| Electrical Factors affecting system impedance -And their consequences on system Q |
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When it comes to designing woofer enclosures, the necessity to increase the volume of enclosures due to
the intrusions of drivers, vents, and bracing are well known, and generally compensated for. A less
considered concern may be the effects of additional electrical impedance to the system. This increased
impedance is due to several factors, including the source and cable impedance, impedance of the
crossover, and thermal effects, and is the focus of this article.
The Math: Any change in series impedance affects the Qes of the driver, and consequently Qts, which of
course is one of the factors used to calculate the optimum enclosure size. The Qes + additional impedance,
Qes' is calculated using the formula:
Qes' = [(Rg + Re) / Re] * Qes
Where:
Re is the DC resistance of the driver
Rg is the additional impedance
Qes is the Electrical Q of the driver
Qts' the new total Q of the driver can then be found by:
Qts' = (Qes' * Qms) / (Qes' + Qms)
Where Qms is the Mechanical Q of the driver. For the purposes of this article, the additional impedance
will be expressed as scalar quantities rather than their complex impedance.
the intrusions of drivers, vents, and bracing are well known, and generally compensated for. A less
considered concern may be the effects of additional electrical impedance to the system. This increased
impedance is due to several factors, including the source and cable impedance, impedance of the
crossover, and thermal effects, and is the focus of this article.
The Math: Any change in series impedance affects the Qes of the driver, and consequently Qts, which of
course is one of the factors used to calculate the optimum enclosure size. The Qes + additional impedance,
Qes' is calculated using the formula:
Qes' = [(Rg + Re) / Re] * Qes
Where:
Re is the DC resistance of the driver
Rg is the additional impedance
Qes is the Electrical Q of the driver
Qts' the new total Q of the driver can then be found by:
Qts' = (Qes' * Qms) / (Qes' + Qms)
Where Qms is the Mechanical Q of the driver. For the purposes of this article, the additional impedance
will be expressed as scalar quantities rather than their complex impedance.
The output impedance of the source amplifier is the first factor affecting Qe. For a tube amplifier, this
can be as much as several ohms. Solid state amps on the other hand will are typically a small fraction of an
ohm. A source impedance of 0.1 ohms will be assumed for the purposes of this discussion, and was
included in all of the following plots.
Speaker cable and interconnect impedance can also be of some minor concern. The resistance of the
cable itself may range from 0.016 to 0.1 ohm typically for a 10 foot length of 12 to 20 gauge wire
respectively. While this is pretty insignificant, the connections at the terminations, speaker, crossover and
driver will all add some small resistance. For this exercise, 0.1 ohm will be assumed as a nominal value.
Passive crossover insertion losses: The DCR of the inductors can significantly increase the series
impedance. This of course will vary depending on the gauge, length of wire in the inductor, and core
material. I'll suggest 0.4 ohms as an average value for a woofer in a 3 way system.
The increase in voice coil resistance with temperature. I have to thank Keith Howard for his article in
the November 2006 issue of Stereophile as the stimulus to write this treatise. While he tested only one
speaker, I suspect his results are reasonably representative of a well-designed driver. I found several things
interesting in his study. One is that the bulk of the increase in voice coil temperature occurred rather
quickly, within 30 seconds or so. Another was the tweeter was relatively immune to thermal effects. Most
significant was with the woofer tested, the voice coil only increased 36 degrees, which resulted in an 8%
increase in Re. The author dismissed this small increase in Re as insignificant, but I suggest that if it is not
considered, along with the other factors I've noted previously, it can make a discernible difference in the
optimum calculated enclosure volume.
can be as much as several ohms. Solid state amps on the other hand will are typically a small fraction of an
ohm. A source impedance of 0.1 ohms will be assumed for the purposes of this discussion, and was
included in all of the following plots.
Speaker cable and interconnect impedance can also be of some minor concern. The resistance of the
cable itself may range from 0.016 to 0.1 ohm typically for a 10 foot length of 12 to 20 gauge wire
respectively. While this is pretty insignificant, the connections at the terminations, speaker, crossover and
driver will all add some small resistance. For this exercise, 0.1 ohm will be assumed as a nominal value.
Passive crossover insertion losses: The DCR of the inductors can significantly increase the series
impedance. This of course will vary depending on the gauge, length of wire in the inductor, and core
material. I'll suggest 0.4 ohms as an average value for a woofer in a 3 way system.
The increase in voice coil resistance with temperature. I have to thank Keith Howard for his article in
the November 2006 issue of Stereophile as the stimulus to write this treatise. While he tested only one
speaker, I suspect his results are reasonably representative of a well-designed driver. I found several things
interesting in his study. One is that the bulk of the increase in voice coil temperature occurred rather
quickly, within 30 seconds or so. Another was the tweeter was relatively immune to thermal effects. Most
significant was with the woofer tested, the voice coil only increased 36 degrees, which resulted in an 8%
increase in Re. The author dismissed this small increase in Re as insignificant, but I suggest that if it is not
considered, along with the other factors I've noted previously, it can make a discernible difference in the
optimum calculated enclosure volume.
Continued...
