iiiinverter - · pdf fileiiiinverter technology ed ... fets have a number of advantages such...
TRANSCRIPT
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Ed Gurdjian amp Carol MaxwellMarch 2000
Please read Direct and Alternating Current and Inverter History articles prior to this articleThis is not meant to be a precise discussion for electrical engineers but rather an attempt to help
the majority of consumers have a better understanding of inverters
nverters have become an im-portant adjunct to the RVelectrical system allowing RV
owners to choose from a variety ofelectronic inverters varying in capac-ity technology and price In order tomake good purchase decisions con-sumers need to be aware of the differ-ent types of inverters available as wellas optional features
Inverter types can be broadly cate-gorized as mechanical or electronicThe mechanical type is the early mo-tor generator which consists of a DCmotor that powers an AC generatorThe output waveform is a sine wavewith low harmonic distortion Theoverall efficiency is between 50 and70 idle power consumption is highand surge capability is poor DC volt-age and current ripple caused by theproduction of AC is minimal Thistype of inverter is no longer used inRV applications but modern versionsare popular in utility trade and emer-gency applications
Electronic inverters can be furthercategorized by output waveformswitch type switching technology andfrequency In order to create alternat-ing current from direct current the
straight line 12 VDC is put through anoscillating circuit which creates 12volt alternating current Other controlcircuits regulate the frequency of theoscillating AC current to 60 cycles persecond The AC output may be squarewave modified square wave (modi-fied sine wave) multi-step sine waveor sine wave A special waveformdescribed as semi sine wave is alsopossible but it is not usually seen inRV applications
The earliest switches used to oscil-late 12 VDC were mechanical vibra-tors Essentially oscillating mechani-cal relays they were inefficient andunreliable but there were no alterna-tives until the development of semi-conductors (transistors) in the 1960sSilicon Controlled Rectifiers (SCRs)were the first solid state relays andfunctioned as electronic latching re-lays Next Darlington transistors wereused SCRs and Darlington transistorswere far more reliable than the me-chanical vibrator but had their owndisadvantages The Metal OxideSemi-conducting Field Effect Tran-sistor (MOSFET or FET) was the an-swer for switching problems FETshave a number of advantages such as
low on resistance and ability tohandle high current They are easy toconnect in a circuit and they workwell in parallel connections The par-allel connections increase the currentcarrying ability and lower the onresistance even more One manufac-turer describes them as ideal for me-dium power applications (1000 wattsto 5000 watts) Some inverters useIGBTs (Insulated Gate Bi-Polar Tran-sistors) These are newer high powerlow loss switching transistors
Switch TypesThere are two main types of
switching topologies Push-Pull and HBridge( Note the term topologyrefers to design layout or landscape)The Push-Pull (Figure 1) uses a trans-former with a center tap attached tothe battery positive Two transistorswitches connect the windings of thetransformer to the battery negativeThe transistors alternately close in aflip-flop pattern every 8 millisecondsThis changes the direction of the cur-rent 120 times per second and creates60-cycle alternating current This typeof circuit is suitable for a square waveinverter When used in a modified
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sine wave inverter a special trans-former with an additional winding toprovide off time shorting must beadded In addition an extra transistorswitch is needed to activate theshorting winding Heart Interfaceproducts do not use this tertiarywinding Off time is accomplished byshorting the primary winding Ac-cording to Heart this results in meas-urably higher efficiency when runningan inductive load than an inverter thatuses a separate tertiary winding Thedisadvantage is that the inverter hasless tolerance to transient voltagespikes or AC miswired to the output
The H Bridge design (Figure 2) hasfour transistors that turn off and on inpairs Since transistor pairs are used inseries current flows through two tran-sistors and power loss doubles Thisdesign was not used until high effi-ciency FETs were available Effi-ciency was further improved by usingFETs in parallel With improved tran-sistor efficiency the H bridge offeredsignificant advantages over the olderpush-pull design The transformerrequires only one primary windingand no off time shorting winding isneeded Off time shorting occurs byswitching on the bottom pair of tran-sistors The oscillating AC is createdby switching diagonal pairs Figure 3displays the H Bridge switching se-quence The H Bridge design is usedwith either FET or IGBT transistorsand in both high and low frequencymulti-step sine wave MSW and sinewave inverters
FrequencyWhen we describe inverters as us-
ing high or low frequency design weare referring to the switching fre-quency used to oscillate the 12 VDCLow frequency inverters create 60cycle AC and then step-up transform-ers create 120 VAC however lowfrequency transformers are large andheavy High frequency inverters os-cillate the DC at frequencies rangingfrom 25000 to 200000 Hz (cyclesper second) The transformers used tocreate 120 VAC in high frequencyapplications on the other hand aresmall and light weight
Like the starter-headlight examplein Direct and Alternating Currentan inverter draws high amperagefrom the battery bank however the
draw fluctuates between zero and themaximum current This fluctuationoccurs 120 times every second Anammeter can not reflect these rapidlypulsating changes and deceptivelyshows a steady draw The pulsatingdraw with high transient spikes causea corresponding voltage ripple (Fig-ure 4) in the DC electrical systemand can cause buzzing in audioequipment interference in radio andtelevision reception and interferencewith other electronic equipment
High transient current spikes andripple voltage also occur on the lowfrequency charger side and based onour testing appear to be significantfactors in the increased battery tem-perature elevations often encounteredduring charging Reliable high outputchargers with high frequency designare difficult to engineer Howeveronce accomplished the high fre-quency chargers offer the possibilityof ripple-free charging One of themajor advantages to the high fre-quency sine wave design is the pres-ence of a DC energy storage bus Thebus stores the high voltage DC used tocreate the 120 VAC and reduces rip-ple current and therefore the ripplevoltage from the DC system (Figure5)
Square Wave OutputAs mentioned previously square
wave inverters by Tripp Lite were thefirst electronic inverters (Figure 6)The mechanical vibrator used a pushpull circuit to oscillate the currentWhen SCR (Silicon Controlled Recti-fier) became available they replacedthe mechanical vibrators but still usedthe push pull design This design es-sentially consists of two transistorsthat alternately switch on and off(Figure 7) As one switch opens theother closes and the current throughthe transformer changes directionThis cycle continues and the result is asquare wave alternating current (Fig-ure 8) In a square wave inverter peakvoltage equals RMS voltage and var-ies directly with battery voltageTherefore when the battery voltage islow the peak AC output voltage andRMS voltage are also low This typeof inverter has high harmonic distor-tion (50) and marginal efficiency(60 to 80) A square wave inverteroften cannot properly power elec-
tronic equipment and motors tend torun hotter Surge capability rangesfrom poor to good depending uponother design features
Modified SineSquare Wave-LowFrequency
Low frequency design means thatthe switches operate at 60 cycles persecond (60 Hz) Present day invertersuse FETs (Field Effect Transistors) orIGBTs (Insulated Gate Bi-Polar Tran-sistor) in the oscillating circuit Forthe most part the H bridge design hasreplaced the push-pull method How-ever there are still some inverterscurrently manufactured with the push-pull design As mentioned previouslya push pull circuit uses an extra tran-sistor to short the transformer betweencurrent oscillations With the H bridgedesign transistors are switched off ina particular pattern to produce eachpart of the waveform The 12 voltmodified sine wave AC is then fed toa step up transformer which convertsit to 120 volts modified sine wave AC(Figure 9) An advantage of the MSWtype inverter is that the RMS (Root-Mean-Square) voltage can be regu-lated and maintained over a range ofbattery voltages by varying the dutycycle (Figures 10 amp 11) Note Fig-ure 11 is exaggerated to illustrate theconcept The peak voltage howeveris not regulated and varies with bat-tery voltage typically from 174 VACwhen battery voltage is 16 VDC to114 VAC when battery voltage is 105VDC For this reason MSW invertersmay not be able to supply full powerto devices that require peak voltagefor optimum performance like micro-wave ovens They have excellentsurge capabilities and efficiency (80to 95) Idle power consumption israted at low to medium Harmonicdistortion ranges from 15 to 35MSW inverters exhibit some incom-patibilities with various types of elec-tronic equipment Timers digitalclocks bread machines and recharge-able power tools or flashlights may beincompatible These appliances oftenuse modern switching type batterychargers and power supplies that onlydraw current at the peak of the sinewave making them susceptible tooverheating which results in prema-ture failure Modified sine waveinverters commonly used in moto-
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rhome applications range in outputfrom 1000 watts to 3600 watts Usinginverters of this size can quite easilydischarge house batteries so provi-sions for recharging must be avail-able
