File:Delta PWM.png

Summary

Principle of the delta Pulse Width Modulation (PWM).

Created using maxima code: freq : 0.05; /* frequency of the reference signal */ hysteresis : 0.15; /* hysteresis of the delta pwm */ currentStep : 0.5; /* rate of increase (or decrease) in the output current */ RefSinSignal(t) := sin(2*%pi*freq*t); UpSineSignal(t) := RefSinSignal(t) + hysteresis; LoSineSignal(t) := RefSinSignal(t) - hysteresis; stepSize : 1e-2; /* step size for calculations */ stepLim : ceiling(1/(freq*stepSize)); /* final step */ myX : makelist(k*stepSize,k,0,stepLim)$ /* X axis points of evaluation */ increasing : 1; /* flag to identify if the current is increasing or decreasing */ currentY : [0]$ /* current signal (input to modulate) */ deltaSignal : [0]$ /* the delta-PWM signal (modulated) */ crossing : [0]$ /* rising and falling times of the PWM signal */ for j:1 thru stepLim do /* create the current waveform and its delta-PWM */

   block(
   if(increasing=1)
       then if(currentY[j]<=UpSineSignal(j*stepSize)) /* if current is increasing and below upper limit */
           then block(
               currentY : append(currentY,[currentY[j]+(currentStep*stepSize)]),
               deltaSignal : append(deltaSignal,[1]))
       else block(
           currentY : append(currentY,[currentY[j]-(currentStep*stepSize)]),
           deltaSignal : append(deltaSignal,[0]),
           crossing : append(crossing,[myX[j]]),
           increasing : 0)
   else
       if(currentY[j]>=LoSineSignal(j*stepSize)) /* if current is decreasing and above lower limit */
           then block(
               currentY : append(currentY,[currentY[j]-(currentStep*stepSize)]),
               deltaSignal : append(deltaSignal,[0]))
       else block(
           currentY : append(currentY,[currentY[j]+(currentStep*stepSize)]),
           deltaSignal : append(deltaSignal,[1]),
           crossing : append(crossing,[myX[j]]),
           increasing : 1)
   );

crossing : setify(crossing)$ /* convert list to set */

 /* Plot them */

load(draw); topPlot : gr2d(points_joined=true,point_type=dot,

   line_width=2,ytics={-1,0,1},font="Times",
   ylabel="Analog signals",font_size=15,
   color=red,key="Reference",explicit(RefSinSignal(x),x,0,20),
   color=green,key="Limits",explicit(UpSineSignal(x),x,0,20),
   key="",explicit(LoSineSignal(x),x,0,20),
   color=blue,key="Output",points(myX,currentY),
   xtics=crossing,grid=true,
   user_preamble="set format x ""; set tmargin 0; 
       set bmargin 0; set xlabel "" 0,1.5",
   title=""

)$ lowPlot : gr2d(points_joined=true,point_type=dot,

   line_width=2,ytics={0,1},font="Times",title="",
   ylabel="Delta-PWM signal",xlabel="Time",
   color=magenta,points(myX,deltaSignal),
   xtics=crossing,grid=true,yrange=[-.25,1.25],
   user_preamble="set format x ""; set tmargin 0;
       set bmargin 1.5"

)$ draw(terminal=svg,file_name="Delta PWM",

   topPlot,lowPlot);

Author Delta_PWM.png: Cyril BUTTAY derivative work: Krishnavedala (talk)

Licensing

This work is licensed under the Creative Commons Attribution-ShareAlike 2.5 License. https://creativecommons.org/licenses/by-sa/2.5/CC-BY-SA-2.5Creative Commons Attribution-ShareAlike 2.5truetrue