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#401
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Distorsion percentage, power or voltage?
Hi,
In message , gecwhite writes The twenty comes in because the "voltage dB" is essentially derived from the "power dB," but power is a non-linear function (square law) of voltage. Yes, I got that; I just needed to know which came first :-) By _Bell System Blue Book definition_: X(dB) = 10*log(P/P_ref) *That's* what I was looking for; many thanks. Is the Bell System Blue book available? Call it sad academic interest. [Much good stuff snipped to the clipboard for later] I hope this clears up some of your questions. All of them. Thanks very much. -- Regards, Glenn Booth |
#402
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in message news:e5d5b$4012a5ca$c247604 .............. Even in that case, a lumped model is good enough, considering all the approximations one uses in that type of anslysis. FET output devices can oscillate at a very high frequency. One would need a speaker cable model that was accurate at very high frequencies The lumped element speakercable models have a limited bandwidth. I doubt that you could write a lumped element model, for a 100 ft of cable, that would be accurate above 200 KHz. So consider the approximations. How accurately can you model the power amp? How about the connection between the output transistors to the terminals at the back of the amp? How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? How about the discontinuity between the cable and the speaker terminals? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. Besides, looking at transmission line loading is the wrong way to analyze such amps. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. One can use Maxwell equations and quantum mechanics to analyze speaker cables, too. Have you thought about doing that? I think that what you are saying is: one can go too far in analyzing speaker cables. Suppose you were writing a circuit analysis program that was to include a model of typical 12 gage speaker cable (any length). Why bother? Suppose you were to write a circuit analysis program based on quantum mechanics? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. Bob Stanton |
#403
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in message news:e5d5b$4012a5ca$c247604 .............. Even in that case, a lumped model is good enough, considering all the approximations one uses in that type of anslysis. FET output devices can oscillate at a very high frequency. One would need a speaker cable model that was accurate at very high frequencies The lumped element speakercable models have a limited bandwidth. I doubt that you could write a lumped element model, for a 100 ft of cable, that would be accurate above 200 KHz. So consider the approximations. How accurately can you model the power amp? How about the connection between the output transistors to the terminals at the back of the amp? How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? How about the discontinuity between the cable and the speaker terminals? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. Besides, looking at transmission line loading is the wrong way to analyze such amps. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. One can use Maxwell equations and quantum mechanics to analyze speaker cables, too. Have you thought about doing that? I think that what you are saying is: one can go too far in analyzing speaker cables. Suppose you were writing a circuit analysis program that was to include a model of typical 12 gage speaker cable (any length). Why bother? Suppose you were to write a circuit analysis program based on quantum mechanics? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. Bob Stanton |
#404
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in message news:e5d5b$4012a5ca$c247604 .............. Even in that case, a lumped model is good enough, considering all the approximations one uses in that type of anslysis. FET output devices can oscillate at a very high frequency. One would need a speaker cable model that was accurate at very high frequencies The lumped element speakercable models have a limited bandwidth. I doubt that you could write a lumped element model, for a 100 ft of cable, that would be accurate above 200 KHz. So consider the approximations. How accurately can you model the power amp? How about the connection between the output transistors to the terminals at the back of the amp? How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? How about the discontinuity between the cable and the speaker terminals? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. Besides, looking at transmission line loading is the wrong way to analyze such amps. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. One can use Maxwell equations and quantum mechanics to analyze speaker cables, too. Have you thought about doing that? I think that what you are saying is: one can go too far in analyzing speaker cables. Suppose you were writing a circuit analysis program that was to include a model of typical 12 gage speaker cable (any length). Why bother? Suppose you were to write a circuit analysis program based on quantum mechanics? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. Bob Stanton |
#405
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in message news:e5d5b$4012a5ca$c247604 .............. Even in that case, a lumped model is good enough, considering all the approximations one uses in that type of anslysis. FET output devices can oscillate at a very high frequency. One would need a speaker cable model that was accurate at very high frequencies The lumped element speakercable models have a limited bandwidth. I doubt that you could write a lumped element model, for a 100 ft of cable, that would be accurate above 200 KHz. So consider the approximations. How accurately can you model the power amp? How about the connection between the output transistors to the terminals at the back of the amp? How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? How about the discontinuity between the cable and the speaker terminals? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. Besides, looking at transmission line loading is the wrong way to analyze such amps. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. One can use Maxwell equations and quantum mechanics to analyze speaker cables, too. Have you thought about doing that? I think that what you are saying is: one can go too far in analyzing speaker cables. Suppose you were writing a circuit analysis program that was to include a model of typical 12 gage speaker cable (any length). Why bother? Suppose you were to write a circuit analysis program based on quantum mechanics? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. Bob Stanton |
#406
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Distorsion percentage, power or voltage?
