Thread: Comparing the Nonlinearity of a Triode and a Junction FET

1. Comparing the Nonlinearity of a Triode and a Junction FET

uneumann (http://music-electronics-forum.com/t44917/) has designed a FET circuit for the first stage of a guitar amp; this stage sounds clean. Why? Is it because the JFET used as the lower device in the cascode is inherently more linear than a triode, or is it the result of the circuit design? The claim here is that it is the latter, and that it is the source resistor that linearizes the JFET. This is supported by modeling, showing that very similar results can be obtained with either device when the feedback from the source resistor is omitted. This post concludes with some suggestions for achieving this in practical FET circuit.

Norman Koren (Improved vacuum tube models for SPICE, Part 1) presents tube models intended for use in Spice. I will use them here in simple algebraic equations solved in Python-Scipy-broyden1 rather than using Spice. He presents two levels of modeling:

1. A simple one, curves in figure 1, uses the equation derived from simple physics in which the plate current is the sum of the plate voltage over the amplification factor and the grid voltage raIsed to the three halves power and divided by a constant. (equation 1).

2. a more complicated (new) equation that is derived from measurements (equation 4). The differences are very significant when plate voltage is high and the plate current low (figure 2, or look at measurements here: Biasing).

From these models, I have constructed a simple circuit using a 100K plate resistor and a power supply of 300V, using tube parameters for a 12AX7. The resulting equations are solved numerically for a sequence of grid voltages consisting of a bias voltage and a superposed sinusoidal variation. The level is set so that the output voltage is large, but not enough to make the grid go positive since there is no consideration of grid current here.

Results are shown here:

The blue line is the simple model; the green line is the more complicated (new) model. The differences are as expected: a triode does not turn off as easily as the simple model predicts. The red line is derived from a junction FET characteristic operation in the so called saturation region (where it behave as a current source). The red line has been derived from the drain current, scaled and shifted as necessary to get it to line up with the tube results. (This is what the upper device in the cascade does.)

In order to get this FET response, it is necessary to adjust both the bias point and gate signal voltage. The equation is IDS = IDSS*(1 - VGS/VP)**2. This equation is explained, for example, here: https://en.wikipedia.org/wiki/JFET. In order to get the red line to agree so well with the green line, it was necessary to adjust four things: the bias voltage, the input signal level, a dc shift, and a scale factor. Of course the agreement is not perfect. The tube response appears to have low levels of higher harmonics that the FET does not have since its model is a perfect square law. In practice, the FET might have such harmonics as well; I do not know.

In practice it is necessary to achieve the two degrees of freedom for adjustment of the FET while keeping the correct load on the pickup and avoiding excessive noise. One way is to start with a source follower. The pickup can be loaded as desired, the output impedance is low, and since JFETs with as low as 50 ohms of noise resistance are available, no significant noise is added. The signal level into the FET gain stage would be expected to need attenuation by several times. This can be accomplished by using a split source resistor in the source follower once the correct attenuation ration has been determined. The FET gain stage (also low noise) can be biased with a source resistor, but it must be bypassed, although it could be partially un-bypassed in some applications. The drain can go to the upper device of a cascode, or perhaps just a resistor in some applications.

tMod.py.zip

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2. Originally Posted by Mike Sulzer
[COLOR=#000000][FONT=Helvetica Neue][SIZE=4]uneumann (http://music-electronics-forum.com/t44917/) has designed a FET circuit for the first stage of a guitar amp; this stage sounds clean. Why? Is it because the JFET used as the lower device in the cascode is inherently more linear than a triode, or is it the result of the circuit design? The claim here is that it is the latter, and that it is the source resistor that linearizes the JFET.
Mike - not sure I followed beyond the basic assertion... but yes, the local feedback from the source resistor is what linearizes the lower stage. The high rail resistors also linearize the current mirror. The point of the circuit is to be clean and quiet - not to add harmonics. Whether tube or FET or transistor, the feedback in the circuit means that the intrinsic NL character of the device has little impact. Once you bypass the source (or cathode) resistance, you remove the feedback and the device character starts to matter.

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3. Originally Posted by uneumann
Mike - not sure I followed beyond the basic assertion... but yes, the local feedback from the source resistor is what linearizes the lower stage. The high rail resistors also linearize the current mirror. The point of the circuit is to be clean and quiet - not to add harmonics. Whether tube or FET or transistor, the feedback in the circuit means that the intrinsic NL character of the device has little impact. Once you bypass the source (or cathode) resistance, you remove the feedback and the device character starts to matter.
Exactly. I wanted to see if you could set up the JFET so that it would have a high signal level response with a shape very similar to the triode, that is, the same nonlinearity. It looks as though you can get pretty close with some effort. I think I recall someone here doing something like this before, different means, same goal, but I do not remember who. Does anyone know?

