Assistance in calculating multiple corners in 3 stage tube amp

[lassoharp]

This question is related to a specific project I'm working on but is more of general basic question on figuring multiple corner frequencies in a 3 stage tube circuit.

The circuit is:

http://www.jlmaudio.com/au300mod.gif

Tube substitutions are V1 & 2 = 6SL7  V3 = 6SN7 All other circuit values stock except for sub of 3K cathode resistors on V1 & V2.  OT = 20K:600  pri 11.4H  Leakage ind = 52.26mH  rated 30Hz-15KHz.  Input transformer 150:20K  rated 30Hz:15K


So far I've got low corner figures for Cc of each stage and the output transformer as well as high attenuation figures for each stage. What I do not know how to do is add them together to get a meaningful figure for what the expected overall response will be front to back with iron included. I'm ignoring the feedback for a moment to simplify things some. The text I'm using shows an involved graphical method for doing this which at the moment I don't understand any better than my attempt here to add them another way.

Lo response

Input transformer:  assumed spec @ 30Hz

V1:  .05uF/~600K  = -3db @ 5.3Hz

V2:  .068/~600K  = -3db @ 3.9Hz

V3:  *not sure on this calc - 4K//10K = 2857r  -3db @ 39.9Hz

Hi response

Input transformer:  assumed spec at 15KHz

V1 & V2:  45K//120K//560K = 30.9K  stage gain = 22.2    30.9K/78.36pf = -3db @ 65.7K

V3:  leakage inductance 52.26mH , 4.9K measured impedance for each half of pri winding  = -3db @ 15K


So, lots of roll offs - How to deal with the addition?  ???  Probably missing the forest for the trees. . . . but I had to ask.

 

[abbey road d enfer]

This question is related to a specific project I'm working on but is more of general basic question on figuring multiple corner frequencies in a 3 stage tube circuit.

Solving this mathematically is quite difficult. The graphic method is what has been employed for about 100 years before computers offered an easy alternative. Using a Spice program is the new way to go (I suggest the free LTSpice program).

The circuit is:

http://www.jlmaudio.com/au300mod.gif

Tube substitutions are V1 & 2 = 6SL7  V3 = 6SN7 All other circuit values stock except for sub of 3K cathode resistors on V1 & V2.  OT = 20K:600  pri 11.4H  Leakage ind = 52.26mH  rated 30Hz-15KHz.   Input transformer 150:20K  rated 30Hz:15K


So far I've got low corner figures for Cc of each stage and the output transformer as well as high attenuation figures for each stage. What I do not know how to do is add them together to get a meaningful figure for what the expected overall response will be front to back with iron included. I'm ignoring the feedback for a moment to simplify things some. The text I'm using shows an involved graphical method for doing this which at the moment I don't understand any better than my attempt here to add them another way.

Lo response

Input transformer:  assumed spec @ 30Hz

  Which is almost meaningless. Source impedance is a major factor here.

V1:  .05uF/~600K  = -3db @ 5.3Hz

V2:   .068/~600K  = -3db @ 3.9Hz

V3:   *not sure on this calc - 4K//10K = 2857r  -3db @ 39.9Hz

Here, it's easy. The latter zero is clearly dominant, by a factor of 10 over the two previous ones, so you can assume the LF response is -3dB @ 40Hz.
But the input xfmr may have a similar response, which would combine in an overdamped 2nd-order (12dB/8ve) response with ca. -6dB @ 40Hz.
But some of your calculations are wrong; in particular your V1: the input impedance of V2 is bootstrapped, so the actual input Z is probably about 10x higher. And NFB around V2 & V3 does matter a lot.

Hi response

Input transformer:  assumed spec at 15KHz

V1 & V2:  45K//120K//560K = 30.9K   stage gain = 22.2    30.9K/78.36pf = -3db @ 65.7K

V3:  leakage inductance 52.26mH , 4.9K measured impedance for each half of pri winding  = -3db @ 15K


So, lots of roll offs - How to deal with the addition?  ???   Probably missing the forest for the trees. . . . but I had to ask.

It seems the HF response also has to take into account two relatively similar dominant poles, which again would produce an overdamped 2nd-order (12dB/8ve) response with ca. -6dB @ 15kHz.
But the 15kHz spec, is it at -3dB?