On Sun, 25 Jan 2004 20:33:59 GMT, gecwhite wrote:
As one who makes his living in the RF field, I say you are flatly wrong. Distortion is an acute matter of concern in modern digital radios that require high linearity. For example, massive amounts of money are spent in feedforward power amplifiers for cell base stations. For example, PA non-linearity is one of the major limiting factors in WLAN OFDM transmitter link budgets (52 subcarriers and up to 64-QAM on each subcarrier). And it goes on and on. My posts have been in accordance with "the generalities" of dB's and dBm's and was prompted in response to a particular posting. With this in mind, it is possible to find exceptions within disciplines. CATV was merely one of these. So is yours. You get no argument from me in this respect. A bandpass filter could be used to reduce out of band signals, sometimes lowpass, even less frequently, highpass. This would be especially the case for RF amplifiers, broadband RF amps and to some extent transmitters etc. BP filters can't remove odd-order intermod products, and no one finds sine waves, by themselves, particularly interesting, even music listeners. Because CATV equipment is so wide-banded, even-order distortion is also major concern. That is why balanced amplifiers dominate that field. No one has argued or proposed that they do. Read what I have said about CATV. However, we are biginning to stray from the original post. It was your second-line statement, above, to which I was makeing an exception I agree. They use dB as a relative level, ... A dB, by itself, it always just "relative," by definition. It is a ratio and nothing else. No one has said otherwise. Thanks ...when it comes to specifying distortion. When I wrote "distortion in -dB(power)", I ment the distortion power *relative* to the signal power. Which I believe should almost go without needing to say so. Hmmm. I checked my posts. I believe you may be quoting someone else. CATV's are outside my experience. Nor did I particularly single them out for distinction. My point was that most people in the side industries (non-audio) which you cited, still use and properly so, dB's as a relative term... It can't be used in any way _but_ relative, because no absolute reference point can be gleaned from it in the absence of other information! Precisely. So we agree even though my points are understated rather than emphatic. ... and dBm's when implying a 'standard' level. Sure it is a "standard" notation, but more importantly it refers to an _absolute_ power level. Precisely. So we agree even though my points are understated rather than emphatic. Now. This really ends my interest in this thread. |
#407
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Distorsion percentage, power or voltage?
On Sun, 25 Jan 2004 20:33:59 GMT, gecwhite wrote:
As one who makes his living in the RF field, I say you are flatly wrong. Distortion is an acute matter of concern in modern digital radios that require high linearity. For example, massive amounts of money are spent in feedforward power amplifiers for cell base stations. For example, PA non-linearity is one of the major limiting factors in WLAN OFDM transmitter link budgets (52 subcarriers and up to 64-QAM on each subcarrier). And it goes on and on. My posts have been in accordance with "the generalities" of dB's and dBm's and was prompted in response to a particular posting. With this in mind, it is possible to find exceptions within disciplines. CATV was merely one of these. So is yours. You get no argument from me in this respect. A bandpass filter could be used to reduce out of band signals, sometimes lowpass, even less frequently, highpass. This would be especially the case for RF amplifiers, broadband RF amps and to some extent transmitters etc. BP filters can't remove odd-order intermod products, and no one finds sine waves, by themselves, particularly interesting, even music listeners. Because CATV equipment is so wide-banded, even-order distortion is also major concern. That is why balanced amplifiers dominate that field. No one has argued or proposed that they do. Read what I have said about CATV. However, we are biginning to stray from the original post. It was your second-line statement, above, to which I was makeing an exception I agree. They use dB as a relative level, ... A dB, by itself, it always just "relative," by definition. It is a ratio and nothing else. No one has said otherwise. Thanks ...when it comes to specifying distortion. When I wrote "distortion in -dB(power)", I ment the distortion power *relative* to the signal power. Which I believe should almost go without needing to say so. Hmmm. I checked my posts. I believe you may be quoting someone else. CATV's are outside my experience. Nor did I particularly single them out for distinction. My point was that most people in the side industries (non-audio) which you cited, still use and properly so, dB's as a relative term... It can't be used in any way _but_ relative, because no absolute reference point can be gleaned from it in the absence of other information! Precisely. So we agree even though my points are understated rather than emphatic. ... and dBm's when implying a 'standard' level. Sure it is a "standard" notation, but more importantly it refers to an _absolute_ power level. Precisely. So we agree even though my points are understated rather than emphatic. Now. This really ends my interest in this thread. |
#408
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Distorsion percentage, power or voltage?
