Not qualified enough to respond but really interested in the answer to this.
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First, kudos on your interest in applying engineering principles to audio, and thereby trying to reduce the randomness that often seems to be inherent in optimizing a system. And in that regard I recall your earlier thread on moving coil stepup math, which I participated in.
For a low pass filter consisting of a resistance and a capacitance, the Fc equation you cited is of course correct. There are two additional equations that are needed to answer your first question:
(a) The ratio of the voltage out of the filter to the voltage into the filter is:
Vout/Vin = 1/sqrt (1 + (f/Fc)^2)
where ^ denotes raised to the power of, i.e. squared in this case, and f is frequency, expressed in the same units as Fc.
(b) (Vout/Vin) expressed in db = 20*log(Vout/Vin)
Where log is the base 10 logarithm.
So as you can see the relevant calculations are definitely non-trivial. Perhaps some Googling would turn up online calculators which have automated some or all of this.
This calculation will be most useful for line-level interfaces. In general the high frequency rolloff caused by speaker cable capacitance will be negligible, because R in that case, the output impedance of the power amplifier, is so low. Capacitance may be relevant in the case of a few speaker cables, however, which achieve ultra-low inductance at the expense of having ultra-high capacitance, which can cause stability or other problems for some amplifiers (if used without a Zobel network). More generally, though, what should be minimized in the case of speaker cables, assuming that the goal is neutral behavior, is resistance and inductance. Resistance should be kept to a tiny fraction of speaker impedance. Inductive reactance, which is the inductive form of impedance and is measured in ohms, should be kept to a small fraction of the impedance of the speakers at high frequencies (i.e., 20 kHz, and possibly higher). Inductive reactance is denoted as Xl (l is a lower case L), and is calculated as follows:
Xl = 2*pi*f*L
where Xl is inductive reactance in ohms, L is inductance in Henries, and f is frequency in Hz.
Special considerations come into play regarding phono cables, involving the interaction of cable capacitance with the inductance of the cartridge.
For moving magnet cartridges, the manufacturer will usually provide a recommended range of load capacitance. Too little or too much capacitance will adversely affect tonal balance in the treble region, as a result of its interaction with the inductance of the cartridge. The load capacitance seen by the cartridge is the sum of the capacitances of the tonearm wiring and its connectors, the phono cable and its connectors, and the input capacitance of the phono stage.
For low output moving coil cartridges, such as the Denon 103 you mentioned, load capacitance should generally be minimized, but the magnitude and character of the difference that will make, and its importance, will depend on the design of the phono stage that is being used. See this post, beginning with the paragraph that starts with I should now debunk another myth ....
Also, see this paper regarding cartridge loading.
Finally, regarding SUTs, they add a whole additional level of complexity to all of this, which Ralph among others can probably speak to more knowledgeably than I can.
I am lost here. Help! LOL.
I looked up RLC circuits and found how to calculate Xc reactive capacitance and XL reactive inductance, and impedance Z.
Xl = 2*pi*F*L
Z = R/sqrt(R^2 +X^2) where X is abs(Xc-XL)
Now I want to figure out how the signal is affected, going from the phono cartridge to the MC Step up, due to the cables R L C parameters across a wide frequency. How do I do this ? What is an appropriate model for this.
If I am using the Denon 103R, and a cinemag 3440 what values do I use and what equation do I put them into to find the voltage change at a given frequency.To my questions above I am guessing that: Once I know this I can change the frequencies for a given cable's C L R to find out the voltage change and convert it to decibles using -20Log (Vin /Vout) and it will become clear exactly what is happening when certain cables are used.
After I figure that out I would also be interested in calculating this wire affect for the connection out of the cinemag into a preamp's phono section. Then the connection from the pre to the power amp, and even amp to speakers would follow.
Perhaps the science will show that the selection of wire for those connections can make a difference within some parameters for R L C as they vary by cable makeup and length, and can help one in selecting an appropriate wire. for each part of the system.