We still have some not-so-fondmemories of trying to recharge bat-teries with a ferroresonant converterA major advancement in the moto-rhome electrical system was the inte-gration of a high powered 3-stagecharger in the inverter package byHeart Interface Most of the othermajor manufacturers have now incor-porated similar chargers into theirproducts When grid voltage is pres-ent either from a generator or shorepower a transfer switch inside theinverter disconnects the units outputcircuit from the inverter output andconnects it to grid AC In additiongrid voltage is supplied to the trans-former A separate winding allows theoutput transformer to step down the120 VAC grid voltage to 16 VAC Itis then rectified to DC (12-16 volts)by using a part of the FETs as diodesControl circuitry provides automatic3-stage charging bulk absorptionand float plus a manual equalizingstage 3-stage charging can rapidlyrecharge house batteries These charg-ers range in output from 100 to 130amps Charging at 100 amps or morerequires 21 to 25 amps of AC powerso it is important to have 120 VACwith a peak voltage of 169 VAC Lowcampground voltage or a low capacitygenerator may not be able to supplythe power required for full outputcharging Unlike the old ferroresonantconverters even when DC loads arepresent these chargers can maintainbattery voltage either at thebulkabsorption set point or the floatset point whichever is in use
It is also important to use tempera-ture compensation when using modi-fied sine wave technology Low fre-quency MSW inverterchargers su-perimpose AC current fluctuations onthe DC wave and thereby produceripple effects We have found that thisvoltage and amperage distortion canproduce undesirable elevations inbattery temperature during high out-put charging Temperature controlcircuits reduce charger output in orderto limit temperature elevations but donot alter the fact that the temperature
rises with high output charging Per-sonally we would never use a modi-fied sine wave invertercharger with-out some method of determining bat-tery temperature and a way to controlcharging output to limit the tempera-ture elevation These inverters and thehigh output chargers are less expen-sive to build than sine wave units andto the consumer this translates tomore watts of power per dollar
Modified SquareSine WaveOutput-High Frequency
High frequency design means theswitches operate between 50000 and200000 cycles per second The trans-formers are much smaller and lighterin weight than the low frequencytransformers Therefore MSW invert-ers using high frequency designweigh a fraction of their low fre-quency counterparts
Battery voltage (12 VDC) is con-verted to high frequency alternatingcurrent using Pulse Width Modulation(PWM) which is then stepped up tohigh voltage AC (Figures 12 amp 13)The high voltage AC is then rectifiedto high voltage DC An H bridge withlow frequency transistor switchesproduces modified sine wave AC Offtime is done on the AC side of the Hbridge (Figures 14 A B amp C)
According to one of our sourcesthrough the years various high fre-quency MSW inverters have producedpeak AC outputs of 155 165 and 170VAC A major advantage of high fre-quency MSW inverters is the peakvoltage produced is not dependent onbattery voltage and remains constantthrough varying levels of battery dis-charge As discussed previously insquare wave output peak voltageequals RMS voltage In low frequencyMSW inverters the length of off timeis varied to regulate and maintainRMS voltage through varying levelsof peak voltage which varies withbattery voltage Because peak voltageis constant in high frequency designsthe off time is calculated to give 120VAC RMS The result is an inverterthat produces consistent peak AC andRMS voltage When inverter peakvoltage is 155 or 165 microwave ov-ens which depend on peak voltagewill operate at reduced power for aselected setting as compared to oper-
ating on shore power However thisreduced level does remain constant forvarious states of battery discharge
Total harmonic distortion is 15 to35 typical efficiency is 85-90and idle power consumption is me-dium Surge capability ranges frompoor to good but generally is lowerthan low frequency MSW invertersThe zero volt transistors on the Hbridge are not isolated from the ACline and are susceptible to voltagespikes There is also a possibility ofTV and radio interference because ofthe high voltage switcher
Semi-Sine Wave OutputAdding a ferroresonant transformer
to a MSW inverter makes a semi-sinewaveform (Figure 15) The harmonicdistortion remains at 15 to 35Typical efficiency is 50 to 70 idlepower consumption is high and surgecapability is poor This type inverter isnot commonly used in RV applica-tions
Sine Wave OutputWe believe that sine wave inverters
will become the inverters of choicefor RV applications As more sophis-ticated and sensitive electronicequipment is added to the chassisthere will be a greater need to reduceelectronic noise on the DC circuits Itis conceivable that some of the prob-lems with the early electronic enginecontrols for diesel engines were asso-ciated with interference frominverterchargers These problemswere seen in RV applications and notseen in trucks Currently automotivemanufacturers are moving toward a36-42 volt system One of the reasonscited is to reduce the effects of elec-tronic noise which can interfere withvarious engine and chassis computercontrols As more sophisticatedequipment is added to the house sideof the RV the seamless performanceand excellent load compatibility of asine wave inverter will become moredesirable to the consumer
Each technology used to make asine wave inverter has advantages anddisadvantages The three main tech-nologies are high frequency multi-step low frequency and hybrid whichis a combination of the high and lowfrequency designs Statpower andExeltech use the high frequency to-
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pology The Exeltech unit is aninverter only and does not have acharger Trace Engineering usesmulti-step low frequency designVanner Inc and Heart Interface usethe hybrid approach To date onlyTrace Engineering and Statpower sinewave products have been used exten-sively in the RV market Both arecombined with high output 3-stagechargers
High Frequency with DC energyBus (Statpower)
The AC waveform of a sine waveinverter is nearly identical to thewaveform of grid AC so incompatibleloads are rare(Figure 16) It has thepotential to offer better frequency andpeak voltage control than a generatorA reliable source from the utility in-dustry tells us that even utility powernow looks worse than that comingfrom a good sine wave inverter Autilitys Total Harmonic Distortionfrequently exceeds 3 Generallysine wave units are more expensive toproduce High charger output is notonly more difficult to achieve butmore expensive to manufacture
Figure 17 shows a block diagramand schematic for the high frequencytechnology Direct Current from thebattery is oscillated through the centertap of a high frequency transformer(s)using unidirectional switching tran-sistors The switch frequency is ap-proximately 120000 to 200000 cy-cles per second This creates an alter-nating voltage that can be stepped upby the high frequency transformers toapproximately 215 volts-slightlyhigher than the peak voltages that willlater be seen on the AC side The al-ternating voltage is then rectified us-ing an H bridge of unidirectionalswitching transistors back to DCThere is now approximately 215 voltsstored in the DC bus energy storagesection The bus serves three pur-poses It stores DC power irrespec-tive of the state of charge of the bat-tery bank it allows continuoustransfer of ripple-free power to andfrom the battery bank and itshields the DC system from the rip-ple effect created by the productionof 60 cycle AC The next stage con-verts the 215 VDC to sinusoidal ACusing a second H bridge of unidi-rectional switching transistors This
creates oscillations at twice the ACfrequency (120 Hz for 60 cycle AC)Pulse Width Modulated (PWM)switching is used to switch the fourtransistors in the H bridge Diago-nally opposite switches function asswitch pairs each pair being turned onor off simultaneously Whenever thecircuit is active one pair is on whilethe other is off The result of thePWM switching is AC produced at 40kHz and at 60 Hz The switchingtechnique for the DC-AC H bridgeis difficult to explain It involves acarrier frequency of 40 kHz and areference frequency of 60 Hz Theresulting AC waveform is sinusoidaland has major components at both 60Hz and 40 kHz A simple low passfilter network is used to remove the 40kHz component leaving only 60 Hzsinusoidal wave AC available at theAC terminals of the inverter In thehigh frequency design 12 VDC iselevated to 215 VDC and then in-verted to 60 Hz AC This high fre-quency design coupled with a DCbus uniquely separates the AC fromthe DC system Voltage and currentripple in the DC system is markedlyreduced from that seen in low fre-quency designs Total harmonic dis-tortion ranges from 1 to 5 typicalefficiency is 84 to 88 and surgecapability is in the medium rangeAlthough this inverter does not offerthe higher efficiency and surge capa-bility seen in low frequency invertersthe Statpower Prosine series has cap-tured the elusive high output 3-stagecharging using high frequency designIn this product reduced efficiency onthe inverter side is compensated by acharger that has a power factor ap-proaching 1 This attribute makes theStatpower charger significantly moreefficient than typical chargers with apower factor of 07 and elevates thecombined efficiency of thisinvertercharger package Since highfrequency transformers are light-weight the Statpower Prosine seriesinverterchargers weigh just 32pounds
Multi-Step Sine Wave Output(Trace Engineering)
To combine the efficiency andsurge capabilities of the low fre-quency design with high output 3-stage charging in a sine wave pack-
