Calculation verification please

Not possible. With a 1:40 SUT into 47000 ohms, the cartridge will see a -30 ohm load. The sum resistance of two parallel resistors cannot exceed the value of the lowest value resistor. So any resistor you place in parallel will reduce the impedance, not augment it. But if your cartridge has internal resistance of 1.4 ohms, it will drive 30 ohms. So why do you want 375 ohms?

I’ve been experimenting into a MC section and the manufacturer says to load between 100 - 800 ohms. I’ve tried 250, 324, 368, 404, 500 & 600 ohms and found I like best the 368 ohm loading. So now want to try using my SUT. Yes it will be fine going directly into the 47K MM section but thought I’d like to try loading it to see around the 375 ohm load.

ChatGPT said:

To determine the load the cartridge sees through the Step-Up Transformer (SUT), we use the following formula:

Rcartridge=Rphonoturns ratio2R_{ ext{cartridge}} = rac{R_{ ext{phono}}}{ ext{turns ratio}^2}Rcartridge​=turns ratio2Rphono​​

Given:

• Turns Ratio = 1:40
• Phono Input = 47,000Ω (47kΩ)

Rcartridge=47000402=470001600=29.375ΩR_{ ext{cartridge}} = rac{47000}{40^2} = rac{47000}{1600} = 29.375ΩRcartridge​=40247000​=160047000​=29.375Ω

So, the cartridge sees a 29.4Ω load.

Adjusting the Load to 375Ω

To achieve a 375Ω load at the cartridge, we need to calculate the required parallel loading resistor at the phono stage.

The formula for the effective load seen by the cartridge when a parallel resistor (RLR_LRL​) is added to the phono input is:

Rcartridge=RL∥Rphonoturns ratio2R_{ ext{cartridge}} = rac{R_L parallel R_{ ext{phono}}}{ ext{turns ratio}^2}Rcartridge​=turns ratio2RL​∥Rphono​​

First, solve for the necessary parallel resistance:

RL∥47000=375×1600R_L parallel 47000 = 375 imes 1600RL​∥47000=375×1600 RL∥47000=600,000ΩR_L parallel 47000 = 600,000ΩRL​∥47000=600,000Ω

Using the parallel resistor formula:

Rparallel=RL×47000RL+47000R_{ ext{parallel}} = rac{R_L imes 47000}{R_L + 47000}Rparallel​=RL​+47000RL​×47000​

Setting this equal to 600,000Ω:

RL×47000RL+47000=600000rac{R_L imes 47000}{R_L + 47000} = 600000RL​+47000RL​×47000​=600000

Solving for RLR_LRL​:

RL×47000=600000(RL+47000)R_L imes 47000 = 600000 (R_L + 47000)RL​×47000=600000(RL​+47000) RL×47000=600000RL+28200000000R_L imes 47000 = 600000 R_L + 28200000000RL​×47000=600000RL​+28200000000 RL(47000−600000)=28200000000R_L (47000 - 600000) = 28200000000RL​(47000−600000)=28200000000 RL(−553000)=28200000000R_L (-553000) = 28200000000RL​(−553000)=28200000000 RL=28200000000553000≈51.0kΩR_L = rac{28200000000}{553000} approx 51.0kΩRL​=55300028200000000​≈51.0kΩ

So, to achieve a 375Ω load at the cartridge, you need to add a 51kΩ resistor in parallel with the 47kΩ phono input.

My phono unit has the ability, via RCA plugs, to load either the MC or MM section. Very easy and simple. 

I refuse to read the gibberish, but if you place a 51K resistor in parallel with a 47K resistor, you will get around 24K resistance. If you use your 1:40 SUT into 24K resistance, you will end up with a phono load of about 15 ohms. In other words, you’re going backwards. I don’t care what the book said. But your cartridge can drive even 15 ohms. So if you do the 51K mod, it will work ok, but the load is not 375 ohms. The only way to increase the resistance of a resistor is to place another resistor in series with that resistor, and obviously you don’t want to do that in this case.

just for the fun of it, if you have an ohm meter, and if you have two 50 K resistors, place them in parallel and measure the resistance across the parallel pair. It will be 25K ohms.

what you could do is replace the 47K load resistance with a 600K load resistor. Then using your 1:40 SUT, the cartridge will see 375 ohms load.

Agree, which is why I titled the thread "Calculation verification please" The answer ChatGPT gave didn’t make sense to me. (and yes a lot of gibberish but fasinating to watch it do the calculations in a matter of seconds).

I can’t replace the 47K load resistor but also came up with a 600K load resistor answer.