Please help me out with modeling this as I am sadly a little lost despite my best efforts to try and figure this out. Thanks again.
I dont have this cartridge or step up, but I think it will be most useful to use it as an example since many people do.
Might as well post the specs.
Denon 103R Specs
Output 0.25 mV
Output impedance 14ohms
(no inductance spec, impedance is total I take it)
37.5,150,600 : 50K
(Into 47K rather than 50K this adjusts to 35 ohms, or 141 ohms depending on tap used)
Output Impedance 2K
(I figure 2k is good to use as most preamps will not be much higher than that value.)
Dfel, the mathematics that is involved in analyzing RLC circuits is quite complex, and probably beyond the scope of what is practical to discuss in a reasonable timeframe in a forum such as this. However, I think that a careful reading of the "cartridge loading" paper I linked to in my previous post, plus the post by JCarr that I also linked to, essentially covers all that needs to be understood for what you are trying to achieve.
Z = R/sqrt(R^2 +X^2) where X is abs(Xc-XL)
That doesn't look right to me, for any possible connection arrangement of an R, an L, and a C. I think that everything after the division sign would be correct for the overall impedance of the three elements connected in a certain configuration, but I don't understand the division into R (perhaps that relates to the cosine of the phase angle of the impedance, rather than the magnitude of the impedance?). And in any event the overall impedance of the three elements is not what is of direct interest. As can be seen in the first figure in the "cartridge loading" paper what is of interest is the relation between the voltage which appears across the capacitance and the voltage (Vc) at the input.
Well, here is what I have done.
The computation does become complex, for spread sheeting etc..once you have to start looking into the differential equations. Do-able but much more practical to handle it using a brute force method, enter the circuit modelling software, which is what I did.
I used the circuit here used in this article: http://www.hagtech.com/loading.html
I adjusted the parameters for the 103R and a cinemag's reflected impedance. Here is the thing, for an MC setup, the capacitance and resistance parameters are of little consequence when the reflected impedance is used, contrary to the article.
Let me explain:
The article is looking at .47k 4.7 and 47k, but in reality the reflected impedance is .47K (470 Ohm) or less for just about any SUT. Now when examining the circuit at > 100 Ohms, minimum recommended loading for the cart we are talking about. It appears that the capacitance can create a huge roll off/tweak the subsonic spike as in the article. So this leads to looking at the assumed inductance. Most MCs have inductance between 5uH and 5mH ( 1mH =1000 uH). Now the results make sense, and rules of thumb/ common observations people have mentioned all come to light. The MC cartridge only becomes sensitive as the inductance moves higher.
For a cartdige with internal inductance 5-250uH, and a cable such as mogami 2549 which has 26pf/ft capacitance, 0.24uH/ft inductance and 0.022/ft Ohms resistance it becomes very difficult to change the subsonic spike by altering length and creating a roll off of even 0.1db at 20khz is just about out of question. The inductance is inconsequential all around, as for the capacitance well it depends.
So at the end of the article, they also explain this. The resonant qualities in a moving coil setup can essentially be reduced to its inductance relationship see . This I verified to be true when the carts output inductance is on the low end of the sliding scale. However as it approaches closer to 5mH this realtionship changes and it becomes very easy to create a less than optimal frequency response.
-Most available wires, used for phono interconnects and for tonearm wiring are suitable for the task and in MC setups do not create meaningful problems in response iff the MC cart's inernal inductance is low.
-As the MC cart's internal inductance approaches 5mh, all of these things become a problem, and it becomes easy to create a substantial roll off by altering interconnect length and by selecting different tone arm wiring. I.E/ The capacitance begins to matter MUCH more.
-Sadly the inductance spec is rarely given for any MC cartridge, so you are essentially in the dark before hand, but experimenting will reveal OBVIOUS results as the response curve can be very responsive when inductance is high, and will give almost no changes in the audible range when they are low.
