Yes only the one between the peaks as you point out. It might not be the minimum impedance across the band, but it will be quite low and always between two peaks.
Assuming of course that you are on about a traditional single vented box, not a double chamber reflex or any other derivative, or bandpass box.
Assuming of course that you are on about a traditional single vented box, not a double chamber reflex or any other derivative, or bandpass box.
If you are interested in finding the resonances that can occur between opposite walls, and between the driver and a wall, I have some software available to work these out for you.
Grab "boxnotes" for free at:
http://www.users.bigpond.com/bcolliso/freesoft.htm
It runs under windows and now supports imperial measurements as well as metric.
regards
Collo
Grab "boxnotes" for free at:
http://www.users.bigpond.com/bcolliso/freesoft.htm
It runs under windows and now supports imperial measurements as well as metric.
regards
Collo
Ok....thanks for all your help guys.........but
It was suggested to me that because the bass reflex box has 2 imepdance humps, it certainly has to have 2 resonances.This puzzles me for shure.My mind keeps telling me that this can't be true.The resonance is based upon the mass of the air in the port and the volume of the box.It's just like a plain and simple spring and mass oscillator......I am kindly asking for some extensive explanations and comments
It was suggested to me that because the bass reflex box has 2 imepdance humps, it certainly has to have 2 resonances.This puzzles me for shure.My mind keeps telling me that this can't be true.The resonance is based upon the mass of the air in the port and the volume of the box.It's just like a plain and simple spring and mass oscillator......I am kindly asking for some extensive explanations and comments
Using simple lumped mass and stiffness models :
A driver has one resonance.
A ported box has one resonance.
A driver in a ported box has two resonances.
The two peaks in the impedance plot are the two resonances of a ported box system. The minimum between the peaks (usually at the frequency where the individual box and driver have resonances) is not a resonance for the combined system. The minimum between the two peaks is the sum of the two mode shapes that cancel driver motion and accentuate port output.
If you do the detailed math treating the driver as a mass and spring in series with a mass and spring for the box, and solve for the eigenvalues and eigenvectors, you can prove to yourself that a driver in a ported box system has two resonances that form the two impedance peaks. You can also look at the mode shapes and understand why a ported box rolls off at 24 dB/octave.
A driver has one resonance.
A ported box has one resonance.
A driver in a ported box has two resonances.
The two peaks in the impedance plot are the two resonances of a ported box system. The minimum between the peaks (usually at the frequency where the individual box and driver have resonances) is not a resonance for the combined system. The minimum between the two peaks is the sum of the two mode shapes that cancel driver motion and accentuate port output.
If you do the detailed math treating the driver as a mass and spring in series with a mass and spring for the box, and solve for the eigenvalues and eigenvectors, you can prove to yourself that a driver in a ported box system has two resonances that form the two impedance peaks. You can also look at the mode shapes and understand why a ported box rolls off at 24 dB/octave.
costin said:
Ah, ok, so I see the reason for your question. Ok looking at the electrical impedance there is actually three or even four or more resonances. A resonance occurs when a mass m is connected to a spring c. The resonance frequency is f=1/sqrt(mc)
The lowest resonance can be estimated by adding the port mass and the driver mass and form a resonator with the driver compliance.
The second resonance (which occurs at the low between the two peaks in the impedance curve) is the helmholtz frequency. This frequency can be estmated by forming a resonator with the port mass and the box compliance.
The third resonance occurs at the second peak in the impedance curve. Its frequency can be estimated by the resonance between the driver mass and the added effect of the driver and box compliances. This resonance is very similar to the single (Ah well...) resonance of the closed box.
The fourth resonance has a slightly akward origin, in that the two reactive components is the voice coil inductance and a capacitance that originates from the driver mass as seen "through" the driver motor. It occurs at the second low to the right of the second peak in the impedance curve, and it is not particularly important.
On top of these resonances, there are also the pipe resonances in the vent.
Now, the great number of resonances is not necessarily bad, most of them have a relatively low Q, which means that they "die" quickly if they are excited. On the contrary, these resonances are used to form the desired response of the speaker.
The BR/driver system does not have a Helmholtz resonance.
