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#81
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Do loudspeaker inductors have audible polarity?
"Svante" wrote in message
om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. |
#82
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Do loudspeaker inductors have audible polarity?
"Arny Krueger" wrote in message ...
"Svante" wrote in message om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26 feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF. Is it possible that it is the skin effect anyway? So far it is the only explanation that I have not been able to rule out. That or my software. Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? |
#83
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Do loudspeaker inductors have audible polarity?
"Arny Krueger" wrote in message ...
"Svante" wrote in message om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26 feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF. Is it possible that it is the skin effect anyway? So far it is the only explanation that I have not been able to rule out. That or my software. Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? |
#84
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Do loudspeaker inductors have audible polarity?
"Arny Krueger" wrote in message ...
"Svante" wrote in message om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26 feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF. Is it possible that it is the skin effect anyway? So far it is the only explanation that I have not been able to rule out. That or my software. Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? |
#85
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Do loudspeaker inductors have audible polarity?
"Arny Krueger" wrote in message ...
"Svante" wrote in message om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26 feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF. Is it possible that it is the skin effect anyway? So far it is the only explanation that I have not been able to rule out. That or my software. Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? |
#86
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Do loudspeaker inductors have audible polarity?
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#87
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Do loudspeaker inductors have audible polarity?
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#88
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Do loudspeaker inductors have audible polarity?
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#89
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Do loudspeaker inductors have audible polarity?
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#90
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Do loudspeaker inductors have audible polarity?
John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante) wrote: Hmm. Pardon me if I am drifting off topic here, but I and a collegue of mine recently noticed a quite noticeable deviance from the Z=wL in the impedance of inductors in the HF range. These inductors were made of standard ~0.3mm (I'll have to check this) wires and no iron core (for loudspeaker crossovers). Any explanation to this, apart from skin? http://www.tolvan.com/coil.gif Note that I don't claim big *audible* effects from this in most applications, though. In a series circuit containing resistance, inductance, and capacitance, the impedance (Z) of the circuit will be equal to the square root of the sums of the squares of the resistance and the square of the difference between the inductive and capacitive reactance. That is, Z = sqrt (R² + (Xl - Xc)²) Of course, in a circuit containing only inductance, the inductive reactance and impedance will be equal. However, such a scenario is impossible and the effects of capacitance and resistance must always be considered if accuracy is important. Looking at just the inductor, since there is a voltage difference between turns and the turns are dielectrically isolated from each other, that gives rise to an inherent capacitance and since there is resistance in the wire used to wind the inductor, that's also part of the inductor and can't be separated from it. There are winding techniques used to minimize the capacitance (which appears to be in _parallel_ with the inductance) but in the case of coils wound for loudspeaker crossovers, I'd seriously doubt whether the slightest consideration was given to them. Just to test the possibility of a parallel capacitance I entered it into the program (it's another coil now, I could not find the first one again). It turns out that I can get a pretty good match if I parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of this circuit will be just above 20 kHz (the limit of the soundcard) and I get the feeling that the match will be very poor at higher frequencies. Also, a stray capacitance of 0.22 uF appears very much, so I don't beleive in it. --- You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. I suddenly realise a possible error source here, but as I check it, it does not appear to be the problem. I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be a measurement error, which will vary with the resistance. Error percentages are likely to be smallest near 47 ohms, and increase as we move away from this resistance. Such an error could cause the impedance curve to bend away from the model as the impedance changes. To test the idea I took three resistors that happened to be on my desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my program showed 10.2 47.0 and 68.5 ohms respectively. That seems to rule out this explanation since impedances in the range 10-68 ohms seems to be measured accurately. Also the impedance curves of the resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20 kHz, which would indicate a low stray capacitance in the equipment) Resistor curves available at: http://www.tolvan.com/10-47-68ohm.gif OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. Be that as it may, at resonance the reactances of the inductor and capacitor will be equal, but opposite in sign, and in a series circuit will cancel, leaving behind only the resistance of the circuit as the impedance. If, then, you connect the resonant circuit in series with your load: Vin----[R]--[L]--[C]--+ | [Rl] | Vret------------------+ And your load is totally resistive, the voltage across the load will peak at the resonant frequency of the LC, whe 1 f = ------------ 2pi(sqrt LC) and will fall away from the peak value on either side of resonance, with the result being that the LC will form a bandpass filter. No problem with that. With the circuit in parallel with the load: Vin----+-----+ | | [R] | | | [L] [Rl] | | [C] | | | Vret----+-----+ The voltage across the load will be at a minimum at the resonant frequency of the LC and will rise on either side of resonance, making the response that of a band-reject, or notch, filter. Ok In a parallel resonant circuit (a "tank"), however, the cancellation of the reactances will give rise to circulating currents in the tank which will only be limited by the series resistance of the elements comprising the tank and the impedance will rise to a very high value. Such being the case, a parallel resonant circuit connected in parallel with a purely resistive load will be a bandpass filter, and connected in series with the load will look like a notch at resonance; exactly the opposite of the series tuned circuit. I'm still with you. Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. My best model fit was 0.22mH, and I think that the resonance in my simulation was slightly above 20 kHz, so everything adds up fine. In the graph http://www.tolvan.com/coil1.gif we see the model impedance without the parallel cap being some 28 ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that model (blue curve) seems OK too. --- I suspect the resistance of the wire is what's causing the deviation from "ideal" inductance, and I also suspect that skin effect has _nothing_ to do with it since that's an effect which starts to become significant at radio frequencies. You say that you suspect the resistance to be responsible for the increased impedance. Is there another effect than the skin effect that could cause the resistance to increase with frequency? --- There shouldn't be. --- The new curve fittings can be seen at: http://www.tolvan.com/coil1.gif blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is the same model paralleled with 0.22uF+33ohm, black is measured data. Don't pay too much attention to the measured phase curve, I have a delay between channels that ruins the HF phase response. A photo of this particular coil is available at: http://www.tolvan.com/coil1.jpg wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm, height 13 mm. Could you or someone else verify that coils really do like this? I have used different soundcards and differenct coils for the measurements, but the same home-brewed program, so it would be nice with a verification from someone else. A 10 ohm resistor produces a straight line within 0.2 ohm using the same equipment (phase is -130 degrees at 20kHz due to the delay I mentioned :-( ). --- Rather than trust a simulator, I'd actually _measure_ the self-resonant frequency of the coil to determine what its distributed capacitance is or, failing that, at the very least measure the resonant frequency at a couple of places using known parallel and series capacitances in order to determine what its true inductance is at different frequencies. Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. So, I still only have the skin effect as a candidate. Hmmm... Thanks, Svante |
#91
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Do loudspeaker inductors have audible polarity?
