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

.

.

.

.

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

_{0}² ∫ t

_{0} dt + U² ∫ 1

_{1} dt + a

_{2}² ∫ t

_{2} dt ] =

= 1 / R [ a

_{0}² t

_{0}³ / 3 + U² t

_{1} + a

_{2}² t

_{2}³ / 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} )