The BR/driver system has two new resonances one above and one below the box Helmholtz resonance. The mode shape of the lower resonance has the driver mass moving into the enclosure and the port air mass moving out of the enclosure ( in phase hence 24 dB/octave roll-off). The second mode shape has the driver mass moving out of the enclosure and the port air mass moving out of the enclosure (out of phase stretching the box "spring").
In between these resonances, the mode shapes combine which produces minimal motion at the driver and maximum motion at the port, people mistake this condition for the resonance of the box (Helmholtz resonance) but it is not a true resonant condition for the BR system.
It is only confusing if you do not have a firm grasp on the math and are considereing only cause and effect types of observations. Once the math is set in your thinking, it makes perfect sense and a clearer insight is obtained into what is going on in a BR system (or TL system) and what options are available for influencing the overall system response.
The BR/driver system has two new resonances one above and one below the box Helmholtz resonance. The mode shape of the lower resonance has the driver mass moving into the enclosure and the port air mass moving out of the enclosure ( in phase hence 24 dB/octave roll-off). The second mode shape has the driver mass moving out of the enclosure and the port air mass moving out of the enclosure (out of phase stretching the box "spring").
In between these resonances, the mode shapes combine which produces minimal motion at the driver and maximum motion at the port, people mistake this condition for the resonance of the box (Helmholtz resonance) but it is not a true resonant condition for the BR system.
It is only confusing if you do not have a firm grasp on the math and are considereing only cause and effect types of observations. Once the math is set in your thinking, it makes perfect sense and a clearer insight is obtained into what is going on in a BR system (or TL system) and what options are available for influencing the overall system response.
Ok, just to set my mind straight on this (I am not used to talking about eigenvalues even though I think I know roughly what they are.):
If you calculate the transfer function of any system, there will be poles and zeroes. The poles are inherent to the system, but the zeroes depend on where you excite it and where you measure. These poles are closely linked to the eigenvalues, as I understand it.
The BR system has two pole pairs, since it is fourth order, and these two pole pairs correspond to the eigenvalues? Am I right? But Hmm... That would make the two eigenvalues of a butterworth design occur at the same frequency (but different Q) ie the helmholtz frequency. Is there such a thing as a Q value for an eigenvalue?
Hmm. Interesting this, there are sooo many ways of looking at loudspeakers
If you calculate the transfer function of any system, there will be poles and zeroes. The poles are inherent to the system, but the zeroes depend on where you excite it and where you measure. These poles are closely linked to the eigenvalues, as I understand it.
The BR system has two pole pairs, since it is fourth order, and these two pole pairs correspond to the eigenvalues? Am I right? But Hmm... That would make the two eigenvalues of a butterworth design occur at the same frequency (but different Q) ie the helmholtz frequency. Is there such a thing as a Q value for an eigenvalue?
Hmm. Interesting this, there are sooo many ways of looking at loudspeakers
Oh no ....... poles and zeros. I am a Mechanical Engineer so my understanding of poles and zeros is minimal. But I think you are correct that the BR system will have four poles (from the denominator of the transfer function). I also believe that the four poles are really two complex conjugates of the form
p1 = a + jb
p2 = a - jb
p3 = c + jd
p4 = c - jd
where the a and c are sometimes labeled as time constants and the b and d are sometimes labeled as damped natural frequencies. The exponential decay damping is derived from a and c while the resonant frequencies are calculated from b and d. Unfortunately that is about the limit of my understanding (at least what I remember from 25+ years ago) of poles, zeros, and transfer functions. Most of the math/analysis work I do now is numerical methods and finite element based so the plotting of a system's response from poles and zeros plots is way back in my distant undergraduate days past.
p1 = a + jb
p2 = a - jb
p3 = c + jd
p4 = c - jd
where the a and c are sometimes labeled as time constants and the b and d are sometimes labeled as damped natural frequencies. The exponential decay damping is derived from a and c while the resonant frequencies are calculated from b and d. Unfortunately that is about the limit of my understanding (at least what I remember from 25+ years ago) of poles, zeros, and transfer functions. Most of the math/analysis work I do now is numerical methods and finite element based so the plotting of a system's response from poles and zeros plots is way back in my distant undergraduate days past.
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