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4. Originally Posted by Mike Sulzer
...very similar results can be obtained with either device when the feedback from the source resistor is omitted.
Mike, are you aware of some of the previous work that's already been done in this area? A lot of people have obsessed, for several decades now, over some of the similarities between JFETs and valves, and the possibility of using JFETS to replace triodes in guitar amps.

1. Interesting reference #1: Dimitri Danyuk presented an AES paper in 2004 in which he calculated that there is an optimum (not zero) JFET source resistor value that makes it behave most like a triode (i.e., approximates the Child-Langmuir three-halves law). Link: https://www.scribd.com/doc/65330169/...Dimitri-Danyuk
2. Interesting reference #2: Using Dimitri's results, Runoffgroove.com operators designed and published a variet of JFET-based guitar effects pedals, all based on using JFETs to emulate triodes. Link: A closer look at the Fetzer Valve
3. Interesting reference #3: Joe Sousa's writeup on his "Trioderizer": The Trioderizer - a solid state triode

It's worth noting that none of these approaches:
1. Emulates the effects of the fall in anode voltage during negative half-cycles of the output waveform in triodes, which "squishes" the negative half-cycles during overdrive.
2. Emulates the effect of grid current flow during overdrive, which clips or rounds off the input voltage signal at the grid.
3. Emulates the effect of "sliding DC bias" caused by grid current flow through the input capacitor. This produces a lot of audible effects, including audible compression of the input signal. Sliding bias caused by grid current flow is a particularly severe problem in output valves biased near class B conditions, where it often causes severe crossover distortion, even blocking distortion, and requires that valves be biased very hot, because they bias themselves cold during overdrive. The problem affects triodes, beam tetrodes, and pentodes as well.

So, even with "trioderizing" and "Fetzer-valving", JFETs remain poor cousins to real valves, because they fail to emulate many of the characteristics of valves that are audibly significant in guitar amps, and have become part of guitar amp sound.

They can sound pretty good, though. Listen to clips of the 'Umble (from Runoff Groove), or clips of the "FET Dream" guitar effects pedal (YouTube), and you can hear some musically useful JFET-based guitar sounds.

IMO, based on some tinkering I've done, JFETS sound better than BJTs for guitar preamp use (i.e. they tend to sound less horrid right away, and can sound good with some effort). They also have all the obvious advantages (small, efficient, long life, no heater power demands, lower cost). But I don't think they sound as good as a good valve preamp, though they can easily sound better than most (all?) BJT guitar preamps.

-Gnobuddy

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5. I saw number 1. sometime ago, but had forgotten the reference. Thanks for pointing it out. The Child-Langmuir three-halves law, used by Danyuk, was also used in the blue line in the plot attached to the first post in this discussion. This is how triodes work in a simple physics derivation, but the actual nonlinearity is significantly larger as shown by the green line. The irony of Danyuk's work is that he adds a (unbypassed) source resistor to make a JFET like a not so good model of how a real triode works when you can get closer to the the actual nonlinearity by leaving out the resistor (for AC, that is, actual resistor bypassed) and just adjusting the bias point and input level.

It looks like the triodeizer emulates the Child-Langmuir three-halves law, and thus misses a significant aspect of the nonlinearity also. In any case, a full emulation is not necessary; it is only the nonlinearity that we must reproduce in the device output current, entirely independent of the other characteristics of the device.

I realize that what I have done only applies to the input stage under the conditions when the signal can get large, but not produce grid current or bias shifts. This seems like a good first step.

Originally Posted by Gnobuddy
Mike, are you aware of some of the previous work that's already been done in this area? A lot of people have obsessed, for several decades now, over some of the similarities between JFETs and valves, and the possibility of using JFETS to replace triodes in guitar amps.

