Treble Peaking formula?

[wakjob]

I know a typical Marshall 470k/470pF gives a corner frequency of about 720Hz, but does anyone know the math to get there?

Much appreciated...wak

 

[JohnH]

id say 720hz is the frequency where the impedance of the cap equals the resistor.

1/(2.Pi.F.C) = R
1/(2.Pi x 720 x 470E-12) = 470000000

 

[South Park]

The cap has a cut off frequency independent of the resister.

 

[mickeydg5]

1 / (6.28 x 470pF x 470k) = 720.8Hz

 

[66 Kicks]

id say 720hz is the frequency where the impedance of the cap equals the resistor.

1/(2.Pi.F.C) = R
1/(2.Pi x 720 x 470E-12) = 470000000

The impedance of the cap equals the resistance of the resistor and the phase shift is 45 degrees and your formula is correct, but your calculation is off.

 

[66 Kicks]

The cap has a cut off frequency independent of the resister.

No it doesn't.

 

[ampmadscientist]

I know a typical Marshall 470k/470pF gives a corner frequency of about 720Hz, but does anyone know the math to get there?

Much appreciated...wak

 

[JohnH]

The impedance of the cap equals the resistance of the resistor and the phase shift is 45 degrees and your formula is correct, but your calculation is off.

yes thanks, too many zeros!. This is better:


1/(2.Pi.F.C) = R
1/(2.Pi x 720 x 470E-12) = 470000

 

[paul-e-mann]

id say 720hz is the frequency where the impedance of the cap equals the resistor.

1/(2.Pi.F.C) = R
1/(2.Pi x 720 x 470E-12) = 470000000

1 / 6.28 x 470pF x 470k = 720.8Hz

Thats what I was gonna say......

 

[South Park]

The circuit is dc to ground the cap is a bypass to ground at a certain frequency it will start to choke off power. To limit the frequency’s to get amp up . Thar is no phase shift no stored power . The filter cap is ware the phase shift happens

 

[wakjob]

I love coffee too.

 

[wakjob]

1 / 6.28 x 470pF x 470k = 720.8Hz

Mickey...where does the 6.28 come from?
Is it the impedance coming into the peaker?

Also, what if there's no reference to ground....
say a 47k bootstrapped with a 2.2uF in the signal path just like a coupling cap or grid stopper.

 

[mickeydg5]

Mickey...where does the 6.28 come from?
Is it the impedance coming into the peaker?

Also, what if there's no reference to ground....
say a 47k bootstrapped with a 2.2uF in the signal path just like a coupling cap or grid stopper.

2 x Pi = 6.28

1 / (6.28 x 2.2uF x 47k) = 1.54Hz

 

[wakjob]

2 x Pi = 6.28

1 / 6.28 x 2.2uF x 47k = 1.54Hz

Thanks a million man...
Helps me a lot!

 

[wakjob]

2 x Pi = 6.28

1 / 6.28 x 2.2uF x 47k = 1.54Hz

I'm getting...
1/6.28 =0.1592356
x 2.2 = 0.3503183
x 47000 = 16,464.96 ???

Sorry,
it's been a LONG time since I've used any advanced math.

 

[neikeel]

No Mickey is right.
Exact answer is 1.5392Hz
ie effectively fully bypassed.
I'll get a Bode plot for each in a minute.
Here:

 

[mickeydg5]

I'm getting...
1/6.28 =0.1592356
x 2.2 = 0.3503183
x 47000 = 16,464.96 ???

Sorry,
it's been a LONG time since I've used any advanced math.

You gotta do your sequence right.
The order of operations
exponentiation and root extraction
multiplication and division
addition and subtraction
(I did forget the parentheses.)

And 2.2uF is .0000022 (because it is micro)

So the formula for Hertz via capacitance and resistance is
1 / [(2Pi) x C x R]
So you do the multiplications first like 2xPi then x C then x R
Last you do the reciprocal or 1 / xxx.
Now you have the final answer.

 

[myersbw]

You can expound on what MDG5 said and also apply it to calculating the cathode bypass cap (or freq, or resistor), but then you should take into consideration the Ra (anode resistance of the given tube...12ax7, etc.) and the anode resistor...and the mu of the tube, too (i.e. 100 for 12ax7). Ra will vary with respect to the biasing circuit (B+, etc.) that the tube is expected to perform in.

So, to calculate the needed value of a cathode bypass cap... you'd use,

Rk= (Rplate + Ra)/(mu+1), where Rplate in that typical 100K in a Marshall preamp...Ra is the anode resistance of the tube based on bias circuit (roughly 60K-80K for a 12ax7 between 100-250V...I usually avg it at 70K)

Once you have Rk...that's the effective anode-to-gnd resistance that's parallel with the cathode resistor (Rcath).

So, let's say you wanted to calculate a cathode cap for a bypass freq down to 1Hz...

C-bypass = 1/(2 x pi x f x (Rk||Rcath)) , and substitute appropriately.

Write it out and then start looking at tube data sheets and you'll see why freq responses change drastically when subbing a 12ay7 for a 12ax7, etc. Do that math on your fave Marshall front end and you'll see where they were headed with certain bypass cap choices. (And, even that calc progression is really "roughing it")...that only gets you to a point, but doesn't tell the whole story. Get close...then sub some values and use your ear. (That's more enjoyable!)

But, you have to love numbers to dive into this. Most mistakes, as MDG5 alluded to, will come from folks forgetting to convert to Farads from uF or pF, etc.

We do something similar with a transistor and usually using norton's or thevenin's theorem to reduce the circuit complexity to idealize it for design.

Yes, I'm deviating from the OP, but bear with me. Take, for example, designing with a transistor and selecting it for a specific gain. If we design the biasing circuit (common voltage divider, etc.) around a specific transistor's spec...then we can get in trouble when replacing the transistor with "something close".

However, if the circuit bias is great enough that it supercedes (what we call.."swamping") a range of transistor spec variations...we can drop about any transistor close to spec in for a replacement and all works fine.

Not much different on the tube front. Where there are solid design parameters in place, you can drop a 12ax7 replacement in and get close to the same operation, save tonal variations based on tube construction. Design on very specific tubes for the desired outcome and you lock yourself in to that brand or manufacturer, etc.

 

[mickeydg5]

Wait a minute.
Rk is the cathode resistor. (in every manual and text I have ever seen)
And how is the cathode resistor in parallel with the Ra or Rp when it is clearly in series?

Rk = cathode resistance
Rg = grid load resistance
Rl = plate/anode load resistance
Ra = plate/anode resistance

The same formula I post above applies to a cathode resistor (Rk) bypass capacitor. It calculates the cutoff/shelf point for roll-off of the resistance/capacitance filter circuit.

Now if you want to calculate the amplification stage nominal frequency I can see using all that sort of criteria.

 

[66 Kicks]

2 x Pi = 6.28

1 / 6.28 x 2.2uF x 47k = 1.54Hz

You're not writing that correctly for single-line notation. Look at how JohnH wrote it. What you wrote equals 0.0165 .

An asterisk is frequently used in multiplication for clarity. 1 / (6.28 * 2.2uF * 47K) = 1.54Hz.