much of a theoretical concept ...
fast schmitt trigger how to :: (uses v12.c from the SN7404's 'Spice alternate)
Dummy 14dB Pulse Amplifier in action
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this is amazing the i-net search can't allocate nor sine nor trapezoidal wave energy formulas ???
as much as i comprehend it'd go like ::
A(work J) = E(nrg J) = P(power W)dt = 1/R∫U²(t)dt
so for sine ::
E = U² / R ∫ Sin²( ωt ) dt = [ 1 - Cos α = 2 Sin ² ( α / 2 ) → { 1 - Cos ( 2 α ) } / 2 = Sin ² α ] =
= U² / ( 2R ) ∫ { 1 - Cos( 2ωt ) } dt = U² / ( 2R ) [ ∫ dt - ∫ Cos( 2ωt ) dt ] =
= [ screw this . . . ------------------------------- . . . , ok] =
= predicting : [ Sin ' ( 2ωt ) / 2ω = const. 1 / 2ω · outer fn. derivate Cos(arg.-s) · inner fn. drvt. 2ω =
= Cos ( 2ωt ) . . . - so - . . . ] = U² / ( 2R ) [ t - Sin( 2ωt ) / 2ω ] = [ for the half cycle ] =
= 2 · U² / ( 2 ... = U² / R [ τ / 4 - Sin{ 2 Pi / τ · ( τ / 4 ) } / ( 2 Pi / τ ) ] =
= U² / R [ τ / 4 - 2 τ · Sin( Pi / 2 ) / ( 4 Pi ) ] = U² / R · τ / 4 [ 1 - Sin( Pi / 2 ) / ( Pi / 2 ) ] =
= U² / R · τ / 4 [ 1 - 1 / ( Pi / 2 ) ] = . . . there's long time since i last did such - - check multiple times before you use any of it !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! . . .
. . . U C :: E = h ν ( in µ-world ) , but here the E became C / f , as for f → ∞ E = 0 it doesn't quite match what i remember about . . . however for ⌂t and P it'd be C · τ / t , IF τ = t THEN P = C for all frequencies likely applies for non relativistic world thus the E.Sine formula might after all be and what it was found here . . . might !!!
&Shit , i gess i see the error (always post error-check myself) :: for each quadrant wave we have a bit different result ::
= U² / R · τ / 4 [ 1 - 1 / ( Pi / 2 ) ] = as infact =
= U² / R · τ / 4 Σ
0,3 [ 1 - Sign( 1 - 2 (( t
LOWER div τ ) mod 2 )) / ( Pi / 2 ) ] = U² / R · τ / 4 =
= not exactly sure what i'm doing (a progressive exacting) // what we should like get is
average U of sine that is ∫ASin(t)dt = -ACos(t)=A at t=(0,Pi/2) for 2Pi 4A relative value for average deviation is thus 2A/Pi . . . as U²/R·τ/4 = (2U)²/R/f , hmm for P the f goes F'd and it's OK, but for NRG ...
oscillation is ± disturbance/deviation from system balance center ??? E = P·t = P/f . . . or dE * = Pdt = ...
... = [ if f = 1/τ = 1/(t/n) → 1/f = t/n → 1/f
const = dt/n * ] = . . . ??? P
MAX · f³(t) / (3f) , f → ∞ 1 / Pi² = 1/(±Arg(-1))² . . . 1/arg , i = exp(ln(i)) = exp(ln(1·e^(i · (2n ± 1)π))) = exp(i · (2n ± 1)π) , ln i = ±iπ , (±iπ)² = -π² , f(-x)=1/f(x) , . . . = this whole computation must be started by some other way (we are missing stuff here ... ) / halt // halt /// halt
& for trapezoid ::
E = 1 / R [ a
0² ∫ t
0 dt + U² ∫ 1
1 dt + a
2² ∫ t
2 dt ] =
= 1 / R [ a
0² t
0³ / 3 + U² t
1 + a
2² t
2³ / 3 ] = [ U = U
MAX = a
i t
i ]
= U² / R [ U / (3a
0) + t
1 + U / (3a
2) ] =
= U² / R [ t
0 / 3 + t
1 + t
2 / 3 ] = [t
0 -- rise time ; t
1 -- ON time ; t
2 -- fall time ]
P = E / ⌂t = E / ( t
0 + t
1 + t
2 )
