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#1
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Loudspeaker Design Cookbook Volume 1 Formula Assistance
I am looking for a formula that was only in Volume 1 of Vance Dickason's
Loudspeaker Design Cookbook. If anybody out there has a copy please email me so I can get the formula from you. Thanks in advance. |
#2
Posted to rec.audio.tech
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Loudspeaker Design Cookbook Volume 1 Formula Assistance
"Chollie" wrote in message ... I am looking for a formula that was only in Volume 1 of Vance Dickason's Loudspeaker Design Cookbook. If anybody out there has a copy please email me so I can get the formula from you. Thanks in advance. I can't help but wonder why it was only in volume one then. Ever think it may be because it was wrong? Why not simply ask what you are looking for instead? MrT. |
#3
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Loudspeaker Design Cookbook Volume 1 Formula Assistance
On Dec 25, 2:47 pm, "Chollie" wrote:
I am looking for a formula that was only in Volume 1 of Vance Dickason's Loudspeaker Design Cookbook. If anybody out there has a copy please email me so I can get the formula from you. Thanks in advance. AS the Loudspeaker Design Cookbook is a derivative work, and is based on the work of Thiele, Small and others, perhaps going to the original sources will work. What was the formula you're looking for supposed to do? |
#4
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Loudspeaker Design Cookbook Volume 1 Formula Assistance
On Dec 25, 11:28 pm, "Chollie" wrote:
On Dec 25, 8:32 pm, wrote: On Dec 25, 2:47 pm, "Chollie" wrote: I am looking for a formula that was only in Volume 1 of Vance Dickason's Loudspeaker Design Cookbook. If anybody out there has a copy please email me so I can get the formula from you. Thanks in advance. As the Loudspeaker Design Cookbook is a derivative work, and is based on the work of Thiele, Small and others, perhaps going to the original sources will work. What was the formula you're looking for supposed to do? The formula was to calculate a resistance value to smooth the roll off below Fs of a tweeter in the crossover. I drew a 2nd order high pass circuit below to illustrate what I thin I remember. I thought the formula stated the total dc resistance of Lx + Rx should be the impedance of Lx at the tweeter's Fs. ---------Cx---|------- + | Lx | Tweeter | Rx | --------------|------- - Thanks for any assistance you can provide. The circuit you drew and your memory are both faulty. First, the "impedance of Lx at the tweeter's Fs" is 0: at resonance, there is no capacitive or inductive component to the impedance: it is purely resistive. Secondly, the circuit you describe cannot "smooth the roll off below Fs of a tweeter ." What you describe is a simple shelving circuit, depending upon the relative values of all the components. Let's assume the LxRx corner frequency is reasonably below the crossover point. The effect of the cricuit you drew would be to convert the 2nd order rolloff into a 1st order rolloff. Perhaps what you are thinkg of is the standard complex conjugate correction (often referred to as a "Zobel") for the inductive component of the driver's impedance ABOVE resonance (and, presumably, the crossover frequency is selected to be above the tweeter's resonance). In the simplest such model, the tweeter's impedance above the resonance behaves like a series resistor and inductor. something like: +---+ | Le | Re | +---+ A shunt conjugate circuit to eliminate the inductive component of the impedance would consist of a series resistor and capacitor, e.g.: +---+ | Cc | Rc | +---+ Assuming the driver resistance and inductance were constant with frequency (they are not), you'd end up with a circuit (including the tweeter model above) which looks like: +---+---+ | | Cc Le | | Rc Re | | +---+---+ Now, again assuming that the values of Re and Le were independent of frequency (and, again, be cautined that, due to secondary effects, they are not), then one would determine the values of Cc and Rc as: Cc = Le / Re^2 and Rc = Re The result will be that instead of a rising impedance with frequency, the load presented to the crossover will be, in essence, constant with frequency and thus resistive. Especially for a first order network, this is important to achieve the correct response (with a rising, partially inductive impedance, you CANNOT get a first-order response from a passive network). Two problems with this approach: First, as I already mentioned, the technique assumes incorrectly that the voice coil resistance and inductance are independent of frequency (I don't mean reactance, I mean inductance). Due to effects such as eddy current losses in the magnet structure, the resistance portion tends to rise as roughly the square root of frequency, and the inductive portion tends to fall as the square root of frequency. Second issue is that it fails to take into account the more important and often more challenging issue of the rise in impedance at the tweeter's mechanical resonance, usually not far below the crossover (like within an octave in many cases). If the tweeter is not well mechanically damped, this rise is often on the order of twice the DC resistance and more, and makes a shambles of any passive crossover response. To adequately correct for that takes much more, essentially a series LRC tank circuit, where the component values are determined, in essence, by the tweeter's moving mass, suspension stiffness and frictional losses. Fortunately, many tweeters, especially those which employ ferrofluid for damping and colling, are highly damped at resonance and present a more constant load. By the way, in later editions of the Loudspeaker Design Cookbook, these and other formulas are found in the chapter on crossovers. |
