A Basic Bias Question

[Lectroid]

So I have a small p-p 6V6 Princeton clone, an AA1164-ish circuit.  Just to understand it better, I worked out load lines for the preamp tubes, working my way through Merlin's book and following his method and instructions.

With the amp running, I measured an actual quiescent bias voltage of 1.8V.  On a 12AX7 Plate characteristics graph, I then drew an anode load line, following the VW's instructions.  Then I calculated points for a cathode load line based on my values of Va=267V, Ra=100.1K, Rk=1491 ohms.  But where they crossed gave a bias point of 1.4V, not 1.8V.

My understanding is that they should be (more or less) at the same spot.  Is the discrepancy due to my ignorance, or to the natural variation of the tube, or what?  Am I just confusing apples for cantaloupes?   

[JPK]

Do you have a "12AX7 average plate characteristics" graph to share? I ask because I plotted one of these too. It was months ago so you got me curious to go revisit it. It looks like I plotted gain stage 2 of an AX84.com High Octane amp. Curious to what yours looks like. I'd share mine but it's kind of a mess. Although my cathode line intersects my load line at -1.0 bias voltage line which is what the schematic shows.

I used this web site to do mine:
https://robrobinette.com/Drawing_Tube_Load_Lines.htm


See PRR's post #16 of this thread. Very good stuff.
https://el34world.com/Forum/index.php?topic=27360.0
.

[tubeswell]

Because everyone knows that plate characteristic charts published by tube manufacturers are standardised advertising propaganda LoL.  They are idealised to enable technical guesstimates about what’s ‘good enough’.
Whereas each tube is a real world thing with various electrodes (each made of its own mixture of metals and other chemical compounds) that have been pre arranged into a ‘more or less the same’ spatial configuration per-tube-type, but electrons flowing between the electrodes don’t conform to exact expectations, and so even Merlin himself says you should conscientiously design the amp first, then adjust the thing after you build it.

[HotBluePlates]

... I measured an actual quiescent bias voltage of 1.8V.  ... I calculated points for a cathode load line based on my values of Va=267V, Ra=100.1K, Rk=1491 ohms.  But where they crossed gave a bias point of 1.4V, not 1.8V.

What is the supply voltage to that tube stage?  Is it 388v?

     (1.8v / 1491Ω = 1.21mA,  1.2mA x 100.1kΩ = 120.85v,   120.85v + 267v = 387.8v ---> "388v")


100.1kΩ = 100kΩ and 1491Ω = 1.5kΩ for all practical purposes (I doubt a meter-error of less than 0.6%).  So I drew a loadline (Red) for a supply voltage of 388v and 100kΩ, then added and a cathode line (Green) of 1.5kΩ.

   -  I found they crossed mighty close to -2v bias, 1.33mA of plate current (Blue dashed line), and 255v on the plate (Purple dashed line).

   -  Your measurements indicate 1.8v bias, and 1.8v/1.5kΩ = about 1.2mA plate current.

   -  Your results are "near enough" those predicted by the loadline.

   -  Your results can be explained by your tube having slightly different curves, with a little lower plate current for a given bias, and possibly higher internal plate resistance.  We don't know if transconductance or gain are different from the "average tube" described by the data sheet.


Loadline below, but you may need to open in a new tab and zoom in to make out the lines.

[JPK]

Nice work HBP. Here's mine cleaned up for the AX84.com High Octain pre-amp stage #2. About -1.0 which is what the schematic states. Click to enlarge.


Edit: Also added schematic screen shot. B+4 was measured at 210VDC.

[Lectroid]

Thanks everyone. 

It sounds like you're all saying "Yes the Q-point and the expected bias point should be fairly close to each other." 

If I'm wrong there, someone please correct.  Attached is my drawing and a schematic if needed. 

@HBP
I get different numbers, maybe you can correct my method?

What is the supply voltage to that tube stage?  Is it 388v?

     (1.8v / 1491Ω = 1.21mA,  1.2mA x 100.1kΩ = 120.85v,   120.85v + 267v = 387.8v ---> "388v")

No, my supply voltage is 267V.  The highest voltage is ~310V at node "A", going to the OT.  By node "D", the supply voltage at the B+ end of the plate resistor is 267V.   After that 100K resistor, the voltage is 144V to the plate.

IF I follow HBP's example method with my actual numbers, I get:
a) 1.8V/1.5K = 1.2mA   
b) 1.2mA * 100K = 121V   
c) 267V - 121V = 156V. 

