Source Bypass Cap Cut off frequency Calculation.

[jcknowles89]

Hello All,

Anyone have a easy way to calculate cut off frequency of source bypass cap on a Mosfet Common source amplifier? from what I have seen its really just the normal calculation with source resistance factored in. But cant seem to find anything like that on Datasheets. Any suggestions. will probably use 2N7000 for these purposes. any info would be great.

Also, Anyone notice that Source bypass caps have less effect in a feedback resistor set up similar to a big muff stage? anyone know possible reasons for this?

thanks guys.

[antonis]

1. Source by-pass cap value should be calculated for cap impedance much lower than 1/g_m..
(and not just much lower than Source resistor value, as some people may think..)

The above should stand for almost complete Source grounding - otherwise 1/gm should be added in series with capacitive reactance..

Calculation formula is the well established f = 0.159/(R x C)..


2. It happens due to voltage gain doesn't solely depends on (simplified) Drain resistor / Source resistor but it's a combination of the former & Feedback resistor / signal source resistor (or any equivalent resistance appears in series with signal)

[PRR]

> a easy way to calculate cut off frequency of source bypass cap

No.

But 100uFd will give full guitar range on almost any MOSFET at almost any likely operating point.

[GibsonGM]

Easy way?   By ear.   Which is not empirical, of course.   100uF, as Paul says (and which you see around in designs) will pass it all.

If you want to selectively boost highs (a common desire), start to decrease from there.  Try 10uF, 1uF, .68uF....etc.   I haven't delved into the region below 1uF, actually.  Maybe I will now that you bring up the topic!

There could be a program out there where someone has already derived all the stuff so you can just enter a few pieces of info, an app or something (?).  I'd hate to be the one to have to figure out the formula though, ha ha. 

[PRR]

The problem is the Gm of MOSFETs is NOT specified at the few-mA we use for amplification.

2N7000 sheet says 100 uMho but at 200 mA. (And 100 uMho  must be a typo?? Curves suggest mMho.)

We know it will be less at 1mA, we know a general tendency, but 200:1 down we can't get any exact result.

[Rob Strand]

100uS is *min* so typ could be somewhat higher.

We know it will be less at 1mA,

Off-hand I'd say 10 mS to 20mS

Working off a different angle,

gm(1mA)  ~   100mS * sqrt(1mA / 200mA)  = 7mS

So that narrows it down quite a bit.

EDIT:
My low-current spice model indicates gm(1mA) at about 7.2mS

[PRR]

.....Off-hand I'd say 10 mS to 20mS
Working off a different angle, ...... 7mS ... So that narrows it down quite a bit.

Yes, to a 3:1 uncertainty. If we aim at say 200Hz, we may get 340Hz or 118Hz. 1-1/2 octaves.

FWIW, I found a 2N7000 model from a local student and let SPICE chew it. For 1mA it gives 13mMho (1/77 Ohms).

But the full-range plot shows a "?" concave kink, below 0.2mA, which is unlikely for a simple device. Much more likely the sub-threshold parameters "miss" the above threshold curve and, not knowing better, just butts them. (I have heard of MOSFET models with sub-threshold parameters missing, which caused "impossible" sim blow-ups.)

Gate voltage swept. Green line is current. Red line is derivative, which is Gm.

[Rob Strand]

But the full-range plot shows a "?" concave kink, below 0.2mA, which is unlikely for a simple device. Much more likely the sub-threshold parameters "miss" the above threshold curve and, not knowing better, just butts them. (I have heard of MOSFET models with sub-threshold parameters missing, which caused "impossible" sim blow-ups.)

MOSFET models are extremely unreliable and yes you see some very weird behaviours.
I pretty much never trust models at low currents.

The model I use is tweaked for low currents.  I don't use it at all for high currents.  The model is simplified in order to keep "good behaviour" over the typical range of current used in effects pedals.

So here's the graph of my model.  Sorry the x-axis is linear.  The results are vastly different to yours but you can see that gm increases linearly.  Since ID is quadratic it keeps the basic gm proportional to sqrt(ID) behaviour.
At Vgs = 2.5V, the model underestimates the current - that's the penalty for matching the small gm at low-currents.

VDS= 10V


IIRC when I wire g to d and plot the VI curve of the "diode connect" MOSFET the simple model produces a reasonable Vds=Vgs upto 10mA.     In this case Vgs is about 2.5V when ID = 10mA.

Here's the log-log,

[Rob Strand]

FWIW, I found a 2N7000 model from a local student and let SPICE chew it. For 1mA it gives 13mMho (1/77 Ohms).

Notice that at 1mA your VGS is very low, like 1V.   On a real device it's more like 2V @ 1mA.

I remember there was a model which had a very sloppy turn-off like that;  IIRC it was from Philips (not NXP).

Winfield Hill (author of Art of Electronics) posted a Philips-like model that wan't too bad.  I think the
slow turn off Philips model had a weird width or length parameter in one of the sub models.  Whatever
it was it looked wrong since the parameter was too large to be real (bigger than a device!).  I don't
know if Winfield Hill just fixed that problem or had a model before that bug got in!
[BTW, your model isn't that one.]