stepup transformer impedance equasion?

[jsn]

Hi nerdz,

I have been playing with various loading of my shiny new Denon DL-103.
I am using a 1:5 stepup transformers and have a pot hooked up instead
of a grid resistor on the input to my phono stage. Turning it makes a
significant difference in the sound.

I would like to be able to accurately calculate the load impedance
seen by the cartridge (in order to compare stepup transformers
independently of cartridge loading). From what I have read, it is
necessary for accuracy (especially with lower-ratio transformers) to
include the DCR of the primary and the secondary in the calculation.

Does this sound right:

DCp = DCR of primary
DCs = DCR of secondary
Rp = impedance seen looking into the primary
Rs = impedance used to terminate the secondary
T = turns ratio of transformer

DCp + Rp = (DCs + Rs) / T^2

Solving for Rs:

Rs = (T^2 (DCp + Rp)) - DCs

I haven't been able to find a very thorough treatment of this that
includes all of the terms as above. Any thoughts?

jsn

[Matt Wiebe]

Jason,
I'm not sure I understand your question. If you are looking for the
best load for your cartridge and you are happy adjusting the pot by
ear than just figure out where the pot is set for your sweet point,
job done. Your equation doesn't include L of the primary which also
determines the load on the cartridge's coil. And you have capacitance
issues with cables between the cartridge and phono pre which can swamp
other issues. I use my DL103 with three different phono preamps and I
load it slightly differently in each case. I think it is mostly a by
ear sort of thing.
Matt

[jsn]

I hate trial and error :) I want to know what is really going on :)

jsn

[Matt Wiebe]

Jason,
I don't think you can know what is going on outside of a general way.
For a better model try Spice and work on getting good inductance
numbers for your SUT and the capacitance of your cables. Measuring the
inductance of your cartridge and its capacitance would be beyond me
but maybe someone has numbers you could google. There is also trial
and better.
Matt

[jsn]

Yeah. I have never seen anything take the inductance into account,
and that probably has a significant contribution.

I guess I'll use my equation to get in the ballpark, and fine tune by ear.

jsn

[Matt Wiebe]

Jason,
I assume you are using an Altec 15095 like I am. One of the things I
haven't tried is bridging the primary and secondary with a cap to see
what that does. Even with such a small core I doubt the tiny current
generated by the cartridge is going to be able to engage the core as
the frequency gets up there, so the highs may be helped by a little
direct capacitance. It's something I've been too lazy to try.
Matt

[jsn]

I have a 15095 and a couple other transformers I want to try. Right
now I'm using an Edcor mx5cs.

How are you terminating your Altec? Does it connect to the standard
47k input resistor or some other resistance?

Interesting idea about the capacitor. I'll have to play with that.

jsn

[Matt Wiebe]

Jason,
When I switched to the Denon I reduced the input resistor but I
cannot remember what value. It's pretty low from what I remember. I've
looked at the Edcor you are using for exactly this purpose. How does
it sound compared with the Altec? Did you spec your MX5CS with a
nickel core?
Matt

[robert taylor]

have you looked @ dave slagle's site?
he's run a lot of spice sims on LCR phonos, etc...
quite a bit of discussion on the forum on this
http://www.intactaudio.com/forum/viewforum.php?f=18&sid=9bc6229e41ad75828c19630222f5e81b

[jsn]

The mx5cs is nickel core. I also got the added electrical shielding
(the cs = copper shield).

I think it sounds good, but my cartridge is brand new, so I have made
too many changes at once to compare it to the Altec. One reason I
would like to get the math down regarding loading is so that I can
compare transformers while keeping the loading at least relatively
constant.

I think the mx8 1:8 would probably be a better match for the phono
stage input spec of 2.5-10mV. 1:5 gives you 1.5mV, which 1:8 gives
you 2.4mA. I talked to edcor and they can wind these on the nickel
core in any ratio you want, and include wire leads instead of PCB
mounting. I'm contemplating getting a 1:10 which would be right on
the money for the DL-103, and would compare almost directly with the
15095. If you are interested, we could probably set up a part number
so that we can order them easily.