On Sun, 25 Jan 2004 20:33:59 GMT, gecwhite wrote:
As one who makes his living in the RF field, I say you are flatly wrong. Distortion is an acute matter of concern in modern digital radios that require high linearity. For example, massive amounts of money are spent in feedforward power amplifiers for cell base stations. For example, PA non-linearity is one of the major limiting factors in WLAN OFDM transmitter link budgets (52 subcarriers and up to 64-QAM on each subcarrier). And it goes on and on. My posts have been in accordance with "the generalities" of dB's and dBm's and was prompted in response to a particular posting. With this in mind, it is possible to find exceptions within disciplines. CATV was merely one of these. So is yours. You get no argument from me in this respect. A bandpass filter could be used to reduce out of band signals, sometimes lowpass, even less frequently, highpass. This would be especially the case for RF amplifiers, broadband RF amps and to some extent transmitters etc. BP filters can't remove odd-order intermod products, and no one finds sine waves, by themselves, particularly interesting, even music listeners. Because CATV equipment is so wide-banded, even-order distortion is also major concern. That is why balanced amplifiers dominate that field. No one has argued or proposed that they do. Read what I have said about CATV. However, we are biginning to stray from the original post. It was your second-line statement, above, to which I was makeing an exception I agree. They use dB as a relative level, ... A dB, by itself, it always just "relative," by definition. It is a ratio and nothing else. No one has said otherwise. Thanks ...when it comes to specifying distortion. When I wrote "distortion in -dB(power)", I ment the distortion power *relative* to the signal power. Which I believe should almost go without needing to say so. Hmmm. I checked my posts. I believe you may be quoting someone else. CATV's are outside my experience. Nor did I particularly single them out for distinction. My point was that most people in the side industries (non-audio) which you cited, still use and properly so, dB's as a relative term... It can't be used in any way _but_ relative, because no absolute reference point can be gleaned from it in the absence of other information! Precisely. So we agree even though my points are understated rather than emphatic. ... and dBm's when implying a 'standard' level. Sure it is a "standard" notation, but more importantly it refers to an _absolute_ power level. Precisely. So we agree even though my points are understated rather than emphatic. Now. This really ends my interest in this thread. |
#409
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Distorsion percentage, power or voltage?
On Sun, 25 Jan 2004 20:33:59 GMT, gecwhite wrote:
As one who makes his living in the RF field, I say you are flatly wrong. Distortion is an acute matter of concern in modern digital radios that require high linearity. For example, massive amounts of money are spent in feedforward power amplifiers for cell base stations. For example, PA non-linearity is one of the major limiting factors in WLAN OFDM transmitter link budgets (52 subcarriers and up to 64-QAM on each subcarrier). And it goes on and on. My posts have been in accordance with "the generalities" of dB's and dBm's and was prompted in response to a particular posting. With this in mind, it is possible to find exceptions within disciplines. CATV was merely one of these. So is yours. You get no argument from me in this respect. A bandpass filter could be used to reduce out of band signals, sometimes lowpass, even less frequently, highpass. This would be especially the case for RF amplifiers, broadband RF amps and to some extent transmitters etc. BP filters can't remove odd-order intermod products, and no one finds sine waves, by themselves, particularly interesting, even music listeners. Because CATV equipment is so wide-banded, even-order distortion is also major concern. That is why balanced amplifiers dominate that field. No one has argued or proposed that they do. Read what I have said about CATV. However, we are biginning to stray from the original post. It was your second-line statement, above, to which I was makeing an exception I agree. They use dB as a relative level, ... A dB, by itself, it always just "relative," by definition. It is a ratio and nothing else. No one has said otherwise. Thanks ...when it comes to specifying distortion. When I wrote "distortion in -dB(power)", I ment the distortion power *relative* to the signal power. Which I believe should almost go without needing to say so. Hmmm. I checked my posts. I believe you may be quoting someone else. CATV's are outside my experience. Nor did I particularly single them out for distinction. My point was that most people in the side industries (non-audio) which you cited, still use and properly so, dB's as a relative term... It can't be used in any way _but_ relative, because no absolute reference point can be gleaned from it in the absence of other information! Precisely. So we agree even though my points are understated rather than emphatic. ... and dBm's when implying a 'standard' level. Sure it is a "standard" notation, but more importantly it refers to an _absolute_ power level. Precisely. So we agree even though my points are understated rather than emphatic. Now. This really ends my interest in this thread. |
#410
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Distorsion percentage, power or voltage?
chung wrote in messag ...
