Phono rig capacitance

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

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

Jonathan, thanks very much for chiming in. Dfel, Jonathan is the designer of Lyra cartridges, so we are privileged to be receiving some exceptionally knowledgeable inputs. He is also the author of the post that I linked to earlier which explained why minimizing capacitive loading of a low inductance low output moving coil cartridge can be important, even in the absence of a SUT.

Regarding your two most recent posts, which I thought were well done summaries of some good work, I just have a couple of comments:

1)With respect to MM's, I would emphasize per my earlier comment that premature rolloff can result from too little capacitance, as well as from too much, since in the case of MM's the LC resonance will in many or most cases directly affect frequency response within the audible range. As I mentioned, in general (and perhaps always) the manufacturer's recommended range of load capacitance should be adhered to.

2)Regarding your point about inductance not being specified for many cartridges, I would expect that in general there would be a significant degree of correlation (albeit probably a very loose one) between a cartridge's inductance and its rated output voltage under the standard test conditions.

And finally, just a very minor quibble: In a couple of places in the longer of your two recent posts the word "subsonic" appears to have been substituted for "ultrasonic," although "ultrasonic" was correctly used toward the end of that post.

Regards,
-- Al

Dfel, what Jonathan said is of course correct. The cartridge does not see the capacitance on the secondary side of the SUT divided by 100 (the square of the turns ratio we are assuming). Since the SUT transforms impedance in proportion to the square of the turns ratio, the cartridge sees the **capacitive reactance** that is on the secondary side divided by 100.

Since as you indicated earlier Xc = 1/(2*pi*f*C), capacitive reactance is inversely proportional to capacitance, and so the cartridge sees the capacitance on the secondary side **multiplied** by 100.

This is all based on an assumption of ideal behavior by the SUT, of course. No transformer will behave in a completely ideal manner, due to many factors. So all of this is of course just an approximation, but it is a good approximation for practical purposes.

Regards,
-- Al

Dfel, as I indicated earlier in the thread I can't speak too knowledgeably about modeling of SUTs. But FWIW the following thoughts occur to me:

1)Depending on how the simulation program you are using works, I think you might have to model the SUT as an "ideal transformer" combined with external elements representing its non-ideal characteristics (i.e., resistance, inductance, and capacitance, to the extent that they may be significant).

2)I would expect that the resistance of its two windings would be significant enough to warrant inclusion in the model, and that it should be modeled as two resistors external to the transformer itself, one of them in series with each of the windings. Or, alternatively, the resistance of the secondary winding could be modeled as reflected into the primary circuit, multiplied by the square of the primary to secondary turns ratio.

3)I don't know how you derived the inductances shown in your model for the two windings, but I suspect that they are not what should be included in the model. I believe that what should be included are series inductances in the primary and secondary circuits representing "leakage inductances." With the secondary circuit leakage inductance alternatively being modeled on the primary side, multiplied by the square of the primary to secondary turns ratio.

4)I don't know if it would be significant enough to warrant inclusion in the model, but including a parallel combination of resistance and inductance across the primary winding MIGHT also be called for, to account for core losses and reactances. (More precisely, those elements would be modeled directly across the primary winding if the impedances in series with the secondary are modeled on the secondary side; if the secondary side impedances are modeled as reflected to the primary side the reflected secondary side impedances should be modeled closer to the primary winding than those elements).

Otherwise your model looks good to me. It assumes that the cable parameters are "lumped elements" rather than "distributed elements," but that assumption seems to me to be reasonable for present purposes.

Regards,
-- Al

... Can you please give some input on the basic structure.... I tried to follow Jcarr's model, but in the end I am still not sure why when modeling a wire connecting devices you would model the RCL in series or in parallel, and in what order you place the RCL for the wire....

As I indicated near the end of my last post, your model looks good to me aside from the SUT issues.

For the cables, R and L are in series, and C is in parallel. Representing these parameters as "lumped" elements, with the capacitance first in the chain, as you have done, rather than as a great many separate elements representing their distribution along the length of the cable, I believe is a reasonable approximation at frequencies of interest.

Regarding the SUT model, the inductances of each of the two windings will probably not be in proportion to the square of the turns ratio, and may be directly proportional to the turns ratio itself (depending on a number of variables). And more significantly, if it is not clear, the inductances that should be represented are not the inductances that each winding would have if it were divorced from the other (i.e., their self-inductance). What should be represented, as I mentioned, is "leakage inductance," in series, and perhaps also a parallel inductance (and resistance). I don't know what values would be reasonably typical for those parameters for typical SUTs.

Also, Lew's comments are good ones IMO. Jonathan's emphasis on minimizing cable capacitance on the secondary side of the SUT should also be kept in mind, of course.

Regards,
-- Al

P.S. to my previous post: Regarding "leakage inductance," see this Wikipedia writeup.

Regards,
-- Al

Looks like you've made some progress. Good!

I'm surprised that relocating the connections of the cable capacitance elements in the model (together with the minor changes you've made in some of the capacitance values) had such a profound impact on the results. I don't know how to explain that.

Also, keep in mind that even though the response peak is way above the range of audible frequencies, its amplitude and frequency are nevertheless important considerations, which stand a good chance of being audibly significant. Again, see Jonathan's post in another thread that I linked to earlier.

Regarding the transformer model, I read through the "Using Transformers in LTspice/SwitcherCAD III" paper you linked to, and I also looked at some of the literature on LTSpice at the linear.com website. Their simulation is done differently than what I was envisioning when I provided my earlier comments. I was envisioning that the transformer would be modeled as an ideal transformer (k = 1; infinite self-inductance of the windings; zero leakage inductance, etc.) in combination with external circuit elements representing its non-ideal characteristics. They are modeling it as a single non-ideal element. So take that into account when considering my earlier comments.

I would expect either approach to yield good results, IF the parameter values are suitably chosen. And again, I have no knowledge of what the appropriate values might be for a typical SUT. Also, you might try re-running your simulation with k values of say 0.9, 0.8, etc., to see how sensitive the results are to that value. k = 1 corresponds to zero leakage inductance, which of course is not possible with a real world transformer.

Finally, a note of caution. It appears that despite statements indicating that LTspice/SwitcherCAD III (or "LTSpice IV" which is what is available for download at their website) is/are "general purpose," it appears that their program is oriented toward facilitating analysis of switching power supplies. As stated in one of their papers, "LTspice is a high performance SPICE simulator, schematic capture and waveform viewer designed to speed the process of power supply design. LTspice adds enhancements and models to SPICE, significantly reducing simulation time compared to typical SPICE simulators, allowing one to view waveforms for most switching regulators in minutes compared to hours for other SPICE simulators." And of course the designs of power supply transformers and cartridge stepup transformers are vastly different.

Regards,
-- Al

IMPORTANT P.S: I just noticed that in the second model the units of the transformer coil inductances appear to be Henries, while in the first model they appear to be microHenries (with the numerical digits being the same in the two models)!!!

That would certainly seem likely to account for the differences in the results!!!

Regards,
-- Al