Cathode bypass caps as noise control

[stratomaster]

On some designs the first gain stage is bypassed my a very large (100uF+). My understanding is that they serve a purpose beyond just fully bypassing the cathode--they swamp noise. 

I've experienced increased noise when reducing the first stage bypass cap of amps without chokes like a Blues Jr. 

This got me to thinking--would a similarly large bypass cap serve the same purpose in things like an AB763 style reverb circuit?  The low end shaping in those circuits is done by the 500pF input coupling cap and .003μF coupling cap at the output of the recovery stage.  These same stages are often sources of noise.  Does it make sense to put big 330μF caps on these stages--especially on Princeton Reverb choke-less builds?

[pdf64]

Noise introduced at the cathode is eliminated by fully bypassing / decoupling the cathode, eg well below mains frequency.
Bypassing down into the subconics seems unnecessary?

[tubeswell]

On some designs the first gain stage is bypassed my a very large (100uF+). My understanding is that they serve a purpose beyond just fully bypassing the cathode--they swamp noise. 

I've experienced increased noise when reducing the first stage bypass cap of amps without chokes like a Blues Jr. 

This got me to thinking--would a similarly large bypass cap serve the same purpose in things like an AB763 style reverb circuit?  The low end shaping in those circuits is done by the 500pF input coupling cap and .003μF coupling cap at the output of the recovery stage.  These same stages are often sources of noise.  Does it make sense to put big 330μF caps on these stages--especially on Princeton Reverb choke-less builds?

You’re almost there. The benefit of a largish Ck at the V1 position (or the reverb recovery position for that matter) is to get the ‘most optimal’ S:N ratio upfront, which you can then manipulate through the following signal chain. The lower the Ck, the less signal BW there is on V1, and so the more ‘other noise’ you end up with by the time to get to the signal output.

[Merlin]

I've experienced increased noise when reducing the first stage bypass cap of amps without chokes like a Blues Jr. 

Reducing it how much? I find it hard to believe there is a noticeable noise difference between a 100uF cap and a traditional 22uF cap  If you're talking about a weeny 1uF cap or something, then sure.

[tdvt]

If you're talking about a weeny 1uF cap or something, then sure.

As reducing the bypass cap is a common way to control/edit extra bass in a stage, what would be the happy medium for bass roll-off vs. generating extra noise?

I have swapped out a few bypass caps to lower values in an effort to roll-off bass, unaware that doing this could be a potential source of noise.

Happy to report those amps are very quiet but maybe I have just been lucky so far.

[tdvt]

...well below mains frequency.

What would be considered "well below"?

[jjasilli]

Things on my mind for discussion.  "Noise" is a broad term - it could be hi-pitched hiss, lo-pitched hum; RF interference; other types of THD; etc.  Different types of noise need different solutions.


Typically more gain increases the noise floor.  Cathode bypass caps increase gain.  So, it seems that the use of any cathode bypass cap would raise the noise floor, making various types of noise more noticeable in relation to signal.  What is the scientific basis for the notion that a large cathode bypass cap swamps noise?


I believe that a 22uF cap increases amplification for the entire frequency range of human hearing.  A larger cap would increase the amplification of frequencies below that of human hearing.  Does this matter?  Maybe.  If frequencies below 20Hz were amplified, then they would act as a LFO.  This would cause intermodulation distortion -- warbling, or a tremolo effect -- for notes within the range of human hearing.  Some might call this "bloom".


A small cathode bypass cap would not boost the amplification of low frequencies; thereby helping to keep low frequency noise less noticeable; though it might increase hiss.

[Merlin]

I have swapped out a few bypass caps to lower values in an effort to roll-off bass, unaware that doing this could be a potential source of noise.

I think the OP is actually talking about hum since he mentioned "amps without chokes". Basically the PSRR is worse unless the bypass cap is big enough to bypass well below 100Hz. But if the power supply is quiet enough to start with, then you won't notice either way.

[jjasilli]

Yes, I would take a direct approach.  Identify the problem.  If it's PS noise, then make the PS itself less noisy.  This may also apply to the heater supply.  Use cathode bypass cap values in gain stages to achieve other design goals.

[tdvt]

Point taken that the initial post may well be about "hum", while I am thinking more hiss, static, white noise kind of stuff.