-Low inductance MCs are clearly preferable and easier to manage within the system
-Loading for MMs, very different story, this can be a substantial problem. Capacitance does matter MUCH more.
-The circuit is simplified and does not give the entire story. The way that a phono stage responds to the ultrasonic information and the RLC can be complex, beyond the scope of a simple model and can be very specific depending on how your preamp operates. The pre/phono amp matters....DUH!.
Oh yeah, one more note on that article. It appears that they have grossly inflated the inductance figure on MCs, as I pointed out, for a typical MC cartridge. Some googling around can confirm that most are really a couple of uH to max a couple hundred uh MAX. However this was done to illustrate the point that they were trying to make, and their calculator is scaled back (but still inflated) to show a worse case scenario which is useful to just about anyone out there using the calculator with modern MC.
Dear Dfel: When using a stepup transformer, any capacitance present on the secondary side of the transformer will be reflected back to the primary side (IOW, the phono cartridge), but multiplied by the square of the primary-secondary turns ratio. It is therefore more important than ever to use super low-capacitance cables to connect a stepup transformer to the phono stage, unless the goal is to build a filter.
As an example of loading sans stepup transformer, the following thread on What's Best forum may be useful reading. The electrical models used are presented in the figures along with the response charts, are more complete than Hagerman's, and are derived from real-world measurements of cartridges, signal cables and phono input stages.
kind regards and hth, jonathan carr
Jonathan, thanks very much for chiming in. Dfel, Jonathan is the designer of Lyra cartridges, so we are privileged to be receiving some exceptionally knowledgeable inputs. He is also the author of the post that I linked to earlier which explained why minimizing capacitive loading of a low inductance low output moving coil cartridge can be important, even in the absence of a SUT.
Regarding your two most recent posts, which I thought were well done summaries of some good work, I just have a couple of comments:
1)With respect to MM's, I would emphasize per my earlier comment that premature rolloff can result from too little capacitance, as well as from too much, since in the case of MM's the LC resonance will in many or most cases directly affect frequency response within the audible range. As I mentioned, in general (and perhaps always) the manufacturer's recommended range of load capacitance should be adhered to.
2)Regarding your point about inductance not being specified for many cartridges, I would expect that in general there would be a significant degree of correlation (albeit probably a very loose one) between a cartridge's inductance and its rated output voltage under the standard test conditions.
And finally, just a very minor quibble: In a couple of places in the longer of your two recent posts the word "subsonic" appears to have been substituted for "ultrasonic," although "ultrasonic" was correctly used toward the end of that post.
Jcarr, thank you very much for posting I appreciate it. I will read through the forum, gather my thoughts, and post in this thread again. I am also wondering, what do you find is the typical inductance of a moving coil cartridge (low output and also high output) ? I get that several generators can be used but I am just curious what your take is on this. Are we in the realm of 5-500uH or are we more in the area of 5-500mH?
I can see what you are saying. I will put it into practical terms for anyone else who is reading so they can follow as well ( all 2 of them). Suppose that you have 100pf cable from the cart -> Sut and another identical one from the SUT->Preamp. and you are using a 1:10 SUT. Then...
The cart sees:
-100Pf + 100pf *sqrt(10)= 416pf
-The 47K load gets reflected back at 470 Ohms
-and the inductance of the wire is meaningless even after -being reflected with a Sqrt(10) multiple tied to it. The -cartdrige inductance is x * sqrt(10) and can be substantial depending.
The SUT sees ( bad phrasing, Through the SUT...):
-100pf *10 +100 pf = 1,100pf
-inductance from the cart x*10 = 10X
-and 40 Ohms from the cart *10 + 47K = 47400, or just 47K
Al, thanks for pointing out those details. You are right. I had not looked at the too little side. On the correlation I would hope so, it would make things easier but there in solid convention for quotation that would make it easy to figure out, but I will have to think about this. I do see what you mean, X MV output and Y resistance into an open circuit figure out ballpark for inductance etc.
