Pulse Width (Duration) Modulators - Updated for Solid State Devices.
by Stephen Cloutier, WA1QIX
Note: The original article, describing vacuum tube Pulse Width Modulators is also available. See link.
This article describes the operation, and presents some practical circuit details of Pulse Width Modulators. Over the years I have designed and built several AM transmitters using the PWM system. If we have spoken on 40, 75 or 160M in the last 10 years or so, then you have probably heard one of my PWM transmitters. Note: The term Pulse Duration and Pulse Width are interchangeable.
SCOPE OF THIS ARTICLE
I will be describing one variation of a PWM system. Other circuit topologies are possible. The one I will describe is the simplest and most straight-forward variation that I have found. This article presents information to allow someone with a reasonable knowledge of radio and electronics to understand how the PWM system works, and to design and build a transmitter using the PWM system. Where ever possible, standard components are used. To properly test a PWM system, you will need access to a 20 MHz or better oscilloscope, and an audio signal or function generator.
The circuits shown are functionally complete. However, to avoid cluttering the diagrams any more than necessary, the usual bypass capacitors at each power lead of each IC have been eliminated, along with the power leads themselves. Since this is standard practice, it is assumed that the builder would include bypasses and such even if they are not shown in a diagram. Since the Pulse Width Modulator uses non-resonant, wide band high frequency RF for its operation, care must be taken to avoid intercircuit coupling, oscillations, ringing and other common problems which plague poor circuit layouts.
PWM TRANSMITTER THEORY OF OPERATION - How and why does it work
NOTE: A Pulse Width MODULATOR differs, in the strict sense of the word, from Pulse Width MODULATION, the latter generally involving the transmission of pulses directly via a carrier, or transmitting RF pulses of varying width. In this discussion, the modulator uses Pulse Width Modulation internally, however, the pulses are removed and the output converted to modulated, standard audio-modulated DC before application to the modulated RF stage. -end Note.
The PWM transmitter consists of a High-level modulated, standard class C, D, E or F amplifier, and in most applications, a very efficient series modulator. A series modulator is just what its name implies - a device in series with the RF amplifier and the power supply.
As far as audio quality is concerned, the series modulator is probably the best high-level modulator circuit that you can use. It uses no transformers, is DC coupled (very important if you use sophisticated audio processing techniques) and is fairly easy to implement. The disadvantage of the class A series modulator is, of course, the low efficiency of the system. The PWM system has all the advantages of the series modulator (no transformers, DC coupled, etc) but does not suffer from the tremendous inefficiency and power loss of the class A amplifier.
In a PWM system, the modulator device or devices (tubes, MOSFETs, transistors, etc) are operated in class D - they are switched between saturation (fully turned on - minimum voltage drop across device) and cutoff (no current flow through device) at a frequency at least 3 or 4 times the highest audio frequency we wish to modulate. The switching frequency is then filtered out so that only original modulating signal remains. Since the modulator devices are always operating at either saturation (very low voltage drop) or cutoff (no current), the power dissipated in the modulator is very low, and therefore the efficiency is very high.
Let us now develop a basic Pulse Width modulator. Since all devices in such a modulator are acting like switches, we will use an actual switch to illustrate how these modulators work. In practice, of course, a MOSFET, tube, or transistor is used as the modulator. Consider the basic circuit shown in figure A:
When the switch is closed, a current will begin to flow in inductor L1 through the load resistor R1, and from C1 as C1 begins to discharge. The current flowing in L1 causes energy to be stored in the magnetic field within the inductor. If the switch is now opened, the current flow through L1 will immediately stop. The magnetic field within the inductor will quickly collapse, producing a current flow in the opposite direction, and therefore a reverse voltage across the inductor. The voltage will quickly rise, until it reaches the power supply voltage. At that point, diode D1 will begin to conduct, and will not allow the voltage to rise any higher. The current developed by the reverse voltage will be conducted through the diode back to the power supply. When the switch is turned back on, the cycle repeats - off, on, off, on, etc... The period of time that the switch is closed is the modulator "on-time".