I generally make extra effort to make the PS fairly quiet; extra filtering, choke, etc. so I wasn't really figuring that in, in my situation(s), but that may certainly be an issue in other cases.


I have (rightly or wrongly) approached the bypass cap as a component to include to increase the gain of a stage, but using a value to try to attenuate unwanted frequencies, &/or roll-off inaudible frequencies to lessen the load on the circuit.

I have generally referred to the AmpBooks calculator for a ballpark idea of response.

[pdf64]

My understanding is DC passing via the cathode resistor generates noise, the degree determined by the current magnitude and resistance.
So an unbypassed input / early stage cathode provides both a noise source and an entry point for it into the sgnal path (maybe the stage kinda acts as common grid WRT signal at the cathode  ).

Additional to that noise, there's the h-k leakage of the valve used, which provides an signal path entry point for heater signal, 50/60Hz and its harmonics. DC elevation / DC heater power can pretty much get rid of this noise.

Fully bypassing the cathode (eg cap's reactive impedance at least 1/10 of Rk//rk at mains frequency) decouples cathode noise and so mitigates both the above, and should provide the best signal to noise ratio for the stage, all else being equal.

Partial bypass allows in low pass filtered heater noise and cathode resistor noise.

Hence typical hot rodded Marshall type designs with 0.68uF // 2k7 partial bypass at input and perhaps 2nd / 3rd stage cathodes may tend towards a rumbly pink / brown kinda noise at high gain settings, rather than white noise.

[tdvt]

Fully bypassing the cathode (eg cap's reactive impedance at least 1/10 of Rk//rk at mains frequency) decouples cathode noise and so mitigates both the above, and should provide the best signal to noise ratio for the stage, all else being equal.

1/10th of Rk as a minimum?

[Merlin]

My understanding is DC passing via the cathode resistor generates noise, the degree determined by the current magnitude and resistance. Anyway it would be tiny for a bias resistance.
 

That's true for carbon comp resistors, but modern resistors don't generate significant hiss with DC current.
All resistors generate Johnson noise of course, which has nothing to do with DC current. But a typical bias resistance is very small and generates so little extra hiss that it is not likely to be noticed in a guitar amp, bypassed or not.

What you say about heater hum is true. Hum from heaters, hum from power supply, this is a altogether an issue of hum. Hiss is just one of those little grooming fish riding on the back of the hum shark; which one should you be worrying about?

[acheld]

My understanding is DC passing via the cathode resistor generates noise, the degree determined by the current magnitude and resistance.

Interesting!  Could expand on that?  How does that work?  I had the simple concept that Rk did not generate noise because it wasn't in the signal path.   You know, the red lines RobRob draws on his schematics . . .

[stratomaster]

I have swapped out a few bypass caps to lower values in an effort to roll-off bass, unaware that doing this could be a potential source of noise.

I think the OP is actually talking about hum since he mentioned "amps without chokes". Basically the PSRR is worse unless the bypass cap is big enough to bypass well below 100Hz. But if the power supply is quiet enough to start with, then you won't notice either way.

This is correct.  I'm primarily thinking of the Blues Jr and Princeton Reverb. 

With the Blues Jr I've attempted to kill off some of the ripple though increased reservoir capacitance.   A 1μF first stage bypass cap with a switch for another 10μF in parallel is quieter when capacitance highest--with audible noise despite the reduced ripple.

This got me thinking about older Tweed era amps with 330μF cathode bypass caps on the first stage and the potential for them to be swamping noise.  10uF would be sufficient to fully bypass the audio spectrum, so I guess a more direct question is "why so high?" What else is the extra capacitance doing? 

Then I thought if it's doing something useful beyond fully bypassing the frequency range, is it useful to combat noise in less than optimal power supply arrangements like the Princeton Reverb? There the reverb transformer derives its high voltage from the screen supply with only a 1k dropper and no choke preceding it. 

Given the cathode and heater have a relationship I don't fully understand (but is implied by a maximum H-K voltage spec) I figured the increased cathode capacitance could potentially be used as a countermeasure in the Princeton and similar circuits against mains and 2x mains noise.  A strategic deployment of 100μF cathode caps on the 1st stage, reverb driver, and reverb recovery triodes would then pay dividends -- assuming there is an actual mechanism of hum reduction provided by those caps.

We would then be free to partially bypass later in the signal chain if desired.

