Simple Equations for Diode Clipping?

[ashcat_lt]

Thanks guys!  This got great (if just a bit deep) real quick.  Unfortunately, the simple answer is that there is no simple answer.  I've got some half-formed idea of how I might get something reasonable, but I'm not there yet.  Like I said, I want to be able to sort of model fairly realistic diodes with some range of properties without having to resort to a drop-down type thing.  

Edit - actually what I guess I want - to be able to set the "threshold" and "curviness" - is pretty close to what I already have.  I kinda wanted to be able to claim that it was "real diode modeling" that we could use to explore concepts and try different things with some reasonable expectation that it would correspond to the real world.  Shrug.  It works pretty well as is.

Half of the point of this thread, I guess, was to just understand better what happens in actual meatspace diodes, and for that...

> Does the "knee" come before or after the forward voltage drop is reached

There's no "knee". The curve is exponential "all the way down". If you plot it on log-lin paper it is a straight line as many decades down as your paper goes.

Well, not quite. There's some current at zero voltage. In Silicon this current is way smaller than we can care about. In Ge we may be able to measure it but at typical audio-circuit impedances it's too small to matter.

It only looks like a knee (or curvy hockey-stick) because plotted lin-lin it looks like "nothing happens" for many decades before it rises. But if you expand those decades you get the *same* shape, just shifted.

...helps a lot.  So IRL, it's not an open circuit up to a "cutoff", it actually follows the curve all the way down, it's just that the curve is really steep up to that point, yes?  

How is the Vf that we see on a datasheet specified?  Is it when the curve hits a specific "small enough" slope, or...?

[PRR]

> How is the Vf that we see on a datasheet specified?

ALWAYS "at XX current".

For one popular diode and its near-kin:
1N4148 IF = 10 mA - max 1 V
1N4448 IF = 5 mA typ 0.62 max 0.72 V

1N4007 Maximum instantaneous forward voltage = 1.0A 1.1V

If you have worked with these diodes, you know the voltage is never 1V. Why? The makers want to sell every part they make. So they set the spec high enough that nearly any functional part is sure to pass the test. And if you want a lower spec, they can sell you another, selected, part at a higher price; like the tight spec on 1N4448.
______________________________________

I said 26mV/octave all the way down. That's not quite right. Bob Pease tested a bunch of diodes.

Open this link in a new window: http://i.imgur.com/udYINT5.gif

Note that the plot is Log-Lin.

Note that the vertical scale, current, covers a hundred million to one range! That's 160dB of audio! We never have that much; in fact we rarely get half that much. And pA are much too small for audio work. Focus on the upper half of the graph. (But it DOES go way-way down.)

Many devices hew to the 26mV/octave (60mV/decade) slope. "All the way down." Just offset.

In a fuzz-circuit, the horizontal scale can be shifted by setting the output gain control. So if two lines would match if shifted left-right, they will be "the same" in your fuzz but at a different point on the output knob.

The vertical scale generally relates to the drive, usually a voltage through a resistor and thus a current. Again, if two curves match if shifted up-down, they are "the same" but at a different point on the Drive knob.

The LEDs far-right act a lot like "stacked" diodes. The usual diode-voltages are scaled-up by a consistent factor due to the doping necessary to get photons excited. Different excitement favors different color photons.

As you see, all the transistor-diodes have very-similar slope; and the LEDs if you factor-out the increase of overall voltage (turn-down the output knob).

Here's where it gets sticky (and I was sloppy). The "general purpose diodes" have a steeper slope! Actually they are two-slope. 1N4148 does follow 26mV/oct up to 50nA. But then it steepens to 35mV/oct. 1N4007 (hard to see in his plot) takes a middle path. The steepness is not parasitic resistance; you can see series resistance at the tops of the LED lines, it is a curve (because of the log-lin plotting). Nor high-level injection, which is similar. I have not seen a good explanation of why common diodes do this. (FWIW: vacuum tube diodes also have a 2-law plot, but they switch from solid-state log-lin to a 3/2-power law at a current level lower than we normally use them at.)

And plot B, the 1N87G Germanium. It isn't the Ge, a *junction* Ge (which I guess Pease did not have, working for a Silicon house) plots a lot like other diodes. 1N87G turns out to be *point-contact*, a technology which faded in the early-mid 1960s, before the greatest growth of consumer electronics. Unlike junctions, which tend to be planar like a sandwich, point-contact is built more like a martini olive on a toothpick. The curve suggests that the center of the "point" has saturated but there's still some action around the edges. Device geometry matters; but the most practical (low-cost) geometries are flat, like a paper-printer. You can buy parts "equivalent to 1N87G", but most of these are really Germanium *junction* not point-contact. Hey, works-near-the-same for many ordinary diode uses. But getting curve B will require much searching (and testing; point-contact is very variable) or elaborate function-generating networks or algorithms. (And I don't think curve G is particularly useful.....)