The voltage (and current) at the output of the filter is directly related to the ratio of modulator on-time vs off-time. Since the voltage at the output of the filter is based on the mathematical average of the pulses appearing at the input of the filter, an expression can be derived which is useful in predicting modulator operation:
Vout = ((t1 * V1) + (t2 * V2)) / (t1 + t2)
where: Vout is the voltage measured at the output of the filter, V1 is one of the voltages in the switching waveform (either high or low), t1 is the time (in any unit) that the switching waveform remains at V1. V2 is the other voltage in the switching waveform, and t2 is the time (in the same units as t1) that the voltage remained at V2. The expression (t1 + t2) is actually the switching rate of the modulator.
In a typical example, a modulator is operating such that the on-time is 4uS and the off time is 6uS. The switching waveform produced by the circuit in figure A would look like this:
The 4uS on time, we'll call t1. The 6uS off time is t2. If the values are substituted into the expression:
Vout = ((4uS * 0V) + (6uS * 1V)) / (4uS + 6uS) = 6uS-V/10uS = .6V
This is the voltage measured at the output of the filter, with respect to ground. The voltage ACROSS the load is, of course, .4V.
If the on-time is increased to, let's say, 7uS, the off-time will then be 3uS, since the switching rate is always the same, in this case 10uS. If the output voltage is now calculated, we will get .3V at the output of the filter, which causes the voltage across the load to increase to .7V.
The on-time is generally called the pulse-width, which is where the name for this type of modulator is derived. Notice that we have controlled the voltage across the load by simply varying the pulse width. That is how the modulator works - controlling the average voltage (pulses filtered out) across the load by changing duty cycle (pulse width or on time) of the modulator.
Any active device, such as a MOSFET, tube, or transistor can be used as the modulator. The diode can be a tube, or fast-recovery solid-state diode. The load resistor R1 represents the final RF amplifier. This comprises most of the Pulse Width Modulator. In a typical operation, the voltage across the RF amplifier is generally set to be 40% of the total supply voltage. The pulse waveform is set up so that, at carrier (no modulation) the modulator device is on for 40% of the total time, and off for 60% of the total time. With this arrangement, the amplifier could be modulated up to 150% positive.
Any circuit which generates variable width pulses can be used as the basis of a pulse width modulator. The modulator could use devices in push pull connected to a transformer whose output is then rectified, multiple modulator devices operating in different phases... etc. The design of these systems is left to the imagination of the reader - and hopefully - future articles.
Basic Pulse Width Modulation Generators
A PWM Generator is any circuit which produces a pulse whose width is proportional to the input amplitude of the applied signal. A simple method of producing such a signal uses a differential comparator and a triangle wave generator. A differential comparator generates either a high or low output (digital signal), based on the voltage difference between 2 input signals. The triangle wave is fed into one input, and the modulating signal is fed to the other input. Referring to figure B (below), the triangle wave generator is fed to the "-" input of the comparator. The audio to the "+" input. The comparator works as follows: When the level of the "+" input is higher than the level of the "-" input, the comparator generates a logic 1 (high) output. When the "-" input is higher than the "+" input, a logic 0 (low) is generated. Let us assume, for the moment, that the triangle generator produces a 10V peak-to-peak output. The "-" input of the comparator is, therefore, varying between +5 and -5 volts (10v P-P). If the signal fed to the "+" input is 0, the output of the comparator will be an exact 50% duty cycle square wave. This is illustrated in figure B(1). Let us now connect a +1 volt DC source to the "+" input of the comparator. If no other factors change, the output from the comparator will very closely resemble the signal shown in figure B(2). The reason that the 1 (high) pulse is longer than the 0 (low) pulse is that the portion of the triangle wave which is less than 1 volt, and therefore makes the "+" input greater than the "-" input, is wider than the portion which is greater than 1 volt. If now, rather than connecting a DC signal to the "+" input, we connect a sine wave to the "+" input, we will produce varying width pulses whose width depends on the width of the triangle wave for the time where the "+" input is greater than the input. The pulse train shown in figure B(3) shows the variable width pulses produced by a sine wave input.
