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MC Step Up Math

Hi all,

after posting a thread on here years ago and becoming exceedingly confused about cartridge step up maths, I gave up, embarrassing for a math major..perhaps I should have studied electrical engineering. Recently I have been reading up on this topic and would like to once and for all figure out how to run the math/electronic theory to find the correct step up to mate with a MC cartridge.

I have looked at 2 different links.

Link (1)

http://www.theanalogdept.com/sut.htm

and

Link (2)
http://www.rothwellaudioproducts.co.uk/html/mc_step-up_transformers_explai.html

Now, everything I read in link 2 falls apart after reading what is on link 1 and I am once again confused about what to look for in a MC step up.

In the second link the author explains that you simply apply a 2 step process: A. multiply the turns ratio by the cartridge output to find the voltage and make sure that it is not overloading the MM phono stage input (i.e/ between 2.5 and 10 MV) and then B. Perform the calculation to show you how much resistance the cartridge actually sees and apply a rule of thumb at least 3 to 10 times ratio between the source impedance and the input. The rule is for the most part out of thin air, though he does explain that matching to equate the 2 is a bad idea.

In the first link however, the author takes a different approach. He explains that a turns ratio cannot just be multiplied to give you the voltage on the other end. For example the cinemag 3440 cart used with the dynavector illustrates the point. The output is .30 MV and the turns ratio is 35.4 resulting in 10.6 MV out.

Now here is the bit I need help with. He explains that in reality the with this combination the output is really 5.1387mV NOT 10.6MV. He uses this equation to adjust the 10.6 MV to 5.1387MV:

(Vout / Vcart) = (R(Load_effective) / (R(Load_effective) + (Rcart)))

he finds Vout and then Multiplies by the turns ratio.

The parameters are as follows:

Rcart: is internal resistance of the MC cartridge
R(Load_effective): resistive load seen at the MC cartridge
Vout: Voltage output at secondary side of tranny
Vcart: Voltage output at MC cartridge

Hi all,

after posting a thread on here years ago and becoming exceedingly confused about cartridge step up maths, I gave up, embarrassing for a math major..perhaps I should have studied electrical engineering. Recently I have been reading up on this topic and would like to once and for all figure out how to run the math/electronic theory to find the correct step up to mate with a MC cartridge.

I have looked at 2 different links.

Link (1)

http://www.theanalogdept.com/sut.htm

and

Link (2)
http://www.rothwellaudioproducts.co.uk/html/mc_step-up_transformers_explai.html

Now, everything I read in link 2 falls apart after reading what is on link 1 and I am once again confused about what to look for in a MC step up.

In the second link the author explains that you simply apply a 2 step process: A. multiply the turns ratio by the cartridge output to find the voltage and make sure that it is not overloading the MM phono stage input (i.e/ between 2.5 and 10 MV) and then B. Perform the calculation to show you how much resistance the cartridge actually sees and apply a rule of thumb at least 3 to 10 times ratio between the source impedance and the input. The rule is for the most part out of thin air, though he does explain that matching to equate the 2 is a bad idea.

In the first link however, the author takes a different approach. He explains that a turns ratio cannot just be multiplied to give you the voltage on the other end. For example the cinemag 3440 cart used with the dynavector illustrates the point. The output is .30 MV and the turns ratio is 35.4 resulting in 10.6 MV out.

Now here is the bit I need help with. He explains that in reality the with this combination the output is really 5.1387mV NOT 10.6MV. He uses this equation to adjust the 10.6 MV to 5.1387MV:

Equation (*)
(Vout / Vcart) = (R(Load_effective) / (R(Load_effective) + (Rcart)))

he finds Vout and then Multiplies by the turns ratio.

The parameters are as follows:
Turns ratio: The turns ratio of the step up device
Rcart: is internal resistance of the MC cartridge
R(Load_effective): resistive load seen at the MC cartridge defined as 47,000/(Turns Ratio)^2
Vout: Voltage output at secondary side of tranny
Vcart: Voltage output at MC cartridge

for this example they using a denon 103 + cinemag 3440 are:
Turns Ratio: 35.4
Rcart: 40
R(Load_effective): 47,000/(35.4^2) = 37.5 ohms
Vout: to be solved for
Vcart: .30 MV

Putting it into equation (*) and solving yields
.1452mV for Vout.

