Understanding cathode caps and cut off frequencies

[Tone Junkie]

Now either Joey or Flemingmras explained how that a 320uf cap on v1a is way over kill and actually could contribute to flubby base by allowing everything to cross. and that in reality 2.2 uf was really all the higher you would want to go. I tried that and actuall prefered a 1uf instead, tightened up everything , the RR mod sounded cruddy with the stock 320 and slightly better but not great with a 2.2uf. Where the 1uf was almost perfect . so my question as Im trying to wrap my tiny little brain around the concept what is the cut off freqency for 1uf with an 820 resister also for v1b what is the cut of frequency for a .68 with a 2k7 and what effect does lowering the resister to a 1k5 have on frequency other than a very slight boost in gain.
thank you Bill

[rsi]

You should go here and fool around with the calculator thing.

http://www.pentodepress.com/home/amplif ... capacitor/" onclick="window.open(this.href);return false;

[flemingmras]

Now either Joey or Flemingmras explained how that a 320uf cap on v1a is way over kill and actually could contribute to flubby base by allowing everything to cross. and that in reality 2.2 uf was really all the higher you would want to go. I tried that and actuall prefered a 1uf instead, tightened up everything , the RR mod sounded cruddy with the stock 320 and slightly better but not great with a 2.2uf. Where the 1uf was almost perfect . so my question as Im trying to wrap my tiny little brain around the concept what is the cut off freqency for 1uf with an 820 resister also for v1b what is the cut of frequency for a .68 with a 2k7 and what effect does lowering the resister to a 1k5 have on frequency other than a very slight boost in gain.
thank you Bill

The equation is -

1 / (6.28 x Rk x Ck) where -

Rk = Cathode Resistor Value in Ohms
Ck = Cathode Bypass Cap Value in Farads

For a typical 820R / 1uF -

1 / (6.28 x 820 x 0.000001) = 194Hz

For the typical 2.7K / 0.68uF -

1 / (6.28 x 2700 x 0.00000068) = 87Hz

This is the corner frequency at which the gain boost starts to come in.

For the 820 / 330uF combo -

1 / (6.28 x 820 x 0.000330) = 0.5Hz

This one should explain why the super high values are way overkill.

The trick is to use cathode bypassing as a way to tune a gain stage to frequencies that are within the guitar's frequency range. Everything below guitar frequencies just becomes mud and noise...especially when added on early stages in an overdrive circuit (muddy bass distortion). When you use low value bypass caps, you turn the gain stage into an "active shelving filter" that applies more gain to upper frequencies than lower ones. This is what's known as "partial bypassing", and it's known as "partial" bypassing because you're only allowing PART OF the audio spectrum to bypass the cathode resistor.

By "shelving" bass early, you end up tightening everything up by eliminating sub-audio frequencies that would just add noise/mud/flub to the guitar signal. Then you can add the bass later in the circuit AFTER the overdrive circuitry either by increasing the value of the bass cap in the tone stack or via a resonance knob in the NFB loop.

Here's a diagram that explains where the term "shelving" came from. You can see that if you were to graph the frequency response pattern of the stage, it looks like a "shelf" -



This particular stage has a gain boost start corner frequency just above 100Hz. Of course, nothing in filter circuitry is "brick wall" so there's a bit of a slope to the curve (roughly 6dB per octave), with all of the gain being in right at the top corner frequency of 200Hz.

[Tone Junkie]

Once again my friend you have givin my knowledge and understanding a great boost. first of all thank you for that equation i can now run my own numbers . By that i mean after playing around with it I can see why 2.2 uf was were you said to go . that comes in at 88hrtz where the low e string on a guitar in standard tuning comes in at 83hrtz. I will reread this a couple more times . Then I will reread a bunch of other things written here and try to understand the peramiters of tuning my gain stages all the way down the line . Im waiting on merlins book know.
The first chapter he gave out free on his site made my head hurt the first time i read it . Unfortunatly thats because a great amount of knowledge was trying to get into my teenie tiny little brain.
I should have quit smokin that good stuff when i was still young enough for it to help me.
Bill

[flemingmras]

Once again my friend you have givin my knowledge and understanding a great boost. first of all thank you for that equation i can now run my own numbers . By that i mean after playing around with it I can see why 2.2 uf was were you said to go . that comes in at 88hrtz where the low e string on a guitar in standard tuning comes in at 83hrtz. I will reread this a couple more times . Then I will reread a bunch of other things written here and try to understand the peramiters of tuning my gain stages all the way down the line . Im waiting on merlins book know.
The first chapter he gave out free on his site made my head hurt the first time i read it . Unfortunatly thats because a great amount of knowledge was trying to get into my teenie tiny little brain.
I should have quit smokin that good stuff when i was still young enough for it to help me.
Bill

Correct...the 80-90Hz pass band is usually where you'd want to start from on a guitar amp. Whichever cap value will give you the 80-90Hz pass band with the cathode resistor that you're using would be the highest you'd want to use, then you'd go lower from there.