I'm not sure how much the added shield has, but it seems like a good
thing to ground the core, and the non-cs versions don't appear to have
a wire to ground the core. They also don't have an electrostatic
shield like most phono stepups, but I haven't investigated what
difference this might make.

jsn

[Matt Wiebe]

Jason,
Well keep reporting on the Altec verses the Edcor. It took my Denon
about 100 hours of playing to really get when I thought it settled in.
Getting the math down will not allow you a baseline for comparison
because you are leaving too many measurements out. Even comparing
similar winding ratios is not apples to apples. There are core
materials difference, air-gap/stacking differences, core dimensional
differences, winding geometry--bobbin or layer wound (if layer wound
how many layers and at what thickness and do the layers scale?) wire
insulation differences of material and thickness, different coppers
and diameters, how well the bobbin fills the core etc. And this is in
addition to impedance and capacitive leakage of the finished product.
This is the same reason there are so many different guitar pickups,
its not an engineering problem. If it sounds good it is.
Matt

[jsn]

I'm becoming convinced :)

jsn

[John Galbraith]

Jason, I agree with Matt that it will be hard to estimate enough factors to build a quantitatively meaningful model (i.e., one that comes close to computing the best sounding grid resistor value). In particular, I think the model you proposed is way too simple and would probably require a lot more poles and zeros (that would be higher order terms of the "s" complex variable that comes from the Laplace transform).

If you were careful and had the right equipment, you could *probably* account for the dominant factors (and maybe some of the links in this thread show that already) but in the end, I suspect you will be fitting the model terms to the measurements; i.e., estimating the R, L, and C terms using empirical data.

The only proper tool to make this measurement is called a "network analyzer" and a commercial one of those would be completely out of reach, financially, for a hobby builder. Even if you had one, I'm still not sure exactly how you would make the so-called "S21" measurement, which is probably the one you want, because the input to the network is not an electrical signal that the network analyzer can synthesize; it is the mechanical grooves on the record. If you could make it, it would measure the transfer function of the tonearm/cartridge/etc. network as the output signal (input to your preamp) as a function of the input signal (the mechanical grooves on the record). The thing that makes the network analyzer so powerful is that it makes a *complex* measurement; i.e., it reports the *phase* of the transfer function in addition to the amplitude. You would probably need this to build your model.

A practical measurement of your tonearm impedance would start with, I suppose, a test record with tones at different frequencies. You would only be able to measure the response at those frequencies, and there is no way you would ever get the phase of your function, just the amplitude terms (rather like a "spectrum analyzer" instead of a network analyzer). You would probably fix a load impedance (the pot in your case) to two known values, and use some linear network theory and algebra do derive the transfer function (amplitude only) at those frequencies.

Here's the other big problem: all the basic theory one could apply, including your initial shot at a model, assumes linearity. The network analyzer does, too, except that you can usually program it to vary the amplitude as well to sort of get at nonlinear behavior. The test record that I have has two volume levels, at least, but only at one or two frequencies. So you would only get four data points.

I suspect that all the information that you want from your model is quite likely confounded significantly by nonlinearities which aren't supposed to be there in theory but probably are, especially in the cartridge. If true, this would render your math and hard work fairly worthless.

I could envision another approach if you had a test record with a really fast step or impulse encoded on it (a scratched record???). The step would have to have at least as wide of frequency content as the bandwidth you wanted to measure, so it would be on the order of 50 microseconds or better. My test record does not have such a track on it and I don't know that any exist. This test would also assume linearity, but would at least measure a continuum of frequencies determined by the sample rate of your scope. (I did mention that you would need a digitizing oscilloscope, right? 8-)

In summary, I like your pot idea combined with your ears...

John

[robert taylor]

 if this helps:
 
http://www.intactaudio.com/forum/viewtopic.php?t=752 
 
 

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[jsn]

Very cool post. Thanks!

jsn