1. INTRODUCTION

With the increasing popularity of alternate power sources, such as solar and wind,

the need for static inverters to convert dc energy stored in batteries to conventional ac

form has increased substantially. Most use the same basic concept: a dc source of

relatively low voltage and reasonably good stability is converted by a high frequency

oscillator and stepup transformer to a dc voltage with magnitude corresponding to the

peak of the desired ac voltage. A power stage at the output then generates an ac voltage

from the higher-voltage dc.

1.1. Current State of the Art:

There are basically two kinds of dc-ac inverters on the market today. One

category is the “pure sine-wave” inverter, which produces sine waves with total harmonic

distortion (THD) in the range of 3% (-30 dB). These are typically used when there is a

need for clean, near-sine-wave outputs for medical, instrument and other critical

applications.

Fig. 1. Most static-power inverters used in solar- and wind-power applications convert

dc to ac using the architecture shown here.

Some, for example, are used in boats and RVs as the main source of electricity,

and some feed energy back into the utility power grid. Waveforms approaching sine

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waves, with minimal distortion, are required in any case. These inverters are available in

sizes up to several thousand watts and typical costs are in the range of $0.50 per watt.

Early techniques for designing these true sine wave inverters incorporated

significant linear technology, reducing their efficiency and contributing to their higher

cost. More recent designs used pulse-width modulation (PWM) to produce a pulsed

waveform that can be filtered relatively easily to achieve a good approximation to a sine

wave. The significant advantage of the PWM approach is that switching techniques are

used in the power stages, resulting in relatively high efficiency.

However, PWM, with the pulse width made to vary according to the amplitude of

a sine wave, requires significant control circuitry and high-speed switching. This is

because the frequency of the PWM signal has to be much higher than that of the sine

wave to be synthesized if the PWM signal is to be filtered effectively. So the PWM

approach introduces significant complexities and switching losses. The second category

consists of relatively inexpensive units, producing modified sine-wave outputs, which

could logically be called “modified square waves” instead.

They are basically square waves with some dead spots between positive and

negative half-cycles. Switching techniques rather than linear circuits are used in the

power stage, because switching techniques are more efficient and thus less expensive.

These inverters require no high-frequency switching, as the switching takes place at line

frequency. Their costs are generally in the range of $0.10 per watt.

The typical modified sine-wave inverter has a waveform as shown in Fig. 2. It is

evident that if the waveform is to be considered a sine wave or a modified sine wave, it is

a sine wave with significant distortion.

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Fig. 2. Modified sine-wave inverters actually generate square waves with dead spots

between the half-cycles, allowing switching techniques rather than linear circuits to be

used in the power stage.

Analysis of Current Technology It is well known that any periodic waveform such

as that mentioned previously can be represented by a Fourier series, an infinite sequence

of sines and cosines, at the fundamental frequency of the waveform and its harmonics.

These harmonics can cause trouble in several areas—particularly in motors and sensitive

applications—and the data sheets for the inverters frequently caution the user that certain

devices may not work with the inverter.

Furthermore, even though the root-mean-square (RMS) value of the waveform

may be a nominal 115 V or 120 V, the peak will be different than that of a true sine wave,

and that factor can cause trouble in applications that depend on the peak value. The actual

percent distortion is not usually quoted in the specifications for inverters other than the

pure sine wave versions.

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So it is instructive to compute the distortion products to get a feel for the relative

distortion involved with the different approaches. For purposes of comparison, let us look

first at a conventional square wave (Fig. 3).

Fig. 3. The square wave provides a benchmark against which we may

compare the THD of the modified sine wave and the waveform generated

by the proposed inverter architecture.

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2. Fourier Analysis

The coefficients of the Fourier series are computed with a pair of integrals that

produce the coefficients of the sine and cosine terms in the series. For a signal f(x) with a

zero dc component, the integrals are:

where an and bn terms are the coefficients of the

cosine and sine terms, respectively, in the series.

The Fourier series is then:

f(x) = a1cos x + a2cos 2x + a3cos 3x + . . . + b1sin x + b2sin

2x + b3sin 3x + . . .

The complete background on Fourier series, as well as treatment of special cases,

is covered in several textbooks on networks or engineering mathematics, and will not be

repeated here.

