Original file (930 × 778 pixels, file size: 148 KB, MIME type: image/png)
Summary
Main signals of a sigma-delta Pulse-Width Modulation (PWM).
The input signal is one period of sinusoidal waveform, the error signal, the integrated signal and the final Σ − Δ\Sigma -\Delta PWM signal.
Created using maxima: freq : 0.05; stepSize : 2e-2; stepLim : ceiling(1/(freq*stepSize)); hyst : 0.15; Xgrid : [0]; Xaxis : makelist(k*stepSize,k,0,stepLim)$ refSignal(t) := sin(2*%pi*freq*t); intSignal : [0]; errVal : [0];
/* this loop takes quite some time to execute */
pwmSignal : block(x:[1],for i:1 thru stepLim step 1 do block(
errVal : append(errVal,[refSignal(i*stepSize) - x[i]]),
intSignal : append(intSignal,[intSignal[i]+(errVal[i]*stepSize)]),
if (intSignal[i+1] > hyst) then
x : append(x, [1])
elseif(intSignal[i+1] < (-hyst)) then
x : append(x, [-1])
else
x : append(x, [x[i]])),
x
)$ Xgrid : block(x:[],for k:2 thru stepLim step 1 do
if(pwmSignal[k-1]#pwmSignal[k]) then
x : append(x,[Xaxis[k]]),
setify(x));
plot1 : gr2d(
user_preamble="set format x \"\";set bmargin 0;
set format y \"\"",
font="Times",grid=true,xtics=Xgrid,
points_joined=true,point_type=dot,
points(Xaxis,errVal),yrange=[-2,2],
color=green,explicit(refSignal(t),t,0,20),
ytics={-2,-1,0,1,2},ylabel="Ref. and Error"
)$ plot2 : gr2d(
user_preamble="set format x \"\"; set tmargin 0;
set bmargin 0",
font="Times",grid=true,xtics=Xgrid,
points_joined=true,point_type=dot,
color=magenta,points(Xaxis,intSignal),
yrange=[-.25,.25],ytics={-.2,0,.2},
ylabel="Integration"
)$ plot3 : gr2d(
user_preamble="set format x \"\";set bmargin 1.75;
set xlabel \"Time\" 0,1.5",
font="Times",grid=true,xtics=Xgrid,
points_joined=true,point_type=dot,
points(Xaxis,pwmSignal),yrange=[-1.25,1.25],
ytics={-1,0,1},ylabel="Sigma-Delta PWM"
)$ draw(terminal=svg,file_name="Sigma-delta PWM",
plot1,plot2,plot3);
Author Sigma_delta.png: Cyril BUTTAY derivative work: Krishnavedala (talk)
Licensing
   | This work is licensed under the Creative Commons Attribution-ShareAlike 2.5 License. |
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:00, 30 August 2023 | | 930 × 778 (148 KB) | Isidore (talk | contribs) | Main signals of a sigma-delta Pulse-Width Modulation (PWM). The input signal is one period of sinusoidal waveform, the error signal, the integrated signal and the final Σ − Δ\Sigma -\Delta PWM signal. Created using maxima: freq : 0.05; stepSize : 2e-2; stepLim : ceiling(1/(freq*stepSize)); hyst : 0.15; Xgrid : [0]; Xaxis : makelist(k*stepSize,k,0,stepLim)$ refSignal(t) := sin(2*%pi*freq*t); intSignal : [0]; errVal : [0]; →this loop takes quite some time to execute: pwmSignal : block... |
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