How to calculate mic input xfmr ratio for tube circuit

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MediaWorksOKC

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Hi, guys.

Hopefully someone can explain to me how to calculate or otherwise determine the 'ideal' or 'proper' ratio to spec. for a mic input transfo.

From what (little) I know it has to do with input noise voltage of the tube used, I think.  ???

I wondering about, really, the lowest ratio I can 'get away with' without penalty (other than the obv. of using a xfmr in the first place) since I don't really 'need' much gain from the transfo itself, just enough to give the tube what it wants to see/hear/feel/eat/etc in order for it to 'act right' in this situation.

I wish to have a mic input transformer made for a balanced tube preamp circuit (the circuit is done, works fine, uses four tubes per channel (I have cases!), two per +/-, provides appr. 60 db of gain, low output imp. and uses no output xfmr, I love it!).

Thank you for your thoughts...

Chris
 

abbey road d enfer

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The Jensen paper is not very helpful in designing tube preamps, because the noise mechanism of tubes (or FET's for that matter) is different than that of bipolar transistors. Bipolar have a clearly defined noise voltage and current. Tubes have a defined noise voltage only. Roughly, the noise performance of a tube preamp could be optimised by increasing the step-up ratio of the transformer, to a point where the tube's self-noise would be irrelevant and the thermal noise of the source (or its reflection at the transformer's secondary) would be dominant. So a 1:100 step-up xfmr would be the ticket for a single-stage tube mic pre with 60dB of gain and 1dB noise factor.
In fact, there are some practical reasons why it's not feasible:
A 1:100 mic input xfmr reflects about 1.5-2Meg at the secondary. Due to the number of turns, the actual parasitic capacitance of the secondary would induce a low-pass filter at about 1-2kHz, with a 12dB/oct roll-off. There are winding techniques that allow reducing parasitic capacitance (I think they are called wave-winding and basket-winding in english, the french term is "nid d'abeille" - bee's nest), but they also increase parasitic resistance and bulk and cost.
Another factor is that the input impedance of a tube is governed at HF by the Miller effect (the plate-to-grid capacitance reflects on the grid multiplied by the gain of the stage. This is another cause of HF degeneration. A pentode or a cascode structure would minimize this effect.
Practically, designers have been content with 1:10 to 1:30 step-up ratio, depending on expected performance and topology.
Abstract from the Jensen website:
If the above calculation is performed for Vacuum Tubes, the value obtained will normally be much higher than the secondary impedance of even our JT-115K-E transformer. We do not manufacture Microphone Input Transformers with ratios higher than 1:10 due to the limited bandwidth that is possible in designs of this type. The JT-115K-E will work very well in most Vacuum Tube applications.
The highest ratio transformer currently available that I'm aware of is Sowter's input xfmr for Ampex 350/351, with a 200R center-tapped primary and a 50k secondary.
 

pstamler

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Here's a good rule of thumb:

Figure out the equivalent noise resistance of the tube circuit. Then use a transformer which raises the mic's source impedance to 4x the tube circuit's equivalent noise resistance.

The equivalent noise resistance has essentially three components, one of them usually minor. These are the tube's own noise, the cathode resistor's noise, and the plate resistor's noise.

The tube's noise resistance typically equals 2.5 / gm, where the gm is measured in Siemenses. The cathode resistor's noise resistance is whatever the resistance is, except when the cathode resistor has a bypass cap, in which case the noise resistance is effectively zero. And the contribution of the plate resistor to the noise resistance is Rp / gain^2 -- that is, the actual plate resistor value divided by the square of the tube's gain. So if the tube gain is 10x and the plate resistor is 30k, the noise resistance is 30,000 / 100 = 300 ohms.

Add all three elements. Let's say gm = 2500uS, so rnoise = 1k. Let's say the cathode resistor is 2.2k, the gain is 10x and the plate resistor 30k as above. The total noise resistance = 1000 + 2200 + 300 = 3500. So a 14,000 ohm transformer secondary would be 4x the total noise resistance, and with that ratio, the tube circuit will add <1dB of noise to the inherent source noise of the mic.

The Jensen JT-115k-E would work in this application. In practice, with a good quiet tube stage you can get away with a JT-13k7, which has a 1:5 turns ratio, better performance in all respects (including saturation), and lower DC resistance in the windings. In real life, you may find that the lower DC resistance yields lower total noise with the JT-13k7 than the JT-115k-E.

Peace,
Paul
 

MediaWorksOKC

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Thanks Mo and Abbey for the references and info.

I'll get to work on the formula that you provided Paul, that's just what I was looking for.

I could have been clearer earlier stating that the circuit I'm having this transformer wound for is fully balanced throughout, so I just need to do the calculations for one polarity and duplicate the results for the other polarity, right? For the sake of this conversation, the transfo will be 1:5, 1:5, basically two transformers on one core, one for each polarity of the circuit.