He then takes Vout and multiplies by the turns ratio.

.1452 * 35.4 = 5.1387mV

NOW: If you take the simple method (from link 2 by multiplying turns with output) you get 10.6 MV, using this adjusted method with equation (*) you get 5.1387 MV. So my question is this. What is equation (*), is there some theory here that I am missing, is this voodoo? I would like a reliable way to select components that match, though I have trouble trusting the equation (*) method without knowing where why he is using it and what it is. I certainly want to get this ironed out before I start buying different transformers to play with, and any help with this would be greatly appreciated. Thanks.
dfel
intactaudio
300 posts
 
In addition to what Al has said above. Once you understand that there are two different things at play here that should have no fixed relationship to each other, it becomes a little easier to understand.

One is the load the cartridge wants to see. This is not a fixed value but something that needs to be selected by ear. There are all kinds of ROT's but ultimately your ears are the only thing to tell you what this value should be.

The other thing at play here is the voltage gain. This is also not a fixed number. Again ROT's abound on this but in order to make a proper choice you need to not only take into consideration the input headroom of your phono but the overall gain structure of your system and your listening habits.

My approach is to get the gain set up properly first then address the load. In the case where Rsource=Rload you will lose 6dB but that is rare.

The mistake I see most making is attempting to link the numbers together to find some sort of convoluted solution. Sure one has the effect on the other but that is only based on other assumptions like the 47K input resistance of a phono. Lets face it, that 47K has no real meaning for a MC cartridge. For MC it should be much higher in value anyway to avoid the situation where the needed turns ratio loads down the cartridge too much.

dave
almarg's avatar
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almarg
9,670 posts
 
Dfel, I'm not sure that I can add much in answer to your recent questions that hasn't already been said. If you haven't already seen it, I would highly recommend that you take a look at the writeup by Bobsdevices for which he provided a link in his post earlier in this thread. He is a well regarded manufacturer of SUTs. And I note, btw, that the models he offers provide ratios that are switchable between two values.
Al, if you don't mind my asking..where the heck did you learn all this stuff? Do you have a background in electrical engineering?
Yes, I am a retired EE, with extensive experience in analog and digital circuit design (not for audio). I've also been an audiophile for about 35 years, and I've read widely on the subject.

Regards,
-- Al
dfel OP
62 posts
 
The only thing to say really is where does 10X come from ?

The answer however from reading many sources, including bobs is: everyone else is doing it. No real science there, just audiophile blind faith I guess. I was hoping to get some insight into why.
bobsdevices
100 posts
 
I personally use 10x as a starting point. It is at the point where the cartridge sounds unconstrained by loading to my ears. I then adjust it lower until it sounds constrained than back it off a bit. With a SUT, use a formula that allows an output of between 2.5 and 10 mV that gives a reflected impedance of between 5 at 10 times the internal impedance to start. It is not an exact science and I adjust it to whatever sounds best. Some cartridges sound better loaded lower and some loaded higher. I wish there was a way to scientfically match it perfectly. From experience with several common cartridges, I know which ones sound best with different step up ratios. But there are so many cartridges out there, that without trying different ratios, you can't tell what is best.
lewm
13,012 posts
 
Golly, Dfel! You are making this much much harder than it really is, and it's somewhat difficult to begin with. "10X" is not a "rule", as others have also written, it's merely a guide. For reasons I, Al, and several others stated, as the ratio approaches 1X and below, you will encounter a perceived loss of HF, a subjectively objectionable (to me) loss of sound quality, and eventually dramatic loss of phono gain. A 10X ratio keeps you safely above any of those phenomena. 5X would probably be fine, too. Depending upon the inductance of a given cartridge (but with an LOMC, inductance is quite low) you will get into trouble at different lower impedance ratios. Just what ratio will start to sound bad is dependent not only upon the cartridge and the phono stage but also on your other equipment, your system sound as a whole, and your ear/brain. For example, there are some who actually seem to prefer the sound of the Denon DL103 at impedance ratios that approach 1X. One guy I know of admits that he loses a lot of gain at that point, but he just likes the sound on other grounds.
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