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Small-signal modelling of self
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2010-08-23
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Introduction
Thisrapportisahand-intotheassignment ]3underthePh.D./Industrialcourse31359on
switch-modeaudiopoweramplifiers.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-oscillatinghystereticamplifiershasanimproved
NTFcomparedtoit’striangular-clockedcounterpart.Theseresultarerecreatedinthisreport
togetherwiththeanalysisofphase-shiftself-oscillatingamplifiers(COM)andmoreadvanced
loopconfigurationsthatincludesanoutputfilterandadditionalnoiseshaping.Inthecaseof
aphase-shiftmodulatedamplifier,theequivalentsmall-signalgainofthecomparatorcanbe
approximatedbyanalysisoftheopen-loopTF(TransferFunction)alone[2].
SinceaPWMmodulatorisinfactasampledsystem,iscanbemodelledasadiscretetime
system[1].Thisexplainsaliasingofnoisedownintheaudiobandandtheexistenceofimage
componentsaroundtheswitchingfrequencyandit’sharmonicswhichcanalsomovedowninto
theaudioband.InrelatingtopredictingtheSTFandNTFthereishowevernoneedsetupa
complicatedz-domainmodel.
Thisrapportisahand-intotheassignment ]3underthePh.D./Industrialcourse31359on
switch-modeaudiopoweramplifiers.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-oscillatinghystereticamplifiershasanimproved
NTFcomparedtoit’striangular-clockedcounterpart.Theseresultarerecreatedinthisreport
togetherwiththeanalysisofphase-shiftself-oscillatingamplifiers(COM)andmoreadvanced
loopconfigurationsthatincludesanoutputfilterandadditionalnoiseshaping.Inthecaseof
aphase-shiftmodulatedamplifier,theequivalentsmall-signalgainofthecomparatorcanbe
approximatedbyanalysisoftheopen-loopTF(TransferFunction)alone[2].
SinceaPWMmodulatorisinfactasampledsystem,iscanbemodelledasadiscretetime
system[1].Thisexplainsaliasingofnoisedownintheaudiobandandtheexistenceofimage
componentsaroundtheswitchingfrequencyandit’sharmonicswhichcanalsomovedowninto
theaudioband.InrelatingtopredictingtheSTFandNTFthereishowevernoneedsetupa
complicatedz-domainmodel.
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