As for the Ultrasonic Subsonic...tomato tom-ah-to LOL, you are correct I goofed on that.
Wait a Minute I had a dull moment let us redo this:
Too bad there are no edits, now the mistakes look silly forever.
Cart[x uh,30Ohms , wire(100pf,2uh,1 Ohm)->SUT->(Same wire)->Preamp(47K)
Cart sees everything on its side and the other side of the SUT DIVIDED by 10^2 or 100:
-100Pf (from the Cart->SUT connection) + 100pr/(10^2) (From the SUT->Preamp) back through the SUT = 101pf
-The 47K load gets reflected back at 47K/(10^2) = 470 Ohms
-and the inductance of the wire is meaningless and even less so after it is divided by 10^2.
-The cartdrige inductance is x and can be substantial depending as explained earlier
Other side ofSUT sees everything stepped up by 10^2:
-100pf *10^2 +100 pf = 10,100pf (WOWZER)
-inductance from the cart x uh*10^2 = 100X uh
-and 40 Ohms from the cart *10^2 = 4K
driven into a pre with a input imp of 47K.
This should be correct, sorry for the mixup, and please let me know if I made a mistake here (again).
Note: I have ignored reactance (Capacitive and Inductive) though I do not think it is substantial and I am also not certain how that follows through the ends of a SUT, If I were to guess Z is altered as sqrt((Xc/10^2)^2 + (XL/10^2)^2) using a linear transform of variable...ditto for the other direction.
Jcarr, Maybe I am off here but on the primary side/ what the cartridge sees: Do you not divide by turns ratio square i.e/ 10^2 or 100 in my example.
47K becomes 470 Ohms
100 pf SUT to Preamp becomes 1 Pf
I would have thought that this implies that the connection from the cartridge to the SUT may be more capacitance critical than the connection from the SUT to the pre.
going to the secondary side however requires multiplication by turns ^2 or by 100.
Please let me know what I am missing here.
Dfel, what Jonathan said is of course correct. The cartridge does not see the capacitance on the secondary side of the SUT divided by 100 (the square of the turns ratio we are assuming). Since the SUT transforms impedance in proportion to the square of the turns ratio, the cartridge sees the **capacitive reactance** that is on the secondary side divided by 100.
Since as you indicated earlier Xc = 1/(2*pi*f*C), capacitive reactance is inversely proportional to capacitance, and so the cartridge sees the capacitance on the secondary side **multiplied** by 100.
This is all based on an assumption of ideal behavior by the SUT, of course. No transformer will behave in a completely ideal manner, due to many factors. So all of this is of course just an approximation, but it is a good approximation for practical purposes.
Dear Dfel: Here is an alternative way to envision what a SUT does.
As a passive device, a SUT cannot create more energy. Its voltage amplification abilities are limited to converting the MC cartridge's output current into voltage. But since a SUT cannot create more energy, the cartridge signal current that gets converted into signal voltage is no longer available at the SUT output.
And since current is what charges and discharges capacitance, inserting a SUT between MC cartridge and phono stage reduces the cartridge's ability to charge and discharge whatever capacitance is present on the SUT secondaries by the square of the primary-secondary turns ratio.
hth, jonathan carr
I can say I only partly understand, I will have to learn a little more to fully wrap my head around how it works. However, for now:
I tried modeling the transformer, not sure why I am running into problems here. I will try to post the image later maybe you can offer some guidance on the schematic/model for simulation. again ,much appreciated thanks guys!
Hi guys, I have been having a lot of trouble modeling this correctly with the SUT in the mix. I am sure I am making some silly mistakes but I can't find them. Here is a link to the image of the simulation + circuit model. I tried to follow the model from the snippets I could find online to the paper by J carr, I would love to read the whole paper one day..please PM me since I cant PM you Jcarr.