#5
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Loudspeaker Design Cookbook Volume 1 Formula Assistance
wrote in message ... On Dec 25, 11:28 pm, "Chollie" wrote: On Dec 25, 8:32 pm, wrote: On Dec 25, 2:47 pm, "Chollie" wrote: I am looking for a formula that was only in Volume 1 of Vance Dickason's Loudspeaker Design Cookbook. If anybody out there has a copy please email me so I can get the formula from you. Thanks in advance. As the Loudspeaker Design Cookbook is a derivative work, and is based on the work of Thiele, Small and others, perhaps going to the original sources will work. What was the formula you're looking for supposed to do? The formula was to calculate a resistance value to smooth the roll off below Fs of a tweeter in the crossover. I drew a 2nd order high pass circuit below to illustrate what I thin I remember. I thought the formula stated the total dc resistance of Lx + Rx should be the impedance of Lx at the tweeter's Fs. ---------Cx---|------- + | Lx | Tweeter | Rx | --------------|------- - Thanks for any assistance you can provide. The circuit you drew and your memory are both faulty. First, the "impedance of Lx at the tweeter's Fs" is 0: at resonance, there is no capacitive or inductive component to the impedance: it is purely resistive. Secondly, the circuit you describe cannot "smooth the roll off below Fs of a tweeter ." What you describe is a simple shelving circuit, depending upon the relative values of all the components. Let's assume the LxRx corner frequency is reasonably below the crossover point. The effect of the cricuit you drew would be to convert the 2nd order rolloff into a 1st order rolloff. Perhaps what you are thinkg of is the standard complex conjugate correction (often referred to as a "Zobel") for the inductive component of the driver's impedance ABOVE resonance (and, presumably, the crossover frequency is selected to be above the tweeter's resonance). In the simplest such model, the tweeter's impedance above the resonance behaves like a series resistor and inductor. something like: +---+ | Le | Re | +---+ A shunt conjugate circuit to eliminate the inductive component of the impedance would consist of a series resistor and capacitor, e.g.: +---+ | Cc | Rc | +---+ Assuming the driver resistance and inductance were constant with frequency (they are not), you'd end up with a circuit (including the tweeter model above) which looks like: +---+---+ | | Cc Le | | Rc Re | | +---+---+ Now, again assuming that the values of Re and Le were independent of frequency (and, again, be cautined that, due to secondary effects, they are not), then one would determine the values of Cc and Rc as: Cc = Le / Re^2 and Rc = Re The result will be that instead of a rising impedance with frequency, the load presented to the crossover will be, in essence, constant with frequency and thus resistive. Especially for a first order network, this is important to achieve the correct response (with a rising, partially inductive impedance, you CANNOT get a first-order response from a passive network). Two problems with this approach: First, as I already mentioned, the technique assumes incorrectly that the voice coil resistance and inductance are independent of frequency (I don't mean reactance, I mean inductance). Due to effects such as eddy current losses in the magnet structure, the resistance portion tends to rise as roughly the square root of frequency, and the inductive portion tends to fall as the square root of frequency. Second issue is that it fails to take into account the more important and often more challenging issue of the rise in impedance at the tweeter's mechanical resonance, usually not far below the crossover (like within an octave in many cases). If the tweeter is not well mechanically damped, this rise is often on the order of twice the DC resistance and more, and makes a shambles of any passive crossover response. To adequately correct for that takes much more, essentially a series LRC tank circuit, where the component values are determined, in essence, by the tweeter's moving mass, suspension stiffness and frictional losses. Fortunately, many tweeters, especially those which employ ferrofluid for damping and colling, are highly damped at resonance and present a more constant load. By the way, in later editions of the Loudspeaker Design Cookbook, these and other formulas are found in the chapter on crossovers. Thanks for the response and excellent explanation. I know my memory is faulty. However, I did not confuse the circuit I mentioned in the LDC 1st edition with a zobel or tank circuit. Your explanation makes me think that whatever the circuit was I referred was determined to not work as desired and was subsequently left out of later LDC editions (Mr. T suggested this in his response). I own the 6th & 7th editions and have been reading the 7th lately as I plan to pursue my hobbies again now that I have time (empty nest). Your response has cleared up some things for me. Thanks again. Charlie |
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