We will just note that because both the square wave and the modified sine wave

have both half-wave symmetry and quarter-wave symmetry, integration is required only

over one-quarter of the waveform, and further that only the sine terms and odd harmonics

are required.

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Thus, the integral used to compute the coefficients for the conventional square

wave becomes:

The series is then

(4/π)sin x + (4/3π)sin(3x)+(4/5π)sin(5x) + . . .

The standard measure of distortion is THD defined as:

Numerical evaluation of the coefficients for the square wave indicates that if the

square wave is to be considered a sine wave with distortion, the THD is in the range of

45% (-7 dB). The third harmonic, the hardest to filter out, is one-third the magnitude of

the fundamental (-10 dB). Turning now to the modified sine wave, let us define the

width of the positive and negative portions as 2α as depicted in Fig. 4.

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Fig. 4. Defining the width of the positive and negative portions of the modified sine wave

as 2α enables us to calculate its Fourier coefficients and then determine its minimum

values of THD.

Again noting that the waveform has both half-wave symmetry and quarter-wave

symmetry, and carrying out the integration from 0 to л /2, we have:

Evaluation of this expression for various values of α indicates that the minimum

harmonic distortion occurs at α = 0.352л, where the THD is 23.8% (-12 dB), about half

that of the square wave. The third harmonic is about 6.5% (-24 dB) of the fundamental,

also a significant improvement over the square wave.

However, these figures indicate that the modified sine wave is far from being a

true sine wave, and suggest that improvement is in order.

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2.1. Proposed Improvement

Consider now a further modification—the addition of another level. The

waveform is shown in Fig. 5.

Fig. 5. Adding another level to the modified sine-wave results in a Fourier series with

four variables that may be varied to minimize distortion, though in practice “B” will be

set equal to 2 A.

Again using the fact that the waveform has both half-wave and quarter wave

symmetry, we carry out the integration over the period 0 to л/2, with the result that:

For odd values of n only.

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This result has four variables, of which all could theoretically be varied to achieve

minimum distortion. However, one particularly efficient approach is to choose a very

simple set of values for A and B—namely B = 2 x A—and then optimize the values of α

and β for minimum distortion.

This approach requires only two positive and two negative power-supply

voltages, all of which can be generated from a single transformer in the high-frequency

oscillator. (Other values of A versus B may be useful, but were not investigated because

the simple relationship of B = 2 x A had very good results as discussed later.)

This result has four variables, of which all could theoretically be varied to achieve

minimum distortion. However, one particularly efficient approach is to choose a very

simple set of values for A and B—namely B = 2 A—and then optimize the values of

and for minimum distortion. This approach requires only two positive and two negative

power-supply voltages, all of which can be generated from a single transformer in the

high-frequency oscillator.

Other values of A versus B may be useful, but were not investigated because the

simple relationship of B = 2 x A had very good results as discussed later. but any filtering

applied to reduce the third through ninth harmonics will be even more effective on those

above the ninth. Therefore, the higher-order harmonics are ignored in this analysis.

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3. IMPLEMENTATION

As demonstrated here, the modified-sine-wave inverter can be modified further to

produce a much closer approximation to a sine wave, at a relatively small increase in

manufacturing costs, simply by incorporating another level into the waveform. The

design still uses switching technology in the power stage, assuring high efficiency. A

patent application has been submitted for the approach described in this article. The

switching stage could be implemented with a combination of bridge and half-bridge

components commonly used in power switching applications.

To produce the proposed multiple-level waveform, several implementations are

possible. In general, they all involve connecting the output lead to a specific voltage level

with switches such as power MOSFETs capable of handling substantial current. Consider

the block diagram shown in Fig. 6 where the voltages A and B correspond to the voltage

levels defined previously.

Fig. 6. The proposed enhancement to the modified sine wave inverter is implemented by

connecting the output lead to a specific voltage level at the correct time with electronic

switches such as power MOSFETs.

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Appropriate digital logic and timing circuits will be used to activate each switch

at the correct time to achieve the α and β pulse widths. A table can be developed to

indicate which switches must be closed for each section of the output waveform. Note

that Switch #3 in Fig. 6 will need to be a bidirectional switch, since it must switch the

output lead V OUT to ground regardless of any voltage present in the load. All other

switches can be unidirectional.