So, 156V is close to my observed plate voltage of 144V.  My load line calculations:

Plate load line:  267 / 100K = ~2.6mA.  So, endpoints of (0mA, 267V) and (2.6mA, 0V) for the load line.

Cathode load line:  1V / 1.5 ohm = 0.7mA,  1.5V / 1.5K ohm = 1.0mA,  2V / 1.5K ohm = 1.3mA

Plotting these points gives an expected grid voltage of ca. 1.4V.  Is that as close as calculated values can be expected to match up with measured values?

Thanks for any and all explanations and corrections.  I'd love to know if I'm doing this right or wrong.

[HotBluePlates]

Bottom-Line:  I think you did the plotting process correctly, but I'm suspicious of your figures or the tube itself.


Let's your figures above using your 100kΩ plate load and 1.5kΩ cathode resistor:

    267v - 144v = 123v  ---> 12AX7 Plate Volts
    123v / 100kΩ = 1.23mA ---> 12AX7 Plate Current
    1.23mA x 1.5kΩ = 1.85v  ---> Cathode Current x Cathode Resistance = Cathode Volts

Those seem to check out, considering only current, volts, and resistance (nothing about the tube used).

Plotting these points gives an expected grid voltage of ca. 1.4V.  Is that as close as calculated values can be expected to match up with measured values?

Your overall process looks correct, even if I would quibble with exactly where you drop some endpoints.

When I plot the 100kΩ loadline on a set of 12AX7 curves, then add a vertical line at 144v it shows I should get about 1.23mA (√) at a bias of about 0.9v.  That's odd... exactly half what you say you have present.

     -   0.9 volt / 0.00123A = 731Ω ---> parallel pair of 1.5kΩ resistors?

     -  I then plotted a horizontal line at a bias of about 1.8v (conveniently double the other bias point).  I get a current of about 0.67mA, so 1.8v / 0.00067A = ~2.7kΩ



Are you sure all your measurements were taken at the same time (with the same cathode resistor value)??  Are we certain this is a 12AX7?

I think either your figures were not all concurrent (and there was a change of cathode resistor value), or you have a not-12AX7 in the socket.   I would be surprised if the 12AX7 curves were drawn this wrong, and nobody noticed for the last 70 years...

[Lectroid]

HBP,

You nailed it. Somewhere in the mists of pandemic time, I'd swapped in a 5751 in the first position and forgotten about it until you brought it up.  Sorry for all the extra work I made for you; I've given myself 50 demerits. 

Using a known good GE 12AX7 I got these new values:  Vg = 1.27,  Vs = 278,  and Vp = 192

Following your method (I think), I get:  278V - 192V = 86V drop across Rp
General rule:    [ Ia = (Vs - Vp)/Rp ]

86V
-----   =  0.86mA = Ia
100K

a) 1.27V/1.5K = 0.85mA   (check)
b) 0.85mA * 100K = 84.67V / ~85V   (check)
c) 278V - 85V = 193V     (check)

So, 193V is close to my observed plate voltage of 192V.  My load line calculations:

Plate load line:  278 / 100K = ~2.78mA.  So, endpoints of (0mA, 278V) and (2.78mA, 0V) for the load line.
Cathode load line:  1V / 1.5 ohm = 0.67mA,  1.5V / 1.5K ohm = 1.0mA,  2V / 1.5K ohm = 1.3mA

Here's a new plot.  Blue dot  is measured bias point, Green is cathode load line, purple lines are dropped from the intersection of the plate loadline and the cathode loadline, and orange show the point intersected by the actual measured values.  None of these line up exactly, but if they look reasonable to you within the range of tube variance, that's good enough for me.

Sorry again for the wild-goose chase!

[shooter]

since you're learn'n well, got the load-line dialed in;
I believe it's on Merlin's site, there's a loadline chart with a sinewave superimposed over it.  That cemented down what all the math was about in one easy pic.  with that understanding you can learn to "shift the line" to get some clipping, compression, OD kinda thing outta the preamp.

[Lectroid]

shooter,

Thanks for the encouragement.  I do know I can shift the bias point more negative to get cold clipping or warmer to get grid clipping.  I just wonder if there's single best way to go about making each one happen, and how to get the "best" overdrive sound out of each one.  I just hope the final's graded on the curve... 

