RE: another explanation...

68.65.204.244

Posted by commentary on May 5, 2012 at 19:16:33

In Reply to: RE: another explanation... posted by Tre' on May 5, 2012 at 09:53:43:

In EE circuit analysis texts, there are two components to describe the sinusoidal signal: either use cartesian, or Rectangular on your calculator (Real and Imaginary) or Polar (Magnitude and Phase). They are convertible using a scientific calculator with R->P and P->R keys. EE's prefer to use "j" as the imaginary number term instead of "i" since "i" is already taken to be AC current.

Real is on the X-axis and Imaginary is on the Y-axis, something that is graphically representative of how the math works in this realm of "phasors".

If a Magnitude is 1 + j1 in Rectangular, then the Polar Magnitude is the length of the diagonal showing, SQRT(1^2 + 1^2) = SQRT(2), and the phase is +45 degrees, with respect to the input reference. Positive phase is lagging, negative is leading.

Now for the example of +1 Vrms vs. -10 Vrms. First we know that the input to the first tube is 1 Vrms Magnitude and is the reference, 0 degrees. That is a vector (arrow) pointing from 0,0 to 1,0 in Rectangular. It's on the real line, in positive direction.

The output is best seen as a real Magnitude of 10 Vrms, but in the opposite direction, +/-180 degrees lagging or leading (it's the same). In Rectangular form, that shows up as a vector pointing from 0,0 to -10,0. The magnitude is ABS(-10) = 10, but the vectors show an important inversion using vector arithmetic, and is represented as a negative number. The entire problem is one of vector addition, not just magnitude addition, because we have phase changes.

Another example for kicks: If you sum +10, zero phase reference, and a partial inverted 1 Magnitude, Phase = +/-180 degrees, you get a net 10 - 1 = 9 Magnitude, zero phase output.

NEXT QUESTION:

How are the harmonics handled in vector arithmetic, not going to the old simple 'magnitude only' addition?

This is helpful if you have a solid understanding of FFT's. But this time I opt to go by observation instead of polarity signs of +/-Acos(wt)+/-Bcos(2wt)...+/-Ksin(wt)+/-Lsin(2wt)... in an infinite series.

Instead of this equation, we can determine by inspection what "polarity" the B coefficient in Bcos(wt) is.

The transfer function of the 2nd harmonic is determined from a simple graph you can create from measurements of such a common cathode stage for Vpk v. Vgk (it's a different special plate curve). We can think of it like this: At about -15 VDC at Vgk, the tube cuts off and we get all the B+ to the output (high voltage) to say +250 VDC. At +1 VDC Vgk (slightly into class A2 in this example), the plate voltage will go down as the tube drains current away from B+. Let's say to +30 VDC.

And then let's say normal bias offers us +140 VDC on the plate. So the cutoff swings up to +250 VDC, or +110 VDC more than quiescent bias point, and small class A2 pull offers +30 VDC, or -110 VDC less than quiescent bias point. Note the bias is centered.

But plot the graph of the output. It will have that 10% 2nd order distortion of asymmetry that is the feature of 2nd order distortion. Now observe the orientation of where the bend is. Since the tube can work slightly into A2, it is still pretty linear over in that part. BUT! The plate curves show that remote cutoffs and all triodes with imperfect linearity towards cutoff really distort more over on this side when in the signal operating range. The upshot for this side of distortion is an elongation of the sinusoidal negative going curve. For odd order distortion, it's about each end with symmetry.

On the other side, it just hit hard clipping at the end of the power supply voltage. Let's ignore the part about overload.

So by observation, we have the polarity of the 2nd harmonic set to distort on the low voltage side every time when not clipping. But let's say the input was pre-distorted where the low voltage output would amplify that distorted end linearly, from a previous stage. What you can picture is that one signal is distorted on one side once, with one stage; but another signal is distorted by a previous stage on one side once, and then let go of linearly the second time.

What we have now is distortion on both ends, moving the distortion to a more odd order problem of distortion. If one end distorted: even order; if two ends distorted: odd order. That was with no math to see this happening.