Unlike conventional PWM-inverter designs, which switch

at high frequencies, the proposed inverter design switches at just three times the line

frequency. As a consequence, the proposed inverter design will reduce switching losses

from that of the PWM-controlled inverter and will save power regardless of the output

power level.

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4. Modified sine wave and true sine wave inverters

The AC output waveform for many inverters is called a quasi-sine wave or a

modified sine wave (MSW). It is a stepped waveform that is designed to have

characteristics similar to the sine wave shape of utility power. A waveform of this type is

suitable for most AC loads, including linear and switching power supplies used in

electronic equipment, transformers, and motors. The modified sine wave produced by the

inverter is designed to have RMS (root mean square) voltage of 115 volts, the same as

standard household power.

Most AC products run fine on MSW inverters. TSW inverters are about two to

three times as expensive per watt due to having more sophisticated design and

manufacturing requirements, and more expensive components. As a result, most people

prefer to use MSW inverters if their applications allow it.

In general, any device that senses either voltage peaks or zero crossings could

have problems when running from MSW. Devices such as these should be run from

TSW inverters. Ham radio and CB radio operators may notice RF noise from MSW

inverters; in that case do not run the radio and the inverter at the same time. Electronics

that modulate RF (radio frequency) signals on the AC line will not work and may be

damaged. You may notice hum or buzz in the audio of TV’s, radios and satellite systems

used with MSW inverters. Audiophiles or professionals using sophisticated audio,

remote measurement, surveillance or telemetry equipment should use TSW.

Examples of problem devices are motor speed controllers employing triacs, and

some small battery rechargers that do not incorporate a transformer between the utility

power and the load. To help you visualize this, if there isn’t a ‘wall wart’ between the

battery charger (or the battery in the device) and the AC plug, don’t use MSW.

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Please note two other common problem loads, electric shavers and emergency

flashlights. Both of these items have batteries in them but connect directly into the wall

to charge, without an external transformer. Don’t use items like these with an MSW

inverter. If you do use an MSW inverter with a transformer-less charger, your product

will likely be damaged. Garage door openers, laser printers and large strobes used in

photography have all been reported as trouble loads for MSW inverters; they either don’t

work at all or stop working entirely, so don’t take a chance – use TSW.

As a general rule, products operating through an AC adapter will work fine from

an MSW inverter. These include laptops and cell phone chargers, video games,

camcorder and digital camera chargers. Televisions generally work well; some VCR’s

with inexpensive power supplies run poorly. Consider switching to another brand of VCR

in that case. A potential solution for RV’ers or off-grid cottagers is to purchase our

smallest TSW inverter (such as the RS400) to run TV, VCR and audio equipment, and a

larger MSW inverter (such as the XPower 1750 Plus) for the coffee maker, hair dryer and

microwave.

Utility grid power supplies pure sine wave alternating current (AC), the most

common form of energy for the majority of electronic appliances. This same energy is

often needed in remote or mobile environments where pure sine wave grid power is not

readily available. In this event, users will turn to dc-ac power inverters using modified

sine wave or pure sine wave technology. While modified sine wave inverters are good for

many applications, pure sine wave inverters are needed because modified sine wave

inverters can have too much harmonic distortion otherwise referred to as noise. Pure Sine

Wave Inverters also known as true sine wave inverters are used because they replicate the

utility grid power allowing the most sensitive electronics to function seamlessly.

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4.1 Quasi-sine inverters (Sometimes called modified sine):

When describing the output from an inverter, people refer to sine, quasi-sine and

square waveforms. It is misleading to claim that any one type is better than another; it is

all a question of compromise of cost, reliability and efficiency. Sine wave output is

closest to replicating the AC mains supply, and at one time would have been costly and

the least efficient. However, developments in power conversion technology mean that

this is no longer the case & sine wave is now the choice for professional applications.

Quasi-sine units are now restricted to very low cost, low end applications and

certain very high inrush applications, such as refrigeration. The descriptions below are

more for historic interest, but remain true.

Square wave inverters, once common, were in their day the cheapest & probably

the most efficient, but were also the most likely to cause operational problems due to

their waveform. The quasi-sine wave is an intermediate approach which can replicate the

key characteristics of the AC mains supply if properly controlled. Given proper control,

and not all quasi-sine wave inverters do, the vast majority of loads can be successfully

operated. At one time, quasi-sine inverters were the best cost-performance compromise,

with true sine-wave restricted to waveform critical applications due to their high cost.

