ZVex SHO / Common source amplifier

[disorder]

I'm playing around with common source MOSFET stages today and have a mental road block regarding biasing. Let's us the SHO booster as an example.

https://hotbottles.files.wordpress.com/2012/03/zvex_sho.gif

What is confusing me is how the GATE bias plays into all of this. I'm assuming bias here is similar to other transistor stages in that more DC voltage = device is more ON. So looking at when the pot is set to 5k (min gain). I get about 7V at the drain and 3.5V at the gate. The 7VDC makes sense to me because when source resistance is 5k you would assume a potential swing from 4.5V to 9V and 7V is close to the middle point of that swing. But why do we want 3.5V (or half the drain voltage) at the gate?

It seems that as you decrease the pot value (increase gain) you are increasing gain because drain current increases by way of there simply being less resistance now from drain resistor to ground through the mosfet BUT the device is also now turned more OFF because the gate voltage is lower. Is this true? Or am I just running in circles?

[disorder]

I guess one of my wonderings is... Could I connect R2 to 9V supply instead of the drain of the FET and still have the circuit operate correctly? Gate will be held at 4.5V and the FET should stay in saturation region for all values of the pot, right? Wondering why the designer chose this arrangement.

[midwayfair]

Try it and see ... But spoiler alert, it was probably designed that way for a reason.

RG Keen has a great article I getting full gain out of a MOSFET. Read the article on the AMZ MOSFET booster too for more explanation on what the gate bias does. (And why it's different form bjt biasing)

[Keppy]

Most MOSFETs are designed for switching use, so they can be a bit touchy when used as a linear amplifier. The range of gate voltages for which the output will be linear is very small. If you use a fixed voltage divider bias like you suggest, the resistor values are critical, and depend on the specific device used. If you search the forum for posts about the AMZ MOSFET booster, you'll find that a lot of people weren't able to get it biased correctly unless they used a trimpot in place of the resistor from gate to V+.

Could I connect R2 to 9V supply instead of the drain of the FET and still have the circuit operate correctly?

I played around with this myself, and found it very difficult to switch from SHO-style drain biasing to AMZ-style fixed biasing. I was unable to get the AMZ scheme to work on the SHO without changing the components on the source of the MOSFET as well, at which point I basically had the AMZ booster rather than the SHO. You might be able to get it to work at one setting, but turning the gain knob would screw it up.

Wondering why the designer chose this arrangement.

There's a thread on here somewhere where Zach Vex explains it himself, but here's my take:

The benefit of drain biasing is that it rather neatly accounts for differences between devices through the use of negative feedback. SHOs don't need trimpots, at least as far as I've found. The feedback also allows you to change the source resistance without screwing up the biasing. You can't do that on the AMZ booster. Tying the source of the MOSFET straight to ground gets the SHO a little bit of extra gain at the max setting.

My observation in testing both circuits was that the SHO seemed to have more gain and distortion available while being somewhat more colored at all levels, while the AMZ booster is cleaner and has a higher, more constant input impedance, and of course doesn't crackle when you turn the knob. None of that comes from measuring, though (except the input impedance), just what I though I heard while swapping components on the breadboard. My observations do appear to match the design goals of each circuit as I understand them, though.

[Transmogrifox]

The bias is a negative feedback arrangement at DC input.  The MOSFET gate is always held at Vout/2,  which guarantees headroom for the range of resistance put in the source.

Because a source impedance (guitar output) is significantly low compared to the feedback resistor there is very little negative feedback at audio frequencies, so you pretty get max gain available from the Rdrain/Rsource ratio.

Keppy above addressed 2 of the reasons you would want a feedback bias:
1)  No trimpots needed, circuit automatically adjusts for variations in components and keeps it balanced somewhere in the middle of its linear operating range.
2)  Easily change source resistance without screwing up biasing (it will change somewhat as you turn the pot, but not enough to ruin the clean amplification range)

What is missed is why would you want to adjust gain by putting a pot in the FET source -- you hear crackle.  Why not configure this for max gain and put a volume pot on the front end?

One reason is noise.  If you have it always configured for max gain, the MOSFET's own noise is amplified but if the input signal is attenuated, then you get a worse signal-noise ratio for low gain settings.  If you adjust the gain in the FET source, then you get less noise as you turn it down so you maximize signal/noise ratio.

Another reason is coloration/distortion.   If always configured for max gain, the FET doesn't have the feedback from the source resistor to help linearize the small-signal response at lower gains.

The SHO gets cleaner and quieter as you reduce the level to unity.

It gets dirtier as you turn the pot toward more boost -- and noisier, but at least you don't have the same amount of noise at low gains.

Another reason is simplicity.  I can't think of a more simple, lower parts-count way to make something as good as the SHO.
This fits into the topic of another thread about elegant circuits.  The only thing that isn't elegant about the SHO is crackle when you turn the pot.  On the other hand, that's an easily accepted trade-off for the benefits granted by adjusting gain in this manner.

[PRR]

> gate voltage is lower. Is this true? Or am I just running in circles?

Circles, yes. Good for your legs, bad for your brain.

Look at Gate-*Source* bias. (The FET can't "feel" ground, so Gate to ground has no meaning to it.)

While the gate-to-ground voltage goes down, the drain-to-ground must go from few-Volts to NO!-Volts.

This is one circuit which I can't analyze by using my fingers as make-believe levers. However I am sure the FET current INcreases when the source resistor goes to zero.

[Transmogrifox]

However I am sure the FET current INcreases when the source resistor goes to zero.

I concur this is a correct. 

If in your imagination you consider the current that would be present in the drain-source bias with minimum resistance you can work your way backward to this.

If you kept the current the same, then adding source resistance would want to turn the FET off by increasing the voltage in the source, reducing Vgs.  In response to turning off, the voltage at the gate needs to go higher to keep the same current.

Well, if the voltage at the gate goes higher, then it means the voltage at the drain would need to go higher.

Voltage at the drain can't go higher without reducing current through the drain.

So...to balance itself out it is forced to reduce drain-source current as source resistance is increased.

[PRR]

Here's a sim-run of the HO circuit.

I varied a 5K variable resistor in steps 0, 0.1, 0.25, 0.5, 0.75, and 1.0. Basically the quarter-points, plus a low-point because I knew things happen faster down there.

My sim only has a very-old MOSFET with high gate voltage and high! maximum current. Your values will be different but the trends will be the same.

One thing to note: the Gate-Source voltage "does not change", only from 2.8543V to 2.8444V. This makes sense: the MOSFET has very high transconductance, so the gate-source voltage hardly has to change to get a large current change. And we don't ask for a large current change, only 3:1. The 0.000,57A change divided by the 0.010V change suggests the MOSFET in this current range has a Gm of 57 milliMhos, or a source resistance of 17 Ohms.

The source pot adds to this which reduces the gain. Ignoring several important details, the minimum gain is 5,000/5,017 or 1, the maximum gain is 5,000/17 or 294(!). So the AC/Audio gain goes from buffer to BOOST. (However meanwhile the input impedance drops from 5Meg to 34K due to Miller, and 34K is a significant load on many guitar-cord sources.)