Choosing cathode bypass values

[Gnobuddy]

According to a calculator a 5uf bypass cap is less than half dB lower in gain at 82Hz than at 10k!?!

With the correct formula, a 5 uF cap calculates to -3 dB at about 117 Hz. That's very close to A#, 6th fret on the low E string. So you can expect to hear some slight bass loss on the first few frets of the low E string. Rhodesplyr has good ears, what he's hearing is real.

Keep in mind that two of the big factors in the formula have big, sloppy tolerances - the gm of the tube, and the value of the capacitor. So we shouldn't really trust these frequency calculations beyond, maybe +/- 20%. For a guitar amp, I find that more than close enough for a starting point. And then adjust to taste by ear, because guitar amps are intended only to please the ears, after all. Measurements and calculations are only to get us to a sane starting point and save us some tedious experimentation time at the workbench.

-Gnobuddy

[Dave H]

a 1uf cap across a 1.5k cathode resistor on a 12ax7 has a +3dB around 150Hz but audibly it predominantly accentuates the upper mids and HF. You can tell me what the numbers say all day, and I'll listen too. But this is what my ears tell me.

That sounds about right to me. It's +3dB at 150Hz but it's +6dB above about 500Hz so that's what you hear (an increase in mid and HF)

[Malcolm Irving]

RDH4, on page 484, gives an exact formula for the effect of cathode bypass capacitors on stage gain. I believe this agrees with @Gnobuddy and Spice, but we would need to build a spreadsheet to check that out.

[Gnobuddy]

That sounds about right to me. It's +3dB at 150Hz but it's +6dB above about 500Hz so that's what you hear (an increase in mid and HF)

Here's an LTSpice simulation - 12AX7, Rk=1.5k, Ck = 1uF. I can't vouch for the accuracy of the 12AX7 model, but the curve matches my back-of-the envelope calculations pretty well. I adjusted input voltage so that the output signal at the anode is 0 dB at the right edge of the plot, to make it easier to eyeball how many decibels of bass loss (of midrange boost if you prefer to think of it in those terms) we're dealing with.

Considering that the fundamental frequencies (not harmonics) from guitar lie roughly in the 100 Hz - 1 kHz range, the frequency response (with the 1 uF bypass cap) is rising through almost that entire range. 500 Hz is already around the 7th fret on the high E string, pretty far up the range of a typical electric guitar.

-Gnobuddy

[Gnobuddy]

RDH4, on page 484, gives an exact formula for the effect of cathode bypass capacitors on stage gain. I believe this agrees with @Gnobuddy and Spice, but we would need to build a spreadsheet to check that out.

Thanks for your input, Malcolm!

My impression is that the books and resources written by real engineers and scientists all get this right. If you know a little bit about complex number algebra and how to apply that to RC circuits, it's not a difficult calculation. It's a simple passive shelving RC filter, and I would guess the math for that was worked out maybe as early as the late 19th century, before electronics existed, but when telephones and AC power and primitive radio transmitters and receivers did exist.

But somewhere along the way, someone with only technician-level knowledge came to the wrong conclusion, and then that wrong conclusion spread like wildfire, maybe because it seems simple and obvious. Many of the easy electronics books I read as a boy had the wrong formula (applied to BJTs, not valves). Eventually the Internet arrived, and now the wrong formula is everywhere.

Even with the formula in hand, though, it didn't use to be easy to turn it into an actual frequency response plot back in the first three-quarters of the 20th century, because it took lots of complex number calculations to do it.

Now we have LTSpice, so anyone who's interested can do a simulation with a few minutes of mouse-clicks. It's so easy, it's incredible!

-Gnobuddy

[Malcolm Irving]

Here's an LTSpice simulation - 12AX7, Rk=1.5k, Ck = 1uF. I can't vouch for the accuracy of the 12AX7 model, but the curve matches my back-of-the envelope calculations pretty well. I adjusted input voltage so that the output signal at the anode is 0 dB at the right edge of the plot, to make it easier to eyeball how many decibels of bass loss (of midrange boost if you prefer to think of it in those terms) we're dealing with.

Considering that the fundamental frequencies (not harmonics) from guitar lie roughly in the 100 Hz - 1 kHz range, the frequency response (with the 1 uF bypass cap) is rising through almost that entire range. 500 Hz is already around the 7th fret on the high E string, pretty far up the range of a typical electric guitar.