To understand how quasi-sine is designed to be a substitute for the mains, it is

helpful to understand what the key characteristics of the mains are. For this discussion we

shall refer to European system which is 50Hz and 230VAC, but the same principles apply

to other voltages and frequencies.

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4.2. The mains has four important characteristics:

Peak voltage: this is the peak voltage at the crest of a true sine wave. It reaches

325 volts on a 230 volt supply. This peak voltage needs to be maintained in order to

successfully operate some electronic equipment, particularly microwave cookers.

Average voltage: this is maximum value reached by the integral against time of

the voltage waveform, or in other words, the average voltage. A 230 volt sine wave

supply has an average voltage 207volts. This characteristic is important for the successful

operation of magnetic devices such as transformers and motors.

RMS voltage: (230V) this is a mathematically derived measure of the heating

effect of a waveform when applied to a resistive load, and has been traditionally used to

specify the magnitude of an AC voltage. This characteristic, which for a 230 volt mains

supply is 230 volts, is important to ensure that heating and tungsten lighting equipment

works to specification. If this is inaccurate or fluctuates then lighting may vary in

intensity.

Stable frequency: (50Hz) this is necessary to ensure that timing devices using

mains frequency operate accurately and that AC motors run at the correct speed. The

following notes give an overview of how the three types of inverter mimics the mains.

The quasi-sine waveform cannot precisely replicate all these key voltage

characteristics at the same time, so a compromise has to be arrived at. The compromise

employed is one of the factors that differentiates different quasi-sine inverters.

Sine wave inverters set out to mimic the mains most closely. At one time. there

were three common types; constant voltage transformer (CVT), pulse width modulated

switch mode units (PWM) and so called linear units. The CVT's are the traditional units

using a large transformer in which an oscillation is established.

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Simple and fairly rugged, they tended to be inefficient, large and heavy, and

sometimes noisy too. The waveform can become quite severely distorted on some types

of load. In contrast, the modern state of the art approach uses switchmode technology to

reconstruct a sine wave; sometimes called PWM units. Relatively small and light, these

are complex units, and used to be expensive, but have now become affordable. However,

they can cause electrical interference and may have difficulty driving loads with a very

high inrush current.

Quasi-sine inverters are simple, efficient and robust. Although they do not give a

true sine wave, they can mimic the key voltage parameters fairly well, allowing the

majority of equipment to run successfully. Not all quasi sine wave units are the same;

many problems with quasi sine inverters stem from poor design, & not from the lack of a

pure sinewave. Older type quasi-sine units can be designed to drive very high inrush

loads; an area where they are still used today.

Square wave inverters are very simple but are really only suited to resistive loads

such as heaters and incandescent lights. Due to their limitations, they are now quite rare.

Rotary inverters; for completeness it is worth being aware of this type of inverter.

It uses a DC motor to drive an AC alternator, which gives a sine wave output. Although

rugged and generally reliable, they suffer the disadvantage of needing brush maintenance

(all static inverters are maintenance free), they are relatively inefficient and can be noisy.

Antares used to offer quasi-sine units, but with a difference. The control

arrangement in our units maintained the key output voltage parameters over a wide range

of operating conditions. Unlike many competitor units, there were no limitations on

capacitive loads, such as presented by electronic equipment or appliances incorporating

power factor correction or motor start capacitors.

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However, Antares now offer exclusively sine wave units as they are now reliable

& cost effective. Our quasi-sine units are no longer in general production, & are only

available to special order when demanded by the application.

4.3. Choose a Power Inverter for RV or Road Trip Vehicle:

Finding a device to convert DC power to AC may seem like it should be a simple

task, but when you start shopping for a power inverter for your RV or road trip vehicle,

you'll soon find that many choices will confront you. With prices ranging from less than

$40 to well into the thousands, it can be difficult to know what features are important and

how to choose a unit appropriate to your needs. While wattage, features, and connections

are obvious considerations, your final choice should take into account the inverter's wave

form output.

There are two general types of power inverters: true-sine wave or modified-sine

wave (square wave). True-sine wave inverters produce power that is either identical or

sometimes slightly better to power from the public utility power grid system. The power

wave when viewed through an oscilloscope is a smooth sine wave.