I must have misunderstood from the get go. I thought your original question was what parallel loading resistors would create a 375 ohm load.  Answer is still that it's not possible by introducing a resistor in parallel with 47K. I personally would do nothing; just run the cartridge into the 30 ohm load.  On the other hand, I don't know why you cannot change the load resistor from 47K to 600K, but I take your word for it. I don't think there would be anything magical about 375 ohms anyway.

@sksos1 The cartridge won't care about the 375 Ohm load. It won't care about 30 Ohms either.

Loads like that are never for the cartridge's benefit; they are to eliminate RFI (Radio Frequency Interference) that LOMC cartridges tend to generate. The resistor detunes the electrical peak (which is usually at some radio frequency) thus preventing it from going into oscillation.

The SUT prevents this problem of course since it lacks the bandwidth, so it blocks RFI.

In addition to what I and Atma have written, I am most amazed that you hear differences in SQ among resistances of 250, 324, 368, 404, 500 & 600 ohms. I don't doubt you, but I have tried such experiments and never heard much if any difference.  Or to put it another way, if there IS a difference among such closely related values, it is so subtle as to be irrelevant.  I set up one of my phono stages to be switchable between 100, 1000, and 47K ohms for LOMC cartridges.  Now I do hear slight differences between 100 and 47K ohms, but both are acceptable and close to being the same.  If I had to say, I would say 47K is slightly more tipped up toward the treble.  This is with cartridges that have internal resistance between 2 and 12 ohms. This phono stage is balanced and the cartridges are hooked up on balanced mode always, straight through to the speakers. (Balanced phono, linestage, and amplifiers.) Speakers are full range ESLs.

Interesting thread!  I always thought loading was to dampen the stylus against any 'ringing' which may occur...

Options, a choice needs to be made, however

I cannot imagine hearing differences of any significance like OP mentions, and the numbers given to OP by his equipment maker do not seem right.

you cannot hear specifics, without not hearing other specifics at any one time. I try hard, and prefer getting others involved to prevent hearing what I want to hear, or simply my brain choosing to hear this this time, then hear that next time. And I try to delay decision making final comparisons until after break-in periods, 

IA (imaging Ability) and SQ (Sound Quality) are separate but equal. A combination of wide channel separation and very importantly tight channel balance is desired for imaging. 

What x factor for decently strong/not too strong signal strength? Downstream volume controls/tubes working easily? Noise free, great! Similar to other source input signal strengths, IOW, it's a copacetic/relative rather than SQ decision

next, load, is it near the 'general formula' coil impedance x ten, in this case 1.4 ohm x ten = 14, the 1:40 x factor (a very high ratio) yields 29 ohms, close enough. What is the signal strength ____? and resultant x40 signal strength _____?

Settings basically correct:

AFTER you break it in: If it isn't already wonderfully INVOLVING playing very familiar content, go for a different cartridge. 

If it doesn't produce great imaging, I would not bother, go for a different cartridge.

refining loading IME is subtle refinement, hard to positively discern, and in my case 4 optional loads are related to the 4 optional xFactors, so there is always a signal strength change too.

 

 

How did I figure out different loading using RCA plugs? (Yes differences are heard, subtle but heard). 

The MC input load of the unit is set at 1000 ohms

                                                  1

For any value                  --------------------

use this formula:               1               1

                                           ---     -     -----

                                           X           1000  

I always thought loading was to dampen the stylus against any 'ringing' which may occur...

@quincy Nope! Especially with LOMC cartridges, which have a very high 'Q' factor in their coils (so as to minimize mass) the result is that the peak I mentioned can be as much as 30dB higher than the signal level. That will mess with a lot of phono sections- it can cause distortion and overload, which is why they sound better when the 'loading' resistor is installed.

When an SUT is involved you have a different situation! The RFI can't make its way past the transformer, but the loading of the transformer becomes critical to prevent it 'ringing' (distorting). If the load is too high an impedance value this will happen; if the value too low the transformer will roll off. If you change the source impedance (the cartridge) that impedance is magnified by the transformer in this case (because its a stepup) so the load value will change with the source impedance.

@lewm I suspect this is why small differences in loading the SUT can be heard.

This process is thus best done with a squarewave generator and an oscilloscope to see how well the squarewave is passing thru the transformer. Most audiophiles don't have access to such equipment and if they did, may not understand how to do this particular critical measurement. So as a result, most of the time its by gosh and by golly unless a lot of care is taken to eliminate variables (like cable capacitance) and also if the manufacturer was careful to specify exact values.

Atmasphere!  Thanks for the clarification!

Atma, Skos wrote: "I’ve been experimenting into a MC section and the manufacturer says to load between 100 - 800 ohms. I’ve tried 250, 324, 368, 404, 500 & 600 ohms and found I like best the 368 ohm loading. So now want to try using my SUT."