This is a big part of the reason why the Marshall DSL amps in stock form exhibit farty bass. The first gain stage in the amp is higher than most (it uses a 220K plate resistor), and then they use a 1.8K cathode resistor with a 4.7uF bypass cap, which starts to boost at about 18Hz (1 / (6.28 x 1800 x 0.0000047) = 18.82Hz)! Way too low a pass band for the very first gain stage.

Now you can reverse a variable in the equation to find which cap value will give you a certain pass band with a particular cathode resistor -

1 / (6.28 x Rk x f) where -

Rk = Cathode resistor value
f = a particular frequency within the pass band you need to start boosting in

What's happening is that a capacitor is basically a frequency dependent resistor. We define this as "capacitive reactance", which means that at a particular frequency the capacitor will exhibit a certain resistance. What we're doing with this singe pole equation is looking for a cap value that exhibits a resistance that is roughly equal to that of the cathode resistor at the frequency we want.

Let's say we have an 820R cathode resistor and we want a capacitor that exhibits 820R of resistance at 200Hz -

1 / (6.28 x 820 x 200) = 000000.9F, or 0.9uF

This means that at 200Hz, the cathode resistor/bypass cap appears to be two 820R resistors in parallel to AC, which would be 1/2 of 820R (410R). From there, frequencies above 200Hz see the cap as the path of least resistance as compared to the cathode resistor value and the boost continues upward. At frequencies below 200Hz, they see the cap as a higher resistance than the cathode resistor, so stuff below 200Hz goes through the cathode resistor instead since it looks like the path of least resistance at those frequencies.

Now what's REALLY happening is that the cathode bypass cap acts like a filter cap. When the input signal at the grid causes the plate current through the preamp tube to fluctuate, this creates a fluctuating voltage drop across the cathode resistor, which causes the cathode voltage to fluctuate. With a fluctuating cathode voltage, this is seen as negative feedback.

By adding the bypass cap, the cap filters out the fluctuations in cathode voltage, which holds the cathode voltage constant and removes the negative feedback, thereby boosting the gain of the stage.

On a fully bypassed stage (high value cap), the cathode bypass cap can act like a filter cap at full bandwidth. But when you drop the bypass cap value...lower cap values exhibit a lower time constant, and as such cannot sustain a slow discharge rate (discharge rate gets slower the lower the frequency), which means that it cannot hold the cathode voltage constant over the longer time period it would have to while it waits for the AC cycle to swing positive again to recharge it. In other words, a lower value cap cannot hold the cathode voltage constant at low frequencies. This is why with lower value bypass caps, lower frequencies get negative feedback while higher frequencies don't, hence the gain boost at higher frequencies while lower frequencies receive the "unbypassed gain" of the stage, which is the gain that the stage would provide if the bypass cap wasn't installed (lower frequencies don't see the bypass cap).

[HTH]

flemingmras, have you ever tried diode/led biasing the first gain stage?

[flemingmras]

flemingmras, have you ever tried diode/led biasing the first gain stage?

Nope. Diode/LED biasing sets the stage up for full bandwidth (decouples everything from DC to light) and pretty much eliminates any possibility of active tone shaping via cathode bypass caps.

You could use a NFB loop from the stage output back to the grid for active tone shaping with diode/LED bias. But you'd have to use an inductor in the NFB loop to shelve the lows though.