For the earlier simulations it was easy to lean on the Hagerman article and simply copy the circuit and play with the parameters. But, in this case it is not so simple, and I would appreciate some help. Thanks.
I am assuming the same cart specs from the paper, and using the specs for the mogami 2549 wire, 0.022 Ohms/foot, 26pf/foot, and 0.72uH. I used a 1:10 Step up ratio for the SUT.
Please tell me how if I have made a mistake here ( I am sure I have), and how to correct it as I am interested in seeing this display something meaningful. Please be gentle with the commentary as I am a rookie and know nothing about Electrical Engineering. Thanks again.
" the mathematics that is involved in analyzing RLC circuits is quite complex"
But not so complex if you use the Complex form of reactive impedance. ;~)
Seriously, the use of Complex (imaginary) numbers makes the process much more easy. The circuit can be reduced to a Complex matrix equation using Ohm's law and then solved. The Complex form keeps track of both the magnitude and the phase of the signal.
Dfel, as I indicated earlier in the thread I can't speak too knowledgeably about modeling of SUTs. But FWIW the following thoughts occur to me:
1)Depending on how the simulation program you are using works, I think you might have to model the SUT as an "ideal transformer" combined with external elements representing its non-ideal characteristics (i.e., resistance, inductance, and capacitance, to the extent that they may be significant).
2)I would expect that the resistance of its two windings would be significant enough to warrant inclusion in the model, and that it should be modeled as two resistors external to the transformer itself, one of them in series with each of the windings. Or, alternatively, the resistance of the secondary winding could be modeled as reflected into the primary circuit, multiplied by the square of the primary to secondary turns ratio.
3)I don't know how you derived the inductances shown in your model for the two windings, but I suspect that they are not what should be included in the model. I believe that what should be included are series inductances in the primary and secondary circuits representing "leakage inductances." With the secondary circuit leakage inductance alternatively being modeled on the primary side, multiplied by the square of the primary to secondary turns ratio.
4)I don't know if it would be significant enough to warrant inclusion in the model, but including a parallel combination of resistance and inductance across the primary winding MIGHT also be called for, to account for core losses and reactances. (More precisely, those elements would be modeled directly across the primary winding if the impedances in series with the secondary are modeled on the secondary side; if the secondary side impedances are modeled as reflected to the primary side the reflected secondary side impedances should be modeled closer to the primary winding than those elements).
Otherwise your model looks good to me. It assumes that the cable parameters are "lumped elements" rather than "distributed elements," but that assumption seems to me to be reasonable for present purposes.
Dfel, Far be it from me to try to amplify on the advice you've been given by either Al or JCarr. However, I don't see where anyone answered your question re the typical range of inductance for a typical MC cartridge. In my personal experience, I have never heard nor read of any MC that has inductance as high as 1 mH. Nearly all MCs seem to have inductance in the low micro-Henry range, less than 100uH. The DL103 may be an outlier as regards MC inductance (don't know the numbers), because it also has a relatively high internal resistance, a sign that there is a large coil inside.
Another source for information, if you are so interested in the math, is to be found on the Jensen Transformer website, in the form of a white paper on how to load their SUTs for flattest frequency response.
Personally, I would just concern myself with impedance loading and be done with it, if I were to be using an MC with a SUT. In other words, let the capacitance and inductance take care of themselves, which will happen if you do nothing crazy, e.g., 10-foot ICs or weird phono input stages.
Thanks Almarg, for you insight.
as to the items:
1) In the K statement I have modeled it as a perfect SUT, this can be seen the by the 1 in the " K L2 L4 1". I can use numbers of less than one to make up for losses due to the SUT, like .6 .7 .9 etc..I figured lets see what happens with a perfect transformer first to isolate the cable effects.
2) Good point, I will sort that once I have the rest of the model making sense. I am concerned that the whole network of connections is completely modeled incorrectly. Can you please give some input on the basic structure, thanks.