How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Bob Stantone news:c0439$40143681$c247604 |
#411
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Distorsion percentage, power or voltage?
chung wrote in messag ...
How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Bob Stantone news:c0439$40143681$c247604 |
#412
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Distorsion percentage, power or voltage?
chung wrote in messag ...
How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Bob Stantone news:c0439$40143681$c247604 |
#413
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Distorsion percentage, power or voltage?
chung wrote in messag ...
How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Bob Stantone news:c0439$40143681$c247604 |
#414
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in messag ... How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. How about the rest of the uncertainties I listed which you snipped? How about the time it would take to carefully measure those parameters of the cable? How closely you think the speaker cables resemble a transmission line? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. Like I said before, that application of determining stability at high frequencies is the only application for using transmission line models for speaker cables in audio application that I can remotely justify. Of course, the transmission line model is very useful in other areas of electronics. But that is neither here nor there in the present discussion. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Note the context here. In audio, there is no need to use a transmission line model for speaker cables. In other areas of electronics, transmission line models are used for the study of, well, transmission lines. Why don't you come up with some reason to use that model in audio? Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. No, I was referring to circuit analysis in general. You know, transisitors, resistors, capacitors and so on? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Give your examples, then. You are looking like someone who has a certain tool and want to solve every problem with that tool. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Look at those approximations again. Those are realistic modelling issues in any application where speaker cables are involved. Bob Stantone news:c0439$40143681$c247604 |
#415
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in messag ... How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. How about the rest of the uncertainties I listed which you snipped? How about the time it would take to carefully measure those parameters of the cable? How closely you think the speaker cables resemble a transmission line? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. Like I said before, that application of determining stability at high frequencies is the only application for using transmission line models for speaker cables in audio application that I can remotely justify. Of course, the transmission line model is very useful in other areas of electronics. But that is neither here nor there in the present discussion. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Note the context here. In audio, there is no need to use a transmission line model for speaker cables. In other areas of electronics, transmission line models are used for the study of, well, transmission lines. Why don't you come up with some reason to use that model in audio? Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. No, I was referring to circuit analysis in general. You know, transisitors, resistors, capacitors and so on? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Give your examples, then. You are looking like someone who has a certain tool and want to solve every problem with that tool. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Look at those approximations again. Those are realistic modelling issues in any application where speaker cables are involved. Bob Stantone news:c0439$40143681$c247604 |
#416
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in messag ... How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. How about the rest of the uncertainties I listed which you snipped? How about the time it would take to carefully measure those parameters of the cable? How closely you think the speaker cables resemble a transmission line? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. Like I said before, that application of determining stability at high frequencies is the only application for using transmission line models for speaker cables in audio application that I can remotely justify. Of course, the transmission line model is very useful in other areas of electronics. But that is neither here nor there in the present discussion. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Note the context here. In audio, there is no need to use a transmission line model for speaker cables. In other areas of electronics, transmission line models are used for the study of, well, transmission lines. Why don't you come up with some reason to use that model in audio? Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. No, I was referring to circuit analysis in general. You know, transisitors, resistors, capacitors and so on? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Give your examples, then. You are looking like someone who has a certain tool and want to solve every problem with that tool. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Look at those approximations again. Those are realistic modelling issues in any application where speaker cables are involved. Bob Stantone news:c0439$40143681$c247604 |
#417
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Distorsion percentage, power or voltage?