 

[emrr]

If another visual helps, you can find two plots of one AU300 here.  The resolution is only 5Hz, so the bottom is a bit fudgy, but you should get the basic idea.  Change to mystery iron, I can't begin to say. 

 

[lassoharp]

Thanks abbey road, Doug.

Solving this mathematically is quite difficult. The graphic method is what has been employed for about 100 years before computers offered an easy alternative. Using a Spice program is the new way to go (I suggest the free LTSpice program).

It was certainly feeling that way and would explain why I couldn't find another(non graphic) treatment of it!

Which is almost meaningless. Source impedance is a major factor here.

I was thinking a lower stage gain with the V1 & 2 substitution to a lower Mu tube affecting the hi corner differently but I think I see what you mean with the source impedance - varying due to the effects of the input transformer?

Here, it's easy. The latter zero is clearly dominant, by a factor of 10 over the two previous ones, so you can assume the LF response is -3dB @ 40Hz.
But the input xfmr may have a similar response, which would combine in an overdamped 2nd-order (12dB/8ve) response with ca. -6dB @ 40Hz.
But some of your calculations are wrong; in particular your V1: the input impedance of V2 is bootstrapped, so the actual input Z is probably about 10x higher. And NFB around V2 & V3 does matter a lot.

Yes, that entire gain control network was a mystery to me. I take it it's not a simple case of adding the extra 39K in series with the grid resistor for low corner calculation?  In my case the optional 250K var resistor is in there between 7 & 19 which looks to change the situation again.

It seems the HF response also has to take into account two relatively similar dominant poles, which again would produce an overdamped 2nd-order (12dB/8ve) response with ca. -6dB @ 15kHz.
But the 15kHz spec, is it at -3dB?

For the input iron it's listed as +/- 1/2 db @ 15KHz,  output gives only range with no deviation.  The measurements were suggesting to me that it was -3db at 15KHz.  I'll have to get a real sweep soon to confirm each case.

So, is it correct to assume the response will always be falling off at 6db per octave on either end regardless of where the corner begins?

If another visual helps, you can find two plots of one AU300 here.  The resolution is only 5Hz, so the bottom is a bit fudgy, but you should get the basic idea.  Change to mystery iron, I can't begin to say.

That looks pretty close to the manual spec on the bottom - allowing for the resolution.  A ways away from some of the others.

 

[emrr]

In my case the optional 250K var resistor is in there between 7 & 19 which looks to change the situation again.

My plots show virtually no frequency deviation from min to max gain, which I did not expect. 

 

[lassoharp]

In my case the optional 250K var resistor is in there between 7 & 19 which looks to change the situation again.

My plots show virtually no frequency deviation from min to max gain, which I did not expect. 

Ah yes, I didn't catch that. The overlay is practically seamless. 

 

[PRR]

> OT = 20K:600  pri 11.4H

11 Henries end to end??

At 20Hz, 11H is 1.38K. To claim 20K impedance we have to get to 290Hz. (If 11H per side, only 72Hz.) That's a remarkably lame OT.

Yes, a low source resistance will improve the -3dB point. However copper resistance may be 10% or 5% of the nominal impedance, so we won't get more than 1/10 or 1/20 better.

The 6SN7 plate impedance is probably around 6K per plate, 12K p-p, so we can't drive with very low source impedance. 11H and 12K||20K is like 108Hz.

Is there negative feedback? V2 gain is dominated by 39K(?) in cathode. 39K?? If true, then this stage gain is barely over 2. The 12AU7 stage is working near-matched so will be near Mu/2, about 10. Gain of 20 around the loop. NFB ratio is 5.6. The loop margin is only 4. Ignoring several "+1" corrections, the LF will be almost 4 times better than it is naked. Near 30Hz.

The 0.47uFd cap can be used to bump the response... but against 180K this is 2Hz and not helping any at 30Hz. If you can verify that the original OT worked to 20Hz, then the 2Hz zero may be the final tweak to compensate several part-dB losses at 20Hz.... but not if your OT is sagging at 290 or even 108Hz and the NFB is needed to get anything like "bass".

