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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
lewm
12,556 posts
 
The math required is high school algebra. The concepts are a bit more difficult to grasp, but one really need not grasp them exactly, if one grasps the math relationships.

The results are "unpredictable" only in the sense that mating any two disparate audio components with a human is unpredictable.

And believe me, I am no EE. I think the manufacturers are to blame for the confusion surrounding SUT use, because there apparently is no agreed upon standard for how to describe what the SUT does electrically. Some talk in terms of db, some in terms of ohms, few in terms of turns ratio. The latter however is most important.
almarg's avatar
Ag insider logo xs@2x
almarg
9,670 posts
 
Lew's post reminds me that one thing that should be described in this thread is how to convert SUT gain that is specified in db into turns ratio.

The relevant relations are:

Voltage out of SUT (Vout) divided by Voltage in (Vin) = turns ratio.

db = 20 x log(Vout/Vin), where "log" is the base 10 logarithm.

So the procedure would be to divide the specified number of db by 20, and raise the number 10 to a power corresponding to that result.

For example a 30 db SUT would have a turns ratio of:

10^(30/20) = 31.6 (^ denotes "raised to the power of")

Similarly, a 20 db SUT would have a turns ratio of 10.

The calculation is easily performed with any scientific calculator, including the one that is built into Windows. If using the one in Windows, which can be found under Start/All Programs/Accessories, set it to "scientific" mode under its "view" menu.

Regards,
-- Al
rodrigaj
32 posts
 
I agree with Swampwalker, an active gain stage, properly done is the best way to go. Unfortunately, in my case, my LFD phono stage did not offer a high enough gain for my Dynavector xx2 cartridge.

At 0.28v output and 43db gain, I was right on the noise edge. Some classical guitar albums that I have had in my collection for years were too noisy at the proper volume level.

I have to hand it to the op, I tried to understand SUTs but gave up and researched some contenders. I went with CineMag (Bob's Devices) 1131 because, he responded quickly, has matched my cartridge / phono stage before and was willing to take it back if I did not like the results.

The package is somewhere in transit now and delayed because of the horrible weather patterns we've been having in the midwest.

I really avoided as long as I could going the SUT route, but in the end I liked my XX2 / LFD combo too much to consider a higher output cartridge.
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