Treble Peaking formula?

Discussion in 'The Workbench' started by wakjob, Nov 30, 2019.

  1. wakjob

    wakjob Well-Known Member

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    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
     
  2. JohnH

    JohnH Well-Known Member

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    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
     
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  3. South Park

    South Park Well-Known Member

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    The cap has a cut off frequency independent of the resister.
     
  4. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    1 / (6.28 x 470pF x 470k) = 720.8Hz
     
    Last edited: Dec 3, 2019
  5. 66 Kicks

    66 Kicks New Member

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    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.
     
  6. 66 Kicks

    66 Kicks New Member

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    No it doesn't.
     
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  7. ampmadscientist

    ampmadscientist Well-Known Member

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    Start the reactor... Free Mars!
    :coffee:
     
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  8. JohnH

    JohnH Well-Known Member

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


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

    pedecamp Well-Known Member

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    Thats what I was gonna say......:ugh:
     
  10. South Park

    South Park Well-Known Member

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    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
     
  11. wakjob

    wakjob Well-Known Member

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    I love coffee too.
     
  12. wakjob

    wakjob Well-Known Member

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    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.
     
    Last edited: Dec 1, 2019
  13. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    2 x Pi = 6.28

    1 / (6.28 x 2.2uF x 47k) = 1.54Hz
     
    Last edited: Dec 3, 2019
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  14. wakjob

    wakjob Well-Known Member

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

    wakjob Well-Known Member

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    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.
     
  16. neikeel

    neikeel Well-Known Member

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    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:[​IMG]
    [​IMG]
     
    Last edited: Dec 2, 2019
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  17. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    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.
     
    Last edited: Dec 3, 2019
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  18. myersbw

    myersbw Well-Known Member

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    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.
     
    Last edited: Dec 3, 2019
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  19. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    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.
     
  20. 66 Kicks

    66 Kicks New Member

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    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.
     

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