Bob-Stanton wrote:
chung wrote in messag ... How accurately do you model the skin effect and resistive losses? How about the loss tangents of the dielectric? How close to an ideal transmission line is a pair of wires side by side? An S-parameter based cable model, would include all of the above factors and more. How about the rest of the uncertainties I listed which you snipped? How about the time it would take to carefully measure those parameters of the cable? How closely you think the speaker cables resemble a transmission line? In the end, you are making many approximations in such calculations. Whether to approximate the cable with a lumped model or a transmission line model is a small difference, compared to the large uncertainties in the rest of the system. You say that the uncentaninties in the rest of the system are greater than the differences between a transmission line model, and a crude components cable model. That is true, in the application you suggested, but that is not the only possible application for a cable model. Like I said before, that application of determining stability at high frequencies is the only application for using transmission line models for speaker cables in audio application that I can remotely justify. Of course, the transmission line model is very useful in other areas of electronics. But that is neither here nor there in the present discussion. It will be like trying to find an answer to 5 significant digits, when all your inputs only have 2 significant digits. You are chasing 4th order effects when you don't even have second order effects under control. ... Besides, looking at transmission line loading is the wrong way to analyze such amps. It was *you*, who in a previous message, suggested using a cable model, for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Much better to vary the output loading and make sure that the amp is stable for all possible loads. And you would model that with resistive, capacitve and inductive loads. Trust me, no one analyzes the stability of an audio amp by using transmission line models of cables. You are the one who suggested using a cable model for testing amplifier stability. Yes, and I was trying really hard to come up with a case where you might want to use the transmission line model in audio. Why bother? Because you can't think of any application that requires an accurate cable model, you think one is not needed. You are being like the man in the 1880's, who suggested closing the US Patent Office, because "all possible inventions" had already been made. Note the context here. In audio, there is no need to use a transmission line model for speaker cables. In other areas of electronics, transmission line models are used for the study of, well, transmission lines. Why don't you come up with some reason to use that model in audio? Suppose you were to write a circuit analysis program based on quantum mechanics? It is not necessary. An S-parameter based cable model, already takes into account *all the factors* that cause cable loss, including quantum effects, if any. No, I was referring to circuit analysis in general. You know, transisitors, resistors, capacitors and so on? This model could be useful for educational perposes, and also would have some pratical applications. Not for audio cables or audio amps. Again, you are being very short sighted. Give your examples, then. You are looking like someone who has a certain tool and want to solve every problem with that tool. Would you write a speaker cable model that was "dead on" accurate, or write a (close approximation) component type model? See all the approximations above. The "approximations above" are only for a limited case. They does not prove there will never be a need for an accurate cable model. Look at those approximations again. Those are realistic modelling issues in any application where speaker cables are involved. Bob Stantone news:c0439$40143681$c247604 |
#418
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Distorsion percentage, power or voltage?
"Bob-Stanton" wrote in message om... chung wrote in message news:eb5e8$400d7230$c247604 snip, not relevant to below There are a lot of different kinds of "dB's": dB - plain old power ratio. dBa - adjusted decibels dBc - referred to a carrier. dBd - gain of an antenna dBi - another gain of an antenna dBk - dB relative to 1000 Watts dBm - obscure reference level, often used by military types. dBm0 - refered to zero transmission level (in dBm) dBmp - dB measured with psophometer weighting. dBmr - dB title for men. dbmV - Very useful CATV reference level, in wide usage. dBrap - Relative power levels of RAP music songs. dBrn - dB used by registered nurses. dBrnc - dB's used by the Republicans? dBV - Output voltage, referred to 1 V input. dBW - dB referred to 1 Watt dBx - Output level, relative to an *unknown* input level. (I may have gotten some of the above definitions wrong.) Bob Stanton LOL!! Thanks. Harry |
#419
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Distorsion percentage, power or voltage?
"Bob-Stanton" wrote in message om... chung wrote in message news:eb5e8$400d7230$c247604 snip, not relevant to below There are a lot of different kinds of "dB's": dB - plain old power ratio. dBa - adjusted decibels dBc - referred to a carrier. dBd - gain of an antenna dBi - another gain of an antenna dBk - dB relative to 1000 Watts dBm - obscure reference level, often used by military types. dBm0 - refered to zero transmission level (in dBm) dBmp - dB measured with psophometer weighting. dBmr - dB title for men. dbmV - Very useful CATV reference level, in wide usage. dBrap - Relative power levels of RAP music songs. dBrn - dB used by registered nurses. dBrnc - dB's used by the Republicans? dBV - Output voltage, referred to 1 V input. dBW - dB referred to 1 Watt dBx - Output level, relative to an *unknown* input level. (I may have gotten some of the above definitions wrong.) Bob Stanton LOL!! Thanks. Harry |
#420
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Distorsion percentage, power or voltage?