age Trace Engineering developed amulti-step design (Figure 18) TheSW series from Trace Engineeringsignificantly alters the modified sinewave technology By strict definitionthis multi-step inverter is not a truesine wave However with 34 to 52stair-steps per cycle the output wave-form approaches a sine wave Thenumber of steps increases as batteryvoltage becomes lower or power re-quirements become higher Trace cre-ates this waveform by using three lowfrequency transformers with the sec-ondary windings wired in series (Fig-ure 19) This allows for 27 possiblevoltages Power MOSFETs (MetalOxide Field Effect Transistors) switchthe primary windings Harmonic dis-tortion of this waveform is typicallyonly 3 to 5 The typical efficiencyis 85 to 95 the idle power con-sumption is low and the surge capa-bility is good
This sinusoidal waveform has sig-nificantly fewer incompatibilitieswhen compared to the modified sinewave This model has a sophisticatedgeneratorshore power transfer relaywhich allows a seamless transfer be-tween the inverter and AC sourcesThere is an automatic generator startfeature and three extra user program-mable voltage controlled relays foraccessories (eg to control solarpanel charging) When using the auto-generator start feature consumersshould be aware of the perils of start-ing a generator indoors in regard tothe possibility of carbon monoxideintoxication and the need for propersafety interlocks so there is no dangerof electrocution Two units can bestacked to provide 240 volt serviceThis product is primarily intended forremote off-grid housing but is fre-quently used in bus conversions The12 volt model is finding its way intohigh end Class A motorhomes
When AC from shore power or agenerator is present the transformersreduce the AC voltage and rectify thelow voltage AC to DC which is thenavailable for charging the batteriesThe integrated 3-stage charger is tem-perature compensated is more effi-cient and has lower AC current dis-tortion when compared to the modi-fied sine wave units This technologyincreases the power factor and lowersthe AC current distortion in the charge
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mode Large pulsating currents remainat the DC port in both inverter andcharger modes Since the low fre-quency transformers are heavy theTrace SW series inverterchargerweighs approximately 105 pounds
Hybrid High-Low Frequency 12 VDC from the battery is
switched using a high frequency tran-sistor H bridge to 12 V sine wave ACIt is then stepped up to 120 volts sinewave AC using a step-up transformerThe 120 volts sine wave AC is used tosupply AC loads (Figure 20) Thismethod yields the high efficiencysurge capabilities and high output 3-stage charging of the low frequencydesign plus the low harmonic distor-tion of the high frequency designTHD ranges from 1 to 5 effi-ciency is 85 to 90 reliability andsurge capability are good and there ismedium idle power consumptionBrutus and IT Series by VannerKenetech from Trace Engineeringand Heart Interface use this approach
CONCLUSIONInverter-chargers must fit the needs
of the individual RV owner Needsrange from none or little to an abso-lute necessity for high capacity pureoutput units Sine wave inverter-chargers may cost up to 50 more
than MSW inverter-chargers but forour application we believe the addedperformance more than justifies theadded expense When we contemplateinvesting in a new inverter-chargerwe first estimate our present and fu-ture needs If future plans includetrading up to a new RV we wouldseriously consider investing in aninverter-charger with a higher capac-ity than currently needed and thenplan to move the inverter to the newRV We would then order the new RVinverter ready but without a stan-dard model installed A manufac-turers willingness to comply with thisplan would be a determining factor inwhich RV to purchase
Most inverterchargers used in RVapplications offer standard or optionalremote controls The remote unitsprovide a means to activatedeactivatethe invertercharger from within theRV They also offer monitor and dis-play features Most models offer someform of a search feature that allowsthe inverter to sleep and therebyreduce power consumption in standbymode It then wakes up when it de-tects a load Almost all chargers havepower sharing although the protocolvaries among manufacturers Generi-cally power sharing limits the amountof power used by the charger so somepower is available for other AC loads
This is a valuable feature when shorepower is limited to 30 amps or lessAcknowledgments
We accept all responsibility forany errors contained in this articleThe subject is complicated and theprocess of accumulating informationand data has been long and difficultThe manufacturers and individualslisted below have contributed equip-ment technical data illustrationsand advice We are grateful to all Ifwe have omitted any company orindividual from this list we are sin-cerely sorry Any omission is purelyunintentional
Ample Power Inc David SmeadExeltechHeart Interface Inc Warren StokesMike Hirata Smitty OvittRedi-line IncStatpower Inc Konrad MauchDerek Pettingale Fred DennertTrace Engineering Mike McCoyGary Baxter Ray Barbee Craig LangEldon WhartonTripp Lite IncVanner Inc Greg Woeste
For more information visit the websites of the contributing companiesTrace Engineering maintains manytechnical articles on their web site intheir Document Depot
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Figure 2
Figure 2 Courtesy of Trace Engineering
Figure 1 Courtesy of Trace Engineering
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Figure 4 Courtesy of Trace Engineering
Figure 3 Courtesy of Trace Engineering
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Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
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Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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sine wave inverter a special trans-former with an additional winding toprovide off time shorting must beadded In addition an extra transistorswitch is needed to activate theshorting winding Heart Interfaceproducts do not use this tertiarywinding Off time is accomplished byshorting the primary winding Ac-cording to Heart this results in meas-urably higher efficiency when runningan inductive load than an inverter thatuses a separate tertiary winding Thedisadvantage is that the inverter hasless tolerance to transient voltagespikes or AC miswired to the output
The H Bridge design (Figure 2) hasfour transistors that turn off and on inpairs Since transistor pairs are used inseries current flows through two tran-sistors and power loss doubles Thisdesign was not used until high effi-ciency FETs were available Effi-ciency was further improved by usingFETs in parallel With improved tran-sistor efficiency the H bridge offeredsignificant advantages over the olderpush-pull design The transformerrequires only one primary windingand no off time shorting winding isneeded Off time shorting occurs byswitching on the bottom pair of tran-sistors The oscillating AC is createdby switching diagonal pairs Figure 3displays the H Bridge switching se-quence The H Bridge design is usedwith either FET or IGBT transistorsand in both high and low frequencymulti-step sine wave MSW and sinewave inverters
FrequencyWhen we describe inverters as us-
ing high or low frequency design weare referring to the switching fre-quency used to oscillate the 12 VDCLow frequency inverters create 60cycle AC and then step-up transform-ers create 120 VAC however lowfrequency transformers are large andheavy High frequency inverters os-cillate the DC at frequencies rangingfrom 25000 to 200000 Hz (cyclesper second) The transformers used tocreate 120 VAC in high frequencyapplications on the other hand aresmall and light weight
Like the starter-headlight examplein Direct and Alternating Currentan inverter draws high amperagefrom the battery bank however the
draw fluctuates between zero and themaximum current This fluctuationoccurs 120 times every second Anammeter can not reflect these rapidlypulsating changes and deceptivelyshows a steady draw The pulsatingdraw with high transient spikes causea corresponding voltage ripple (Fig-ure 4) in the DC electrical systemand can cause buzzing in audioequipment interference in radio andtelevision reception and interferencewith other electronic equipment
High transient current spikes andripple voltage also occur on the lowfrequency charger side and based onour testing appear to be significantfactors in the increased battery tem-perature elevations often encounteredduring charging Reliable high outputchargers with high frequency designare difficult to engineer Howeveronce accomplished the high fre-quency chargers offer the possibilityof ripple-free charging One of themajor advantages to the high fre-quency sine wave design is the pres-ence of a DC energy storage bus Thebus stores the high voltage DC used tocreate the 120 VAC and reduces rip-ple current and therefore the ripplevoltage from the DC system (Figure5)
Square Wave OutputAs mentioned previously square
wave inverters by Tripp Lite were thefirst electronic inverters (Figure 6)The mechanical vibrator used a pushpull circuit to oscillate the currentWhen SCR (Silicon Controlled Recti-fier) became available they replacedthe mechanical vibrators but still usedthe push pull design This design es-sentially consists of two transistorsthat alternately switch on and off(Figure 7) As one switch opens theother closes and the current throughthe transformer changes directionThis cycle continues and the result is asquare wave alternating current (Fig-ure 8) In a square wave inverter peakvoltage equals RMS voltage and var-ies directly with battery voltageTherefore when the battery voltage islow the peak AC output voltage andRMS voltage are also low This typeof inverter has high harmonic distor-tion (50) and marginal efficiency(60 to 80) A square wave inverteroften cannot properly power elec-