3)Derived to have a 1:10 ratio, no other "genius" there (Strong emphasis on the quotation marks). The values I chose were arbitrary, so long as they had at square of quotient to give 10. Maybe that is incorrect.
4) I hear you, but I want to make sure that model itself I.E/ series/parallel resistors ground inductors and everything else are placed correctly in the circuit to model that part of a stereo system. I tried to follow Jcarr's model, but in the end I am still not sure why when modeling a wire connecting devices you would model the RCL in series or in parallel, and in what order you place the RCL for the wire connectors. I am a little lost on it and hoping someone can look at the images of the model circuit I have done and help me tweak it to the one that is correct.
... Can you please give some input on the basic structure.... I tried to follow Jcarr's model, but in the end I am still not sure why when modeling a wire connecting devices you would model the RCL in series or in parallel, and in what order you place the RCL for the wire....As I indicated near the end of my last post, your model looks good to me aside from the SUT issues.
For the cables, R and L are in series, and C is in parallel. Representing these parameters as "lumped" elements, with the capacitance first in the chain, as you have done, rather than as a great many separate elements representing their distribution along the length of the cable, I believe is a reasonable approximation at frequencies of interest.
Regarding the SUT model, the inductances of each of the two windings will probably not be in proportion to the square of the turns ratio, and may be directly proportional to the turns ratio itself (depending on a number of variables). And more significantly, if it is not clear, the inductances that should be represented are not the inductances that each winding would have if it were divorced from the other (i.e., their self-inductance). What should be represented, as I mentioned, is "leakage inductance," in series, and perhaps also a parallel inductance (and resistance). I don't know what values would be reasonably typical for those parameters for typical SUTs.
Also, Lew's comments are good ones IMO. Jonathan's emphasis on minimizing cable capacitance on the secondary side of the SUT should also be kept in mind, of course.
According to this link the:
the inductance is proportional to the
square of the turns ratio. In the ex ample above, a turns ratio of 1:3 gives a 1:9 inductance ratio..."
they they proceed to use 100uH : 900 uH.
I have not even got the slightest clue where to get the actual figures for the SUTs, as none of them publish this information. I suppose I can try to email cinemag, Jensen etc... to see if I can get it.
Now, I followed this guide to implement the SUT. Worth repeating: I know very VERY little about electrical engineering. However, in the current model as I raise Capacitance massively on either side of the SUT is makes NO difference to the frequency plot. Also the Freq plot is offside by over -50db...as it should be reading +20 after going through the SUT. Hence Why I think there may still be something off. I dont know enough EE to figure out what the "something" is. Please experts, lend a helping hand, CALLING ALL EXPERTS PLEASE!
It would be great if I could attach the model so you can open it in your own software without re-sketching it. If you know of a way please tell me, I cant seem to attach files on audiogon.
I tweaked the model, after reading another paper on tranmission lines etc.. I found a model that made sense and demonstrated the correct db gain and presented a familiar looking bode plot. I think this lumped model may be correct, or at least "better".
See the link
I tested this model with some extreme values, and compared to the baseline case outlined in Jcars white paper. I used the specs from the Mogami 2549 out to as much as 20 feet worth of RCL, tried changing the cartrdige parameters for impedance up to 50 Ohms and 500 Uh etc...
The only changes I have noticed in the response curve are in the ultrasonic peak shape and neighborhood, though this activity occurred far away from the audible band (100K or more). The Subsonic roll off was very slightly affected and was still very low (<15Hz) across the values used. Of course this is under the "Perfect" transformer assumption. So this model is showing that a cable with the characteristics of the 2549 is capable of reproducing the signal without an drastic changes to the frequency response in an MC Phono rig, provided that the parameters of the cable are "reasonable" and inline with what most people would use anyways.
Looks like you've made some progress. Good!
I'm surprised that relocating the connections of the cable capacitance elements in the model (together with the minor changes you've made in some of the capacitance values) had such a profound impact on the results. I don't know how to explain that.