(BTW, this 0.47u cap may affect the simple approximation for bootstrapping the 560K; but with OT spec given, this is moot.)

In addition: the distortion of a P-P OT is related to inductance, and in P-P OTs we usually want enough inductance that the small-signal response extends FAR below the band. Loudspeaker OTs routinely pass 10hz or lower, if you stay far-far below max power.

If you like good sound, build a good no-NFB amp. I'm guessing you want <2% THD at 50Hz at 50 milliwatts. If you also must meet a 20-20KHz -2dB spec or a <1% THD @ 50Hz spec, build it with a little extra gain and apply NFB. In solid-state you can sometimes add so much stable gain that the raw amp may be somewhat crummy (and also too high-gain to use at all). In tubes you can't get huge NFB, you gotta get the core amp solid first.

> correct to assume the response will always be falling off at 6db per octave on either end

A single reactance will be 6dB/oct.

The L-C inside the hi-Z input transformer has probably been optimized for mild-Q resonance and then 12dB/oct.

If you cascade three identical stages with say 20KHz corner, response will be -9dB at corner, -3dB an octave lower, and asymtotic to 18dB/oct.

V2 input Miller C is nowhere near the 50-100pFd we'd get from a "normal stage" due to bootstrap. As a rough guess the Miller multiplier is maybe 2. So 10pFd? Since extravagant wiring or big fat coupling caps can add 20-30pFd of stray, you need a nice layout to take advantage of this low grid C.

> no frequency deviation from min to max gain

Oh, wait!!

Points 7 and 19 have a resistor across? Then some gain-margin stays somewhat constant as gain is changed. This is "current feedback opamp theory". V2 gain rises from 2 to 20 or 20dB as gain-pot turns from infinite to zero. That 20dB is also the amount of claimed gain-change. Like a CFB opamp's frequency response top-end changes little for gain of 2 to 20, this will change little. Secondary effects like weak bootstrapping will show at the extremes


> How to deal with the addition?

Same way they did it back then.

Fix any terrible on-paper problem, like a 5KHz top-loss (or a 108Hz OT limit).

Build it. Measure.

If it is a little out, fiddle it. NFB can depress the midband gain so it is level with selected bass or treble gain (but only so far). Since this plan has local NFB, you can use small (0.005uFd) cathode caps to bump the treble.

If a lot out, see if some slight change fixes it. I have project reports from my dad, he wrote to the coil-winder and asked if a different spec was possible and how bad cost would go up. That was data-heads but obviously the old console makers talked to their winders too. Maybe an X13 core at three times the price would buy another octave. Now the problem is profit, not electronic.

 

[lassoharp]

  Thanks PRR for  the excellent breakdown!                                                                                                                                                                                                                                                                               


                                   

> OT = 20K:600  pri 11.4H

11 Henries end to end??

At 20Hz, 11H is 1.38K. To claim 20K impedance we have to get to 290Hz. (If 11H per side, only 72Hz.) That's a remarkably lame OT.

Probably more my lame calculations.  Here's how I (re)figured it.  I measured 6.3K and 11H end to end @ 120Hz (measured ~18.5K @ 1K).  From CT to either end I get 2.0K and 2.75H @ 120Hz.  I'm not sure if it's equivalent to say that 6.3K//12K = 4.1K/11H = 58Hz  is the same as 2K//6K = 1.5K/2.75H = 86Hz.  Neither figure is close to 30Hz.  It looks like the source impedance needs to be around 4K to get near the 30Hz corner.  The factory iron lit states designed for 6C5 family tubes. A 6C5 would look to offer 16K p to p at best.

It may be the inductance meter measurement. I didn't state it above but those figures were measured with a test tone of 120Hz and the secondary was loaded with a 600r resistor.  Unloaded, the inductance measures 15.9H @ 120Hz. The end to end calc looks better at a 41.4Hz corner. Which will be more accurate in circuit?  Also, the inductance could creep to 17-18H @ 30Hz could it not? 

Is there negative feedback?

Gain wise it measures like hardly any -  With NFB total gain:  54.8db
                                                    No-NFB  total gain:  54.26db


I will post some sweeps at a later date.