[sdiy] Harmonics Question

[Donald Tillman]

On Nov 2, 2011, at 8:51 PM, Kyle Stephens wrote:

> Just how do vacuum tubes tend to produce predominantly even harmonics, and likewise why do transistors rock the odd harmonics?


They don't; it's a complete myth.  And like many myths, there's a weird little grain of truth to it.

In a college level electrical engineering class you often get to study the input-to-output transfer function nonlinearities in various devices.  Tubes have a curve shaped somewhere between Vin^1.5 to Vin^2.0, FET's have curve of Vin^2, and bipolar transistors have a curve of e^Vin.  And at this point in the curriculum the student has also just studied Fourier Transforms in a math course.  So in a rare moment of serendipity, it's possible to put these two bits of learning together and calculate the sine wave distortion products of these devices.  Whoopee!

The sine wave distortion product of a Vin^2 curve is only a second harmonic.  The sine wave distortion of a bipolar transistor exponential curve is all harmonics, mostly second, less third, less fourth, etc.  And this result was warped into "tubes even, transistors odd".  Even though second harmonic distortion is predominant in a bipolar transistor.

The problem with this is that 1. it assumes that this particular theoretical curve is all that's going on, 2. it assumes that there's no negative feedback, and 3. it assumes there's only one transistor in the entire piece of equipment.  All those assumptions are wildly incorrect (with the possible exception of the Nelson Pass Zen amplifier).

For instance, if you have a single tube or FET with only second harmonic distortion, and you add a little feedback, which most circuits do, that second harmonic content is reduced, and third, fourth, fifth and other harmonics are added.  Likewise, if you have a balanced circuit, such as a diff amp or a push-pull output section, even harmonics are mostly nulled out, to a degree depending upon component matching.

  -- Don

--
Don Tillman
Palo Alto, California
don at till.com
http://www.till.com