As we mentioned earlier, the output from the comparator is a digital signal - that is, the signal has only 2 possible states, high and low. The information (modulation), rather than appearing as an amplitude change, as in the input, appears as a change in the ratio between the times that the signal is high and low. The amount of change is directly related to the amplitude of the input signal, and the rate of change is the frequency of the input signal. One of the nicest aspects of pulse width signals is that they can be amplified without regard to amplitude linearity - in fact, the best amplifiers for this application are amplifiers designed to operate in the saturation/cutoff, or switch mode.
The triangle wave generator must produce perfectly linear triangles if good modulation linearity is to be expected. The distortion characteristic of the transmitter is determined more by the design of the triangle wave generator than any other part of the modulator. Care must be taken to ensure that the output of the triangle generator is unaffected by the input signal, power line variations, RF or any other outside factor. The tips of the triangles should be sharp and pointy. If they are rounded, nonlinearity and distortion of the modulating signal will occur. The sides of the triangles need not be identical in length. Often, the output will more resemble a sawtooth than a triangle. This is OK as long as both sides are perfectly straight and linear. A good circuit for a triangle wave generator will be presented later as part of a complete PWM generator.
The switching frequency (determined by the frequency of the triangle wave generator) should be at least 4 times as high as the highest audio frequency you want to modulate. This ensures adequate resolution of the high frequencies and reduces the possibility of aliasing, a type of distortion caused by the mixing of the switching frequency and the input signal. It also makes design of the output filter easier. However, if the switching frequency is too high, the pulse generator and amplifier design will become difficult, due to the higher bandwidth required for high switching frequencies. Switching frequencies of between 50kHz and 100kHz are used in most Pulse Width Modulators with 70kHz being very popular with broadcast equipment designers.
Functional Design of the Overall System
Figure C shows a functional diagram of a PWM transmitter. Each functional component will be discussed separately.
Triangle Wave Generator and Comparator
As discussed above, the triangle wave generator produces a triangle (or sawtooth) signal which is fed into one input of a comparator. The switching (or sample) frequency is set by the frequency of the triangle wave generator.
Low Pass Filter
Before audio is applied to the comparator, it passes through a low pass filter. This filter prevents any harmonics or other audio signals near to the switching frequency from reaching the comparator. If the filter were not present, high frequency audio harmonics or other signals may mix with the switching frequency to produce unwanted signals in the audio range. This type of distortion is known as aliasing. It is very noticeable, but easy to prevent with a proper input filter.
Pulse Modulator (Amplifier)
The pulse modulator/amplifier is the final stage of amplification is a PWM system. The amplifier may consist of several stages, but the ultimate function is to amplify the 5V TTL signal produced by the comparator to a level sufficient to directly handle the power required by the RF amplifier. An extremely important consideration in designing the pulse modulator/amplifier is the bandwidth, or 'speed' of the circuit. Inadequate amplifier bandwidth will generally cause distortion to appear at the extremes of modulation, both positive and negative, but is much more of a problem on the negative peak. If the rise and fall time of the pulse is too long, very short pulses will be stretched out, or may disappear entirely. If you want your pulse width modulator to be able to modulate your transmitter up to 99% negative, without distortion, then the pulse modulator/amplifier should be capable of passing a pulse which is 1/100th of the total period of the switching waveform. With switching frequencies below 100kHz, this is not terribly difficult to achieve, as we will see later.