But the math using vectors and polarity changed to plus and minus Rectangular coordinates offers a way to get a calculation. The harmonics are being played out in different mathematical phases through different polarity orientations.

That's the best I can do to try to explain this. I hope you got something from this.

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Follow Ups Full Thread

Topic - Does any one feel vindicated by TAS' editorial? nt - HiFiOd 12:05:44 04/26/12 (41)

RE: Does any one feel vindicated by TAS' editorial? nt - RGA 18:06:29 05/01/12 (0)

Harley should have asked some designers before saying that. - Ralph 13:05:03 04/30/12 (0)

another commentary... - commentary 00:27:58 04/28/12 (28)

RE: another commentary... - dave slagle 23:43:06 04/28/12 (8)

RE: another commentary... - commentary 00:10:35 04/29/12 (7)

RE: another commentary... - Tre' 21:52:36 04/30/12 (6)

RE: another explanation... - commentary 22:02:08 05/04/12 (4)

RE: another explanation... - Tre' 09:53:43 05/05/12 (2)

RE: another explanation... - commentary 19:16:33 05/05/12 (1)

RE: another explanation... Editing all of "NEXT QUESTION" reply - commentary 19:38:21 05/05/12 (0)

I forgot important details in the above explanation. To remove my mistakes... - commentary 02:59:56 05/05/12 (0)

RE: another commentary... - TubeDriver 09:08:12 05/01/12 (0)

RE: another commentary... - Stuben 12:07:28 04/28/12 (18)

Type 50 Monos - vacuumtube1954 16:19:53 04/28/12 (16)

RE: Type 50 Monos - Stuben 04:39:08 04/30/12 (15)

RE: Type 50 Monos - vacuumtube1954 15:20:44 04/30/12 (1)

RE: Type 50 Monos - Stuben 17:14:34 04/30/12 (0)

RE: Type 50 Monos - vacuumtube1954 13:49:01 04/30/12 (3)

RE: Type 50 Monos - Stuben 17:27:23 04/30/12 (2)

RE: Type 50 Monos - vacuumtube1954 14:30:32 05/01/12 (1)

RE: Type 50 Monos - Stuben 15:00:15 05/01/12 (0)

RE: Type 50 Monos - drummerwill 08:53:45 04/30/12 (8)

RE: Type 50 Monos - Stuben 10:07:24 04/30/12 (7)

RE: Type 50 Monos - dave slagle 19:32:48 04/30/12 (0)

Don't Forgret The... - Gerry E. 10:50:53 04/30/12 (5)

RE: Don't Forgret The... - Stuben 11:26:53 04/30/12 (4)

RE: Don't Forgret The... - Sidewinder 17:25:51 04/30/12 (3)

RE: Don't Forgret The... - Stuben 15:07:14 05/01/12 (2)

Thanks. I'll wait for the files NT - Sidewinder 20:46:48 05/01/12 (1)

RE: Thanks. I'll wait for the files NT - Stuben 14:41:06 05/18/12 (0)

RE: another commentary... - SETdude 13:41:17 04/28/12 (0)

I think TAS' comments are now vindicated by the SET amp owners here. (: NT - commentary 00:19:09 04/28/12 (0)

Not really news. - mwhitmore 08:05:01 04/27/12 (1)

Ain'tcha smart! - HiFiOd 08:23:54 04/27/12 (0)

Rant - Frihed89 03:35:23 04/27/12 (0)

What did it say? nt - Salectric 16:15:37 04/26/12 (1)

RE: What did it say? nt - HiFiOd 09:39:21 04/27/12 (0)

RE: Does any one feel vindicated by TAS' editorial? nt - adaug 15:08:39 04/26/12 (3)

of course, Harley wasn't listening to just ANY ol' SET - triode 22:44:20 04/26/12 (2)

The whole M2.2 design is unlike most SET amps. - Timbo in Oz 23:49:14 04/27/12 (1)

no feedback adjustment on my ML2s - triode 10:20:57 04/28/12 (0)

Follow Ups

RE: another explanation... - commentary 19:16:33 05/05/12 (1)

RE: another explanation... Editing all of "NEXT QUESTION" reply - commentary 19:38:21 05/05/12 (0)

RE: another explanation...

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