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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
dfel OP
62 posts
 
Yeah I guess I just have to roll with it, the rule of thumb as a guide along with the formula + testing by ear.

However, applying the rule becomes tricky since the data spec quotations on several transformers are not quoted at 47,000. For example:

1.Cinemag 3440AHPC has.....37.5 or 150 : 50K

2. Another RCA has..... 600 or 150: 15K

For the above trafos do I have to adjust the calculations since they are not into 47,000 ohms, one is into 50K and the other is into 15K, to find the effective load?

To find the turns ratios please tell me if this is correct:
1. 50,000/x^2 = 37.5 solve x-> implies x=36.5 turns ratio

then to find impedance do I standardize to 47,000 in the following way?

47,000/36.5^2 -> 35 Ohms ?

I will repaeat the logic for the second cartridge as well which using the 150 tap with the quotation value 15K.

2. 15,000/x^2 = 150 solve x-> implies x = 10 turns ratio

then to find impedance 47,000/10^2 -> 470 ohms

My point is most transformers out there are not quoted into 47,000 ohms like the phono section is, they are often 50,000 or even 15,000. So if using those quotations, do you not have to solve for the turns ratio with their quotation values first, then use 47,000/turns^2 to find the effective load ?

If you look at the above example 2. it is quoted at

"600, 150: 15K"...so using the 150 tap I get a turns ratio of 10, and this provides and effective load @ 47,000 of 470 and not 150 the way it was quoted.

Then once this is done which set of turns ratios and effective impedances to I put into equation (*) to find the voltage?

dfel OP
62 posts
 
You can see in example 1. it did not make much difference 35Ohms vs 37.5 quoted.

But in example 2 that 470 vs 150 quoted is a huge difference. If you were trying to match a 40 ohm cart 150 would be rejected since it is much lower than a 10 multiple, but after converting (if I am doing this right) it shows that it is in fact 470 which is ideal for a 40 ohm cartridge.

It is very hard to explain and ask, via the message board and it takes forever to type these things out. But I would like a workable way to find transformers that are suitable regardless of how they are quoted. I would also like for anyone reading this thread who does not know how to match correctly to understand as well.
almarg's avatar
Ag insider logo xs@2x
almarg
8,673 posts
 
Your calculations look correct to me, Dfel.

As you've found, and as might be expected, 47K vs. 50K makes little difference, and is probably not worth correcting for. Imprecision in cartridge output voltage specs, resulting in part because at least two different measurement standards exist, will often make more of a difference. Significantly larger discrepancies, though, certainly need to be taken into account.
Then once this is done which set of turns ratios and effective impedances to I put into equation (*) to find the voltage?
The effective load impedance will be the actual input impedance of the particular phono stage that is being used (often but not always 47K) divided by the square of the turns ratio.

The turns ratio that should be used, if it is not explicitly specified, is calculated per the examples you cited.

Regards,
-- Al
lewm
6,770 posts
 
Those data you start with are unnecessarily complex, and are paradoxically offered to make life simple. Just know the turns ratio of the transformer. (Call up the maker and ask, if it's not published.) Then know the input impedance of your MM phono stage and the internal resistance of your cartridge. All else flows from those numbers.
dfel OP
62 posts
 
Good call lewm, sure simplicity is good and when possible that is the best path. How about if it was made in 1930-1950 by a company that is long gone, or does not have the specs available any more? By applying the simple calculation, you know what you are dealing with even if that information is not available...figuring out the which tap does what (ground, phase, impedance etc..) can still be a pain.

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