John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante) wrote: Hmm. Pardon me if I am drifting off topic here, but I and a collegue of mine recently noticed a quite noticeable deviance from the Z=wL in the impedance of inductors in the HF range. These inductors were made of standard ~0.3mm (I'll have to check this) wires and no iron core (for loudspeaker crossovers). Any explanation to this, apart from skin? http://www.tolvan.com/coil.gif Note that I don't claim big *audible* effects from this in most applications, though. In a series circuit containing resistance, inductance, and capacitance, the impedance (Z) of the circuit will be equal to the square root of the sums of the squares of the resistance and the square of the difference between the inductive and capacitive reactance. That is, Z = sqrt (R² + (Xl - Xc)²) Of course, in a circuit containing only inductance, the inductive reactance and impedance will be equal. However, such a scenario is impossible and the effects of capacitance and resistance must always be considered if accuracy is important. Looking at just the inductor, since there is a voltage difference between turns and the turns are dielectrically isolated from each other, that gives rise to an inherent capacitance and since there is resistance in the wire used to wind the inductor, that's also part of the inductor and can't be separated from it. There are winding techniques used to minimize the capacitance (which appears to be in _parallel_ with the inductance) but in the case of coils wound for loudspeaker crossovers, I'd seriously doubt whether the slightest consideration was given to them. Just to test the possibility of a parallel capacitance I entered it into the program (it's another coil now, I could not find the first one again). It turns out that I can get a pretty good match if I parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of this circuit will be just above 20 kHz (the limit of the soundcard) and I get the feeling that the match will be very poor at higher frequencies. Also, a stray capacitance of 0.22 uF appears very much, so I don't beleive in it. --- You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. I suddenly realise a possible error source here, but as I check it, it does not appear to be the problem. I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be a measurement error, which will vary with the resistance. Error percentages are likely to be smallest near 47 ohms, and increase as we move away from this resistance. Such an error could cause the impedance curve to bend away from the model as the impedance changes. To test the idea I took three resistors that happened to be on my desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my program showed 10.2 47.0 and 68.5 ohms respectively. That seems to rule out this explanation since impedances in the range 10-68 ohms seems to be measured accurately. Also the impedance curves of the resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20 kHz, which would indicate a low stray capacitance in the equipment) Resistor curves available at: http://www.tolvan.com/10-47-68ohm.gif OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. Be that as it may, at resonance the reactances of the inductor and capacitor will be equal, but opposite in sign, and in a series circuit will cancel, leaving behind only the resistance of the circuit as the impedance. If, then, you connect the resonant circuit in series with your load: Vin----[R]--[L]--[C]--+ | [Rl] | Vret------------------+ And your load is totally resistive, the voltage across the load will peak at the resonant frequency of the LC, whe 1 f = ------------ 2pi(sqrt LC) and will fall away from the peak value on either side of resonance, with the result being that the LC will form a bandpass filter. No problem with that. With the circuit in parallel with the load: Vin----+-----+ | | [R] | | | [L] [Rl] | | [C] | | | Vret----+-----+ The voltage across the load will be at a minimum at the resonant frequency of the LC and will rise on either side of resonance, making the response that of a band-reject, or notch, filter. Ok In a parallel resonant circuit (a "tank"), however, the cancellation of the reactances will give rise to circulating currents in the tank which will only be limited by the series resistance of the elements comprising the tank and the impedance will rise to a very high value. Such being the case, a parallel resonant circuit connected in parallel with a purely resistive load will be a bandpass filter, and connected in series with the load will look like a notch at resonance; exactly the opposite of the series tuned circuit. I'm still with you. Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. My best model fit was 0.22mH, and I think that the resonance in my simulation was slightly above 20 kHz, so everything adds up fine. In the graph http://www.tolvan.com/coil1.gif we see the model impedance without the parallel cap being some 28 ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that model (blue curve) seems OK too. --- I suspect the resistance of the wire is what's causing the deviation from "ideal" inductance, and I also suspect that skin effect has _nothing_ to do with it since that's an effect which starts to become significant at radio frequencies. You say that you suspect the resistance to be responsible for the increased impedance. Is there another effect than the skin effect that could cause the resistance to increase with frequency? --- There shouldn't be. --- The new curve fittings can be seen at: http://www.tolvan.com/coil1.gif blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is the same model paralleled with 0.22uF+33ohm, black is measured data. Don't pay too much attention to the measured phase curve, I have a delay between channels that ruins the HF phase response. A photo of this particular coil is available at: http://www.tolvan.com/coil1.jpg wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm, height 13 mm. Could you or someone else verify that coils really do like this? I have used different soundcards and differenct coils for the measurements, but the same home-brewed program, so it would be nice with a verification from someone else. A 10 ohm resistor produces a straight line within 0.2 ohm using the same equipment (phase is -130 degrees at 20kHz due to the delay I mentioned :-( ). --- Rather than trust a simulator, I'd actually _measure_ the self-resonant frequency of the coil to determine what its distributed capacitance is or, failing that, at the very least measure the resonant frequency at a couple of places using known parallel and series capacitances in order to determine what its true inductance is at different frequencies. Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. So, I still only have the skin effect as a candidate. Hmmm... Thanks, Svante |
#92
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Do loudspeaker inductors have audible polarity?