[SISKO]

Here's where it gets sticky (and I was sloppy). The "general purpose diodes" have a steeper slope! Actually they are two-slope. 1N4148 does follow 26mV/oct up to 50nA. But then it steepens to 35mV/oct. 1N4007 (hard to see in his plot) takes a middle path. The steepness is not parasitic resistance; you can see series resistance at the tops of the LED lines, it is a curve (because of the log-lin plotting). Nor high-level injection, which is similar. I have not seen a good explanation of why common diodes do this. (FWIW: vacuum tube diodes also have a 2-law plot, but they switch from solid-state log-lin to a 3/2-power law at a current level lower than we normally use them at.)

Recombination current?

Te total forward bias current density is the sum of the recombination and ideal diffusion current densities. At low current density, teh recombination current dominates, and at higier current density, the ideal diffusion current dominates.
Thats where the ideality factor (if.) comes from. For large forward-bias voltage, if. =1, when diffusion dominates, and for low forward-bias voltage if. =2  when recombination dominates. There is a transition region where 1 < if < 2.

Do you happen to have a copy of  the semiconductor physics and devices book by Neamen?

[PRR]

> Recombination current?

I'll have to think on that.

> Do you happen to have a copy of  the semiconductor physics and devices book by Neamen?

No; and at $100+ I can't afford a recent edition. I've just ordered (at your prod) a 1992 edition (assuming Silicon has changed little in 20 years).

[SISKO]

http://es.scribd.com/doc/140464131/Semiconductor-Physics-and-Devices-Donald-Neamen

Page 323 on the navigation bar. Figure 8.21 is of interest

[noisette]

Hello, I hope it is not an emberrasment for you, a semi-moron like me entering the discussion  
Also sorry for OT...

This is all most interesting and after some time also understandable for me, but what sticks to the brain of
an undereducated hack is ´point-contact´ diodes    
First time I heard about them. The mentioned model 1N87G seems to be still available:
http://www.ralphselectronics.com/ProductDetails.aspx?itemnumber=SEMI-1N87G&source=oemsecrets

With regards to the plot posted by PRR, and given that it´s curve can be shifted via input/output level, shouldn´t it be
interesting to listen to one(two) in a typical circuit?
Seems to be nonlinear nonlinearity  
Or would it be just a dead end road, not expected to make that much difference?

[PRR]

Play with point-contact diodes if you like.

The reason we don't use them, the reason Shockley gave up on them and developed the Junction devices, is that the fabrication and resulting action is very unpredictable.

As for the "predictable" devices.... Nature does not invent new action for every physical system. The math for a thermionic vacuum diode is the *same* as the math for a square notch in a water-dam: current (water or electric) is 3/2 power of pressure (water or voltage). A triangular dam notch gives a 5/3-power law which is difficult but possible in specially tapered electronic "dams" (notably some V-groove MOSFETs over part of their range).

[noisette]

I was just thinking, like in the plot the steeper the slope the harder the clipping, other way round the gentler the slope the softer the clipping?
Like reported for LEDs (I would like to see BS170 on that plot) . Would make some sense.

So 1N87G has the softest looking slope of em all.
Or is it magical thinking?

And btw., what is a ´big old stud rectifier´. Sounds like something from the goldrush era...

[PRR]

> what is a ´big old stud rectifier´.

You are too young. (Whatever age you are.)

Google is your friend.

[PRR]

> Figure 8.21 is of interest

Copy for critical review: http://i.imgur.com/hUO5WDv.gif

> Recombination current?

Offhand.... I think it bends the wrong way. And that the effect shown in 8.21 will happen at extremely small currents, far below what we care about.

But the ice-storm outside may have frosted my brain. I'll have to think on that, and see if more-educated lurkers can explain it to me.

[mac]

I posted a simple code to solve numerically a simple transistor bias using newton-rapshon.
Not exactly what you aks but hope it helps.

http://www.diystompboxes.com/smfforum/index.php?topic=105208.msg946684#msg946684

mac

[guitar_paul]

Have you seen the Christophe Rapp equation?
It works very simply.