"Bob-Stanton" wrote in message om... chung wrote in message news:eb5e8$400d7230$c247604 snip, not relevant to below There are a lot of different kinds of "dB's": dB - plain old power ratio. dBa - adjusted decibels dBc - referred to a carrier. dBd - gain of an antenna dBi - another gain of an antenna dBk - dB relative to 1000 Watts dBm - obscure reference level, often used by military types. dBm0 - refered to zero transmission level (in dBm) dBmp - dB measured with psophometer weighting. dBmr - dB title for men. dbmV - Very useful CATV reference level, in wide usage. dBrap - Relative power levels of RAP music songs. dBrn - dB used by registered nurses. dBrnc - dB's used by the Republicans? dBV - Output voltage, referred to 1 V input. dBW - dB referred to 1 Watt dBx - Output level, relative to an *unknown* input level. (I may have gotten some of the above definitions wrong.) Bob Stanton LOL!! Thanks. Harry |
#421
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Distorsion percentage, power or voltage?
"Bob-Stanton" wrote in message om... chung wrote in message news:eb5e8$400d7230$c247604 snip, not relevant to below There are a lot of different kinds of "dB's": dB - plain old power ratio. dBa - adjusted decibels dBc - referred to a carrier. dBd - gain of an antenna dBi - another gain of an antenna dBk - dB relative to 1000 Watts dBm - obscure reference level, often used by military types. dBm0 - refered to zero transmission level (in dBm) dBmp - dB measured with psophometer weighting. dBmr - dB title for men. dbmV - Very useful CATV reference level, in wide usage. dBrap - Relative power levels of RAP music songs. dBrn - dB used by registered nurses. dBrnc - dB's used by the Republicans? dBV - Output voltage, referred to 1 V input. dBW - dB referred to 1 Watt dBx - Output level, relative to an *unknown* input level. (I may have gotten some of the above definitions wrong.) Bob Stanton LOL!! Thanks. Harry |
#422
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Distorsion percentage, power or voltage?
Glenn Booth wrote: Hi, In message , gecwhite writes The twenty comes in because the "voltage dB" is essentially derived from the "power dB," but power is a non-linear function (square law) of voltage. Yes, I got that; I just needed to know which came first :-) By _Bell System Blue Book definition_: X(dB) = 10*log(P/P_ref) *That's* what I was looking for; many thanks. I would like to add that I don't believe the "origin" notes at http://www.madengineer.com/blunders/decibels.htm. There are no sources cited and the author fails to decently answer his own questions: "Why is the log multiplied by twenty? If it's deci, why not multiply (or divide!) by 10? That is, why the deci?" It is "deci" because of the '10' multiplying the log. The -bel was "already" log-based-10; so that would not explain it. The only thing that made it deci- was the 10 multiplier for the log-base-10. For electrical work, how the '20' comes in has been demonstrated. I'll leave the '20,' as a sound pressure, as an exercise for the student, hah hah. On the other hand, the site http://www.sizes.com/units/decibel.htm does cite sources and very old ones at that. I have many engineering texts, and *every one* defines the original dB as a power ratio. One of my physics texts (R. Serway) gives the original definition in the chapter on sound waves as / I \ x(dB) = 10*log(-----) \ Io/ where the intensity 'I' of a sound wave is P_sound_wave I := --------------. Area So the definition is definitely a power (or energy) relationship, and the work is relevent to that carried in an acoustical wave. 'Io' is defined as the intensity of a sound wave at the threshold of hearing. Note that the area of any individual's ear is constant, regardless of wave intensity. Therefore, the above acoustically related definition has the area simply "drop out," since it is identical in the numerator and denominator. We are then left with / P_sound_wave \ x(dB) = 10*log(------------------). \P_sound_wave_ref/ This is a _power ratio_ and once it is reduced to that, it makes no difference "where" the power is. It could be in an acoustical wave, a resistor, a light wave..... the definition does not then require the statement of any particular medium, or energy carrying means; although it probably was _sourced_ in the acoustical world. The basic power definition of the dB is therefore a highly generalized one. It is doubtful that the original work was concerned with anything other than sound intensity. So bet 20*log(pressure_ratio), as an original definition, to be wrong. A good rule is to demand citations. Is the Bell System Blue book available? You might see them on ebay from time to time. They seem to get high prices ($50). I should note my language is sloppy. The term "Blue Book" is not well defined and I know Bell labs published more than one. How many were "blue," I don't know. My particular "blue book" is _Transmission Systems for Communications_ 3rd Ed, (c) 1964 Bell Telephone Laboratories, Inc. Still an excellent text, ime. [Much good stuff snipped to the clipboard for later] I hope this clears up some of your questions. All of them. Thanks very much. You're welcome! |
#423
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Distorsion percentage, power or voltage?
