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19th February 2014, 04:22 AM  #1 
diyAudio Member
Join Date: Nov 2013

Moving Coil Step Up Maths and Optimal Matching
Hi all,
after posting a thread 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) SUT and Link (2) mc stepup transformers explained 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 them in terms of impedence 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 denon 103 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 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. 
19th February 2014, 09:21 AM  #2 
diyAudio Member
Join Date: Nov 2003
Location: Melbourne (Oz, not Florida!)

Mmmm, my belief is that using a SUT and attempting to get the correct LOMC cart loading ... is like p*ss*ng into the wind!
If you want to get serious about LOMC cart loading and you have a MM phono stage, use an (active) head amp. If it's built right, this will have a parallel pair of input RCAs: * one pair is for the phono stage. * the second is for "Rloaded" plugs. Regards, Andy 
19th February 2014, 07:46 PM  #3 
diyAudio Member

Archiekaras your link 2 is the more useful for showing the effects that impedance loading has on the transformer.The only aspect missing concerns how the combined source impedance of the cartridge with the xformer effects the noise figures of the preamplifier.As a rule of thumb,as there are a myriad of variations in topologies, valve stages give lower noise with about four times the source impedance of transistor ccts which typically have their lowest noise with a source impedance of 5000 Ohm.

19th February 2014, 10:11 PM  #4 
Sin Bin
Join Date: Nov 2003
Location: Brighton UK

Hi,
The maths in both links is right but the theory in SUT is wrong. The Denon DL103 simply needs a 1:10 step up like : Denon Step Up transformer,Denon AU300LC Step Up transformer,Denon AU 300LC Step Up transformer,Denon AU300LC Step Up transformer,Denon AU300LC MC Step Up transformer,Denon AU 300LC MC Step Up transformer,Denon AU300LC MC Step Up transformer Its not more complicated. The 40ohm cartridge sees 470 ohms, load, and conversely the 47K input sees a 4K ohm drive source. Gain is x10, 0.3mV goes to 3mV, moreorless which is just fine. The SUT post shows your really wasting your time using any transformer that breaks the > 3 times loading rule, The above is the ~ x10 case. So with a 1:33 transforrner the cartridge sees 47 ohms as a load and the input sees a 40K ohms driving source. So you will get high voltages losses both ends and about the same real output as the first case, nowhere near 10mV. In reality 1:20 would work, the cartridge sees around 120 ohms and the input is driven by about 16K ohms. This will give you the "highest" voltage gain, about 5mV. This is the ~ x3 case. However its easier to build lower ratio high quality transformers. Here the DL103 is fine with a ratio of 1: 10 to 20, and most MC's are fine using a transformer that fits into x3 to x10 case. rgds, sreten. 
21st February 2014, 10:47 PM  #5 
diyAudio Member
Join Date: May 2006
Location: Behind the Cheddar Curtain

archiekaras
sreten has the most practical answer. If you are still wondering where the math is coming from, it has to do with how they rate the output of the cartridge. If .3mV is the open circuit voltage output of the coil, then the 2nd link is the most accurate. Transformers don't really have an impedance unto themselves, they transform the impedance from one side as seen by the other side by a factor of the turns ratio squared. So a 34.5 turns ratio xfmr will transform the 40K Ohm load impedance to 37.5 Ohms on the other (cartridge) side of the xfmr. The cartridge then sees a load of 37.5 Ohms which forms a simple resistive divider as shown in the attached image. The voltage developed across the cartridge side of the xfmr is then .3mV x 37.5/77.5 or .1452mV. The xfmr steps this voltage up by a factor of the turns ratio (x 35.4) so it delivers 5.186mV across 40K. If the cartridge output is rated .3mV into a 40 Ohm load, then the 1st link is most accurate. In that case, the resistive divider is already factored in and the cartridge will deliver .3mV across 40 Ohms since it would have .6mV output open circuit (the 40 Ohm load and the 40 Ohm source imp form a voltage divider that will halve the open circuit voltage or 40/80). If the xfmr presents a 37.5 Ohm load instead of 40 Ohms, the voltage would then be .29mV since the voltage divider would be 37.5/77.5 x .6mV. The xfmr steps this up by 35.4x or 10.28mV. 
21st February 2014, 11:34 PM  #6 
Sin Bin
Join Date: Nov 2003
Location: Brighton UK

Hi,
The error in post #1 and #5 and point 1) is only considering one side of the transformer matching for alleged gain. Work out what happens with : 4047, 33 gain and 40K47K. Compare to : 40120, 20 gain and 16K47K And : 40470, 10 gain and 40047K. rgds, sreten. Last edited by sreten; 21st February 2014 at 11:40 PM. 
22nd February 2014, 01:47 AM  #7 
diyAudio Member
Join Date: Nov 2013

I do not understand what was said. The open circuit/drive into terminology has confused me. When I look at a cartridge, specification it is called output voltage measured at 5cm/sec. The impedance is called internal impedance. So I am not sure which of the 2 scenarios you are talking about is in play with a MC cartridge. So it leaves me confused how to apply voltage divider theory, also does it apply the same way when a passive transformer is in the circuit as it does with the typical resistor in circuit examples they give online for voltage dividing.
If I were to guess I would think that it is putting out 0.3 MV from the output pins after being run though a 40 ohm (internal impedance) load. Is the voltage drop/adjustment equation correct ? Under what scenario will it correctly give you the real voltage seen by the MM phono section. 
5th March 2014, 02:35 PM  #8 
diyAudio Member
Join Date: May 2006
Location: Behind the Cheddar Curtain

dfoe
It all depends upon how the output is specified (I actually don't know which method they use). Think of the cartridge as an AC generator with an internal impedance. If it has and internal impedance of 40 Ohms and you measure the output with no load, it will appear ~twice as high as if it were terminated into a 40 Ohm load. So the question becomes: Is the 0.3mV output measured open circuit or into a 40 Ohm load? Regarding the xfmr, per my previous post, xfmrs do not exhibit an impedance of their own when operated within their specified range. The 40 Ohm load presented by the xfmr to the cartridge is the result of the 40K termination on the other side being transformed by the square of the turns ratio. The xfmr does not have a 40 Ohm input impedance unless it is terminated on its output by 40K. You do not have to apply the voltage divider reduction again on the output side of the xfmr. If you run the xfmr with no output load, the input side will be essentially open circuit as well and the voltage seen by the input will double (and so will the output voltage). Terminating the output with 40K will restore the voltage ratio as it now properly terminates the cartridge with 40 Ohms. Not sure what sreten is alluding to... The question still remains then: How is the cartridge output voltage specified; open circuit or terminated into the specified impedance? 
5th March 2014, 02:44 PM  #9 
diyAudio Member
Join Date: Mar 2009

not to be rude but why use a step up transformer when you could build a nice MC phono stage that can be configured to any MC cartridge loading with the change of a few resistors. then all you do is plug the phono stage into any line level input of your pre/integrated amp.
or am i missing an important point of step up transformers. 
5th March 2014, 03:13 PM  #10 
diyAudio Moderator

Noise and CMR.
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“Instead of Rational Law, objective truths perceptible to any who will undergo the necessary intellectual discipline, Knowledge will degenerate into a riot of subjective visions. . ."  Auden 
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