The output filter network usually consists of a multi-section L-C filter which must be specifically designed for the particular transmitter in which it is to be used. The number of filter sections will depend on the switching frequency, and how much attenuation of the switching frequency is desired. It is highly recommended that the switching frequency be attenuated at least 60dB or more. If your signal is 60dB over s9, and you only have 40dB of filtering, you will produce 2 sidebands, 20dB over s9 at plus and minus the switching frequency!! If you are building a powerful transmitter, more than 60dB of filtering should be used. There are many different types of filter arrangements which will work with these modulators. I will describe the method I use to design the filters in my transmitters. It is reasonably straight forward, and uses filter information which is available in the ARRL handbook and other common sources.
The filter I use has a Butterworth response. It is a 6 element filter, using 3 inductors and 3 capacitors. The corner (the frequency at which the filter begins attenuation) is set at 12.5kHz. I use a switching frequency of 100kHz. A 6 element filter with the corner set at 12.5kHz should attenuate the 100kHz switching frequency more than 60dB. Each reactive element in the filter should, theoretically, give 6dB of attenuation per octave above the corner frequency. Design of the filter is dependent on basically 3 things: the impedance that the filter operates at, the corner frequency of the filter, and the number of elements in the filter. The load on the output of the filter is the DC resistance of the RF amplifier. I designed the filter to have the same input and output impedance. This approach has always given excellent results.
It is highly important that the filter input inductor have sufficient inductance to allow the waveform to remain in the "off" (when the modulator devices are not switched on) state without colapsing. If the inductance is not sufficient, when the modulator switching device (tube, MOSFET, etc.) is in the off state, particularly with a large off pulse, the waveform will colapse (either rise or fall - depending on your modulator design) before the modulator device switches on again. This will cause SERIOUS distortion. Observe the switching waveform on an oscilloscope and verify that no such waveform distortion is present. The filter is not difficult to build. The input inductor is the most critical.
It is possible to write an entire article on the filter design alone. Space does not permit that, however. The newer ARRL handbook, West Coast Handbook, and many other sources have filter tables which will aid in designing the filter. The design of the filter is not particularly difficult when using the filter tables. In practice, there is considerable room for slop in the filter design - so it's not quite as critical as it may seem to get the "exact" values for all the components.
When the modulator devices turn "off", the energy stored in the filter network is released, and will flow in the opposite direction of the current through the pulse modulator output devices. Without a damper diode, energy stored in the filter network, when released, would cause the voltage to rise to very high levels as a result of the flyback effect. The damper diode clamps this voltage and conducts the energy back to the power supply and to the load. The damper diode must be a fast recovery diode, and particularly in solid state designs, must be located immediately next to the switching transistors or MOSFETs, and connected with VERY short leads.
RF Amplifier and RF Coupling Network
The RF amplifier is a conventional class C, D, E or F amplifier which is operating in some type of saturation or switching mode. Like all high-level modulated amplifiers, it must follow a linear square law (straight line) and be capable of handling the maximum positive power which the modulator can deliver.
PRACTICAL PWM TRANSMITTERS - making it work in the real world
Here we present practical details for building a PWM transmitter. I have included circuits of a good PWM generator and modulator output stages. While these are actual, working circuits, they are just one possible implementation. Your implementation may use some of these circuits, or parts of them. The circuit examples presented have the modulator and RF amplifier both at DC ground, except for the last modulator stage which is floating. The modulated DC is applied to the positive (drain) side of the RF amplifier.
Figure D shows the schematic of a good PWM generator. Note that this generator will produce a two-phase output allowing the generator to be used with a multiphase system. Multiphase PWM functions much like a full wave rectifier - doubling (or multiplying) the switching frequency. One modulator output stage, including the first stage of the filter network is used for each phase of a multiphase system. This generator may be used in a standard single-phase PWM system by using only one of the outputs.
Triangle wave generator
The triangle wave generator MUST be of good quality. As explained earlier, the distortion characteristics of the transmitter are directly determined by the quality of the triangle generator. I use a multivibrator (square wave generator) followed by an active integrator.
