Cartridge Loading- Low output M/C

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.

The recording process (particularly analog) imposes restrictions in the frequency response- limiting the HF and LF responses. These restrictions are not set in any standard and are usually due to limitations in the equipment used (Tape recorder and lathe frequency responses and dynamic ranges for examples). Good recording engineers try to minimize the effects, but they still exist.

Hello Wyn, when I saw this comment, because I run a small LP mastering operation, I thought you might like to know that the bandwidth of most LP mastering systems can go pretty high (and down to about 5Hz). Our Westerex system is bandwidth limited by a filter on the mastering amplifiers at 42KHz. This is mostly done to prevent damage to the cutter head from errant signals at the input, since the RIAA preemphasis causes a wee bit of extra gain at that frequency!  As far as dynamic range is concerned, the limitation of LP dynamic range is on the playback side, not record (although many LPs are compressed, this is mostly due to the fact that if no compression is to be used, the mastering engineer will have to spend a bit more time with the project, so compression is there to save money, not because the LP format can't do it). The cutter head can easily cut grooves that no modern arm/cartridge combination could track; the mastering engineer's task is to make sure that the cutter head does not exceed those playback limits!
Just to be clear about the effects of RFI on a preamp, the designer's concern is not so much about RFI from external sources like a radio station (although that certainly is a concern) but the RFI generated by the cartridge and interconnect cable combination (and also the input capacitance of the preamp itself). If immune to the latter, it will also be immune to the former.