tronic equipment and motors tend torun hotter Surge capability rangesfrom poor to good depending uponother design features
Modified SineSquare Wave-LowFrequency
Low frequency design means thatthe switches operate at 60 cycles persecond (60 Hz) Present day invertersuse FETs (Field Effect Transistors) orIGBTs (Insulated Gate Bi-Polar Tran-sistor) in the oscillating circuit Forthe most part the H bridge design hasreplaced the push-pull method How-ever there are still some inverterscurrently manufactured with the push-pull design As mentioned previouslya push pull circuit uses an extra tran-sistor to short the transformer betweencurrent oscillations With the H bridgedesign transistors are switched off ina particular pattern to produce eachpart of the waveform The 12 voltmodified sine wave AC is then fed toa step up transformer which convertsit to 120 volts modified sine wave AC(Figure 9) An advantage of the MSWtype inverter is that the RMS (Root-Mean-Square) voltage can be regu-lated and maintained over a range ofbattery voltages by varying the dutycycle (Figures 10 amp 11) Note Fig-ure 11 is exaggerated to illustrate theconcept The peak voltage howeveris not regulated and varies with bat-tery voltage typically from 174 VACwhen battery voltage is 16 VDC to114 VAC when battery voltage is 105VDC For this reason MSW invertersmay not be able to supply full powerto devices that require peak voltagefor optimum performance like micro-wave ovens They have excellentsurge capabilities and efficiency (80to 95) Idle power consumption israted at low to medium Harmonicdistortion ranges from 15 to 35MSW inverters exhibit some incom-patibilities with various types of elec-tronic equipment Timers digitalclocks bread machines and recharge-able power tools or flashlights may beincompatible These appliances oftenuse modern switching type batterychargers and power supplies that onlydraw current at the peak of the sinewave making them susceptible tooverheating which results in prema-ture failure Modified sine waveinverters commonly used in moto-
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rhome applications range in outputfrom 1000 watts to 3600 watts Usinginverters of this size can quite easilydischarge house batteries so provi-sions for recharging must be avail-able
We still have some not-so-fondmemories of trying to recharge bat-teries with a ferroresonant converterA major advancement in the moto-rhome electrical system was the inte-gration of a high powered 3-stagecharger in the inverter package byHeart Interface Most of the othermajor manufacturers have now incor-porated similar chargers into theirproducts When grid voltage is pres-ent either from a generator or shorepower a transfer switch inside theinverter disconnects the units outputcircuit from the inverter output andconnects it to grid AC In additiongrid voltage is supplied to the trans-former A separate winding allows theoutput transformer to step down the120 VAC grid voltage to 16 VAC Itis then rectified to DC (12-16 volts)by using a part of the FETs as diodesControl circuitry provides automatic3-stage charging bulk absorptionand float plus a manual equalizingstage 3-stage charging can rapidlyrecharge house batteries These charg-ers range in output from 100 to 130amps Charging at 100 amps or morerequires 21 to 25 amps of AC powerso it is important to have 120 VACwith a peak voltage of 169 VAC Lowcampground voltage or a low capacitygenerator may not be able to supplythe power required for full outputcharging Unlike the old ferroresonantconverters even when DC loads arepresent these chargers can maintainbattery voltage either at thebulkabsorption set point or the floatset point whichever is in use
It is also important to use tempera-ture compensation when using modi-fied sine wave technology Low fre-quency MSW inverterchargers su-perimpose AC current fluctuations onthe DC wave and thereby produceripple effects We have found that thisvoltage and amperage distortion canproduce undesirable elevations inbattery temperature during high out-put charging Temperature controlcircuits reduce charger output in orderto limit temperature elevations but donot alter the fact that the temperature
rises with high output charging Per-sonally we would never use a modi-fied sine wave invertercharger with-out some method of determining bat-tery temperature and a way to controlcharging output to limit the tempera-ture elevation These inverters and thehigh output chargers are less expen-sive to build than sine wave units andto the consumer this translates tomore watts of power per dollar
Modified SquareSine WaveOutput-High Frequency
High frequency design means theswitches operate between 50000 and200000 cycles per second The trans-formers are much smaller and lighterin weight than the low frequencytransformers Therefore MSW invert-ers using high frequency designweigh a fraction of their low fre-quency counterparts
Battery voltage (12 VDC) is con-verted to high frequency alternatingcurrent using Pulse Width Modulation(PWM) which is then stepped up tohigh voltage AC (Figures 12 amp 13)The high voltage AC is then rectifiedto high voltage DC An H bridge withlow frequency transistor switchesproduces modified sine wave AC Offtime is done on the AC side of the Hbridge (Figures 14 A B amp C)
According to one of our sourcesthrough the years various high fre-quency MSW inverters have producedpeak AC outputs of 155 165 and 170VAC A major advantage of high fre-quency MSW inverters is the peakvoltage produced is not dependent onbattery voltage and remains constantthrough varying levels of battery dis-charge As discussed previously insquare wave output peak voltageequals RMS voltage In low frequencyMSW inverters the length of off timeis varied to regulate and maintainRMS voltage through varying levelsof peak voltage which varies withbattery voltage Because peak voltageis constant in high frequency designsthe off time is calculated to give 120VAC RMS The result is an inverterthat produces consistent peak AC andRMS voltage When inverter peakvoltage is 155 or 165 microwave ov-ens which depend on peak voltagewill operate at reduced power for aselected setting as compared to oper-
ating on shore power However thisreduced level does remain constant forvarious states of battery discharge
Total harmonic distortion is 15 to35 typical efficiency is 85-90and idle power consumption is me-dium Surge capability ranges frompoor to good but generally is lowerthan low frequency MSW invertersThe zero volt transistors on the Hbridge are not isolated from the ACline and are susceptible to voltagespikes There is also a possibility ofTV and radio interference because ofthe high voltage switcher
Semi-Sine Wave OutputAdding a ferroresonant transformer
to a MSW inverter makes a semi-sinewaveform (Figure 15) The harmonicdistortion remains at 15 to 35Typical efficiency is 50 to 70 idlepower consumption is high and surgecapability is poor This type inverter isnot commonly used in RV applica-tions
Sine Wave OutputWe believe that sine wave inverters
will become the inverters of choicefor RV applications As more sophis-ticated and sensitive electronicequipment is added to the chassisthere will be a greater need to reduceelectronic noise on the DC circuits Itis conceivable that some of the prob-lems with the early electronic enginecontrols for diesel engines were asso-ciated with interference frominverterchargers These problemswere seen in RV applications and notseen in trucks Currently automotivemanufacturers are moving toward a36-42 volt system One of the reasonscited is to reduce the effects of elec-tronic noise which can interfere withvarious engine and chassis computercontrols As more sophisticatedequipment is added to the house sideof the RV the seamless performanceand excellent load compatibility of asine wave inverter will become moredesirable to the consumer
Each technology used to make asine wave inverter has advantages anddisadvantages The three main tech-nologies are high frequency multi-step low frequency and hybrid whichis a combination of the high and lowfrequency designs Statpower andExeltech use the high frequency to-
wwwrvtechstopcom 4
pology The Exeltech unit is aninverter only and does not have acharger Trace Engineering usesmulti-step low frequency designVanner Inc and Heart Interface usethe hybrid approach To date onlyTrace Engineering and Statpower sinewave products have been used exten-sively in the RV market Both arecombined with high output 3-stagechargers
High Frequency with DC energyBus (Statpower)
The AC waveform of a sine waveinverter is nearly identical to thewaveform of grid AC so incompatibleloads are rare(Figure 16) It has thepotential to offer better frequency andpeak voltage control than a generatorA reliable source from the utility in-dustry tells us that even utility powernow looks worse than that comingfrom a good sine wave inverter Autilitys Total Harmonic Distortionfrequently exceeds 3 Generallysine wave units are more expensive toproduce High charger output is notonly more difficult to achieve butmore expensive to manufacture
Figure 17 shows a block diagramand schematic for the high frequencytechnology Direct Current from thebattery is oscillated through the centertap of a high frequency transformer(s)using unidirectional switching tran-sistors The switch frequency is ap-proximately 120000 to 200000 cy-cles per second This creates an alter-nating voltage that can be stepped upby the high frequency transformers toapproximately 215 volts-slightlyhigher than the peak voltages that willlater be seen on the AC side The al-ternating voltage is then rectified us-ing an H bridge of unidirectionalswitching transistors back to DCThere is now approximately 215 voltsstored in the DC bus energy storagesection The bus serves three pur-poses It stores DC power irrespec-tive of the state of charge of the bat-tery bank it allows continuoustransfer of ripple-free power to andfrom the battery bank and itshields the DC system from the rip-ple effect created by the productionof 60 cycle AC The next stage con-verts the 215 VDC to sinusoidal ACusing a second H bridge of unidi-rectional switching transistors This
