifying a complex problem?

Also, I was under the impression that if I reduced the port power handling capacity too much I would get chuffing, but you suggest that compression would be the more likely outcome. What does port compression do to the response of the cab?

David

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winISD calculates the tuning based upon speaker volume being linked to drive-unit parameters. It's giving an optimum result at one signal level only. As the amp signal/voltage increases, the speaker is pushed harder and increases the air pressure inside the cabinet. The tuning will stay the same, but the air pressure within the port  rises and rises.

 Do you still only need to run the speakers at half your amplifiers rated output (150w)?  I've run a variety of models with different amplifier inputs & enclosure volumes using your earlier rough guide to the speaker, and I 've found that with an 11.4L enclosure and a 75w signal from the amplifier, the 30Hz speaker output is at least -30dB below the output at 60Hz. With filters switched in, the difference is even larger; so large, it goes off the bottom of the scale.

With a rectangular vent of 3.8 x 10cm (internal) and tuning set to 64Hz, the calculated port length is 19.26cm. Is this port length impracticable?

 The peak air velocity through the port is only 15.7 @ 63Hz. At the same frequency and with the 60Hz filter switched in, output from the speaker is down -4.6dB. Chuffing is not going to be an issue.

With a 75w input the speaker is calculated to deliver 108dB from 80Hz & upwards, and with the 60Hz filter in the chain, xmax is not exceeded, even down to Zero Hz.

 

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24 minutes ago, Balcro said:

... Do you still only need to run the speakers at half your amplifiers rated output (150w)?  I've run a variety of models with different amplifier inputs & enclosure volumes using your earlier rough guide to the speaker, and I 've found that with an 11.4L enclosure and a 75w signal from the amplifier, the 30Hz speaker output is at least -30dB below the output at 60Hz. With filters switched in, the difference is even larger; so large, it goes off the bottom of the scale.

With a rectangular vent of 3.8 x 10cm (internal) and tuning set to 64Hz, the calculated port length is 19.26cm. Is this port length impracticable?

 The peak air velocity through the port is only 15.7 @ 63Hz. At the same frequency and with the 60Hz filter switched in, output from the speaker is down -4.6dB. Chuffing is not going to be an issue.

With a 75w input the speaker is calculated to deliver 108dB from 80Hz & upwards, and with the 60Hz filter in the chain, xmax is not exceeded, even down to Zero Hz.

 

My earlier thoughts were to use the two 4 ohm speakers, each fed from a 20 W amplifier, with the option to connect them in series to connect to a 75 W @ 8 ohm / 150 W @ 4 ohm amplifier when I needed more volume. I've since found a 50+50 W @ 4 ohms module so I'm going up from 75 W total input to 100 W total input.

We all seem to agree that the 30-60 Hz octave is unlikely to be a problem, so  I am interested in your thoughts on porting at 64 Hz - do I need to allow for 100W at that frequency, and if not, how do you decide how many watts to design for?

With my current layout of components, I can accommodate a 200mm long port.

David

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I'm not an expert on the maths around fluid dynamics. the only time I studied it was back in the 60's so this is really broad brush. The thing that causes compression and the wind noise is turbulence in the port at high velocities. Turbulence will add in an additional resistive element to the port reducing the radiation of the cab around the tuning frequency. The port only really radiates sound at the tuning frequency so isn't going to affect the frequency response apart from around the tuning range.

I don't think anyone can reliably answer the question about 'allowing' for 100W. Without knowing exactly how you play and what eq you will use in the future it's almost impossible to say what level of discount you could reasonably apply and how frequently and by how much you'd exceed 15m/sec in the port. Remember too that these guideline port velocities are just that, guidelines. The people that developed the theories behind all this differ in what sort of port speed is acceptable and I've seen figures between 14 and 20 given as ideal.

To give you a wattage figure we'd need some basis in theory to make a calculation and we don't have that. If you look at the port velocity at 50W you are looking at 3dB down, if it is 6dB down it is 25W.

Port dimensions around the sizes you are thinking of seem fine to me and so does a 64 hz tuning. 

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If you calculate upon a 100W input, nothing changes except the pressure within the port as I said previously. Remember Phil's comment about squeezing a balloon.

The up-side:-  if you change the smaller vent dimension to 3.8cm you are given a port length of 19.26cm i.e 19.3cm. You will need an air gap beyond the end of the port. If it's possible, make it equal to at least 3.8cm.

The down-side:-  the air velocity calculation shows a rise to 18m/s at 63Hz. Balloon squeezed, but still within recommended bounds.

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5 hours ago, Phil Starr said:

I'm not an expert on the maths around fluid dynamics. the only time I studied it was back in the 60's so this is really broad brush. The thing that causes compression and the wind noise is turbulence in the port at high velocities. Turbulence will add in an additional resistive element to the port reducing the radiation of the cab around the tuning frequency. The port only really radiates sound at the tuning frequency so isn't going to affect the frequency response apart from around the tuning range.

I don't think anyone can reliably answer the question about 'allowing' for 100W. Without knowing exactly how you play and what eq you will use in the future it's almost impossible to say what level of discount you could reasonably apply and how frequently and by how much you'd exceed 15m/sec in the port. Remember too that these guideline port velocities are just that, guidelines. The people that developed the theories behind all this differ in what sort of port speed is acceptable and I've seen figures between 14 and 20 given as ideal.

To give you a wattage figure we'd need some basis in theory to make a calculation and we don't have that. If you look at the port velocity at 50W you are looking at 3dB down, if it is 6dB down it is 25W.

Port dimensions around the sizes you are thinking of seem fine to me and so does a 64 hz tuning. 

 

4 hours ago, Balcro said:

If you calculate upon a 100W input, nothing changes except the pressure within the port as I said previously. Remember Phil's comment about squeezing a balloon.

The up-side:-  if you change the smaller vent dimension to 3.8cm you are given a port length of 19.26cm i.e 19.3cm. You will need an air gap beyond the end of the port. If it's possible, make it equal to at least 3.8cm.

The down-side:-  the air velocity calculation shows a rise to 18m/s at 63Hz. Balloon squeezed, but still within recommended bounds.

Thank you both, and contributors to the previous thread.

In summary, I have a viable design based on the maths and the experience of others and no defined route, other than trial and error, to making the cab smaller by using a smaller volume port. I only want to build this once, so that sounds like a good place to stop.

David

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13 hours ago, Mottlefeeder said:

 

Thank you both, and contributors to the previous thread.

In summary, I have a viable design based on the maths and the experience of others and no defined route, other than trial and error, to making the cab smaller by using a smaller volume port. I only want to build this once, so that sounds like a good place to stop.

David

Hope it works out well for you, let us know how you get on. Good luck.

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