1. Interesting reference #1: Dimitri Danyuk presented an AES paper in 2004 in which he calculated that there is an optimum (not zero) JFET source resistor value that makes it behave most like a triode (i.e., approximates the Child-Langmuir three-halves law). Link: https://www.scribd.com/doc/65330169/...Dimitri-Danyuk
2. Interesting reference #2: Using Dimitri's results, Runoffgroove.com operators designed and published a variet of JFET-based guitar effects pedals, all based on using JFETs to emulate triodes. Link: A closer look at the Fetzer Valve
3. Interesting reference #3: Joe Sousa's writeup on his "Trioderizer": The Trioderizer - a solid state triode

It's worth noting that none of these approaches:
1. Emulates the effects of the fall in anode voltage during negative half-cycles of the output waveform in triodes, which "squishes" the negative half-cycles during overdrive.
2. Emulates the effect of grid current flow during overdrive, which clips or rounds off the input voltage signal at the grid.
3. Emulates the effect of "sliding DC bias" caused by grid current flow through the input capacitor. This produces a lot of audible effects, including audible compression of the input signal. Sliding bias caused by grid current flow is a particularly severe problem in output valves biased near class B conditions, where it often causes severe crossover distortion, even blocking distortion, and requires that valves be biased very hot, because they bias themselves cold during overdrive. The problem affects triodes, beam tetrodes, and pentodes as well.

So, even with "trioderizing" and "Fetzer-valving", JFETs remain poor cousins to real valves, because they fail to emulate many of the characteristics of valves that are audibly significant in guitar amps, and have become part of guitar amp sound.

They can sound pretty good, though. Listen to clips of the 'Umble (from Runoff Groove), or clips of the "FET Dream" guitar effects pedal (YouTube), and you can hear some musically useful JFET-based guitar sounds.

IMO, based on some tinkering I've done, JFETS sound better than BJTs for guitar preamp use (i.e. they tend to sound less horrid right away, and can sound good with some effort). They also have all the obvious advantages (small, efficient, long life, no heater power demands, lower cost). But I don't think they sound as good as a good valve preamp, though they can easily sound better than most (all?) BJT guitar preamps.

-Gnobuddy

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6. Originally Posted by Mike Sulzer
I realize that what I have done only applies to the input stage under the conditions when the signal can get large, but not produce grid current or bias shifts. This seems like a good first step.
You will find some interesting work here... Main page

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7. Originally Posted by uneumann
You will find some interesting work here... Main page
Thanks for the link! I have run across that website before, lots of very interesting (and very complete) designs to ponder.

It's funny how attempts to use solid state components to emulate even the simplest valve circuits, usually end up requiring very considerable complexity. The most extreme case being today's digital signal processing guitar amp and effect emulations, which use several tens or hundreds of millions of MOSFETs to emulate something originally done by a handful of valves.

I should add that I appreciate and enjoy solid-state electronics, and consider it vastly superior to ancient valve technology, in every application except guitar amplification.

-Gnobuddy

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8. Originally Posted by Gnobuddy
I should add that I appreciate and enjoy solid-state electronics, and consider it vastly superior to ancient valve technology, in every application except guitar amplification.
For perfomance of ancient valve technology nothing really beats it. But there are VERY good reasons why one also likes to get rid of that ancient valve technology.

Besides the obvious benefits of solid-state technology I do also find it very nice in guitar amps. It's not that a solid-state amp can sound like (insert name) tube guitar amp. It's that with a flick of a switch it can also sound like dozens of other nice tube guitar amps out there, and it does this in a lunchbox size that does not run hot like a toaster, weighs next to nothing and provides consistent tone and reliable performance up to the day it dies... when its maybe at least half a century old or something. Don't really know... These solid-state thingies just seem to keep going, and going, and going... My 40+ -year old Sansui domestic HiFi stereo amp is still running solid. With no service under its belt at all, may I add. Could as well run another 40+.

Show me a genuine tube amp that beats that.

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9. Originally Posted by teemuk
I do also find it very nice in guitar amps. It's not that a solid-state amp can sound like (insert name) tube guitar amp. It's that with a flick of a switch it can also sound like dozens of other nice tube guitar amps out there
This is where we differ. I have tried many - too many - solid state guitar amps and multiFX/amp emulation devices, including three different Line 6 products (stupid me). All the amp emulation hardware I've tried sounds like dozens of different (horrible) kazoos in one box, not dozens of different nice guitar amps!

I know the emulations are getting better (Atomic Amplifire, etc), and software running on a powerful computer CPU is better yet. Right now, the good digital hardware solutions cost much more than building my own valve amps. I do most of my playing live, and the software solutions running on a PC are not that appealing in that context.

Originally Posted by teemuk
Show me a genuine tube amp that beats that.
It's like solid-body electric violins versus 17th-century Stradivarius'. The electric violin has a lot of obvious conveniences, but doesn't sound good enough for serious musicians.

-Gnobuddy

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