Modified-sine wave and square wave inverters are the most common types of

power inverters on the market. Modified-sine wave power inverters produce a power

wave that is sufficient for most devices. The power wave is not exactly the same as

electricity from the power grid. It has a wave form that appears as a choppy squared-off

wave when viewed through an oscilloscope.

What does that mean to the everyday user? Not much. Most household electrical

devices will run perfectly fine on either type of wave form. Most of our customers who

are using a power inverter to run a laptop, a/c cell phone charger, fan, or camera find that

a modified-sine wave power inverter that operates through the cigarette lighter socket the

easiest to use.

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Usual suggestion is choosing power inverters that are rated under 300 watts when

using the 12-volt cigarette lighter socket found in most vehicles. We suggest this because

after reaching 300 watts of draw on the inverter, the fuses in your car will begin to blow.

The xPower 175 Micro ($35.00) is a great choice for dash boarders who would like an

easy solution to power their devices. It has only one outlet, but since plugging it into a 12

volt socket is all that is required for operation, it can't be beat for ease of use. This little

inverter can supply 140 watts of continuous operation and has a built-in surge protector.

Square wave inverters, which are appropriate for most roadtrippers, fall into the

following four groups:

300 watts ($40-$60): For household appliances, TVs (up to 27"), VCR, desktop

computers, other mobile office equipment. Most of these connect via a 12-Volt plug.

600 watts ($100-$120): For household appliances, large screen TVs, 5-amp power

tools, and bread machines. Most such inverters are connected directly to the 12-volt

battery and have three or more grounded outlets for powering several products at the

same time.

1750 watts ($199-$380): For household appliances, larger power tools,

microwave ovens, toasters, and hair dryers. All of these inverters are designed for direct

connection to the battery network and can generally supply 1500 watts of continuous

power.

3000 watts ($395-$750): With output power generally rated at 2500 watts for

continuous load, these inverters can power virtually all household appliances and office

equipment. For loads of this magnitude, special wiring and battery banks may be

required.

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The problem with wave form only comes into play when specialized pieces of

equipment need to be powered. Here are a few devices which could have problems when

they are connected to an inverter producing a modified-sine wave signal: oxygen

concentrators, fax machines, laser printers, high voltage cordless tool chargers,

equipment with variable speed motors, electric shavers, and garage door openers.

There are a few other applications -- high-end audio video units, plasma displays,

gaming systems, and certain scientific testing equipment -- for which true-sine wave is

not usually required. Even so, these applications can usually benefit from the improved

clarity of the electrical signal produced by a true-sine wave power inverter. Users of these

particular items have usually spent a lot of money to achieve optimal results from their

equipment, and it would be a shame to have a cheaper modified-sine wave signal cause

inaccurate readings on a piece of scientific equipment. It would be equally disheartening

to have small distortion lines appear on a $3000 plasma TV because the user saved

$250.00 by buying a modified-sine wave power inverter.

4.4. The Xantrex XS400 true-sine inverter

It is also important to understand that there is no way to upgrade or clean a

modified-sine wave signal. If your item does not work on a modified-sine wave inverter,

you will need to purchase a new true-sine wave power inverter. We often recommend

that users on a tight budget purchase only enough true-sine wave power to run required

equipment and purchase a less expensive modified-sine wave inverter to run the rest of

the load. The Xantrex XS400 ($375-$400), a true-sine wave power inverter, is often used

to power only the audio video loads in RV applications. The rest of the RV's electrical

loads are often powered by a larger modified-sine wave power inverter.

Many people are surprised at the overall improvement in signal quality when

using inverters on audio/video applications. They notice that there are fewer distortions

and few if any interference lines. While we don't recommend true-sine wave inverters to

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most of our customers, we do advise customers with no budgetary concerns to choose a

true-sine wave product. They can then rest assured that their inverter will be able to

handle anything they plug into it.

Many stores do not carry true-sine wave power inverters because the price is often

significantly higher than their modified-sine cousins -- usually two to five times more.

Generally, expect to pay $200 to $3,000 for pure-sine wave inverters depending upon

how many output watts are needed. Our firm, 4lots.com has had great experience with

two brands of true-sine wave power inverters, namely the Xantrex Prosine line and the

Go Power! true-sine wave line.

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