creates oscillations at twice the ACfrequency (120 Hz for 60 cycle AC)Pulse Width Modulated (PWM)switching is used to switch the fourtransistors in the H bridge Diago-nally opposite switches function asswitch pairs each pair being turned onor off simultaneously Whenever thecircuit is active one pair is on whilethe other is off The result of thePWM switching is AC produced at 40kHz and at 60 Hz The switchingtechnique for the DC-AC H bridgeis difficult to explain It involves acarrier frequency of 40 kHz and areference frequency of 60 Hz Theresulting AC waveform is sinusoidaland has major components at both 60Hz and 40 kHz A simple low passfilter network is used to remove the 40kHz component leaving only 60 Hzsinusoidal wave AC available at theAC terminals of the inverter In thehigh frequency design 12 VDC iselevated to 215 VDC and then in-verted to 60 Hz AC This high fre-quency design coupled with a DCbus uniquely separates the AC fromthe DC system Voltage and currentripple in the DC system is markedlyreduced from that seen in low fre-quency designs Total harmonic dis-tortion ranges from 1 to 5 typicalefficiency is 84 to 88 and surgecapability is in the medium rangeAlthough this inverter does not offerthe higher efficiency and surge capa-bility seen in low frequency invertersthe Statpower Prosine series has cap-tured the elusive high output 3-stagecharging using high frequency designIn this product reduced efficiency onthe inverter side is compensated by acharger that has a power factor ap-proaching 1 This attribute makes theStatpower charger significantly moreefficient than typical chargers with apower factor of 07 and elevates thecombined efficiency of thisinvertercharger package Since highfrequency transformers are light-weight the Statpower Prosine seriesinverterchargers weigh just 32pounds
Multi-Step Sine Wave Output(Trace Engineering)
To combine the efficiency andsurge capabilities of the low fre-quency design with high output 3-stage charging in a sine wave pack-
age Trace Engineering developed amulti-step design (Figure 18) TheSW series from Trace Engineeringsignificantly alters the modified sinewave technology By strict definitionthis multi-step inverter is not a truesine wave However with 34 to 52stair-steps per cycle the output wave-form approaches a sine wave Thenumber of steps increases as batteryvoltage becomes lower or power re-quirements become higher Trace cre-ates this waveform by using three lowfrequency transformers with the sec-ondary windings wired in series (Fig-ure 19) This allows for 27 possiblevoltages Power MOSFETs (MetalOxide Field Effect Transistors) switchthe primary windings Harmonic dis-tortion of this waveform is typicallyonly 3 to 5 The typical efficiencyis 85 to 95 the idle power con-sumption is low and the surge capa-bility is good
This sinusoidal waveform has sig-nificantly fewer incompatibilitieswhen compared to the modified sinewave This model has a sophisticatedgeneratorshore power transfer relaywhich allows a seamless transfer be-tween the inverter and AC sourcesThere is an automatic generator startfeature and three extra user program-mable voltage controlled relays foraccessories (eg to control solarpanel charging) When using the auto-generator start feature consumersshould be aware of the perils of start-ing a generator indoors in regard tothe possibility of carbon monoxideintoxication and the need for propersafety interlocks so there is no dangerof electrocution Two units can bestacked to provide 240 volt serviceThis product is primarily intended forremote off-grid housing but is fre-quently used in bus conversions The12 volt model is finding its way intohigh end Class A motorhomes
When AC from shore power or agenerator is present the transformersreduce the AC voltage and rectify thelow voltage AC to DC which is thenavailable for charging the batteriesThe integrated 3-stage charger is tem-perature compensated is more effi-cient and has lower AC current dis-tortion when compared to the modi-fied sine wave units This technologyincreases the power factor and lowersthe AC current distortion in the charge
wwwrvtechstopcom 5
mode Large pulsating currents remainat the DC port in both inverter andcharger modes Since the low fre-quency transformers are heavy theTrace SW series inverterchargerweighs approximately 105 pounds
Hybrid High-Low Frequency 12 VDC from the battery is
switched using a high frequency tran-sistor H bridge to 12 V sine wave ACIt is then stepped up to 120 volts sinewave AC using a step-up transformerThe 120 volts sine wave AC is used tosupply AC loads (Figure 20) Thismethod yields the high efficiencysurge capabilities and high output 3-stage charging of the low frequencydesign plus the low harmonic distor-tion of the high frequency designTHD ranges from 1 to 5 effi-ciency is 85 to 90 reliability andsurge capability are good and there ismedium idle power consumptionBrutus and IT Series by VannerKenetech from Trace Engineeringand Heart Interface use this approach
CONCLUSIONInverter-chargers must fit the needs
of the individual RV owner Needsrange from none or little to an abso-lute necessity for high capacity pureoutput units Sine wave inverter-chargers may cost up to 50 more
than MSW inverter-chargers but forour application we believe the addedperformance more than justifies theadded expense When we contemplateinvesting in a new inverter-chargerwe first estimate our present and fu-ture needs If future plans includetrading up to a new RV we wouldseriously consider investing in aninverter-charger with a higher capac-ity than currently needed and thenplan to move the inverter to the newRV We would then order the new RVinverter ready but without a stan-dard model installed A manufac-turers willingness to comply with thisplan would be a determining factor inwhich RV to purchase
Most inverterchargers used in RVapplications offer standard or optionalremote controls The remote unitsprovide a means to activatedeactivatethe invertercharger from within theRV They also offer monitor and dis-play features Most models offer someform of a search feature that allowsthe inverter to sleep and therebyreduce power consumption in standbymode It then wakes up when it de-tects a load Almost all chargers havepower sharing although the protocolvaries among manufacturers Generi-cally power sharing limits the amountof power used by the charger so somepower is available for other AC loads
This is a valuable feature when shorepower is limited to 30 amps or lessAcknowledgments
We accept all responsibility forany errors contained in this articleThe subject is complicated and theprocess of accumulating informationand data has been long and difficultThe manufacturers and individualslisted below have contributed equip-ment technical data illustrationsand advice We are grateful to all Ifwe have omitted any company orindividual from this list we are sin-cerely sorry Any omission is purelyunintentional
Ample Power Inc David SmeadExeltechHeart Interface Inc Warren StokesMike Hirata Smitty OvittRedi-line IncStatpower Inc Konrad MauchDerek Pettingale Fred DennertTrace Engineering Mike McCoyGary Baxter Ray Barbee Craig LangEldon WhartonTripp Lite IncVanner Inc Greg Woeste
For more information visit the websites of the contributing companiesTrace Engineering maintains manytechnical articles on their web site intheir Document Depot
wwwrvtechstopcom 6
Figure 2
Figure 2 Courtesy of Trace Engineering
Figure 1 Courtesy of Trace Engineering
wwwrvtechstopcom 7
Figure 4 Courtesy of Trace Engineering
Figure 3 Courtesy of Trace Engineering
wwwrvtechstopcom 8
Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
wwwrvtechstopcom 9
Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
wwwrvtechstopcom 10
Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
wwwrvtechstopcom 11
Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
wwwrvtechstopcom 12
Figure 13 Courtesy of Trace Engineering
wwwrvtechstopcom 13
Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
wwwrvtechstopcom 14
Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
wwwrvtechstopcom 15
Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
wwwrvtechstopcom 16
Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
wwwrvtechstopcom 3
rhome applications range in outputfrom 1000 watts to 3600 watts Usinginverters of this size can quite easilydischarge house batteries so provi-sions for recharging must be avail-able
We still have some not-so-fondmemories of trying to recharge bat-teries with a ferroresonant converterA major advancement in the moto-rhome electrical system was the inte-gration of a high powered 3-stagecharger in the inverter package byHeart Interface Most of the othermajor manufacturers have now incor-porated similar chargers into theirproducts When grid voltage is pres-ent either from a generator or shorepower a transfer switch inside theinverter disconnects the units outputcircuit from the inverter output andconnects it to grid AC In additiongrid voltage is supplied to the trans-former A separate winding allows theoutput transformer to step down the120 VAC grid voltage to 16 VAC Itis then rectified to DC (12-16 volts)by using a part of the FETs as diodesControl circuitry provides automatic3-stage charging bulk absorptionand float plus a manual equalizingstage 3-stage charging can rapidlyrecharge house batteries These charg-ers range in output from 100 to 130amps Charging at 100 amps or morerequires 21 to 25 amps of AC powerso it is important to have 120 VACwith a peak voltage of 169 VAC Lowcampground voltage or a low capacitygenerator may not be able to supplythe power required for full outputcharging Unlike the old ferroresonantconverters even when DC loads arepresent these chargers can maintainbattery voltage either at thebulkabsorption set point or the floatset point whichever is in use