[yladrd61]

Bump good explanation

[dazzlindino]

Now either Joey or Flemingmras explained how that a 320uf cap on v1a is way over kill and actually could contribute to flubby base by allowing everything to cross. and that in reality 2.2 uf was really all the higher you would want to go. I tried that and actuall prefered a 1uf instead, tightened up everything , the RR mod sounded cruddy with the stock 320 and slightly better but not great with a 2.2uf. Where the 1uf was almost perfect . so my question as Im trying to wrap my tiny little brain around the concept what is the cut off freqency for 1uf with an 820 resister also for v1b what is the cut of frequency for a .68 with a 2k7 and what effect does lowering the resister to a 1k5 have on frequency other than a very slight boost in gain.
thank you Bill

The equation is -

1 / (6.28 x Rk x Ck) where -

Rk = Cathode Resistor Value in Ohms
Ck = Cathode Bypass Cap Value in Farads

For a typical 820R / 1uF -

1 / (6.28 x 820 x 0.000001) = 194Hz

For the typical 2.7K / 0.68uF -

1 / (6.28 x 2700 x 0.00000068) = 87Hz

This is the corner frequency at which the gain boost starts to come in.

For the 820 / 330uF combo -

1 / (6.28 x 820 x 0.000330) = 0.5Hz

This one should explain why the super high values are way overkill.

The trick is to use cathode bypassing as a way to tune a gain stage to frequencies that are within the guitar's frequency range. Everything below guitar frequencies just becomes mud and noise...especially when added on early stages in an overdrive circuit (muddy bass distortion). When you use low value bypass caps, you turn the gain stage into an "active shelving filter" that applies more gain to upper frequencies than lower ones. This is what's known as "partial bypassing", and it's known as "partial" bypassing because you're only allowing PART OF the audio spectrum to bypass the cathode resistor.

By "shelving" bass early, you end up tightening everything up by eliminating sub-audio frequencies that would just add noise/mud/flub to the guitar signal. Then you can add the bass later in the circuit AFTER the overdrive circuitry either by increasing the value of the bass cap in the tone stack or via a resonance knob in the NFB loop.

Here's a diagram that explains where the term "shelving" came from. You can see that if you were to graph the frequency response pattern of the stage, it looks like a "shelf" -



This particular stage has a gain boost start corner frequency just above 100Hz. Of course, nothing in filter circuitry is "brick wall" so there's a bit of a slope to the curve (roughly 6dB per octave), with all of the gain being in right at the top corner frequency of 200Hz.

can someone explain to a total newbie in this amp thingy just how the math works in the formula...
1/ ( ooo X ooo X ooo ) = HZ

[Janglin_Jack]

It is awesome that these guys post the math, (or even know the equations) as it is a real opportunity to learn. I cheat and use charts that provide the frequency cutoff values... Again, kudos to the experts. Great info.

Mike

[neikeel]

It is awesome that these guys post the math, (or even know the equations) as it is a real opportunity to learn.

Yes those things are all in my dusty books too

I cheat and use charts that provide the frequency cutoff values

Yes me too

[dazzlindino]

Did a little homework, the formula for
820R / 1uf
1/ ( 6.28 x 820 x 0.000001 ) = Hz
1 means 1 second
6.28 is pi + pi, thusly it is 3.14 + 3.14 = 6.28
so 6.28 x 820 x 0.000001= .0051496
1 second divided by .0051496= 194 Hz
can someone explain why pi is doubled?

[arledgsc]

can someone explain why pi is doubled?

2 * pi falls out of time domain to frequency domain conversions. 2 * pi in math comes from the equation for circumference of a circle = 2 * pi * r where "r" is the radius of a circle. If you can picture a sine wave completing one cycle in 2 * pi radians then you can begin to understand why 2*pi shows up at every turn in calculations of frequency response for filters. For more information see this wiki which sheads some light on (wt) "omega t"...
http://en.wikipedia.org/wiki/Sine_wave

[dazzlindino]

can someone explain why pi is doubled?

2 * pi falls out of time domain to frequency domain conversions. 2 * pi in math comes from the equation for circumference of a circle = 2 * pi * r where "r" is the radius of a circle. If you can picture a sine wave completing one cycle in 2 * pi radians then you can begin to understand why 2*pi shows up at every turn in calculations of frequency response for filters. For more information see this wiki which sheads some light on (wt) "omega t"...
http://en.wikipedia.org/wiki/Sine_wave

Thanks!, that was an awesome read at that link....
Now I can clearly see / understand that one completed sine wave + / - = pi ( 3.14 )...
but still not understanding the doulbling of pi....hmmm...
me needs to think harder I guess...

[antosimoni]

reviving this great topic.... just to be sure of my math : so a .68uF+820r (=285 Hz) combo is "brighter" than a .68uF+2.7k one (=86 Hz) ???
Thanks for clarifying this to me