The triangle wave generator must have its own voltage regulators to improve the isolation from other circuits. It is of the utmost importance that the triangle generator and all other low level circuits in a PWM transmitter be completely isolated from RF and other circuits in the system. If the frequency, amplitude or waveshape of the triangle generator is affected by external events, distortion of the modulated signal will result. The triangle generator in the circuit shown will generate a triangle wave around 100kHz. Referring to the oscillator section of figure D, the 74s04 is set up as a free running square wave oscillator. The square wave oscillator output feeds the integrator, which is made from an LM318 (or equiv.) op amp. The integrator integrates the square wave and produces a triangle wave output. The output of the generator should be carefully checked on an oscilloscope before any use is attempted.
Negative Peak Limiter, Filter and Pulse Generator
Referring to figure D, the audio circuitry includes a negative peak limiter (clipper), low pass filter, and carrier level contol. The pulse outputs are 5 Volt TTL. Audio is fed to the first op amp, which includes the negative peak limiter (clipper). The output from the clipper is then amplified and filtered by the following three op amp stages. The output of the audio amplifier/filter is then fed into the "+" input of the comparator.
The output from the triangle wave generator is fed to a resistor load/divider network through a coupling capacitor to the "-" input of comparator. The triangle wave input to the comparator is offset by a DC level determined by the setting of the Carrier Level control. This establishes the quiescent pulse width, which determines the carrier level.
The pulse output from the comparator is fed to a buffer consisting of two sections of a 74s04 inverter in parallel. The output from the buffer feeds the modulator high level circuitry. Although not specifically shown in the diagram, each power lead of each IC is bypassed with a 10uF capacitor to the ground plane. Short bypass leads are very important. Remember, this is an RF circuit. Lead bypassing, lead dress, and inter-lead coupling must be considered. Lumped reactances at the end of long leads can cause ringing on, and integration of, the waveforms. The system bandwidth will be reduced. Oscillations are also possible. Please keep these factors in mind when building your PWM circuits.
Pulse Amplifier, Modulator Output and Damper Diode
Figure E shows the pulse amplifier and output section. This implementation applies the modulation to the positive side of the load (RF amplifier), which simplifies the RF amplifier design and implementation. The modulator FETs are operated as source-followers - the output is taken from the sources of the FETs rather than from the drains, and the drains are connected to the power supply. The gate-source drive for the modulator FETs is accomplished by using a floating driver stage. The sources of the modulator FETs are connected to the "ground" of the driver. The driver is assembled on a small piece of copper clad board, which is insulated from the chassis and connected by very short leads to the sources of the modulator FETs. A fast optical isolator is used to transfer the input signal to the floating driver circuitry, and to isolate the floating driver from ground. DC power for the driver circuitry is supplied through a charge pump consisting of a fast recovery rectifier diode which charges a capacitor each time the modulator FETs turn "off".
The modulator works as follows: [Assuming a proper load connected to the output of the filter] The 100kHz PWM signal is fed to the input of the opto-isolator. The output of the opto-isolator drives the MC34151 driver ICs. There are two amplifiers in each IC, and one amplifier is used for each of the modulator MOSFETs. When the input signal goes low, the output of the opto-isolator also goes low, driving the inputs of the MC34151s low. The MC34151 is an inverter, so the outputs of the MC34151s go high - driving the gates of the modulator MOSFETs high and turning the FETs on. When the modulator FETs turn on, the source voltage will quickly rise to the power supply input voltage, which is applied to the drains (in this case, 100V). 100 V will appear at the input of the input filter network inductor, and energy will be stored in the inductor. When the PWM input signal switches to the high state, everything will reverse. The gates of the modulator MOSFETs will be driven low, and the devices will turn off. The energy stored in the filter network input inductor will be released, and the modulator output (FET source) voltage will quickly fall. The modulator FET output voltage will be clamped at 0v by the damper diodes, and energy will be conducted through the diodes to the negative side of the load (RF amplifier) and the negative side of the power supply. This cycle repeats again and again, at the switching rate of the modulator (in this case, 100kHz). The filter network will integrate (filter and average) the output of the modulator, resulting in a steady-state signal, which is fed to the RF amplifier.