-Gnobuddy

I've hand calculated the RDH4 formula for the above example at 200Hz. It gives -2.2dB which is spot on the LTSpice value from the graph.

[Rhodesplyr]

Thanks for your compliment on the ears. When you get right down to it, it's not that hard when you know the general ballpark to experiment with different values and pick what seems to sound right.

This is a single 6V6 amp with moderately-sized OPT and a 10" Quam speaker, and it's easy to turn it up to overdrive levels. Too much bass in this one sounds like garbage when you start to hit overdrive. I wanted a reasonably full, balanced bass sound, but I wanted to minimize the ugly sound of too much bass distortion. And I'm a strong believer in bandwidth-limiting in terms of not throwing signals at a speaker that it can't turn into musical sounds.

But I will look up the cathode bypass math. I've run across it before. It's disappointing that an online calculator would be based on the wrong formula. You'd think that someone who went to that much trouble to set it up would get it right....

[cjenrick]

put a 6 way rotary sw in there and stuff it with different caps, maybe try non polarized vs polarized and get out the scope to see if it changes anything,

got an old Jensen you do not want to blow up? scale back the bypass cap,

[Gnobuddy]

It's disappointing that an online calculator would be based on the wrong formula.

It surely is. Remember a few decades ago, when we used to hear the phrase "garbage in, garbage out" a lot?

-Gnobuddy

[Gnobuddy]

...disappointing...online calculator

I just coded up a little Javascript calculator that contains the correct formula. Its a little HTML file you open in your browser. I don't have a personal or professional website these days, so I'll just attach the calculator program to this post.

To use it, you enter your valve's conductance in umho, external cathode resistance in kilo ohms, and desired -3 dB frequency in Hertz. Click to see the proper cathode bypass capacitor value to use, in uF. (Screenshot attached, based on numbers we discussed in an earlier post on this thread.)

This forum doesn't accept HTML file attachments, so I zipped it up and attached that. Unzip, and open "capval.html" with a standards-compatible browser. It should open automatically if you click on it. If not, right-click, select "open with" and choose your browser. I tested with Firefox and Google Chrome, both work fine. I don't use Windows and can't speak for whatever browser Microsoft is pushing these days. Let's hope it's better than their previous garbage.

This is a very simple little program, so it doesn't do any error checking - if you type "Fluffy" where you should be entering the valve conductance in umho, the calc will choke!

These days one has to be careful about opening any kind of file in a browser. Feel free to run any virus checkers you want on the calculator HTML file, or open it up in a text editor, and see what's in it for yourself. It's only a few lines of code, you can easily tell that there is no evilness lurking within.

-Gnobuddy

[g1]

Awesome. Thanks.
What would you call something that goes viral to cure a 'virus'?

[nickb]

The object of the thread, I think, was to correct a commonly found error. I fear we have introduced another one.

If I use the script and compare using LtSpice it's obviously incorrect:





The expression for the gain from RHD4 is



You can see that there is a 'zero' around where the gain starts to rise at w=1/Rk/Ck and a 'pole' where the gain levels off at (1+(u+1)*rk/Rl+Rp) times this. Rp is the plate resistance, Rl is the total external plate resistance. Neither of these use the parallel combination of Rk and 1/gm at all.

The -3dB point occurs where the numerator is half the denominator. Using this the script was recoded to give the correct value for the cap. You can see this now corresponds very well using LtSpice:



Here is the corrected script:

TruCapVal.zip

[tedmich]

put a 6 way rotary sw in there and stuff it with different caps, maybe try non polarized vs polarized and get out the scope to see if it changes anything,

got an old Jensen you do not want to blow up? scale back the bypass cap,

switching bypass caps is said to be quite noisy; the Jensen may blow anyway!

[Enzo]

If you use a simple switch. You need to keep the caps charged, so you would wire a high value resistor across each switch. I use 1 meg, but 470k or something would work. The resistance essentially disables the cap, close the switch, it shorts the resistor bringing the cap into circuit.

[Dave H]

If you use a simple switch. You need to keep the caps charged, so you would wire a high value resistor across each switch.

I think it's more effective to switch the value of the coupling cap feeding the vol pot. I managed to get away with just a single 10M resistor to keep DC off the caps.