It is also important to use tempera-ture compensation when using modi-fied sine wave technology Low fre-quency MSW inverterchargers su-perimpose AC current fluctuations onthe DC wave and thereby produceripple effects We have found that thisvoltage and amperage distortion canproduce undesirable elevations inbattery temperature during high out-put charging Temperature controlcircuits reduce charger output in orderto limit temperature elevations but donot alter the fact that the temperature
rises with high output charging Per-sonally we would never use a modi-fied sine wave invertercharger with-out some method of determining bat-tery temperature and a way to controlcharging output to limit the tempera-ture elevation These inverters and thehigh output chargers are less expen-sive to build than sine wave units andto the consumer this translates tomore watts of power per dollar
Modified SquareSine WaveOutput-High Frequency
High frequency design means theswitches operate between 50000 and200000 cycles per second The trans-formers are much smaller and lighterin weight than the low frequencytransformers Therefore MSW invert-ers using high frequency designweigh a fraction of their low fre-quency counterparts
Battery voltage (12 VDC) is con-verted to high frequency alternatingcurrent using Pulse Width Modulation(PWM) which is then stepped up tohigh voltage AC (Figures 12 amp 13)The high voltage AC is then rectifiedto high voltage DC An H bridge withlow frequency transistor switchesproduces modified sine wave AC Offtime is done on the AC side of the Hbridge (Figures 14 A B amp C)
According to one of our sourcesthrough the years various high fre-quency MSW inverters have producedpeak AC outputs of 155 165 and 170VAC A major advantage of high fre-quency MSW inverters is the peakvoltage produced is not dependent onbattery voltage and remains constantthrough varying levels of battery dis-charge As discussed previously insquare wave output peak voltageequals RMS voltage In low frequencyMSW inverters the length of off timeis varied to regulate and maintainRMS voltage through varying levelsof peak voltage which varies withbattery voltage Because peak voltageis constant in high frequency designsthe off time is calculated to give 120VAC RMS The result is an inverterthat produces consistent peak AC andRMS voltage When inverter peakvoltage is 155 or 165 microwave ov-ens which depend on peak voltagewill operate at reduced power for aselected setting as compared to oper-
ating on shore power However thisreduced level does remain constant forvarious states of battery discharge
Total harmonic distortion is 15 to35 typical efficiency is 85-90and idle power consumption is me-dium Surge capability ranges frompoor to good but generally is lowerthan low frequency MSW invertersThe zero volt transistors on the Hbridge are not isolated from the ACline and are susceptible to voltagespikes There is also a possibility ofTV and radio interference because ofthe high voltage switcher
Semi-Sine Wave OutputAdding a ferroresonant transformer
to a MSW inverter makes a semi-sinewaveform (Figure 15) The harmonicdistortion remains at 15 to 35Typical efficiency is 50 to 70 idlepower consumption is high and surgecapability is poor This type inverter isnot commonly used in RV applica-tions
Sine Wave OutputWe believe that sine wave inverters
will become the inverters of choicefor RV applications As more sophis-ticated and sensitive electronicequipment is added to the chassisthere will be a greater need to reduceelectronic noise on the DC circuits Itis conceivable that some of the prob-lems with the early electronic enginecontrols for diesel engines were asso-ciated with interference frominverterchargers These problemswere seen in RV applications and notseen in trucks Currently automotivemanufacturers are moving toward a36-42 volt system One of the reasonscited is to reduce the effects of elec-tronic noise which can interfere withvarious engine and chassis computercontrols As more sophisticatedequipment is added to the house sideof the RV the seamless performanceand excellent load compatibility of asine wave inverter will become moredesirable to the consumer
Each technology used to make asine wave inverter has advantages anddisadvantages The three main tech-nologies are high frequency multi-step low frequency and hybrid whichis a combination of the high and lowfrequency designs Statpower andExeltech use the high frequency to-
wwwrvtechstopcom 4
pology The Exeltech unit is aninverter only and does not have acharger Trace Engineering usesmulti-step low frequency designVanner Inc and Heart Interface usethe hybrid approach To date onlyTrace Engineering and Statpower sinewave products have been used exten-sively in the RV market Both arecombined with high output 3-stagechargers
High Frequency with DC energyBus (Statpower)
The AC waveform of a sine waveinverter is nearly identical to thewaveform of grid AC so incompatibleloads are rare(Figure 16) It has thepotential to offer better frequency andpeak voltage control than a generatorA reliable source from the utility in-dustry tells us that even utility powernow looks worse than that comingfrom a good sine wave inverter Autilitys Total Harmonic Distortionfrequently exceeds 3 Generallysine wave units are more expensive toproduce High charger output is notonly more difficult to achieve butmore expensive to manufacture
Figure 17 shows a block diagramand schematic for the high frequencytechnology Direct Current from thebattery is oscillated through the centertap of a high frequency transformer(s)using unidirectional switching tran-sistors The switch frequency is ap-proximately 120000 to 200000 cy-cles per second This creates an alter-nating voltage that can be stepped upby the high frequency transformers toapproximately 215 volts-slightlyhigher than the peak voltages that willlater be seen on the AC side The al-ternating voltage is then rectified us-ing an H bridge of unidirectionalswitching transistors back to DCThere is now approximately 215 voltsstored in the DC bus energy storagesection The bus serves three pur-poses It stores DC power irrespec-tive of the state of charge of the bat-tery bank it allows continuoustransfer of ripple-free power to andfrom the battery bank and itshields the DC system from the rip-ple effect created by the productionof 60 cycle AC The next stage con-verts the 215 VDC to sinusoidal ACusing a second H bridge of unidi-rectional switching transistors This
creates oscillations at twice the ACfrequency (120 Hz for 60 cycle AC)Pulse Width Modulated (PWM)switching is used to switch the fourtransistors in the H bridge Diago-nally opposite switches function asswitch pairs each pair being turned onor off simultaneously Whenever thecircuit is active one pair is on whilethe other is off The result of thePWM switching is AC produced at 40kHz and at 60 Hz The switchingtechnique for the DC-AC H bridgeis difficult to explain It involves acarrier frequency of 40 kHz and areference frequency of 60 Hz Theresulting AC waveform is sinusoidaland has major components at both 60Hz and 40 kHz A simple low passfilter network is used to remove the 40kHz component leaving only 60 Hzsinusoidal wave AC available at theAC terminals of the inverter In thehigh frequency design 12 VDC iselevated to 215 VDC and then in-verted to 60 Hz AC This high fre-quency design coupled with a DCbus uniquely separates the AC fromthe DC system Voltage and currentripple in the DC system is markedlyreduced from that seen in low fre-quency designs Total harmonic dis-tortion ranges from 1 to 5 typicalefficiency is 84 to 88 and surgecapability is in the medium rangeAlthough this inverter does not offerthe higher efficiency and surge capa-bility seen in low frequency invertersthe Statpower Prosine series has cap-tured the elusive high output 3-stagecharging using high frequency designIn this product reduced efficiency onthe inverter side is compensated by acharger that has a power factor ap-proaching 1 This attribute makes theStatpower charger significantly moreefficient than typical chargers with apower factor of 07 and elevates thecombined efficiency of thisinvertercharger package Since highfrequency transformers are light-weight the Statpower Prosine seriesinverterchargers weigh just 32pounds
Multi-Step Sine Wave Output(Trace Engineering)
To combine the efficiency andsurge capabilities of the low fre-quency design with high output 3-stage charging in a sine wave pack-
age Trace Engineering developed amulti-step design (Figure 18) TheSW series from Trace Engineeringsignificantly alters the modified sinewave technology By strict definitionthis multi-step inverter is not a truesine wave However with 34 to 52stair-steps per cycle the output wave-form approaches a sine wave Thenumber of steps increases as batteryvoltage becomes lower or power re-quirements become higher Trace cre-ates this waveform by using three lowfrequency transformers with the sec-ondary windings wired in series (Fig-ure 19) This allows for 27 possiblevoltages Power MOSFETs (MetalOxide Field Effect Transistors) switchthe primary windings Harmonic dis-tortion of this waveform is typicallyonly 3 to 5 The typical efficiencyis 85 to 95 the idle power con-sumption is low and the surge capa-bility is good
This sinusoidal waveform has sig-nificantly fewer incompatibilitieswhen compared to the modified sinewave This model has a sophisticatedgeneratorshore power transfer relaywhich allows a seamless transfer be-tween the inverter and AC sourcesThere is an automatic generator startfeature and three extra user program-mable voltage controlled relays foraccessories (eg to control solarpanel charging) When using the auto-generator start feature consumersshould be aware of the perils of start-ing a generator indoors in regard tothe possibility of carbon monoxideintoxication and the need for propersafety interlocks so there is no dangerof electrocution Two units can bestacked to provide 240 volt serviceThis product is primarily intended forremote off-grid housing but is fre-quently used in bus conversions The12 volt model is finding its way intohigh end Class A motorhomes