John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante) wrote: Hmm. Pardon me if I am drifting off topic here, but I and a collegue of mine recently noticed a quite noticeable deviance from the Z=wL in the impedance of inductors in the HF range. These inductors were made of standard ~0.3mm (I'll have to check this) wires and no iron core (for loudspeaker crossovers). Any explanation to this, apart from skin? http://www.tolvan.com/coil.gif Note that I don't claim big *audible* effects from this in most applications, though. In a series circuit containing resistance, inductance, and capacitance, the impedance (Z) of the circuit will be equal to the square root of the sums of the squares of the resistance and the square of the difference between the inductive and capacitive reactance. That is, Z = sqrt (R² + (Xl - Xc)²) Of course, in a circuit containing only inductance, the inductive reactance and impedance will be equal. However, such a scenario is impossible and the effects of capacitance and resistance must always be considered if accuracy is important. Looking at just the inductor, since there is a voltage difference between turns and the turns are dielectrically isolated from each other, that gives rise to an inherent capacitance and since there is resistance in the wire used to wind the inductor, that's also part of the inductor and can't be separated from it. There are winding techniques used to minimize the capacitance (which appears to be in _parallel_ with the inductance) but in the case of coils wound for loudspeaker crossovers, I'd seriously doubt whether the slightest consideration was given to them. Just to test the possibility of a parallel capacitance I entered it into the program (it's another coil now, I could not find the first one again). It turns out that I can get a pretty good match if I parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of this circuit will be just above 20 kHz (the limit of the soundcard) and I get the feeling that the match will be very poor at higher frequencies. Also, a stray capacitance of 0.22 uF appears very much, so I don't beleive in it. --- You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. I suddenly realise a possible error source here, but as I check it, it does not appear to be the problem. I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be a measurement error, which will vary with the resistance. Error percentages are likely to be smallest near 47 ohms, and increase as we move away from this resistance. Such an error could cause the impedance curve to bend away from the model as the impedance changes. To test the idea I took three resistors that happened to be on my desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my program showed 10.2 47.0 and 68.5 ohms respectively. That seems to rule out this explanation since impedances in the range 10-68 ohms seems to be measured accurately. Also the impedance curves of the resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20 kHz, which would indicate a low stray capacitance in the equipment) Resistor curves available at: http://www.tolvan.com/10-47-68ohm.gif OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. Be that as it may, at resonance the reactances of the inductor and capacitor will be equal, but opposite in sign, and in a series circuit will cancel, leaving behind only the resistance of the circuit as the impedance. If, then, you connect the resonant circuit in series with your load: Vin----[R]--[L]--[C]--+ | [Rl] | Vret------------------+ And your load is totally resistive, the voltage across the load will peak at the resonant frequency of the LC, whe 1 f = ------------ 2pi(sqrt LC) and will fall away from the peak value on either side of resonance, with the result being that the LC will form a bandpass filter. No problem with that. With the circuit in parallel with the load: Vin----+-----+ | | [R] | | | [L] [Rl] | | [C] | | | Vret----+-----+ The voltage across the load will be at a minimum at the resonant frequency of the LC and will rise on either side of resonance, making the response that of a band-reject, or notch, filter. Ok In a parallel resonant circuit (a "tank"), however, the cancellation of the reactances will give rise to circulating currents in the tank which will only be limited by the series resistance of the elements comprising the tank and the impedance will rise to a very high value. Such being the case, a parallel resonant circuit connected in parallel with a purely resistive load will be a bandpass filter, and connected in series with the load will look like a notch at resonance; exactly the opposite of the series tuned circuit. I'm still with you. Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. My best model fit was 0.22mH, and I think that the resonance in my simulation was slightly above 20 kHz, so everything adds up fine. In the graph http://www.tolvan.com/coil1.gif we see the model impedance without the parallel cap being some 28 ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that model (blue curve) seems OK too. --- I suspect the resistance of the wire is what's causing the deviation from "ideal" inductance, and I also suspect that skin effect has _nothing_ to do with it since that's an effect which starts to become significant at radio frequencies. You say that you suspect the resistance to be responsible for the increased impedance. Is there another effect than the skin effect that could cause the resistance to increase with frequency? --- There shouldn't be. --- The new curve fittings can be seen at: http://www.tolvan.com/coil1.gif blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is the same model paralleled with 0.22uF+33ohm, black is measured data. Don't pay too much attention to the measured phase curve, I have a delay between channels that ruins the HF phase response. A photo of this particular coil is available at: http://www.tolvan.com/coil1.jpg wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm, height 13 mm. Could you or someone else verify that coils really do like this? I have used different soundcards and differenct coils for the measurements, but the same home-brewed program, so it would be nice with a verification from someone else. A 10 ohm resistor produces a straight line within 0.2 ohm using the same equipment (phase is -130 degrees at 20kHz due to the delay I mentioned :-( ). --- Rather than trust a simulator, I'd actually _measure_ the self-resonant frequency of the coil to determine what its distributed capacitance is or, failing that, at the very least measure the resonant frequency at a couple of places using known parallel and series capacitances in order to determine what its true inductance is at different frequencies. Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. So, I still only have the skin effect as a candidate. Hmmm... Thanks, Svante |
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Do loudspeaker inductors have audible polarity?