Thanks again!
 

ruffrecords

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pstamler said:
Here's a good rule of thumb:

The tube's noise resistance typically equals 2.5 / gm, where the gm is measured in Siemens

I have often seen this quoted but I do not believe it is true. I have searched for original measurements made at audio frequencies and can find none. |As far as I can make out the original work this formula came from was rf not audio. My own extensive measurements indicate that at audio frequencies a tube's self noise if much higher, several times higher than this formula suggests. In practice you need a 10:1 ratio transformer to achieve even a 3dB noise figure.

Cheers

Ian
 

ruffrecords

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pstamler said:
Ian, could you share the data from your measurements with us?

Peace,
Paul

OK, here is a broad summary. First, in a 20K bandwidth, at room temperature the Johnson noise in a resistor is approximately:

(Vn)^2 = R/3096  in (microvolts)^2

or the noise voltage in a 3096 ohm resistor is about 1uV or -120dBV

A triode with a gm of 2.5mA/V ought, by the 2.5/gm formula, to have an equivalent input noise resistance of 1000 ohms which is a noise voltage of about 0.57uV. So such a tube with a stage gain of 20 should have a measured noise at its output of 20 x 0.57 = 11.4uV assuming there are no other dominant noise sources.

I have measured a large  number of stages  (well over 100) , all with bypassed cathode bias resistors,with dc supplies in screened boxes, with stage gains of 20 times. The measured output noise has never been better than 45uV and varies typically between 60 and 120uV within any tube type. I have tested 6AU6 wired as triodes, 6SN7, 6CG7, ECC88, ECC81, ECC82 and ECC83 tubes all with very similar results.

This means the equivalent input noise voltage is in the region of 2 to 6uV representing equivalent input noise resistances of over 12K and 111K respectively.

The noise in a 150R resistor is about 0.22uV. Via a 10:1 transformer this becomes 2.2 uV which is very close to the lowest equivalent input noise I have ever measured - hence my comment about the 3dB noise factor.

Cheers

Ian
 

pstamler

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Ian, are you sure those tubes were really running at an operating point which produced a gm of 2.5mS? An ECC83 (12AX7) won't get up that high under typical conditions. The kind of results you're measuring make sense on a 12AX7 but are noisier than I've encountered with things like 6SN7s.

It'd help to know the operating points (cathode current, plate or grid voltage) for some of these experiments.

Peace,
Paul
 

ruffrecords

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pstamler said:
Ian, are you sure those tubes were really running at an operating point which produced a gm of 2.5mS? An ECC83 (12AX7) won't get up that high under typical conditions. The kind of results you're measuring make sense on a 12AX7 but are noisier than I've encountered with things like 6SN7s.

No, quite a few of them are not operating where gm = 2.5 and I did not mean to imply that they were. I was simply using it as an example to show the sort of output noise you would expect.  Having said that, I measured the gm for all the triode strapped 6AU6 tubes I tested at the same operating point that the noise was measured and in all cases the gm was in the 3.5 mA/V region and it was on a one of these that I measured the lowest noise at 45uV. These were the first tests I did and what first made me wonder about the old 2.5/gm formula. I tested about 30 6AU6 tubes.

All the 6SN7 and 6CG7 tests were done at 5 or 8mA idle current where gm is typically just over 2mA/V. I have tested about 80 of these. I only tested a few ECC88 and Russian equivalents at the same idle current where gm should be well over 2.5 mA/V. I agree the higher mu tests are inconclusive but I did note that the measured output noise was roughly proportional to the tube mu and the 12AX7 measurements were in excess of 200uV.


I would be interested to hear what results you have obtained with the likes of the 6SN7 and friends.

Cheers

Ian
 

pstamler

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Well, it's been ten years since I did the experiments, but as I recall the tests came out within a dB of predictions based on 2.5/gm. I was running 6SN7s at about 4.5mA with a 325V supply; I think the plate was sitting at about 180V.

We've got a class starting up today where we'll be looking at stuff like this; perhaps measuring some of this can be our in-class exercise in about five weeks, when I start talking about tube design and noise.

Peace,
Paul
 

ruffrecords

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pstamler said:
Well, it's been ten years since I did the experiments, but as I recall the tests came out within a dB of predictions based on 2.5/gm. I was running 6SN7s at about 4.5mA with a 325V supply; I think the plate was sitting at about 180V.

That is very interesting. My plates are running slightly lower at around 145V with a 300V supply so not different enough to account for the much higher levels I measured.

We've got a class starting up today where we'll be looking at stuff like this; perhaps measuring some of this can be our in-class exercise in about five weeks, when I start talking about tube design and noise.

That would be very interesting indeed. I would love the 2.5/gm rule to be right but I have not yet been able to confirm it. As you are no doubt aware, measuring such small noise voltages is non-trivial and I would be interested to hear how you would approach it.

Cheers

Ian
 

PRR

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I'm real interested. Tell the class the World is watching.

If we must over-rule "2.5/gm" let's have good estimates of Gm. Explain that datasheets often cite show-off conditions, good-enough system design may work much leaner, and Gm runs roughly as square-root of current. The 10mA spec for 12AU7 is way-off if you run 250V and 150K, less than 1mA.

