Hi,
In the code you sent you used a division for phase detection as far as I
can tell.
Yes, but it is the Matlab model code, so I dont care about division. In 'real
life' I multiply with the conjugate complex value. It has the same angle and
different length, but I normalize anyway.
And the 'atan' is always 'atan2', sure.
For a non-complex PLL I beat down to zero the angle of the phase discriminator.
In this complex PLL I beat down to zero the imaginary part of the quotient.
Another very interesting detail: The carrier I pll on is at 2400Hz, I have to
demodulate with a synched 1800Hz. This means that I have to find the complex
value which has 3/4 of the angle without atan/cos/sin, sqrt is ok.
This C-Code does the trick:
cpl4.re=sqrt((1.0+cpl3.re)/2.0f);
cpl4.im=sqrt((1.0-cpl3.re)/2.0f);
cpl5.re=sqrt((1.0+cpl4.re)/2.0f);
cpl5.im=sqrt((1.0-cpl4.re)/2.0f);
CMUL(cpl5,cpl5,cpl4);
CMUL(cpl4,cpl5,cpl3);
CROT(T3,cpl3);
much fun !
Math rulez !
Cheers
Detlef
Am 19.03.2021 um 13:23 schrieb Magnus Danielson:
Hi,
On 2021-03-18 13:59, Detlef Schuecker via time-nuts wrote:
Hi,
yes, got it, I think, thanks.
I calculate the complex quotient of the incoming complex signal and the
local complex oscillator. I feed the imaginary part of the quotient to the
PI controller, thus forcing it to zero. The local oscillator is updated by
multiplying it with ( real(quotient)+j*PIOutput ). Forcing the imaginary
part of the quotient to zero means that incoming signal and local
oscillator are in phase.
See Matlab code and the image.
No atan/cos/sin, just mere multiplication :))
In the code you sent you used a division for phase detection as far as I
can tell.
The modeling approach you used is different enough that it took some
time to decode it, and maybe I would have used a different set of
variable names, but that's more me than the model.
I often use a phase-accumulator / integrator to model (and synthesize)
in PLL simulations.
Anyway, good that you are on track. Once you have that basic I think you
can quickly enough vary the theme.
You could move over from imag to real and it would only change subtly.
Cheers,
Magnus
Thanks
Cheers
Detlef Schücker
DD4WV
clear
n=10000;
T1=0;
T2=0.01;
s0=exp(j*2*pi*200*(0:n-1)/n);
s1=zeros(1,n);
s2=zeros(1,n);
s3=zeros(1,n);
for(k=1:n)
s1(k)=(s0(k)/T2);
T1=T1+imag(s1(k))/4000;
s2(k)=0.03*imag(s1(k))+T1;
s3(k)=T2;
T2=T2*(real(s1(k))+j*s2(k));
end;
plot(1:n,real(s3),'b.-',1:n,real(s0),'r.-')
return
"Magnus Danielson" <[email protected]> schrieb am 17.03.2021 19:20:49:
Von: "Magnus Danielson" <[email protected]>
An: [email protected]
Datum: 17.03.2021 19:59
Betreff: [time-nuts] Re: Complex PLL
Hi,
On 2021-03-17 17:20, Detlef Schuecker via time-nuts wrote:
Hi time-nuts,
a PLL takes the phase difference of the incoming signal and the
synthesized signal and feeds that in a loop filter. The output of the
loop
filter is used to steer the local oscillator.
In my setup I have an incoming complex signal and my local oscillator
is
generating a complex signal as well. So calculation of the phase
difference is just the quotient of the incoming signal and the local
oscillator, it is a sampled system. I take the quotient, calculate the
angle using the atan function and then I feed it in the loop filter, a
PI
controller. The output of the loop filter is converted to a complex
phase
increment for the local oscillator with the sin and cos function.
Now I have to get rid of the atan, cos and sin functions.
I am looking for a loop filter which takes the quotient of the
incoming/synthesized signal as a complex value. The output of this
loop
filter should be the phase increment for the local oscillator. It
should
not use the angle of the complex value explicitly, as this will
involve
the atan/cos/sin functions.
Is someone aware of such a loop filter? I surfed through Gardners'
'Phaselock Techniques' but did not find a hint.
That book is full of hints. Costas loop is one. Actually, you could just
do complex multiplication and only use the real output (and thus remove
half the complex multiplication) and use that output of the
multiplication as input to normal PI-regulator, that will lock up and
achieve everything you want. You can then also remove the sine with a
squarewave. There is some benefits and losses in doing that, which may
or may not be relevant.
There is a richness of complex detectors to be found in GPS literature,
such as that of "Understanding GPS principles and applications" of
Kaplan and Hegarty. You can also look at "Phase-locked loop circuit
design" by Wolaver for additional inspiration. You end up finding that
Garners' book is actually very comprehensive if you only take time to
dwell into it.
Let me know if you need more hints.
Cheers and 73,
Magnus SA0MAD
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