[Merlin]

10uF would be sufficient to fully bypass the audio spectrum, so I guess a more direct question is "why so high?" What else is the extra capacitance doing? 

You mean the amps that used a shared 820R resistor between two triodes? With two cathode impedances effectively in parallel you need more capacitance. You'd need 22uF to just barely cover the audio spectrum. Rule of thumb, use ten times more than you just barely need, especially with electrolytics. So Fender used 250uF, presumably a convenient value that his supplier had in stock.
Does it deliver the best available PSRR? Yes. Does it shunt heater hum? Yes. Would 22uF do the same thing? Just barely. I think you may be over-thinking the rest!

[pdf64]

My understanding is DC passing via the cathode resistor generates noise, the degree determined by the current magnitude and resistance. Anyway it would be tiny for a bias resistance.
 

That's true for carbon comp resistors, but modern resistors don't generate significant hiss with DC current.
All resistors generate Johnson noise of course, but a typical bias resistance is very small and generates so little extra hiss that it is not likely to be noticed in a guitar amp, bypassed or not.
 ...

So is the noise generated by the input grid stopper resistance due to a different mechanism than the main chunk of any noise generated by the cathode resistor?
My thinking was that they may be at least somewhat related, with the grid stopper noise being due to a much larger resistance but vastly lower current. Compared to the low cathode resistance but much higher cathode current.

What's the mechanism by which noise (or any signal at the cathode) appears at the anode?
Might it be due to the stage acting as a common grid (and hence noise voltage at the cathode being amplified), or is it just that the noise signal modulates cathode, and hence anode, current?

[tdvt]

With two cathode impedances effectively in parallel you need more capacitance. You'd need 22uF to just barely cover the audio spectrum. Rule of thumb, use ten times more than you just barely need, especially with electrolytics. So Fender used 250uF, presumably a convenient value that his supplier had in stock.
Does it deliver the best available PSRR? Yes. Does it shunt heater hum? Yes. Would 22uF do the same thing? Just barely. I think you may be over-thinking the rest!

So carrying this further, & towards the goal of minimizing noise the traditional noisy sections, would a larger-than-typical bypass cap be beneficial on the parallel Fender reverb driver stage?

[stratomaster]

So carrying this further, & towards the goal of minimizing noise the traditional noisy sections, would a larger-than-typical bypass cap be beneficial on the parallel Fender reverb driver stage?

That was my takeaway.  Alternatively in that amp you can go one supply node over and render it pointless at the expense of some plate voltage.

On the larger 2 channel AB763 style amps the reverb recovery and 3rd triode also have a common cathode.  People tend to have noise problems around V4 on those amps.  A larger cap here could also prove beneficial. 

[tdvt]

I am there with you. I have all of the amps you mentioned earlier; a BlJr, a Princeton Reverb & a few AB763s & the tube-driven reverb circuit is usually the culprit when it comes to noise. But I was able to get them to an acceptable noise floor overall.

With the Princeton, I was able to re-purpose the unused B+ node for the reverb. I can't say whether that was THE fix but it certainly helped. 

The others are not really tweaked much (I did split the V4 cathodes) & have some reverb circuit noise, but could still be quieter.


The ones I have built are generally quiet, but I am presently building an EL84 Princeton for a friend & I am having noise issues with the 2-tube reverb circuit.

[pdf64]

...
So carrying this further, & towards the goal of minimizing noise the traditional noisy sections, would a larger-than-typical bypass cap be beneficial on the parallel Fender reverb driver stage?

I can't think how?
The input signal to the driver is heavily LPFed.
The output of the stage is also heavily LPFed (very inductive load).
Noise of whatever type would have to be really bad for it to appear at the tank output, and be anywhere near the magnitude of the recovery stage noise.

[stratomaster]

I am there with you. I have all of the amps you mentioned earlier; a BlJr, a Princeton Reverb & a few AB763s & the tube-driven reverb circuit is usually the culprit when it comes to noise. But I was able to get them to an acceptable noise floor overall.

The others are not really tweaked much (I did split the V4 cathodes) & have some reverb circuit noise, but could still be quieter.

With respect to the Blues Jr I've had an idea to lift the ground end of the heater artificial center tap resistors, solder them together and run a jumper from the junction to the cathode of D6, the rectifier for the 15V supply.  This will give 26.6V of elevation according to the Rev D schematic (TP31).  This also leaves another pole of filtering before the 15v is generated for the opamp that can decouple any effects of this addition.