John Fields wrote in message . ..
On 12 Feb 2004 00:15:25 -0800, (Svante) wrote: Hmm. Pardon me if I am drifting off topic here, but I and a collegue of mine recently noticed a quite noticeable deviance from the Z=wL in the impedance of inductors in the HF range. These inductors were made of standard ~0.3mm (I'll have to check this) wires and no iron core (for loudspeaker crossovers). Any explanation to this, apart from skin? http://www.tolvan.com/coil.gif Note that I don't claim big *audible* effects from this in most applications, though. In a series circuit containing resistance, inductance, and capacitance, the impedance (Z) of the circuit will be equal to the square root of the sums of the squares of the resistance and the square of the difference between the inductive and capacitive reactance. That is, Z = sqrt (R² + (Xl - Xc)²) Of course, in a circuit containing only inductance, the inductive reactance and impedance will be equal. However, such a scenario is impossible and the effects of capacitance and resistance must always be considered if accuracy is important. Looking at just the inductor, since there is a voltage difference between turns and the turns are dielectrically isolated from each other, that gives rise to an inherent capacitance and since there is resistance in the wire used to wind the inductor, that's also part of the inductor and can't be separated from it. There are winding techniques used to minimize the capacitance (which appears to be in _parallel_ with the inductance) but in the case of coils wound for loudspeaker crossovers, I'd seriously doubt whether the slightest consideration was given to them. Just to test the possibility of a parallel capacitance I entered it into the program (it's another coil now, I could not find the first one again). It turns out that I can get a pretty good match if I parallel the coil (0.22mH, 0.7 ohm) with a (capacitor in series with a resistor) of 0.22 uF and 33 ohm. However, the resonance frequency of this circuit will be just above 20 kHz (the limit of the soundcard) and I get the feeling that the match will be very poor at higher frequencies. Also, a stray capacitance of 0.22 uF appears very much, so I don't beleive in it. --- You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. I suddenly realise a possible error source here, but as I check it, it does not appear to be the problem. I'll describe it anyway. If the Rs isn't exactly 47 ohms there will be a measurement error, which will vary with the resistance. Error percentages are likely to be smallest near 47 ohms, and increase as we move away from this resistance. Such an error could cause the impedance curve to bend away from the model as the impedance changes. To test the idea I took three resistors that happened to be on my desk, 9.9 ohms 46.5 and 68.3 ohms (according to my multimeter) and my program showed 10.2 47.0 and 68.5 ohms respectively. That seems to rule out this explanation since impedances in the range 10-68 ohms seems to be measured accurately. Also the impedance curves of the resistors are very flat (the 47 ohm curve drops to 46.6 ohms at 20 kHz, which would indicate a low stray capacitance in the equipment) Resistor curves available at: http://www.tolvan.com/10-47-68ohm.gif OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. Be that as it may, at resonance the reactances of the inductor and capacitor will be equal, but opposite in sign, and in a series circuit will cancel, leaving behind only the resistance of the circuit as the impedance. If, then, you connect the resonant circuit in series with your load: Vin----[R]--[L]--[C]--+ | [Rl] | Vret------------------+ And your load is totally resistive, the voltage across the load will peak at the resonant frequency of the LC, whe 1 f = ------------ 2pi(sqrt LC) and will fall away from the peak value on either side of resonance, with the result being that the LC will form a bandpass filter. No problem with that. With the circuit in parallel with the load: Vin----+-----+ | | [R] | | | [L] [Rl] | | [C] | | | Vret----+-----+ The voltage across the load will be at a minimum at the resonant frequency of the LC and will rise on either side of resonance, making the response that of a band-reject, or notch, filter. Ok In a parallel resonant circuit (a "tank"), however, the cancellation of the reactances will give rise to circulating currents in the tank which will only be limited by the series resistance of the elements comprising the tank and the impedance will rise to a very high value. Such being the case, a parallel resonant circuit connected in parallel with a purely resistive load will be a bandpass filter, and connected in series with the load will look like a notch at resonance; exactly the opposite of the series tuned circuit. I'm still with you. Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. My best model fit was 0.22mH, and I think that the resonance in my simulation was slightly above 20 kHz, so everything adds up fine. In the graph http://www.tolvan.com/coil1.gif we see the model impedance without the parallel cap being some 28 ohms, which is in line with Xl=2*pi*2.0E4*0.22E-3=27.6 ohms so that model (blue curve) seems OK too. --- I suspect the resistance of the wire is what's causing the deviation from "ideal" inductance, and I also suspect that skin effect has _nothing_ to do with it since that's an effect which starts to become significant at radio frequencies. You say that you suspect the resistance to be responsible for the increased impedance. Is there another effect than the skin effect that could cause the resistance to increase with frequency? --- There shouldn't be. --- The new curve fittings can be seen at: http://www.tolvan.com/coil1.gif blue curve is the impedance of a model (0.22mH 0.7 ohm), red curve is the same model paralleled with 0.22uF+33ohm, black is measured data. Don't pay too much attention to the measured phase curve, I have a delay between channels that ruins the HF phase response. A photo of this particular coil is available at: http://www.tolvan.com/coil1.jpg wire diameter 0.9mm, inner diameter 28 mm, outer diameter 38 mm, height 13 mm. Could you or someone else verify that coils really do like this? I have used different soundcards and differenct coils for the measurements, but the same home-brewed program, so it would be nice with a verification from someone else. A 10 ohm resistor produces a straight line within 0.2 ohm using the same equipment (phase is -130 degrees at 20kHz due to the delay I mentioned :-( ). --- Rather than trust a simulator, I'd actually _measure_ the self-resonant frequency of the coil to determine what its distributed capacitance is or, failing that, at the very least measure the resonant frequency at a couple of places using known parallel and series capacitances in order to determine what its true inductance is at different frequencies. Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. So, I still only have the skin effect as a candidate. Hmmm... Thanks, Svante |
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ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: "Arny Krueger" wrote in message ... "Svante" wrote in message om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26 feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF. Is it possible that it is the skin effect anyway? So far it is the only explanation that I have not been able to rule out. That or my software. Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? John's dad say: "Never trust measurement that give wrong answer." :-) Right, but I think I have tested the equipment in a post right after yours, and I think it is OK. Measurning 10, 47 and 68 ohm resistors give straight lines at 10 47 and 68 ohms, http://www.tolvan.com/10-47-68ohm.gif Adding a parallel cap of 0.47uF gives the "right" resonance frequency of 15600Hz: http://www.tolvan.com/coil1+047uF.gif but the Q is wrong. I think the impedance curve is correct. I keep being left with the skin effect here, which is the only effect I cannot do the math for yet. Ideas? (original measurement at: http://www.tolvan.com/coil1.gif , black curve ) |
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Do loudspeaker inductors have audible polarity?
ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: "Arny Krueger" wrote in message ... "Svante" wrote in message om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26 feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF. Is it possible that it is the skin effect anyway? So far it is the only explanation that I have not been able to rule out. That or my software. Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? John's dad say: "Never trust measurement that give wrong answer." :-) Right, but I think I have tested the equipment in a post right after yours, and I think it is OK. Measurning 10, 47 and 68 ohm resistors give straight lines at 10 47 and 68 ohms, http://www.tolvan.com/10-47-68ohm.gif Adding a parallel cap of 0.47uF gives the "right" resonance frequency of 15600Hz: http://www.tolvan.com/coil1+047uF.gif but the Q is wrong. I think the impedance curve is correct. I keep being left with the skin effect here, which is the only effect I cannot do the math for yet. Ideas? (original measurement at: http://www.tolvan.com/coil1.gif , black curve ) |
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Do loudspeaker inductors have audible polarity?
ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: "Arny Krueger" wrote in message ... "Svante" wrote in message om Do you think that a 0.22 uF stray capacitance is likely in this case? That is what the red curve is (+ 33 ohm in series with the capacitance for best fit, modeled). How many feet of wire in that coil? There might be something like 30 pF of stray capacitance per foot of wire in the coil. Hmm... Looks like 13 by 6 windings, average diameter 34 mm, which would be about 13*6*34*pi=8000 mm or 8 metres (wow!). That would be 26 feet if I calculate correctly, and 26*30=780pF. Far less than 0.22uF. Is it possible that it is the skin effect anyway? So far it is the only explanation that I have not been able to rule out. That or my software. Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? John's dad say: "Never trust measurement that give wrong answer." :-) Right, but I think I have tested the equipment in a post right after yours, and I think it is OK. Measurning 10, 47 and 68 ohm resistors give straight lines at 10 47 and 68 ohms, http://www.tolvan.com/10-47-68ohm.gif Adding a parallel cap of 0.47uF gives the "right" resonance frequency of 15600Hz: http://www.tolvan.com/coil1+047uF.gif but the Q is wrong. I think the impedance curve is correct. I keep being left with the skin effect here, which is the only effect I cannot do the math for yet. Ideas? (original measurement at: http://www.tolvan.com/coil1.gif , black curve ) |
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Do loudspeaker inductors have audible polarity?
On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote: You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. --- I don't know what your equipment setup looks like, but offhand I'd say your measurement technique may be flawed in that you seem to be treating the LR combination as a simple voltage divider without taking phase into consideration. --- OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. --- What has happened that has caused the peak to broaden is that the Q of the circuit has been lowered. That can happen because of either series resistance _in_ the tank or parallel resistance _across_ the tank. Take a look at the impedance of what you're using to measure the voltage across the tank with and you may find it there. --- Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). --- 2.2E-5 actually, but yes, you're right. Good catch. --- Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. --- Plugging in the 36 ohms for Xl gives us L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH which is a 70µH error. That comes out to about 32% referred to your 220µH, but when you consider the tolerance of the coil, the cap, and whatever you used to measure the resonant frequency with, it's in the ball park. --- Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. --- Apparently. Another test you may want to run is to parallel the coil with various capacitors while it's being excited with your cal square wave and see what happens. You should certainly see the ringing with 0.2µF across the coil. You'll notice that as you decrease the capacitance the ringing frequency will increase and the ringing envelope will become shorter and shorter until you'll just see the LdI/Dt spikes your photos show. BTW, at that point there'll still be some ringing happening, but it'll be so fast you won't be able to see it unless the bandwidth of your scope's vertical amplifier(s) is wide enough. So, I still only have the skin effect as a candidate. Hmmm... --- No, you still have Q to consider, and I believe that if you look into it, you'll find that's what's causing the broadening. After all, the resonances are where they're supposed to be for the values of the components, so as the impedance of the tank rises as it gets nearer to resonance, any resistance in the circuit will tend to swamp out the nice high impedance peak which would be there without the extra R spoiling it. Kind of like if you try to measure the voltage across a 10Mohm resistor with a voltmeter having an input resistance of 10Mohms! -- John Fields |
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Do loudspeaker inductors have audible polarity?
