Cartridge Loading- Low output M/C

What I don’t understand is why any of the purported effects of heavy resistive loading you state could be definitively true- certainly not on tracking which is demonstrably false based on IM tests on tracking performance that I have incidentally performed as a function of load. While mechanical impact does occur as a result of electrical load- there is some back emf necessarily generated by the signal current that affects the mechanical motion, but a quick back of the envelope calculation using Lenz's law and the 10uH cartridge suggests a 2 orders of magnitude difference between the generated signal and the back EMF for a 100 ohm load at 20kHz- certainly not enough to cause tracking issues I would think. As for the rest, well, take the Madake for instance- the resistive load that people (reviewers) claim is best literally varies by nearly four orders of magnitude! I load mine with 60 ohms (as do many users) and I find that the resolution and dynamics is excellent while maintaining a natural timbre, tonal balance and micro/macro dynamics while not creating the unnatural etched image that many "high resolution" MC cartridges produce.
In any case, I’ll have to research this to see what technical white papers or similar exist on the subject.

Wyn, I am glad that JCarr finally mentioned the fact that most LOMCs I know about have a much lower nominal inductance than the 0.5mH, on which you based your first set of calculations, and thank you for re-calculating your results based on more realistic values of inductance.  I also want to thank you, Al, JCarr, Ralph, and others for this civil and erudite discussion.  Such educational interchanges are all too rare on audiophile websites.  I only recently experimented with reducing the load on my LOMC cartridges, which is to say I am running them at 47K ohms routinely now.  I find the sonics to be more open and airy that way, and I feel no impulse to move back to the more typical 100R value.  I am sure my results have most to do with the nature of my particular phono stage, my downstream components, and my two ears,

Yes, it has been quite interesting and informative for neophytes like myself.
By the way, I constructed a model for the cartridge back EMF using Lenz's law and incorporated it into my simulations.
For those who are interested, the simplest version of the law is V(t)= -LdI/dt.
In this case the parameters can be measured (the LC100A meter from Ebay is a great way to do it) and the back EMF acts to oppose the voltage developed in the coil. The fractional change (attenuation) in the signal voltage is easy to calculate as it approx. equal to -L*2*pi*frequency of interest/Rload. So, it's inversely proportional to the load R and proportional to the frequency.
For example, for a 11.8uH cartridge, with a 100 ohm load the error at 20kHz is c. 1.5%.
The model measures the current through the coil and adds a correction of the form -k*s to the source voltage.
The effect can be seen both on the frequency response and on the transient response of the Phono preamp that I'm simulating.
Is anyone interested in this, or the simulation results?

Hi Wyn,

Yes, that is of interest. And I agree with your math, of course, while having two comments:

First, I’m not sure that "back EMF" would be the best terminology to apply to what you are calculating, or the best way of considering it (see the next paragraph for my perspective on that). As you no doubt realize, that term is commonly used in the context of speakers, where a signal is applied by an external source, and back EMF is generated by the speaker as motion of a driver coil in its surrounding magnetic field continues beyond what is called for by the signal. In this case, of course, it is motion of the cartridge’s coil which generates the signal, as opposed to coil motion that occurs in response to an applied signal.

Second, I believe that what your calculation reflects is simply the high frequency rolloff which occurs as a result of the interaction of cartridge inductance and load resistance, putting aside the effects of capacitance. In your example, 2 x pi x f x L (i.e., inductive reactance) would become equal to the 100 ohm load impedance at a frequency of about 1.35 MHz, resulting in a 3 db bandwidth equal to that amount. So the error you are calculating, if indeed it can be considered to be an error, would seem to be insignificant at audible frequencies.

Regards,
-- Al

Yes, it really is back EMF- it's calculated using Lentz's law and is a consequence of Faraday's Law of Induction and it occurs as a result of the change in current through the coil- that's where the frequency dependent term comes from (the derivative). The term is subtracted from the voltage generated by the cartridge and in that way it acts to reduce the output voltage and hence the current, so there's a degree of negative feedback. I chose to use the full inductance rather than the MC inductance alone as a way to add a bit of correction for the physical displacement of the stylus/cantilever/coil that occurs as a result of the generated force. I did it that way as I don't believe that true reciprocity occurs and I have no idea what the losses are. The "gain" can be scaled to increase the mechanical feedback- for example the value of multiplier for the s term in the feedback could be increased to Icart*1.5 for example. What I actually calculate is 
FBvoltage= k.Lcart*Icart*s, where K is the scale factor mentioned above (a default of 1), s=jw as usual, Lcart is the extended inductance and Icart is the actual cartridge current in the coil which I measure using a very small R as sucky LTspice doesn't include the right components to let me do it easily.
In any case, yes, the error is small for the Madake, and the effect on the 1kHz square wave versus an ideal RIAA is miniscule. I'm currently running sims with varying load Rs to see what significant effects I see. My initial look suggests that 100 ohms has a faster rise time than 47K, for example- but it's early days.
By the way, higher inductance carts will need proportionally higher load Rs to achieve the same level of non-interaction.