When AC from shore power or agenerator is present the transformersreduce the AC voltage and rectify thelow voltage AC to DC which is thenavailable for charging the batteriesThe integrated 3-stage charger is tem-perature compensated is more effi-cient and has lower AC current dis-tortion when compared to the modi-fied sine wave units This technologyincreases the power factor and lowersthe AC current distortion in the charge
wwwrvtechstopcom 5
mode Large pulsating currents remainat the DC port in both inverter andcharger modes Since the low fre-quency transformers are heavy theTrace SW series inverterchargerweighs approximately 105 pounds
Hybrid High-Low Frequency 12 VDC from the battery is
switched using a high frequency tran-sistor H bridge to 12 V sine wave ACIt is then stepped up to 120 volts sinewave AC using a step-up transformerThe 120 volts sine wave AC is used tosupply AC loads (Figure 20) Thismethod yields the high efficiencysurge capabilities and high output 3-stage charging of the low frequencydesign plus the low harmonic distor-tion of the high frequency designTHD ranges from 1 to 5 effi-ciency is 85 to 90 reliability andsurge capability are good and there ismedium idle power consumptionBrutus and IT Series by VannerKenetech from Trace Engineeringand Heart Interface use this approach
CONCLUSIONInverter-chargers must fit the needs
of the individual RV owner Needsrange from none or little to an abso-lute necessity for high capacity pureoutput units Sine wave inverter-chargers may cost up to 50 more
than MSW inverter-chargers but forour application we believe the addedperformance more than justifies theadded expense When we contemplateinvesting in a new inverter-chargerwe first estimate our present and fu-ture needs If future plans includetrading up to a new RV we wouldseriously consider investing in aninverter-charger with a higher capac-ity than currently needed and thenplan to move the inverter to the newRV We would then order the new RVinverter ready but without a stan-dard model installed A manufac-turers willingness to comply with thisplan would be a determining factor inwhich RV to purchase
Most inverterchargers used in RVapplications offer standard or optionalremote controls The remote unitsprovide a means to activatedeactivatethe invertercharger from within theRV They also offer monitor and dis-play features Most models offer someform of a search feature that allowsthe inverter to sleep and therebyreduce power consumption in standbymode It then wakes up when it de-tects a load Almost all chargers havepower sharing although the protocolvaries among manufacturers Generi-cally power sharing limits the amountof power used by the charger so somepower is available for other AC loads
This is a valuable feature when shorepower is limited to 30 amps or lessAcknowledgments
We accept all responsibility forany errors contained in this articleThe subject is complicated and theprocess of accumulating informationand data has been long and difficultThe manufacturers and individualslisted below have contributed equip-ment technical data illustrationsand advice We are grateful to all Ifwe have omitted any company orindividual from this list we are sin-cerely sorry Any omission is purelyunintentional
Ample Power Inc David SmeadExeltechHeart Interface Inc Warren StokesMike Hirata Smitty OvittRedi-line IncStatpower Inc Konrad MauchDerek Pettingale Fred DennertTrace Engineering Mike McCoyGary Baxter Ray Barbee Craig LangEldon WhartonTripp Lite IncVanner Inc Greg Woeste
For more information visit the websites of the contributing companiesTrace Engineering maintains manytechnical articles on their web site intheir Document Depot
wwwrvtechstopcom 6
Figure 2
Figure 2 Courtesy of Trace Engineering
Figure 1 Courtesy of Trace Engineering
wwwrvtechstopcom 7
Figure 4 Courtesy of Trace Engineering
Figure 3 Courtesy of Trace Engineering
wwwrvtechstopcom 8
Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
wwwrvtechstopcom 9
Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
wwwrvtechstopcom 10
Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
wwwrvtechstopcom 11
Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
wwwrvtechstopcom 12
Figure 13 Courtesy of Trace Engineering
wwwrvtechstopcom 13
Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
wwwrvtechstopcom 14
Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
wwwrvtechstopcom 15
Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
wwwrvtechstopcom 16
Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
wwwrvtechstopcom 4
pology The Exeltech unit is aninverter only and does not have acharger Trace Engineering usesmulti-step low frequency designVanner Inc and Heart Interface usethe hybrid approach To date onlyTrace Engineering and Statpower sinewave products have been used exten-sively in the RV market Both arecombined with high output 3-stagechargers
High Frequency with DC energyBus (Statpower)
The AC waveform of a sine waveinverter is nearly identical to thewaveform of grid AC so incompatibleloads are rare(Figure 16) It has thepotential to offer better frequency andpeak voltage control than a generatorA reliable source from the utility in-dustry tells us that even utility powernow looks worse than that comingfrom a good sine wave inverter Autilitys Total Harmonic Distortionfrequently exceeds 3 Generallysine wave units are more expensive toproduce High charger output is notonly more difficult to achieve butmore expensive to manufacture
Figure 17 shows a block diagramand schematic for the high frequencytechnology Direct Current from thebattery is oscillated through the centertap of a high frequency transformer(s)using unidirectional switching tran-sistors The switch frequency is ap-proximately 120000 to 200000 cy-cles per second This creates an alter-nating voltage that can be stepped upby the high frequency transformers toapproximately 215 volts-slightlyhigher than the peak voltages that willlater be seen on the AC side The al-ternating voltage is then rectified us-ing an H bridge of unidirectionalswitching transistors back to DCThere is now approximately 215 voltsstored in the DC bus energy storagesection The bus serves three pur-poses It stores DC power irrespec-tive of the state of charge of the bat-tery bank it allows continuoustransfer of ripple-free power to andfrom the battery bank and itshields the DC system from the rip-ple effect created by the productionof 60 cycle AC The next stage con-verts the 215 VDC to sinusoidal ACusing a second H bridge of unidi-rectional switching transistors This
creates oscillations at twice the ACfrequency (120 Hz for 60 cycle AC)Pulse Width Modulated (PWM)switching is used to switch the fourtransistors in the H bridge Diago-nally opposite switches function asswitch pairs each pair being turned onor off simultaneously Whenever thecircuit is active one pair is on whilethe other is off The result of thePWM switching is AC produced at 40kHz and at 60 Hz The switchingtechnique for the DC-AC H bridgeis difficult to explain It involves acarrier frequency of 40 kHz and areference frequency of 60 Hz Theresulting AC waveform is sinusoidaland has major components at both 60Hz and 40 kHz A simple low passfilter network is used to remove the 40kHz component leaving only 60 Hzsinusoidal wave AC available at theAC terminals of the inverter In thehigh frequency design 12 VDC iselevated to 215 VDC and then in-verted to 60 Hz AC This high fre-quency design coupled with a DCbus uniquely separates the AC fromthe DC system Voltage and currentripple in the DC system is markedlyreduced from that seen in low fre-quency designs Total harmonic dis-tortion ranges from 1 to 5 typicalefficiency is 84 to 88 and surgecapability is in the medium rangeAlthough this inverter does not offerthe higher efficiency and surge capa-bility seen in low frequency invertersthe Statpower Prosine series has cap-tured the elusive high output 3-stagecharging using high frequency designIn this product reduced efficiency onthe inverter side is compensated by acharger that has a power factor ap-proaching 1 This attribute makes theStatpower charger significantly moreefficient than typical chargers with apower factor of 07 and elevates thecombined efficiency of thisinvertercharger package Since highfrequency transformers are light-weight the Statpower Prosine seriesinverterchargers weigh just 32pounds
Multi-Step Sine Wave Output(Trace Engineering)
To combine the efficiency andsurge capabilities of the low fre-quency design with high output 3-stage charging in a sine wave pack-
age Trace Engineering developed amulti-step design (Figure 18) TheSW series from Trace Engineeringsignificantly alters the modified sinewave technology By strict definitionthis multi-step inverter is not a truesine wave However with 34 to 52stair-steps per cycle the output wave-form approaches a sine wave Thenumber of steps increases as batteryvoltage becomes lower or power re-quirements become higher Trace cre-ates this waveform by using three lowfrequency transformers with the sec-ondary windings wired in series (Fig-ure 19) This allows for 27 possiblevoltages Power MOSFETs (MetalOxide Field Effect Transistors) switchthe primary windings Harmonic dis-tortion of this waveform is typicallyonly 3 to 5 The typical efficiencyis 85 to 95 the idle power con-sumption is low and the surge capa-bility is good
This sinusoidal waveform has sig-nificantly fewer incompatibilitieswhen compared to the modified sinewave This model has a sophisticatedgeneratorshore power transfer relaywhich allows a seamless transfer be-tween the inverter and AC sourcesThere is an automatic generator startfeature and three extra user program-mable voltage controlled relays foraccessories (eg to control solarpanel charging) When using the auto-generator start feature consumersshould be aware of the perils of start-ing a generator indoors in regard tothe possibility of carbon monoxideintoxication and the need for propersafety interlocks so there is no dangerof electrocution Two units can bestacked to provide 240 volt serviceThis product is primarily intended forremote off-grid housing but is fre-quently used in bus conversions The12 volt model is finding its way intohigh end Class A motorhomes