[stratomaster]

...
So carrying this further, & towards the goal of minimizing noise the traditional noisy sections, would a larger-than-typical bypass cap be beneficial on the parallel Fender reverb driver stage?

I can't think how?
The input signal to the driver is heavily LPFed.
The output of the stage is also heavily LPFed (very inductive load).
Noise of whatever type would have to be really bad for it to appear at the tank output, and be anywhere near the magnitude of the recovery stage noise.

Aggressively high passed. But point taken. 

I don't think signal-side filtering eliminates the problems.  Single coil noise is still audible through a tight overdrive amp.  There may be high passes down to 300Hz or higher, but then you switch to positions 1,3,5 on the strat you still get the noise in all its glory.

The mechanisms are different, though.  With the reverb driver in a Princeton it's a single ended amp (no benefit of common mode rejection) with inadequate filtering sharing the screen node.  Noise from the power supply there would be present downstream of the HPF feeding the grid.  Same with filament noise.

[tdvt]

I can't think how?
The input signal to the driver is heavily LPFed.
The output of the stage is also heavily LPFed (very inductive load).
Noise of whatever type would have to be really bad for it to appear at the tank output, and be anywhere near the magnitude of the recovery stage noise.

It wouldn't be my first guess as a source of noise, but ever hopeful, as it is a link in that chain. 

I would agree that the recovery stage tends to be a very noisy section.

With respect to the Blues Jr I've had an idea to lift the ground end of the heater artificial center tap resistors, solder them together and run a jumper from the junction to the cathode of D6, the rectifier for the 15V supply.

I have had this same thought regarding the amp I am currently working on. I haven't tried it yet as the heaters don't seem to be a big issue (did the 6V battery test; marginally better) but as Merlin mentioned earlier, the noise can be riding on the heater hum, so maybe worth experimenting.

I also wasn't sure about elevating through the artificial center tap & I would have to create a +DC reference, as this one has fixed bias.

[shooter]

noise can be riding on the heater hum

noise can sneak along a sketchy ground, sketchy solder joint,  cross-coupling through parallel wires...
scopes are real handy, especially if it's got a FFT (frequency based) option.


this chart doesn't help noise, but it kinda handy for bypass caps, even got the math if you're so inclined

[pdf64]

... I also wasn't sure about elevating through the artificial center tap & I would have to create a +DC reference, as this one has fixed bias.

There's +/-15V supplies https://el34world.com/charts/Schematics/files/Fender/Fender_blues_jr.pdf
The suggestion is to use the +15V to elevate the heater circuit.

[HotBluePlates]

On some designs the first gain stage is bypassed my a very large (100uF+). My understanding is that they serve a purpose beyond just fully bypassing the cathode--they swamp noise.

... thinking about older Tweed era amps with 330μF cathode bypass caps on the first stage and the potential for them to be swamping noise.  10uF would be sufficient to fully bypass the audio spectrum, so I guess a more direct question is "why so high?" What else is the extra capacitance doing?

You mean the amps that used a shared 820R resistor between two triodes? With two cathode impedances effectively in parallel you need more capacitance. You'd need 22uF to just barely cover the audio spectrum. Rule of thumb, use ten times more than you just barely need, especially with electrolytics. So Fender used 250uF, presumably a convenient value that his supplier had in stock.
Does it deliver the best available PSRR? Yes. Does it shunt heater hum? Yes. Would 22uF do the same thing? Just barely. I think you may be over-thinking the rest!

I have experience with a specific type of hum:  heater-to-cathode leakage.

There are a couple ways to conceptualize this, but the easiest is to think of the leakage as a sneak-path for audio (at mains frequency), and a larger & larger & larger capacitance as a lower impedance.  The leakage is a current, so by minimizing the impedance-to-ground you also minimize the resulting hum-volts.

   25µF = ~106Ω at 60Hz
  250µF = ~10.6Ω at 60Hz

Where do you see a 250µF cap in tweed amps?  Only the the Bassman, and Fender also opted for the new-ish special 12AY7 whose data sheet specifically mentions low-noise and hum in input stages of audio equipment.  Fender gave it a 1-2 punch for keeping the hum out (though not-sharing a cathode resistor would have made the job easier).


