[sdiy] Generating acyclic waveforms?

[Jerry Gray-Eskue]

Theta - the "phase angle"
Schaum's Outlines Electric Circuits 4th edition pg 103 6.3

a sinusoidal voltage v(t) is given by

	v(t)= Vo cos(wt+ phase angle)
----------


*2 to double the frequency. 2w I expect is a more standard representation.



-----Original Message-----
From: Ian Fritz [mailto:ijfritz at comcast.net]
Sent: Monday, March 22, 2010 4:27 PM
To: Jerry Gray-Eskue; Synth-diy at dropmix.xs4all.nl
Subject: Re: [sdiy] Generating acyclic waveforms?


At 03:01 PM 3/22/2010, Jerry Gray-Eskue wrote:

>I am not quite sure how to express this properly but here is a shot at it:
>
>A signal v(t) is periodic with period T if
>
>         v(t) = v(t+T) for all t
>         In other words the waveform is precisely repeating over the period
T.
>
>The Fundamental sine wave  v(t)= Vo cos(wt+ phase angle). ( or is that a
>cosine wave? )
>v(t) is +- around zero and the Sum of (v(t) over the period T) = 0.
>
>
>Now if we take the first harmonic its value is vh(t)= Vo cos(wt+ (phase
>angle * 2)).
>So if we vary the Harmonic thus  vh(t)= Vo cos(wt+ ((phase angle +
>SomeFunctionOf(v(t))* 2)).
>That is the harmonic is frequency shifted using the fundamental sine's v(t)
>as the control.
>Assuming this is a sine not cosine wave, we have the phase angel
accelerated
>during the first T/2 and decelerated during the second half with a net
>acceleration of zero.
>
>So the waveform repeats each T and
>
>Vo cos(wt+ ((phase angle + SomeFunctionOf(v(t))* 2)) = Vo cos(w(t+T)+
>((phase angle + SomeFunctionOf(v(t+T))* 2)).
>
>
>Clear as mud???


Right. Sorry, but it doesn't make any sense to me.  I don't see any
harmonics (2w, 3w, etc), so how is this relevant to the discussion at
all?  Why are you multiplying the "phase angle" (which it is not) by 2?  I
think you need to back up and study the fundamentals of waves and signals.

Ian