Treble Peaking formula?

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

  1. 66 Kicks

    66 Kicks New Member

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    Upper case letters tend to designate components external to the tube while lower case letters tend to designate internal characteristics.
     
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  2. 66 Kicks

    66 Kicks New Member

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    The absence of a readily available subscript and superscript key is a little annoying on a forum that discusses mathematics.

    R(sub)g was the grid stopper resistor and R(sub)c was the grid leak resistor here in the 'States for a long time, but R(sub)g seems to be used for the grid leak more and more. The resistor that comprises the load on the plate was referred to as R(sub)c2 or R(sub)cf. The resistor from the plate to the power supply still seems to be called R(sub)p.

    The internal characteristics at your operating point can be found from the average characteristics graphs supplied by the manufacturer.

    You need to know the resistance of the parallel combination of R(sub)p and R(sub)cf in order to calculate the internal cathode resistance r(sub)k. R(sub)p' = [R(sub)p * R(sub)cf] / [R(sub)p + R(sub)cf]

    Now you can calculate r(sub)k. r(sub)k = [R(sub)p' + r(sub)p] / [mu + 1]

    There are two knees for the frequency response of a partially bypassed cathode. There is the knee where the gain decreases from the maximum gain and there is the knee where the gain increases from the minimum gain. Neither one of these knees necessarily have anything to do with -3dB.

    The frequency for the knee decreasing from the maximum gain is:

    f = [R(sub)k + r(sub)k] / [2 * pi * R(sub)k * r(sub)k * C(sub)k]

    The frequency for the knee increasing from the minimum gain is:

    f = 1 / [2 * pi * R(sub)k * C(sub)k]
     
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  3. myersbw

    myersbw Well-Known Member

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    Until the solidstate era when all that's taught is upper case is relative to DC values and lowercase usually denotes ac values. Much depends on the book you were taught from in regard to circuit analysis.

    Now for the important question...how many subs do you need before you get a discount at subway? :)

    The bottom line is that, if you understand the theory to begin with, the notation is secondary. You'll remember...and write it...as you were taught. Keep in mind there are many lurkers here that won't understand the variation of super and sub-scripts and where that comes into play.
     
  4. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    I forgot to place parentheses. Sorry.
     
    Last edited: Dec 3, 2019
  5. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    Sorry I forgot the parentheses which caused confusion. :confused: I edited my post. :erk:
     
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  6. myersbw

    myersbw Well-Known Member

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    I don't know, MDG5. I think this forum is "Workbench" and I'd expect anyone wanting to dig into design and it's associated formulas to have put the time in to education at this point. Sure, we take some individuals through some basic procedures, but it's a forum at its roots...not a lab where we're building and writing up lab reports. A strive to be accurate is merited, but I won't lose sleep over a bit of misquote in a media that doesn't support scientific or mathematical notation. It really isn't the intention here.

    That's one reason I'll comment with caution on anyone uneducated trying even some basic measurements. Because, as soon as the chassis is exposed, there's another analogy for a "1 inch death punch" besides Bruce Lee. I'll refuse to say,"You can do this." Because, just maybe they can't...yet!
     
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  7. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    Yes, I agree.
    Being use to the way I do and think about things through habit keeping it simple as possible I sometimes forget everyone does not think and do the same.
     
    Last edited: Dec 4, 2019
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  8. wakjob

    wakjob Well-Known Member

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    No problem brother...
    You've helped so many of us tech-deficient tinkers over the years I can let it slide.:h5:
     
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  9. 66 Kicks

    66 Kicks New Member

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    Fine. R(sub)p is upper case and it is the DC resistance of the plate resistor. r(sub)p is lower case and it is the AC resistance of the plate.
     
  10. South Park

    South Park Well-Known Member

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    When you are talking treble peaking thar is no formula . It is a power roll off . You need to put it on a graff chart. If you combine the resister and the tone cap what information are you getting
     
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  11. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    I agree with @myersbw in that various text and documentation indicate different callouts for components and characteristics.
    Though most text and manuals I use seem to be in line I have also noticed differences in eras and manufacturers using their own systems to describe particular circumstances.

    (no, I am not typing all those subscripts (sub) :))

    Also to note I have witnessed the use of Pb for plate and would think the use of Gc for grid would follow suit. Those designations are from specific use in olden days gone by relating to battery supplies as B for plate, C for control grid and A for filament.
     
  12. 66 Kicks

    66 Kicks New Member

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    Whereas there is a lot of variation in the subscripts (though they cluster around a small number), the convention for upper and lower case is remarkably consistent.

    It is actually faster for me to type "(sub)" than it is to track down the "sub" button, place the cursor, type the value, then place the cursor again. Especially after I get the pattern down.
     
  13. myersbw

    myersbw Well-Known Member

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    Careful! It's also a faster way to achieve carpal tunnel! :cheers:
     
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  14. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    Why doesn't the Ctrl+comma or Ctrl+= work (properly) on this site?
    Isn't that for subscript, maybe?
     
  15. neikeel

    neikeel Well-Known Member

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    Ah, so you mean the Bode plots I referred to on page 1. Useful charts from a Dutch-American a bit less well know than EVH!
     
  16. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    There most definitely is a formula for calculating cutoff, shelf, knee or whatever anyone wants to call it.
    By power roll off I take it you mean attenuation which is why we want to calculate the cutoff.
    It can be placed on a chart if you want but that does not make it any more real.
    The resistor and the capacitor form a band-stop type frequency filter. That is the information we are getting.
    Thar hugo.
     
    Last edited: Dec 6, 2019
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  17. myersbw

    myersbw Well-Known Member

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    I suppose I'd expand that maybe to say...you'll find no "one" particular formula as it takes a series of mathematical equations. For a treble peak or a bright cap, you can look at the RC network in that leg. However, if you want a bit more accuracy then you need to consider the impedance of the stage after, etc. The only times singular equations come into play is when there is, 1 - isolative impedances in devices where the preceding or successive stages are negligible (I was always taught a factor of 10x is close enough to ignore in low voltage circuits.)...or...2 - you string the needed equations together and "fill in the blanks" in a rather large equation...and, one created specifically for the device at hand. This is where a lot of reading & study come into play.

    Yet, sometimes the basic equations per a given leg of circuit are just enough to get you in the ballpark. Then, you can sub out values above and below...and manufactured types (carbon film, metal film, foil caps, etc.)...to get the tone you're seeking.
     
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  18. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    That second paragraph is much more simple and user oriented. :)
     
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  19. myersbw

    myersbw Well-Known Member

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    Agreed...especially after at least one bourbon on the rocks! ;)
     
  20. mickeydg5

    mickeydg5 Well-Known Member VIP Member

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    Most people reading will need at least a double on the rocks for your first paragraph up there. :D
     

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