First, kudos on your interest in applying engineering principles to audio, and thereby trying to reduce the randomness that often seems to be inherent in optimizing a system. And in that regard I recall your earlier thread on moving coil stepup math, which I participated in.
For a low pass filter consisting of a resistance and a capacitance, the Fc equation you cited is of course correct. There are two additional equations that are needed to answer your first question:
(a) The ratio of the voltage out of the filter to the voltage into the filter is:
Vout/Vin = 1/sqrt (1 + (f/Fc)^2)
where ^ denotes raised to the power of, i.e. squared in this case, and f is frequency, expressed in the same units as Fc.
(b) (Vout/Vin) expressed in db = 20*log(Vout/Vin)
Where log is the base 10 logarithm.
So as you can see the relevant calculations are definitely non-trivial. Perhaps some Googling would turn up online calculators which have automated some or all of this.
This calculation will be most useful for line-level interfaces. In general the high frequency rolloff caused by speaker cable capacitance will be negligible, because R in that case, the output impedance of the power amplifier, is so low. Capacitance may be relevant in the case of a few speaker cables, however, which achieve ultra-low inductance at the expense of having ultra-high capacitance, which can cause stability or other problems for some amplifiers (if used without a Zobel network). More generally, though, what should be minimized in the case of speaker cables, assuming that the goal is neutral behavior, is resistance and inductance. Resistance should be kept to a tiny fraction of speaker impedance. Inductive reactance, which is the inductive form of impedance and is measured in ohms, should be kept to a small fraction of the impedance of the speakers at high frequencies (i.e., 20 kHz, and possibly higher). Inductive reactance is denoted as Xl (l is a lower case L), and is calculated as follows:
Xl = 2*pi*f*L
where Xl is inductive reactance in ohms, L is inductance in Henries, and f is frequency in Hz.
Special considerations come into play regarding phono cables, involving the interaction of cable capacitance with the inductance of the cartridge.
For moving magnet cartridges, the manufacturer will usually provide a recommended range of load capacitance. Too little or too much capacitance will adversely affect tonal balance in the treble region, as a result of its interaction with the inductance of the cartridge. The load capacitance seen by the cartridge is the sum of the capacitances of the tonearm wiring and its connectors, the phono cable and its connectors, and the input capacitance of the phono stage.
For low output moving coil cartridges, such as the Denon 103 you mentioned, load capacitance should generally be minimized, but the magnitude and character of the difference that will make, and its importance, will depend on the design of the phono stage that is being used. See this post, beginning with the paragraph that starts with I should now debunk another myth ....
Also, see this paper regarding cartridge loading.
Finally, regarding SUTs, they add a whole additional level of complexity to all of this, which Ralph among others can probably speak to more knowledgeably than I can.
Best regards,
-- Al
For a low pass filter consisting of a resistance and a capacitance, the Fc equation you cited is of course correct. There are two additional equations that are needed to answer your first question:
(a) The ratio of the voltage out of the filter to the voltage into the filter is:
Vout/Vin = 1/sqrt (1 + (f/Fc)^2)
where ^ denotes raised to the power of, i.e. squared in this case, and f is frequency, expressed in the same units as Fc.
(b) (Vout/Vin) expressed in db = 20*log(Vout/Vin)
Where log is the base 10 logarithm.
So as you can see the relevant calculations are definitely non-trivial. Perhaps some Googling would turn up online calculators which have automated some or all of this.
This calculation will be most useful for line-level interfaces. In general the high frequency rolloff caused by speaker cable capacitance will be negligible, because R in that case, the output impedance of the power amplifier, is so low. Capacitance may be relevant in the case of a few speaker cables, however, which achieve ultra-low inductance at the expense of having ultra-high capacitance, which can cause stability or other problems for some amplifiers (if used without a Zobel network). More generally, though, what should be minimized in the case of speaker cables, assuming that the goal is neutral behavior, is resistance and inductance. Resistance should be kept to a tiny fraction of speaker impedance. Inductive reactance, which is the inductive form of impedance and is measured in ohms, should be kept to a small fraction of the impedance of the speakers at high frequencies (i.e., 20 kHz, and possibly higher). Inductive reactance is denoted as Xl (l is a lower case L), and is calculated as follows:
Xl = 2*pi*f*L
where Xl is inductive reactance in ohms, L is inductance in Henries, and f is frequency in Hz.
Special considerations come into play regarding phono cables, involving the interaction of cable capacitance with the inductance of the cartridge.
For moving magnet cartridges, the manufacturer will usually provide a recommended range of load capacitance. Too little or too much capacitance will adversely affect tonal balance in the treble region, as a result of its interaction with the inductance of the cartridge. The load capacitance seen by the cartridge is the sum of the capacitances of the tonearm wiring and its connectors, the phono cable and its connectors, and the input capacitance of the phono stage.
For low output moving coil cartridges, such as the Denon 103 you mentioned, load capacitance should generally be minimized, but the magnitude and character of the difference that will make, and its importance, will depend on the design of the phono stage that is being used. See this post, beginning with the paragraph that starts with I should now debunk another myth ....
Also, see this paper regarding cartridge loading.
Finally, regarding SUTs, they add a whole additional level of complexity to all of this, which Ralph among others can probably speak to more knowledgeably than I can.
Best regards,
-- Al