[HotBluePlates]

Using a known good GE 12AX7 I got these new values:  Vg = 1.27,  Vs = 278,  and Vp = 192

Following your method (I think), I get:  278V - 192V = 86V drop across Rp
General rule:    [ Ia = (Vs - Vp)/Rp ]

86V
-----   =  0.86mA = Ia
100K

a) 1.27V/1.5K = 0.85mA   (check)
b) 0.85mA * 100K = 84.67V / ~85V   (check)
c) 278V - 85V = 193V     (check)

So, 193V is close to my observed plate voltage of 192V.  My load line calculations:

Plate load line:  278 / 100K = ~2.78mA.  So, endpoints of (0mA, 278V) and (2.78mA, 0V) for the load line.
Cathode load line:  1V / 1.5 ohm = 0.67mA,  1.5V / 1.5K ohm = 1.0mA,  2V / 1.5K ohm = 1.3mA

Here's a new plot.  ...

Nice work!  Yep, you have it down now!

... Somewhere in the mists of pandemic time, I'd swapped in a 5751 in the first position and forgotten about it until you brought it up. ...

So now you have a valuable data point:  Real tubes almost never land exactly on the printed curves, but they're "pretty close."  When something is way off like you encountered then ask, "Where did I goof?"  We all do it sooner or later.

[Lectroid]

@HBP,

Oh, I've had ample proof of how easily I can overlook something obvious but maybe one more data point will finally cement the lesson.      At least I have more confidence in my math now.

Thanks again for checking my work.

[PRR]

...193V is close to my observed plate voltage of 192V....

That's half-percent 'error'. That's amazing precision. All tube-work is +/-20% slop. 170V to 210V should not make much difference.

Done here.

[Lectroid]

That's amazing precision. All tube-work is +/-20% slop.

Thanks, just dumb luck.  But I'll quit wondering why my numbers aren't closer to Leo's..

170V to 210V should not make much difference.

So (all else being equal) the tube will behave roughly the same, and the amp sound the same, over that voltage range.  Got it.

[shooter]

I just hope the final's graded on the curve...

after the Navy, I used my GI-bill, went to college.  I'm in physics 200 level, the teacher grades on a curve, tells us that even then the best he's had so far was a B, so don't expect the curve to help.
I was getting A without the curve, the Instructor steps out during a mid-term, the "jock-kid" says "man you're smart, how bout helping the rest of us by taking a C, it's still a A for you"  I laughed, said how bout studying as much as me and EARN an A

[JPK]

I just hope the final's graded on the curve...

after the Navy, I used my GI-bill, went to college.  I'm in physics 200 level, the teacher grades on a curve, tells us that even then the best he's had so far was a B, so don't expect the curve to help.
I was getting A without the curve, the Instructor steps out during a mid-term, the "jock-kid" says "man you're smart, how bout helping the rest of us by taking a C, it's still a A for you"  I laughed, said how bout studying as much as me and EARN an A

I had a very similar experience. First Physics exam we had the entire class bombed it. I got a 97%. It was graded on a curve so they all hated me and called me the curve buster, but I guarantee not one of them studied as hard as I did. So yeah EARN it!!!

[Lectroid]

In 2002 I went back to college in Connecticut to major in American History.  18 units the first semester and when I discovered how easy it was to get straight "A"s, I took 21 units the second semester.  I had to apply to the Dean both times.  The first time it took about 30 seconds to convince her; the second time she looked up, said, "Oh, it's you," and just signed it.

Sadly, I think most of the younger students were wasting parental money.  Too many of them never should have gotten a HS diploma.  They just didn't have the academic skills they needed for a university degree.  After working in corporate for 20 years, I was amazed to learn that undergrad classes actually were not difficult at all.  And if you liked the material, it was fun.  In fairness, a small number of them really dug in and worked for the good grades.  But most were just there to get their ticket punched, and had no idea how to do real academic work.  They clearly didn't have HS-level skills, let alone college-level.  We need more technical ed. in this country.  College is just not for everyone.

[shooter]

The start of my 2nd year the department head came to me an ask if I could teach a couple classes 
We made a deal, I got credit for that year, he got an instructor. 
day 1 i asked how many wanted to be here, how many had to be here, was an even split, so I said all that wanted to be here, you have a A, those that have to be here have a B as long as you don't disrupt the class, now lets try an learn something now that grades are out of the way.


I got called into the College VP office, where he tried to explain I couldn't grade that way, so I quit, the next day I was teaching again 

[Lectroid]

so I quit, the next day I was teaching again