Quadrature oscillator question

Hello Jon,

Sorry about the delay in responding. My news server/browser seems to
be kinda hosed these days. Many messages don't even appear on my
server. What a pain!



You are correct in that there is a typo in my figure 5. (Good Catch)
The
inputs to the upper summer should both be positive. When this is done,
then
the matrix (given in the paper) agrees with the figure. And yes this
is the
same as your oscillator.

> To summarize, the equations I am using are:
>   sin(t) = sin(t-1)-(freq*cos(t-1))                  (1)
>   cos(t) = cos(t-1)+(freq*sin(t))                    (2)

C = C + f(S-fC)  -> C(1-f^2) + fS
S = S - fC           -> C(-f) + S

In matrix form this is

[  1-f^2        f   ]
[                      ]
[    -f           1   ]


Now since the upper left and the lower right elements are disimilar,
we know
immediately that this is not a quadrature osc. In the limit as f->0,
it will
tend to be quadrature. However since the upper right and lower left
elements
are negatives of each other, then this an equiamplitude osc. Also the
allowable conditions for osc require   -2 < 2-f^2 < 2 and the
determinant to
be one (of which it is). If you work out the matrix for the case where
I had
my typo, the determinant was not one so it couldn't be an osc.

Clay

Sorry about the typo - I lost the sign when doing the drawings in
photoshop.








"Jon Harris" <jon_harrisTIGER@hotmail.com> wrote in message news:<3f6a430b$1_3@newsfeed.slurp.net>...
> Clay,
> 
> After reading your paper, it looks like my oscillator doesn't exactly match
> any of the ones you list.  It is very similar to the Equi-amplitude,
> staggered update oscillator of Fig. 5, but it differs by a minus sign
> (assuming I'm interpretting this correctly.).  When I change the signs to
> make it match Fig. 5 it doesn't seem to oscillate at all.  So either I'm
> doing something wrong or maybe there is an error in that figure?
> 
> To summarize, the equations I am using are:
>   sin(t) = sin(t-1)-(freq*cos(t-1))                  (1)
>   cos(t) = cos(t-1)+(freq*sin(t))                    (2)
> This seems to work as expected.
> 
> When I change them to match Fig. 5 they become:
>   sin(t) = sin(t-1)-(freq*cos(t-1))                  (1)
>   cos(t) = cos(t-1)-(freq*sin(t))                    (2b)
> This doesn't seem to oscillate.
> 
> Any thoughts?
> 
> -Jon