Also, keep in mind that even though the response peak is way above the range of audible frequencies, its amplitude and frequency are nevertheless important considerations, which stand a good chance of being audibly significant. Again, see Jonathan's post in another thread that I linked to earlier.
Regarding the transformer model, I read through the "Using Transformers in LTspice/SwitcherCAD III" paper you linked to, and I also looked at some of the literature on LTSpice at the linear.com website. Their simulation is done differently than what I was envisioning when I provided my earlier comments. I was envisioning that the transformer would be modeled as an ideal transformer (k = 1; infinite self-inductance of the windings; zero leakage inductance, etc.) in combination with external circuit elements representing its non-ideal characteristics. They are modeling it as a single non-ideal element. So take that into account when considering my earlier comments.
I would expect either approach to yield good results, IF the parameter values are suitably chosen. And again, I have no knowledge of what the appropriate values might be for a typical SUT. Also, you might try re-running your simulation with k values of say 0.9, 0.8, etc., to see how sensitive the results are to that value. k = 1 corresponds to zero leakage inductance, which of course is not possible with a real world transformer.
Finally, a note of caution. It appears that despite statements indicating that LTspice/SwitcherCAD III (or "LTSpice IV" which is what is available for download at their website) is/are "general purpose," it appears that their program is oriented toward facilitating analysis of switching power supplies. As stated in one of their papers, "LTspice is a high performance SPICE simulator, schematic capture and waveform viewer designed to speed the process of power supply design. LTspice adds enhancements and models to SPICE, significantly reducing simulation time compared to typical SPICE simulators, allowing one to view waveforms for most switching regulators in minutes compared to hours for other SPICE simulators." And of course the designs of power supply transformers and cartridge stepup transformers are vastly different.
IMPORTANT P.S: I just noticed that in the second model the units of the transformer coil inductances appear to be Henries, while in the first model they appear to be microHenries (with the numerical digits being the same in the two models)!!!
That would certainly seem likely to account for the differences in the results!!!
AL, thanks for pointing that out!!!!
You are right I must have not typed in uh or mh and it defaulted to full henries, and I completely missed this. I will have to look at this later when I get a chance.
But now that, that is a thing I might as well figure out what the inductance is in acutal step up transformers. I emailed cinemag hopefully they respond.
Looks like so long as L4 is at least 100mh things look normal. The pairwise inductance have been chosen to give a 1:10 ratio i.e/ as per the source it is the sqrt of the inductance ratio. (L4,L5)->(1uH, 100uH) ; (10uH, 1mH) ; (100uh, 10mh) ; ( 1mH, 100 mH) ; (10mH, 1000mH) were all giving weird results as in the first circuit and the gain was below the approximate 20 Db I was expecting as per the normal calculation given the turns ratio.
Once I used values in the form of ( X, 100X) where X was greater than 100mh things normalized and stayed normal. I tried (100mH, 10000mH) all the way to (10H,1000H) the gain stayed constant, the low freq roll-off disappeared as the values got pumped up, though it makes little difference as much of this activity was below 20 HZ. The ultrasonic peak remained above 100K and well outside of the audible range, its shape was slightly altered as the values went higher.
So as it sits now. I am very curious know exactly what an actual spec for the prm/sec inductance values are in transformers that we use. NO manufacturer has this spec on their website that I have been able to locate, so hopefully cinemag emails me back. I will report back once I know OR if anyone else has a reliable source for these specs please post.
Go here: http://www.jensen-transformers.com/
That's the home page. On the left hand margin you will see a vertical listing of links. Click on any or all of the links listed under "Applications". Plus, the principles of Jensen are some very nice, very smart, and very knowledgeable guys, when it comes to SUT design and implementation. They typically will share their expertise over the phone, if you have a specific question. (Disclaimer: I have no affiliation with Jensen whatsoever. I don't even use a SUT.)