Glenn Booth wrote: Hi, In message , gecwhite writes The twenty comes in because the "voltage dB" is essentially derived from the "power dB," but power is a non-linear function (square law) of voltage. Yes, I got that; I just needed to know which came first :-) By _Bell System Blue Book definition_: X(dB) = 10*log(P/P_ref) *That's* what I was looking for; many thanks. I would like to add that I don't believe the "origin" notes at http://www.madengineer.com/blunders/decibels.htm. There are no sources cited and the author fails to decently answer his own questions: "Why is the log multiplied by twenty? If it's deci, why not multiply (or divide!) by 10? That is, why the deci?" It is "deci" because of the '10' multiplying the log. The -bel was "already" log-based-10; so that would not explain it. The only thing that made it deci- was the 10 multiplier for the log-base-10. For electrical work, how the '20' comes in has been demonstrated. I'll leave the '20,' as a sound pressure, as an exercise for the student, hah hah. On the other hand, the site http://www.sizes.com/units/decibel.htm does cite sources and very old ones at that. I have many engineering texts, and *every one* defines the original dB as a power ratio. One of my physics texts (R. Serway) gives the original definition in the chapter on sound waves as / I \ x(dB) = 10*log(-----) \ Io/ where the intensity 'I' of a sound wave is P_sound_wave I := --------------. Area So the definition is definitely a power (or energy) relationship, and the work is relevent to that carried in an acoustical wave. 'Io' is defined as the intensity of a sound wave at the threshold of hearing. Note that the area of any individual's ear is constant, regardless of wave intensity. Therefore, the above acoustically related definition has the area simply "drop out," since it is identical in the numerator and denominator. We are then left with / P_sound_wave \ x(dB) = 10*log(------------------). \P_sound_wave_ref/ This is a _power ratio_ and once it is reduced to that, it makes no difference "where" the power is. It could be in an acoustical wave, a resistor, a light wave..... the definition does not then require the statement of any particular medium, or energy carrying means; although it probably was _sourced_ in the acoustical world. The basic power definition of the dB is therefore a highly generalized one. It is doubtful that the original work was concerned with anything other than sound intensity. So bet 20*log(pressure_ratio), as an original definition, to be wrong. A good rule is to demand citations. Is the Bell System Blue book available? You might see them on ebay from time to time. They seem to get high prices ($50). I should note my language is sloppy. The term "Blue Book" is not well defined and I know Bell labs published more than one. How many were "blue," I don't know. My particular "blue book" is _Transmission Systems for Communications_ 3rd Ed, (c) 1964 Bell Telephone Laboratories, Inc. Still an excellent text, ime. [Much good stuff snipped to the clipboard for later] I hope this clears up some of your questions. All of them. Thanks very much. You're welcome! |
#424
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Distorsion percentage, power or voltage?