IOW, he heard differences in SQ among those listed load resistances BEFORE he decided to implement a SUT. So, using a step-up had nothing to do with his observation.  So many hear differences using load resistances that differ by only a few tens of ohms that I am convinced the observations are valid.  I just don't hear it, or better to say I do hear subtle differences between widely different loads (e.g., 100 ohms vs 47K ohms, with LOMCs that can drive 100 ohms) but none worth a damn. In those cases I slightly prefer 47K ohms. I do think my system is low enough in distortion that I should hear it if my brain says it's there.  That suggests my ears and brain are tuned differently or are superannuated or both.

My wife is a brunette and I don't have the gut that guy has, but otherwise there is some relevance.

So yeah:

• For a typical fixed 47Kohm MM input, a 40x SUT gives your cart a 29 ohm load. You CAN’T raise that 29 by paralleling anything. If you try to add resistance in series, you will lose almost all of your actual signal before it hits the MM input (voltage divider). As mentioned earlier, you have to either modify the phono stage to get higher than 47K input (600K = 375 * 40 * 40, as mentioned ealier) or switch to an MM stage that has non-standard loading options above 47K.
• Rogue Ares has an MM option for 100K and 1 MEG ohm loading in MM mode. Phono stages with this kind of option are few and far between. 1 MEG would give you 625 ohms off a 40x SUT (1 million / 40 / 40). 100K is 62.5 ohms. Still, you target 375 eludes you. 
• A 1.4 ohm cart will be FINE into 29 ohms. Like lewm, I don’t see much value in going higher. I don’t hear much difference in small gradiations of load, at least until you’ve gone way too far (low ohms) for the coils at hand.
• Your 1.4 ohms screams "My Sonic Labs". If so, these carts also have high outputs - like 0.5mV. A 40x on this (20mV) is going to push you way towards the overload margins of most phono stages, which will likely have a very negative sonic impact - much more so than your loading concerns.

By normal convention "40/40" means 40 divided by 40, which is 1.  Just so not to confuse anyone, you probably meant 40-squared or 40 X 40, or 1600. 600,000 divided by 1600 (or 600,000/1600) equals 375 ohms, the load that Skos desires. I know you know that but some might have been confused by the way you wrote it. That Rogue with a built in option for a 1Megohm input impedance on its MM stage would work too, but 47K works as well.

Good point overlooked by me and everyone else: What LOMC requires a 1:40 SUT? If you guessed correctly that it is a Mysoniclabs with 0,5mV output, then your point is very well taken. 20mV of signal voltage at the standard stylus velocity will definitely overload nearly any MM phono stage, because the stylus velocity can go way higher than the standard 3.54 cm/sec or 5.0 cm/sec (the two standards for which cartridge output is calculated).  To justify a 1:40 SUT, you would expect that the cartridge output is not more than 0.15mV or preferably less.

By normal convention "40/40" means 40 divided by 40, which is 1.

Good point - division is not associative. Indeed I meant ((1 MEG / 40) / 40), same as applying the div operator strictly left-to-right without groupings. 

@sksos1 could you share which cartridge you're using? 1.4 ohm coils are fairly unsual, and "usually" a good match to 40x SUT - but not if it's an MSL, which are extra unusual cartridges.

Perhaps off topic, but does anyone know how MSL gets as much as 0.5 mV from only 1.4 ohm coils? No other cartridge maker gets close to this ratio. MSL's marketing blurb goes like "magic SH-μX core", but it's hard to believe a core material could net that much more generator efficient versus iron-based cores of other manufacturers. Could they possibly be using larger-than-usual gauge coil wire, which nets more mass but lower DC ohms for a given number of turns? If so, that feels like "cheating" 

Magnets and their proximity to the coils plus core material must be how they do it. The math for such calculations is complex, and I don’t know the equations. So off the top of my head, I can’t be amazed unless I knew the math and physics involved.

Dear @sksos1  : Other that the LOMC cartridges are not sensible to load changes and with all respect I can't understand that you want to use a SUT when you own an active high gain phonolinepreamp. Just my curiosity.

Any cartridge will sound and performs with higher quality levels in that phonolinepreamp than in any SUT at any price where the best that can does the SUT the BEST is to degrade the quality sensible cartridge signal. So you will listen a degraded quality sound through any SUT.

 

In the other side as @lewm  posted you are really better that a bat hwn can hear differences between  between a difference of only 36 ohms whe the cartridge is insensible to changes on load impedance. Makes sense to you what you are listen it? or maybe is what you just want to hear. Obviously that's what you like and is ok for me or any one else.

 

Regards and enjoy the MUSIC NOT DISTORTIONS,

R.

By my calculations, I load the cartridge to what sounds best to me.