Gm may be checked in place. Put 100mV input. Use large coupling cap and load the output to 100mV out. Now Gm is approximately 1/RL. (Small correction for other resistances; may be significant on lower Mu tubes.)

One pitfall comes to mind: 1/f noise. And rather than speculate on causes and effects, let's do some tests with 6dB/8ve 400Hz low-cut and if possible a steeper higher wack (12dB-1KHz).

(A spectral analysis may be interesting, and is now cheap. I've used that for insights into room noise and PC soundcard noise, but not a tube.)

Some tubes left hot overnight (or morning to late afternoon if overnight smoke could be a problem) just to cook the cathodes and cathode-caps.

Of course measured with dead-short grids. Also with 1Meg on grids, but in practice this should reveal all the hum in the room, negligible grid-current noise.

Of course with grids mostly negative of their cathodes, though there are some zero-bias amps which are quite quiet.

> 12AX7 measurements were in excess of 200uV.

200uV/50 = 4uV in? Seems high. But the same number (3uV-6uV) appears in a test of open-grid operation:

http://i.imgur.com/4jY7Y.gif
http://i.imgur.com/qHEgj.gif
 

abbey road d enfer

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The attached formula, from the J B Johnson 1928 publication, seems to yield more practical results.
 

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lassoharp

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PRR, thanks for those papers.

My observation from the effects of plate voltage on noise is that 90V +/- 10V or so is a common V1 plate voltage for a number of classic tube pres using the J/SJ7 - iron to open grid.

Interesting to see how that ties in to figuring best ratio in terms of all other considerations - headroom, noise, needed gain etc.  Maybe coincidence?



 

ruffrecords

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abbey road d enfer said:
The attached formula, from the J B Johnson 1928 publication, seems to yield more practical results.

Which is very interesting because with a stage gain of 20 and an idle current of 5mA this yields 37K5 which is roughly equivalent to 3.5uV which is much closer to the values I have measured.

I would be very interested top get hold of this publication. Can you let me know its full title and publishing details please?

Cheers

Ian
 

ruffrecords

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Just to add a note to PRR's comments.

My test rig for noise measurement is built in a screened box, the grid is shorted and the measuring meter has a 400Hz HPF built in.

I have seen several times people say 1 or 2 uVinput noise is achievable but never have such claims been accompanied by measurements - except once where it was mis-read. I sent the guy an email pointing out the error but never received a reply.

Cheers

Ian
 

PRR

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> ...90V +/- 10V or so is a common V1 plate voltage for a number of classic tube pres

Yeah, well, what choice do you have? Classic preamps run 180V-300V supply, often 250V. For best large-signal we run plate maybe over half of B+, for best gain we go lower than half B+. Talking about input stages in a non-Rock studio, signals are small, gain is the goal, aim 1/4 to 1/2 of B+, 62V to 125V, so nominal 90V.

A _few_ of the old-time spec-sheets give noise claims. I thought 12AY7 did, using an oddly small 20K load, but I can't find the uV number. There is a number on Tung-Sol 12AX7A 1963:
http://www.mif.pg.gda.pl/homepages/frank/sheets/127/1/12AX7A.pdf
Note that the cathode resistor for this test is far higher than is suggested in the R-C table for 250V 100K working. And the bandwidth is 25CPS to 10,000CPS. Corrected for 20KHz it would be 2.5uV noise+hum.

> how that ties in to figuring best ratio in terms of all other considerations - headroom, noise, needed gain etc.

The optimum noise-figure comes with the HIGHEST practical transformer ratio. Tubes have significant hiss voltage and teeny hiss current. You don't have to worry about "too high ratio" spoiling your noise-figure until dozens of Meg Ohms. However a wideband audio transformer can't be wound-up to Megs. First you can't buy or wind wire thin enough. Second any reasonable bass means a physically large core and winding and hundreds of pFd of stray capacitance. Be optimistic: 50pFd. At 1Meg nominal impedance, 50pFd loads-down the source above 3KHz, which isn't good enuff for gitar, let alone soprano or piano.

Depending on goals and definitions, transformer windings can go 5K easily and 50K with significant compromise (ringy/falling at 15KHz or very expensive and ringy/falling at 25KHz). This leads to ratios like 1:5 to 1:15. OTOH if mike hiss is 200 ohms or 0.25uV, that levers to 1.3uV to 4uV at the grid. If grid hiss is 0.5uV as sometimes stated, no big deal. If grid hiss is 3+uV as Ian is seeing, then even higher ratios are not insignificant noise figure.

Does it matter? I said gitar, but amp-hiss will overwhelm any semi-decent preamp. Piano, is hard to find a room that is flattering to the piano and has low ambient noise. And so many of us use condenser mikes where the actual PRE-amp is in the mike, and often the self-hiss low in acoustic terms yet electrically is way in excess of even poor NF console amps.
 
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