A boutique builder messaged me on this forum maybe 15 years ago.  He was having hum issues with a new design that was a Bassman spin-off.  If he used the 25µF cap he wanted (or smaller) there was hum, but there was no-hum with a 220µF cap.  He was certain it couldn't be "a tube problem" because he'd tried 10 different preamp tubes in the first stage.

Turns out, the whole case lot of 12AX7s he had exhibited heater-to-cathode leakage.  The large 220µF cap swamped the resulting hum, but smaller caps were too-high an impedance and allowed enough 60Hz voltage to develop to be audible in the amplified signal.


Later, I experienced this all over again after buying 100+ tubes of a particular odd triode.  I built a design that allowed using a 1µF cathode bypass cap (I prefer the bass trimmed in the input stage), or paralleled by another 25µF.  I can use that amp to sort "leaking" tubes from "no-leak" tubes, simply by listening for hum in the 1µF position.

Since then, I have acquired a tube tester that directly measures heater-to-cathode leakage in the µA range.

[tubeswell]

Where do you see a 250µF cap in tweed amps?

Not strictly 'tweed', but reverb recovery in 6G15 is also 250uF Ck

[Merlin]

Where do you see a 250µF cap in tweed amps?  Only the the Bassman

Sorry, I was looking at the bassman schematic. Got a link to a schem showing 330uF?

[Merlin]

Guys, can we not use the word noise if we're talking about hum? It's really confusing. In electronics theory, noise means hiss.

[So carrying this further, & towards the goal of minimizing noise the traditional noisy sections, would a larger-than-typical bypass cap be beneficial on the parallel Fender reverb driver stage?

It depends what the hum mechanism is in your particular amp:

Magnetic coupling from the power transformer into the reverb transformer or input coil: Cathode cap makes this better.
Ripple on the power supply (PSRR): Cathode cap makes this worse in a transformer coupled reverb driver.* But it makes it better in a resistor loaded gain stage.
Parasitic coupling from heater to cathode: Cathode cap makes this better.

Apart from PSRR in the reverb driver, a bigger cathode cap gives better immunity to hum, but there is the law of dimishing returns. 100uF may be somewhat better than 22uF, but that doesn't mean you get the same improvement again by stepping to 1000uF. But it won't hurt to try it.

*There is a super secret mod to get enhanced PSRR from the Fender driver, but y'all are not ready for that conversation.

[jjasilli]

@hotblue:  great explanation of heater to cathode leakage, and how a large cathode bypass cap reduces hum!  Now it makes sense.


However, the word "swamp" has been swamping my understanding of this.  I think "swamp", in electronics, means that one signal is dominating another signal, often with the negative connotation that this is undesirable in the particular application.  So, the large bypass cap is not swamping hum -- dominating it with another, unwanted, signal -- rather it is bleeding the hum to ground.


Still, it appears that imprecise terminology, in spite of itself, is a path to knowledge; albeit the scenic route.

[tdvt]

Still, it appears that imprecise terminology, in spite of itself, is a path to knowledge; albeit the scenic route.

I agree that this has been a bit of a quagmire regarding terminology, & as always, I appreciate everyone's input.


With my present project, I am dealing with noise (static, hiss...) & not hum,  & have tried to stick with that description.


So while we are kind of landing more on the topic of hum, the way I am understanding it to this point, much of what has been shared still seems relevant to the issues I am tackling, & that is why I have been following the thread with interest.

[stratomaster]

Where do you see a 250µF cap in tweed amps?  Only the the Bassman

Sorry, I was looking at the bassman schematic. Got a link to a schem showing 330uF?

That was my fault. Confused it with the Marshall variant.  The JTM45 used a 330μF cathode cap.

[jjasilli]

I can see for economic reasons why a mass manufacturer would use a "cheap trick" to mask a hum issue -- like using a huge value, low voltage, cathode bypass cap @ the input stage  --  especially since they're going to put a cap there anyway.  But DIY or boutique builders need not imitate that.

[sluckey]

I can see for economic reasons why a mass manufacturer would use a "cheap trick" to mask a hum issue -- like using a huge value, low voltage, cathode bypass cap @ the input stage  --  especially since they're going to put a cap there anyway.  But DIY or boutique builders need not imitate that.

Cheap trick or good engineering? Sunn put a 250µF cap on the cathode of the first triode in all their tube amps.

