Phono rig capacitance

Not qualified enough to respond but really interested in the answer to this.

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

I am lost here. Help! LOL.

I looked up RLC circuits and found how to calculate Xc reactive capacitance and XL reactive inductance, and impedance Z.

Xc= 1/(2*pi*F*C)
Xl = 2*pi*F*L
Z = R/sqrt(R^2 +X^2) where X is abs(Xc-XL)

Now I want to figure out how the signal is affected, going from the phono cartridge to the MC Step up, due to the cables R L C parameters across a wide frequency. How do I do this ? What is an appropriate model for this.

If I am using the Denon 103R, and a cinemag 3440 what values do I use and what equation do I put them into to find the voltage change at a given frequency.To my questions above I am guessing that: Once I know this I can change the frequencies for a given cable's C L R to find out the voltage change and convert it to decibles using -20Log (Vin /Vout) and it will become clear exactly what is happening when certain cables are used.

After I figure that out I would also be interested in calculating this wire affect for the connection out of the cinemag into a preamp's phono section. Then the connection from the pre to the power amp, and even amp to speakers would follow.

Perhaps the science will show that the selection of wire for those connections can make a difference within some parameters for R L C as they vary by cable makeup and length, and can help one in selecting an appropriate wire. for each part of the system.

Please help me out with modeling this as I am sadly a little lost despite my best efforts to try and figure this out. Thanks again.

I dont have this cartridge or step up, but I think it will be most useful to use it as an example since many people do.

Might as well post the specs.

Denon 103R Specs
Output 0.25 mV
Output impedance 14ohms
(no inductance spec, impedance is total I take it)

Cinemag 3440AH:
37.5,150,600 : 50K
(Into 47K rather than 50K this adjusts to 35 ohms, or 141 ohms depending on tap used)

Phono Section:
47K

Preamp:
Output Impedance 2K
(I figure 2k is good to use as most preamps will not be much higher than that value.)