Glenn Booth wrote: Hi, In message , gecwhite writes The twenty comes in because the "voltage dB" is essentially derived from the "power dB," but power is a non-linear function (square law) of voltage. Yes, I got that; I just needed to know which came first :-) By _Bell System Blue Book definition_: X(dB) = 10*log(P/P_ref) *That's* what I was looking for; many thanks. I would like to add that I don't believe the "origin" notes at http://www.madengineer.com/blunders/decibels.htm. There are no sources cited and the author fails to decently answer his own questions: "Why is the log multiplied by twenty? If it's deci, why not multiply (or divide!) by 10? That is, why the deci?" It is "deci" because of the '10' multiplying the log. The -bel was "already" log-based-10; so that would not explain it. The only thing that made it deci- was the 10 multiplier for the log-base-10. For electrical work, how the '20' comes in has been demonstrated. I'll leave the '20,' as a sound pressure, as an exercise for the student, hah hah. On the other hand, the site http://www.sizes.com/units/decibel.htm does cite sources and very old ones at that. I have many engineering texts, and *every one* defines the original dB as a power ratio. One of my physics texts (R. Serway) gives the original definition in the chapter on sound waves as / I \ x(dB) = 10*log(-----) \ Io/ where the intensity 'I' of a sound wave is P_sound_wave I := --------------. Area So the definition is definitely a power (or energy) relationship, and the work is relevent to that carried in an acoustical wave. 'Io' is defined as the intensity of a sound wave at the threshold of hearing. Note that the area of any individual's ear is constant, regardless of wave intensity. Therefore, the above acoustically related definition has the area simply "drop out," since it is identical in the numerator and denominator. We are then left with / P_sound_wave \ x(dB) = 10*log(------------------). \P_sound_wave_ref/ This is a _power ratio_ and once it is reduced to that, it makes no difference "where" the power is. It could be in an acoustical wave, a resistor, a light wave..... the definition does not then require the statement of any particular medium, or energy carrying means; although it probably was _sourced_ in the acoustical world. The basic power definition of the dB is therefore a highly generalized one. It is doubtful that the original work was concerned with anything other than sound intensity. So bet 20*log(pressure_ratio), as an original definition, to be wrong. A good rule is to demand citations. Is the Bell System Blue book available? You might see them on ebay from time to time. They seem to get high prices ($50). I should note my language is sloppy. The term "Blue Book" is not well defined and I know Bell labs published more than one. How many were "blue," I don't know. My particular "blue book" is _Transmission Systems for Communications_ 3rd Ed, (c) 1964 Bell Telephone Laboratories, Inc. Still an excellent text, ime. [Much good stuff snipped to the clipboard for later] I hope this clears up some of your questions. All of them. Thanks very much. You're welcome! |
#425
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Distorsion percentage, power or voltage?
Glenn Booth wrote: Hi, In message , gecwhite writes The twenty comes in because the "voltage dB" is essentially derived from the "power dB," but power is a non-linear function (square law) of voltage. Yes, I got that; I just needed to know which came first :-) By _Bell System Blue Book definition_: X(dB) = 10*log(P/P_ref) *That's* what I was looking for; many thanks. I would like to add that I don't believe the "origin" notes at http://www.madengineer.com/blunders/decibels.htm. There are no sources cited and the author fails to decently answer his own questions: "Why is the log multiplied by twenty? If it's deci, why not multiply (or divide!) by 10? That is, why the deci?" It is "deci" because of the '10' multiplying the log. The -bel was "already" log-based-10; so that would not explain it. The only thing that made it deci- was the 10 multiplier for the log-base-10. For electrical work, how the '20' comes in has been demonstrated. I'll leave the '20,' as a sound pressure, as an exercise for the student, hah hah. On the other hand, the site http://www.sizes.com/units/decibel.htm does cite sources and very old ones at that. I have many engineering texts, and *every one* defines the original dB as a power ratio. One of my physics texts (R. Serway) gives the original definition in the chapter on sound waves as / I \ x(dB) = 10*log(-----) \ Io/ where the intensity 'I' of a sound wave is P_sound_wave I := --------------. Area So the definition is definitely a power (or energy) relationship, and the work is relevent to that carried in an acoustical wave. 'Io' is defined as the intensity of a sound wave at the threshold of hearing. Note that the area of any individual's ear is constant, regardless of wave intensity. Therefore, the above acoustically related definition has the area simply "drop out," since it is identical in the numerator and denominator. We are then left with / P_sound_wave \ x(dB) = 10*log(------------------). \P_sound_wave_ref/ This is a _power ratio_ and once it is reduced to that, it makes no difference "where" the power is. It could be in an acoustical wave, a resistor, a light wave..... the definition does not then require the statement of any particular medium, or energy carrying means; although it probably was _sourced_ in the acoustical world. The basic power definition of the dB is therefore a highly generalized one. It is doubtful that the original work was concerned with anything other than sound intensity. So bet 20*log(pressure_ratio), as an original definition, to be wrong. A good rule is to demand citations. Is the Bell System Blue book available? You might see them on ebay from time to time. They seem to get high prices ($50). I should note my language is sloppy. The term "Blue Book" is not well defined and I know Bell labs published more than one. How many were "blue," I don't know. My particular "blue book" is _Transmission Systems for Communications_ 3rd Ed, (c) 1964 Bell Telephone Laboratories, Inc. Still an excellent text, ime. [Much good stuff snipped to the clipboard for later] I hope this clears up some of your questions. All of them. Thanks very much. You're welcome! |
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