Higher Impedance MC Carts on Transimpedance Stages?

Mathematically, current (I) is defined as the Voltage (V) divided by the Resistance (R):

I = V/R

The current (I) is inversely proportional to the resistance (R) , i.e., the higher the current, the lower the resistance and vice versa, the lower the current, the higher the resistance.  Therefore if the resistance of your cartridge is high, you will get lower current and as a result also lower voltage.  High impedance cartridges will result in lower output and will sound like your phonostage doesn’t have adequate gain.

I worked this out. Bandwidth is where current is half of maximum. This occurs when impedance from cart inductance equals cart resistance. If the bandwidth is acceptable, cart will run fine.  Bandwidth is given as:

f = R/(6.3*L);

Or you can use the handy calculator I placed on this web page:

https://www.hagtech.com/loading.html

Hagtech, In your equation, I assume R is the internal resistance of the cartridge and L is the cartridge inductance. Since you speak of "bandwidth", "f" must be bandwidth. Further I assume R is in ohms and L is in henries. I must have something wrong, because if those assumptions are correct, then LOMCs with high internal R (>>10 ohms), like the Kiseki, would have much greater bandwidth than a typical LOMC with an internal R of ~10 or less. This happens because LOMCs have very low inductance, usually less than 50 microhenries, and therefore the denominator is always going to <<1.0. Further, I would think an equation to determine bandwidth resulting from a specific match between cartridge and phono would have to include parameters of both the cartridge and the phono stage.

For example, the Kiseki with an internal resistance of 40 ohms and an inductance of say 50 microhenries or .000050 Henries (cannot find the actual value on line) would have a bandwidth in excess of 100KHz. Whereas a more typical LOMC with an internal R of 4 ohms and similar inductance would have a ten-fold narrower bandwidth.  Even if such a cartridge has also a lower inductance, that would not help much; the predicted value for f would still be well below 100kHz.

Thanks to everyone who has contributed to the thread so far. The explanations and the equations provided are very helpful in understanding how to find a good match.

@hagtech, I'm curious to your response on lewm's reply as I can see where the way you're calculating bandwidth may not be accurate.

I did see on Steve Hoffman Forums that there is a user using a BMC with a different Kiseki cartridge also with 40 Ohm impedance and doesn't seem to be experiencing any issues with it. It may be that Kiseki has lower than typical inductance?

It's a shame that cartridge manufacturers do not provide all the specs an end user may need to make better-informed decisions.

The inductance of an LOMC is trivial, in the sense that it’s very low, on the order of 1000 times lower than MI which is already much lower than MM. Your acquaintance is probably happy because it works and he has yet to try an LOMC with truly low internal resistance. I feel that I must be misinterpreting Hagtech’d equation .