[tdvt]

As a real-world follow-up, trying to distill all the information here, in my efforts to quiet down a noisy reverb section in a new build, I implemented (temped in) a couple of the things that were mentioned &/or pointed out earlier that to my mind, might be relevant.


Project is an AB763 pre & 2-tube reverb (V1,V2,V3) into a LTPI/EL84 output (V4, V5, V6). The issue was an unacceptable level of static/white noise, seemingly from the reverb section, reverb knob would not completely quiet it but would significantly add to it. 10uF & 4uF for V1A/V1B which I was hoping to leave, so I started with modding V2 & V3 values.


In trying to zero in, noise was;

• reduced by disconnecting the mixer triode bypass cap,
• no change pulling V1,
• slightly better pulling V2,
• eliminated by pulling V3 (power amp section then dead quiet)
• also eliminated by jumpering V1 directly to the PI (had sound)

In the query about dual cathodes it was mentioned that the 22uF value might be marginal, so I subbed in a 68uF bypass (value on-hand) & it was also pointed out that the 6G15 used a 220uF in the recovery triode, which I also had on-hand, & that was also subbed in. The only other reverb section change was going to 4.7K on the V2 dual cathode.


Results so far are a nearly silent reverb section. While I need to really test drive it more, the amp is now very quiet overall.

[stratomaster]

Results so far are a nearly silent reverb section. While I need to really test drive it more, the amp is now very quiet overall.

This is great.  Is your reverb recovery triode sharing a cathode like in the AB763 with the 3rd gain stage, or does it have a dedicated network?

[tdvt]

Is your reverb recovery triode sharing a cathode like in the AB763 with the 3rd gain stage, or does it have a dedicated network?

They are separate as it is based on a modded Hoffman PR board (which are already separated), then modified to a no-trem/LTPI version as per a Sluckey drawing.

So presently, it has a 220uF on V3A & a 25uF on V3B.

[stratomaster]

Is your reverb recovery triode sharing a cathode like in the AB763 with the 3rd gain stage, or does it have a dedicated network?

They are separate as it is based on a modded Hoffman PR board (which are already separated), then modified to a no-trem/LTPI version as per a Sluckey drawing.

So presently, it has a 220uF on V3A & a 25uF on V3B.

And finally, which node is your reverb driver connected to? And are you using a choke?

Sorry for the barrage. 

[tdvt]

No worries, avoiding yard work being online...

The power rail is still 4 node but seasoned a little. The reverb driver is connected to B+2 which has a choke & resistor  between B+. I was trying out an idea that was part of this thread.
(Post #23 has the final drawing)

I thought I would try it to lower the screen voltage (in relation to B+) of the EL84s, more than just a choke would. I could also have added another node, but was running out of room.

So in this one, I have a choke with a 1K/5W presently tacked in. It is putting the screens about 10V-ish lower than full B+.


As I mentioned earlier, I DID put the reverb driver on it's own node in my actual PR, thinking it is probably a good idea in general if you have the opportunity.

In production amp practice, I have to think that there was/is always a back & forth between what works OK, what might be better & if better is worth the higher cost.

Luckily, we have the option to take things a little further without spending all that much more.

[pullshocks]

noise can be riding on the heater hum

this chart doesn't help noise, but it kinda handy for bypass caps, even got the math if you're so inclined

Not to get off topic, but what does the response of an UNbypassed stage (as seen in V1A of the Tone King Imperial) look like?

[stratomaster]

noise can be riding on the heater hum

this chart doesn't help noise, but it kinda handy for bypass caps, even got the math if you're so inclined

Not to get off topic, but what does the response of an UNbypassed stage (as seen in V1A of the Tone King Imperial) look like?

Flat, same as a fully bypassed stage, but with about 6dB less gain across the board. At least in theory. 

You can see this as the horizontal lines formed by the S curves in the plot above.  Imagine the capacitance keeps shrinking to where the transition from the lower gain line to the higher gain line occurs above the audible range.  You'll end up with just a flat line so lower gain.

Check out the ampbooks calculators to get a feel for this stuff.  Put a 1000μF cathode cap and run the sim, then out a 1pF cap and repeat.

*Correction* I mistakenly thought someone had attached the image below somewhere in the thread previously.  The hadn't.  Theirs includes a ratio which makes this effect harder to see.  Image taken from https://www.valvewizard.co.uk/OtherStuff.html