Phono rig capacitance

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.)

Dfel, the mathematics that is involved in analyzing RLC circuits is quite complex, and probably beyond the scope of what is practical to discuss in a reasonable timeframe in a forum such as this. However, I think that a careful reading of the "cartridge loading" paper I linked to in my previous post, plus the post by JCarr that I also linked to, essentially covers all that needs to be understood for what you are trying to achieve.

Also, regarding:

Z = R/sqrt(R^2 +X^2) where X is abs(Xc-XL)

That doesn't look right to me, for any possible connection arrangement of an R, an L, and a C. I think that everything after the division sign would be correct for the overall impedance of the three elements connected in a certain configuration, but I don't understand the division into R (perhaps that relates to the cosine of the phase angle of the impedance, rather than the magnitude of the impedance?). And in any event the overall impedance of the three elements is not what is of direct interest. As can be seen in the first figure in the "cartridge loading" paper what is of interest is the relation between the voltage which appears across the capacitance and the voltage (Vc) at the input.

Best regards,
-- Al

Well, here is what I have done.

The computation does become complex, for spread sheeting etc..once you have to start looking into the differential equations. Do-able but much more practical to handle it using a brute force method, enter the circuit modelling software, which is what I did.

I used the circuit here used in this article: http://www.hagtech.com/loading.html

I adjusted the parameters for the 103R and a cinemag's reflected impedance. Here is the thing, for an MC setup, the capacitance and resistance parameters are of little consequence when the reflected impedance is used, contrary to the article.

Let me explain:

The article is looking at .47k 4.7 and 47k, but in reality the reflected impedance is .47K (470 Ohm) or less for just about any SUT. Now when examining the circuit at > 100 Ohms, minimum recommended loading for the cart we are talking about. It appears that the capacitance can create a huge roll off/tweak the subsonic spike as in the article. So this leads to looking at the assumed inductance. Most MCs have inductance between 5uH and 5mH ( 1mH =1000 uH). Now the results make sense, and rules of thumb/ common observations people have mentioned all come to light. The MC cartridge only becomes sensitive as the inductance moves higher.

For a cartdige with internal inductance 5-250uH, and a cable such as mogami 2549 which has 26pf/ft capacitance, 0.24uH/ft inductance and 0.022/ft Ohms resistance it becomes very difficult to change the subsonic spike by altering length and creating a roll off of even 0.1db at 20khz is just about out of question. The inductance is inconsequential all around, as for the capacitance well it depends.

So at the end of the article, they also explain this. The resonant qualities in a moving coil setup can essentially be reduced to its inductance relationship see . This I verified to be true when the carts output inductance is on the low end of the sliding scale. However as it approaches closer to 5mH this realtionship changes and it becomes very easy to create a less than optimal frequency response.

Final notes:
-Most available wires, used for phono interconnects and for tonearm wiring are suitable for the task and in MC setups do not create meaningful problems in response iff the MC cart's inernal inductance is low.

-As the MC cart's internal inductance approaches 5mh, all of these things become a problem, and it becomes easy to create a substantial roll off by altering interconnect length and by selecting different tone arm wiring. I.E/ The capacitance begins to matter MUCH more.

-Sadly the inductance spec is rarely given for any MC cartridge, so you are essentially in the dark before hand, but experimenting will reveal OBVIOUS results as the response curve can be very responsive when inductance is high, and will give almost no changes in the audible range when they are low.

-Low inductance MCs are clearly preferable and easier to manage within the system

-Loading for MMs, very different story, this can be a substantial problem. Capacitance does matter MUCH more.

-The circuit is simplified and does not give the entire story. The way that a phono stage responds to the ultrasonic information and the RLC can be complex, beyond the scope of a simple model and can be very specific depending on how your preamp operates. The pre/phono amp matters....DUH!.

Oh yeah, one more note on that article. It appears that they have grossly inflated the inductance figure on MCs, as I pointed out, for a typical MC cartridge. Some googling around can confirm that most are really a couple of uH to max a couple hundred uh MAX. However this was done to illustrate the point that they were trying to make, and their calculator is scaled back (but still inflated) to show a worse case scenario which is useful to just about anyone out there using the calculator with modern MC.