When AC from shore power or agenerator is present the transformersreduce the AC voltage and rectify thelow voltage AC to DC which is thenavailable for charging the batteriesThe integrated 3-stage charger is tem-perature compensated is more effi-cient and has lower AC current dis-tortion when compared to the modi-fied sine wave units This technologyincreases the power factor and lowersthe AC current distortion in the charge
wwwrvtechstopcom 5
mode Large pulsating currents remainat the DC port in both inverter andcharger modes Since the low fre-quency transformers are heavy theTrace SW series inverterchargerweighs approximately 105 pounds
Hybrid High-Low Frequency 12 VDC from the battery is
switched using a high frequency tran-sistor H bridge to 12 V sine wave ACIt is then stepped up to 120 volts sinewave AC using a step-up transformerThe 120 volts sine wave AC is used tosupply AC loads (Figure 20) Thismethod yields the high efficiencysurge capabilities and high output 3-stage charging of the low frequencydesign plus the low harmonic distor-tion of the high frequency designTHD ranges from 1 to 5 effi-ciency is 85 to 90 reliability andsurge capability are good and there ismedium idle power consumptionBrutus and IT Series by VannerKenetech from Trace Engineeringand Heart Interface use this approach
CONCLUSIONInverter-chargers must fit the needs
of the individual RV owner Needsrange from none or little to an abso-lute necessity for high capacity pureoutput units Sine wave inverter-chargers may cost up to 50 more
than MSW inverter-chargers but forour application we believe the addedperformance more than justifies theadded expense When we contemplateinvesting in a new inverter-chargerwe first estimate our present and fu-ture needs If future plans includetrading up to a new RV we wouldseriously consider investing in aninverter-charger with a higher capac-ity than currently needed and thenplan to move the inverter to the newRV We would then order the new RVinverter ready but without a stan-dard model installed A manufac-turers willingness to comply with thisplan would be a determining factor inwhich RV to purchase
Most inverterchargers used in RVapplications offer standard or optionalremote controls The remote unitsprovide a means to activatedeactivatethe invertercharger from within theRV They also offer monitor and dis-play features Most models offer someform of a search feature that allowsthe inverter to sleep and therebyreduce power consumption in standbymode It then wakes up when it de-tects a load Almost all chargers havepower sharing although the protocolvaries among manufacturers Generi-cally power sharing limits the amountof power used by the charger so somepower is available for other AC loads
This is a valuable feature when shorepower is limited to 30 amps or lessAcknowledgments
We accept all responsibility forany errors contained in this articleThe subject is complicated and theprocess of accumulating informationand data has been long and difficultThe manufacturers and individualslisted below have contributed equip-ment technical data illustrationsand advice We are grateful to all Ifwe have omitted any company orindividual from this list we are sin-cerely sorry Any omission is purelyunintentional
Ample Power Inc David SmeadExeltechHeart Interface Inc Warren StokesMike Hirata Smitty OvittRedi-line IncStatpower Inc Konrad MauchDerek Pettingale Fred DennertTrace Engineering Mike McCoyGary Baxter Ray Barbee Craig LangEldon WhartonTripp Lite IncVanner Inc Greg Woeste
For more information visit the websites of the contributing companiesTrace Engineering maintains manytechnical articles on their web site intheir Document Depot
wwwrvtechstopcom 6
Figure 2
Figure 2 Courtesy of Trace Engineering
Figure 1 Courtesy of Trace Engineering
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Figure 4 Courtesy of Trace Engineering
Figure 3 Courtesy of Trace Engineering
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Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
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Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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mode Large pulsating currents remainat the DC port in both inverter andcharger modes Since the low fre-quency transformers are heavy theTrace SW series inverterchargerweighs approximately 105 pounds
Hybrid High-Low Frequency 12 VDC from the battery is
switched using a high frequency tran-sistor H bridge to 12 V sine wave ACIt is then stepped up to 120 volts sinewave AC using a step-up transformerThe 120 volts sine wave AC is used tosupply AC loads (Figure 20) Thismethod yields the high efficiencysurge capabilities and high output 3-stage charging of the low frequencydesign plus the low harmonic distor-tion of the high frequency designTHD ranges from 1 to 5 effi-ciency is 85 to 90 reliability andsurge capability are good and there ismedium idle power consumptionBrutus and IT Series by VannerKenetech from Trace Engineeringand Heart Interface use this approach
CONCLUSIONInverter-chargers must fit the needs
of the individual RV owner Needsrange from none or little to an abso-lute necessity for high capacity pureoutput units Sine wave inverter-chargers may cost up to 50 more
than MSW inverter-chargers but forour application we believe the addedperformance more than justifies theadded expense When we contemplateinvesting in a new inverter-chargerwe first estimate our present and fu-ture needs If future plans includetrading up to a new RV we wouldseriously consider investing in aninverter-charger with a higher capac-ity than currently needed and thenplan to move the inverter to the newRV We would then order the new RVinverter ready but without a stan-dard model installed A manufac-turers willingness to comply with thisplan would be a determining factor inwhich RV to purchase
Most inverterchargers used in RVapplications offer standard or optionalremote controls The remote unitsprovide a means to activatedeactivatethe invertercharger from within theRV They also offer monitor and dis-play features Most models offer someform of a search feature that allowsthe inverter to sleep and therebyreduce power consumption in standbymode It then wakes up when it de-tects a load Almost all chargers havepower sharing although the protocolvaries among manufacturers Generi-cally power sharing limits the amountof power used by the charger so somepower is available for other AC loads
This is a valuable feature when shorepower is limited to 30 amps or lessAcknowledgments
We accept all responsibility forany errors contained in this articleThe subject is complicated and theprocess of accumulating informationand data has been long and difficultThe manufacturers and individualslisted below have contributed equip-ment technical data illustrationsand advice We are grateful to all Ifwe have omitted any company orindividual from this list we are sin-cerely sorry Any omission is purelyunintentional
Ample Power Inc David SmeadExeltechHeart Interface Inc Warren StokesMike Hirata Smitty OvittRedi-line IncStatpower Inc Konrad MauchDerek Pettingale Fred DennertTrace Engineering Mike McCoyGary Baxter Ray Barbee Craig LangEldon WhartonTripp Lite IncVanner Inc Greg Woeste
For more information visit the websites of the contributing companiesTrace Engineering maintains manytechnical articles on their web site intheir Document Depot
wwwrvtechstopcom 6
Figure 2
Figure 2 Courtesy of Trace Engineering
Figure 1 Courtesy of Trace Engineering
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Figure 4 Courtesy of Trace Engineering
Figure 3 Courtesy of Trace Engineering
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Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
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Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 2
Figure 2 Courtesy of Trace Engineering
Figure 1 Courtesy of Trace Engineering
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Figure 4 Courtesy of Trace Engineering
Figure 3 Courtesy of Trace Engineering
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Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
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Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 4 Courtesy of Trace Engineering
Figure 3 Courtesy of Trace Engineering
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Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
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Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 6 Courtesy of Trace Engineering
Figure 5 Courtesy of Statpower
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Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 7 Courtesy of Trace Engineering
Figure 8 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 9 Courtesy of Trace Engineering
Figure 10 Courtesy of Statpower
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 11 Courtesy of Trace Engineering
Figure 12 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 13 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 14 B
Figure 14 C
Figure 14 A B amp C Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 15 Courtesy of Trace Engineering
Figure 16 Courtesy of Statpower
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering
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Figure 17 Courtesy of Statpower
Figure 18 Courtesy of Trace Engineering
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Figure 19 Courtesy of Trace Engineering
Figure 20 Courtesy of Trace Engineering