On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote: You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. --- I don't know what your equipment setup looks like, but offhand I'd say your measurement technique may be flawed in that you seem to be treating the LR combination as a simple voltage divider without taking phase into consideration. --- OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. --- What has happened that has caused the peak to broaden is that the Q of the circuit has been lowered. That can happen because of either series resistance _in_ the tank or parallel resistance _across_ the tank. Take a look at the impedance of what you're using to measure the voltage across the tank with and you may find it there. --- Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). --- 2.2E-5 actually, but yes, you're right. Good catch. --- Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. --- Plugging in the 36 ohms for Xl gives us L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH which is a 70µH error. That comes out to about 32% referred to your 220µH, but when you consider the tolerance of the coil, the cap, and whatever you used to measure the resonant frequency with, it's in the ball park. --- Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. --- Apparently. Another test you may want to run is to parallel the coil with various capacitors while it's being excited with your cal square wave and see what happens. You should certainly see the ringing with 0.2µF across the coil. You'll notice that as you decrease the capacitance the ringing frequency will increase and the ringing envelope will become shorter and shorter until you'll just see the LdI/Dt spikes your photos show. BTW, at that point there'll still be some ringing happening, but it'll be so fast you won't be able to see it unless the bandwidth of your scope's vertical amplifier(s) is wide enough. So, I still only have the skin effect as a candidate. Hmmm... --- No, you still have Q to consider, and I believe that if you look into it, you'll find that's what's causing the broadening. After all, the resonances are where they're supposed to be for the values of the components, so as the impedance of the tank rises as it gets nearer to resonance, any resistance in the circuit will tend to swamp out the nice high impedance peak which would be there without the extra R spoiling it. Kind of like if you try to measure the voltage across a 10Mohm resistor with a voltmeter having an input resistance of 10Mohms! -- John Fields |
#108
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Do loudspeaker inductors have audible polarity?
On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote: You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. --- I don't know what your equipment setup looks like, but offhand I'd say your measurement technique may be flawed in that you seem to be treating the LR combination as a simple voltage divider without taking phase into consideration. --- OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. --- What has happened that has caused the peak to broaden is that the Q of the circuit has been lowered. That can happen because of either series resistance _in_ the tank or parallel resistance _across_ the tank. Take a look at the impedance of what you're using to measure the voltage across the tank with and you may find it there. --- Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). --- 2.2E-5 actually, but yes, you're right. Good catch. --- Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. --- Plugging in the 36 ohms for Xl gives us L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH which is a 70µH error. That comes out to about 32% referred to your 220µH, but when you consider the tolerance of the coil, the cap, and whatever you used to measure the resonant frequency with, it's in the ball park. --- Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. --- Apparently. Another test you may want to run is to parallel the coil with various capacitors while it's being excited with your cal square wave and see what happens. You should certainly see the ringing with 0.2µF across the coil. You'll notice that as you decrease the capacitance the ringing frequency will increase and the ringing envelope will become shorter and shorter until you'll just see the LdI/Dt spikes your photos show. BTW, at that point there'll still be some ringing happening, but it'll be so fast you won't be able to see it unless the bandwidth of your scope's vertical amplifier(s) is wide enough. So, I still only have the skin effect as a candidate. Hmmm... --- No, you still have Q to consider, and I believe that if you look into it, you'll find that's what's causing the broadening. After all, the resonances are where they're supposed to be for the values of the components, so as the impedance of the tank rises as it gets nearer to resonance, any resistance in the circuit will tend to swamp out the nice high impedance peak which would be there without the extra R spoiling it. Kind of like if you try to measure the voltage across a 10Mohm resistor with a voltmeter having an input resistance of 10Mohms! -- John Fields |
#109
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Do loudspeaker inductors have audible polarity?
On 13 Feb 2004 02:07:37 -0800, (Svante)
wrote: You haven't described what you mean by a "match" or how the circuit is implemented, so it's difficult to keep from guessing about what you're trying to accomplish. By "match" I mean tweaking the values of R1, R2, C and L (see graphs below) by hand to make the curves fit the measured black curve as well as possible. I tried to indicate the circuit I used with my way of writing the parantheses, but anyway, here is a go with ASCII graphics instead (view with courier): -------------- | L=0.22mH Z = | R1=0.7ohm | -------------- That was the blue curve in my simulation ( http://www.tolvan.com/coil1.gif ), and here is the red one: ----------*------------ | | C=0.22uF L=0.22mH Z = | | R2=33ohm R1=0.7ohm | | ----------*------------ My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. --- I don't know what your equipment setup looks like, but offhand I'd say your measurement technique may be flawed in that you seem to be treating the LR combination as a simple voltage divider without taking phase into consideration. --- OK, another experiment: Paralleling the coil with a 0.47uF cap yields a resonance frequency of 15800 Hz, as seen from the location of the peak of the measured black curve in: http://www.tolvan.com/coil1+047uF.gif The green curve is a model ----------*------------ | | 0.47uF 0.22mH Z = | | | 0.7ohm | | ----------*------------ The resonance frequency is consistent with 1 f = ------------ 2pi(sqrt LC) which turns out to be 1/(2*pi*sqrt(0.22e-3*0.47e-6))=15600 Hz. This pretty much rules out a stray capacitance of 0.22 uF, the resonance frequency should then have been 1/(2*pi*sqrt(0.22e-3*(0.22e-6+0.47e-6)))=12900 Hz. The broadening of the resonance peak, compared to the model, indicates to me that something has happened to the resistance rather than with the reactance at high frequencies. --- What has happened that