Introduction
Thisrapportisahand-intotheassignment ]3underthePh.D./Industrialcourse31359on
switch-modeaudiopowerampli?ers.Theassignmenttargetsmodellingthesmallsignalgainof
theonlyintendednonlinearcomponentincontinuousPWMmodulators,namelythecomparator.
Itisderivedin[1]thatthecomparatorinanypulse-widthmodulatedsystem,clockedorself-
oscillating,canbemodelledasaconstantgain.ThiscanbeexploitedtocalculatetoSTF(Signal
TransferFunction)andNTF(NoiseTransferFunction)ofaPWMmodulator,withoutdoing
timeconsumingsingle-tonebode-plotsimulationsinthetimedomain.
Itisshown[1]thattheconstantgainisdirectlyrelatedtotheslopeofthecarrieratzerocrossing
attheinputofthecomparatortogetherwiththeamplitudeofthesupplyvoltage.Thishasled
tothemathematicalproofthatthesimplestself-oscillatinghystereticampli?ershasanimproved
NTFcomparedtoit’striangular-clockedcounterpart.Theseresultarerecreatedinthisreport
togetherwiththeanalysisofphase-shiftself-oscillatingampli?ers(COM)andmoreadvanced
loopcon?gurationsthatincludesanoutput?lterandadditionalnoiseshaping.Inthecaseof
aphase-shiftmodulatedampli?er,theequivalentsmall-signalgainofthecomparatorcanbe
approximatedbyanalysisoftheopen-loopTF(TransferFunction)alone[2].
SinceaPWMmodulatorisinfactasampledsystem,iscanbemodelledasadiscretetime
system[1].Thisexplainsaliasingofnoisedownintheaudiobandandtheexistenceofimage
componentsaroundtheswitchingfrequencyandit’sharmonicswhichcanalsomovedowninto
theaudioband.InrelatingtopredictingtheSTFandNTFthereishowevernoneedsetupa
complicatedz-domainmodel.