has caused the peak to broaden is that the Q of the circuit has been lowered. That can happen because of either series resistance _in_ the tank or parallel resistance _across_ the tank. Take a look at the impedance of what you're using to measure the voltage across the tank with and you may find it there. --- Since the inductive and capacitive reactances will be equal at resonance, for 0.22µF and 20kHz we have: Xc = 1/2piFc = 1/6.28*2.0E4*2.2E-6 ~ 3.6 ohms I get 36 ohms (typo here I think, should be 0.22E-6). --- 2.2E-5 actually, but yes, you're right. Good catch. --- Then, for the inductance to have a reactance of 3.6 ohms, we have: Xl = 2pifL so, rearranging to solve for L, L = Xl/2pif = 3.6/6.28*2.0E4 ~ 2.9E-5H ~ 29µH Is that what the inductance of the coil at 20kHz is supposed to be? Actually, 0.2 mH, but given the typo above you are close. --- Plugging in the 36 ohms for Xl gives us L = Xl/2pif = 36/6.28*2.0E4 ~ 2.9E-4H ~ 290µH which is a 70µH error. That comes out to about 32% referred to your 220µH, but when you consider the tolerance of the coil, the cap, and whatever you used to measure the resonant frequency with, it's in the ball park. --- Ok, lacking equipment to measure other than audio frequency at home, I grabbed my old oscilloscope and connected this circuit to the probe calibration square wave. probe cal -----1 kohm------*-------ch2 | coil | GND ----------------- http://www.tolvan.com/coilresonanceconnection.jpg There is definitely no 20 kHz ringing http://www.tolvan.com/coilresonancetrace1.jpg and expanding the time scale http://www.tolvan.com/coilresonancetrace2.jpg reveals no resonances either. Sorry about the poor focus. Obviously the scope does not deliver a perfect square wave, but if there were (high Q) resonances they should be seen here as ringings anyway. This tells me that the stray capacitance of the coil is low, or at least not 0.22uF, which IMO rules out the parallel capacitance theory as an explanation to the increasing impedance of the coil in the upper audio band. --- Apparently. Another test you may want to run is to parallel the coil with various capacitors while it's being excited with your cal square wave and see what happens. You should certainly see the ringing with 0.2µF across the coil. You'll notice that as you decrease the capacitance the ringing frequency will increase and the ringing envelope will become shorter and shorter until you'll just see the LdI/Dt spikes your photos show. BTW, at that point there'll still be some ringing happening, but it'll be so fast you won't be able to see it unless the bandwidth of your scope's vertical amplifier(s) is wide enough. So, I still only have the skin effect as a candidate. Hmmm... --- No, you still have Q to consider, and I believe that if you look into it, you'll find that's what's causing the broadening. After all, the resonances are where they're supposed to be for the values of the components, so as the impedance of the tank rises as it gets nearer to resonance, any resistance in the circuit will tend to swamp out the nice high impedance peak which would be there without the extra R spoiling it. Kind of like if you try to measure the voltage across a 10Mohm resistor with a voltmeter having an input resistance of 10Mohms! -- John Fields |
#110
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Do loudspeaker inductors have audible polarity?
Svante wrote:
My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. If I understand you correctly, you are making an error here. You are assuming that the voltage divider formula works like this: mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs) This is wrong. I would give a counter example to show that you are wrong, and you can work out the right equation. Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to your equation, you would have that being 0.5*mag(Lin). Given that, I did not read the rest of your post. |
#111
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Do loudspeaker inductors have audible polarity?
Svante wrote:
My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. If I understand you correctly, you are making an error here. You are assuming that the voltage divider formula works like this: mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs) This is wrong. I would give a counter example to show that you are wrong, and you can work out the right equation. Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to your equation, you would have that being 0.5*mag(Lin). Given that, I did not read the rest of your post. |
#112
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Do loudspeaker inductors have audible polarity?
Svante wrote:
My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. If I understand you correctly, you are making an error here. You are assuming that the voltage divider formula works like this: mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs) This is wrong. I would give a counter example to show that you are wrong, and you can work out the right equation. Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to your equation, you would have that being 0.5*mag(Lin). Given that, I did not read the rest of your post. |
#113
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Do loudspeaker inductors have audible polarity?
Svante wrote:
My computer program measures Z by means of this circuit: Lout ---------- | Lin ----------* | Rs=47 ohm | Rin ----------* | Z | GND ---------- And calculates |Z| as Rs*|Rin|/(|Lin|-|Rin|), Lin amd Rin being the voltages on left and right inputs. If I understand you correctly, you are making an error here. You are assuming that the voltage divider formula works like this: mag(Voltage at Rin) = mag (Voltage at Lin) * mag (Z)/(mag(Z)+Rs) This is wrong. I would give a counter example to show that you are wrong, and you can work out the right equation. Assuming Rs =47, and Z = 47j. Then magnitude of the voltage at Rin would be mag of voltage at Lin * 1/sq.rt(2), or 0.707* mag(Lin). According to your equation, you would have that being 0.5*mag(Lin). Given that, I did not read the rest of your post. |
#114
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Do loudspeaker inductors have audible polarity?
ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html Great, this page gives a hint, at 10 kHz the penetration depth into copper would be 0.65 mm, which would make the current in the centre of the conductor (my coil had a wire diameter of 0.9 mm) noticeably less than for DC. I cannot find on the page how this would affect the resistance of the circular wire though even if it gives a hint on the order of magnitude of the effect. I wonder if the math for this is terribly complex, I recall doing web searchs for this before and ending up with penetration depths, but not that magic frequency dependent factor for the circular conductor resistance. Anyway, does it appear likely a penetration depth of 0.65 mm into a 0.9 mm wire would increase the resistance of 0.7 ohms to the sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33 ohms I see at 20 kHz? Hmm... |
#115
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Do loudspeaker inductors have audible polarity?
ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html Great, this page gives a hint, at 10 kHz the penetration depth into copper would be 0.65 mm, which would make the current in the centre of the conductor (my coil had a wire diameter of 0.9 mm) noticeably less than for DC. I cannot find on the page how this would affect the resistance of the circular wire though even if it gives a hint on the order of magnitude of the effect. I wonder if the math for this is terribly complex, I recall doing web searchs for this before and ending up with penetration depths, but not that magic frequency dependent factor for the circular conductor resistance. Anyway, does it appear likely a penetration depth of 0.65 mm into a 0.9 mm wire would increase the resistance of 0.7 ohms to the sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33 ohms I see at 20 kHz? Hmm... |
#116
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Do loudspeaker inductors have audible polarity?
ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html Great, this page gives a hint, at 10 kHz the penetration depth into copper would be 0.65 mm, which would make the current in the centre of the conductor (my coil had a wire diameter of 0.9 mm) noticeably less than for DC. I cannot find on the page how this would affect the resistance of the circular wire though even if it gives a hint on the order of magnitude of the effect. I wonder if the math for this is terribly complex, I recall doing web searchs for this before and ending up with penetration depths, but not that magic frequency dependent factor for the circular conductor resistance. Anyway, does it appear likely a penetration depth of 0.65 mm into a 0.9 mm wire would increase the resistance of 0.7 ohms to the sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33 ohms I see at 20 kHz? Hmm... |
#117
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Do loudspeaker inductors have audible polarity?
ow (Goofball_star_dot_etal) wrote in message ...
On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html Great, this page gives a hint, at 10 kHz the penetration depth into copper would be 0.65 mm, which would make the current in the centre of the conductor (my coil had a wire diameter of 0.9 mm) noticeably less than for DC. I cannot find on the page how this would affect the resistance of the circular wire though even if it gives a hint on the order of magnitude of the effect. I wonder if the math for this is terribly complex, I recall doing web searchs for this before and ending up with penetration depths, but not that magic frequency dependent factor for the circular conductor resistance. Anyway, does it appear likely a penetration depth of 0.65 mm into a 0.9 mm wire would increase the resistance of 0.7 ohms to the sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33 ohms I see at 20 kHz? Hmm... |
#118
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Do loudspeaker inductors have audible polarity?
On 13 Feb 2004 11:35:52 -0800, (Svante)
wrote: (Goofball_star_dot_etal) wrote in message ... On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html Great, this page gives a hint, at 10 kHz the penetration depth into copper would be 0.65 mm, which would make the current in the centre of the conductor (my coil had a wire diameter of 0.9 mm) noticeably less than for DC. I cannot find on the page how this would affect the resistance of the circular wire though even if it gives a hint on the order of magnitude of the effect. I wonder if the math for this is terribly complex, I recall doing web searchs for this before and ending up with penetration depths, but not that magic frequency dependent factor for the circular conductor resistance. Anyway, does it appear likely a penetration depth of 0.65 mm into a 0.9 mm wire would increase the resistance of 0.7 ohms to the sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33 ohms I see at 20 kHz? Hmm... --- Google for "skin depth" and you'll get a lot of hits. Basically, when the effect comes into play, you have to consider the wire a tube with a wall thickness which goes inversely with frequency, and the area of that annular ring now becomes the area through which current flows. -- John Fields |
#119
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Do loudspeaker inductors have audible polarity?
On 13 Feb 2004 11:35:52 -0800, (Svante)
wrote: (Goofball_star_dot_etal) wrote in message ... On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html Great, this page gives a hint, at 10 kHz the penetration depth into copper would be 0.65 mm, which would make the current in the centre of the conductor (my coil had a wire diameter of 0.9 mm) noticeably less than for DC. I cannot find on the page how this would affect the resistance of the circular wire though even if it gives a hint on the order of magnitude of the effect. I wonder if the math for this is terribly complex, I recall doing web searchs for this before and ending up with penetration depths, but not that magic frequency dependent factor for the circular conductor resistance. Anyway, does it appear likely a penetration depth of 0.65 mm into a 0.9 mm wire would increase the resistance of 0.7 ohms to the sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33 ohms I see at 20 kHz? Hmm... --- Google for "skin depth" and you'll get a lot of hits. Basically, when the effect comes into play, you have to consider the wire a tube with a wall thickness which goes inversely with frequency, and the area of that annular ring now becomes the area through which current flows. -- John Fields |
#120
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Do loudspeaker inductors have audible polarity?
On 13 Feb 2004 11:35:52 -0800, (Svante)
wrote: (Goofball_star_dot_etal) wrote in message ... On 12 Feb 2004 22:59:28 -0800, (Svante) wrote: Is there an equation somewhere describing the resistance of a conductor as a function if frequency, including the skin effect? http://www.st-andrews.ac.uk/~www_pa/...rt7/page3.html Great, this page gives a hint, at 10 kHz the penetration depth into copper would be 0.65 mm, which would make the current in the centre of the conductor (my coil had a wire diameter of 0.9 mm) noticeably less than for DC. I cannot find on the page how this would affect the resistance of the circular wire though even if it gives a hint on the order of magnitude of the effect. I wonder if the math for this is terribly complex, I recall doing web searchs for this before and ending up with penetration depths, but not that magic frequency dependent factor for the circular conductor resistance. Anyway, does it appear likely a penetration depth of 0.65 mm into a 0.9 mm wire would increase the resistance of 0.7 ohms to the sqrt(18^2-15^2)=10 ohms I see at 10 kHz, or the sqrt(43^2-28^2)= 33 ohms I see at 20 kHz? Hmm... --- Google for "skin depth" and you'll get a lot of hits. Basically, when the effect comes into play, you have to consider the wire a tube with a wall thickness which goes inversely with frequency, and the area of that annular ring now becomes the area through which current flows. -- John Fields |
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