The driver circuitry power is supplied from a 24 to 30 volt supply through an MR856 fast recovery diode, which forms a charge pump. When the modulator MOSFET sources are high (modulator on state), the MR856 diode is back-biased and no current flows through the diode. When the modulator devices are in the off state (0 V modulator output), energy is conducted from the 24 to 30 volt supply, through the MR856, to the 2200uF "storage" capacitor. The capacitor will be fully charged to approximately 24 volts after a few modulator on-off cycles. 5V and 12V regulators supply regulated DC to the driver components.
The Damper Diodes are fast-recovery, high current diodes. In the actual implementation, 6 IXYS DESI 30-06 (600V, 30 amp) diodes are used. These diodes are mounted on a heat sink, and are connected directly, and with heavy, short leads to the sources of the modulator MOSFETs and to the ground plane. The 150uF capacitor which is connected from the modulator drains to ground is actually made up of 3 50uF capacitors, connected along the source bus to ground. Again, short, heavy leads are important.
Output Filter Design and Construction
The design and construction of the output filter is very important. One of the biggest problems encountered in filters of this type is ringing. Any ringing in the switching waveform will cause distortion of the modulated signal. Another problem to avoid is self-resonance in the inductive elements. Once a filter is constructed, and the modulator completed, the waveform occurring at the input to the filter must be checked over the entire range of pulse widths to ensure that no ringing, waveform distortion or other anomalies exist which will cause distortion.
The best kind of inductor I have found for use in these filters, at least for the input inductor, is an air-wound coil. For modulators designed to modulate RF amplifiers with an impedance of around 6 to 8 ohms, values in the range of 26uH to 40uH are typical for the input inductor. All of the inductors in the filter network need to be wound from very heavy wire to avoid voltage drop and losses. #10 wire is a good wire size for transmitters operating at up to 10 Amps of DC load current.
The capacitors should be connected between the ground plane and the filter inductors with short leads. The inductors should be located at right angles to each other, with sufficient spacing the inductors, to prevent coupling.
The recommended filter consists of L-C sections. A Butterworth or constant K low pass filter will work very well in this application. Filter tables and data is available in the ARRL handbook and from many other sources. The filter input and output impedance should be the same. The filter corner frequency should be around 10 to 12 kHz.
Be absolutely sure that the modulator output waveform, measured at the sources of the output MOSFETs, is a good square wave, and that the waveform contains no ringing or other anomalies over the entire range of pulse widths. Most problems will occur when the modulator is turned "off" most of the time (very small "on" pulse width - as will occur during high levels of negative modulation.
The RF amplifier
Up to now, there has been little discussion of the RF amplifier. The RF amplifier is a standard class C, D, E or F amplifier. The output of the RF amplifier should directly and linearly reflect the DC input voltage.
It is highly recommended that the last capacitor in the PWM filter be located at the RF amplifier, as part of the RF amplifier. This will result in the most stable RF design, while still maintaining the proper value for the filter.
The power supply in a PWM transmitter must supply the full voltage required to modulate the RF amplifier to whatever positive modulation is desired. If you want to run 40VDC (at carrier) on your RF amplifier, and you want to be able to modulate the RF stage to 150% modulation, the power supply must deliver 100VDC. The current that the supply must deliver is related to the RF amplifier power input, ratio of total power supply voltage to RF amplifier voltage, and the efficiency of the modulator. As an example, let's say the RF stage runs at 40V at 10A (400W) total power input. All power which passes through the modulator must be added together to get the TOTAL power which the modulator will handle. The transmitter is to have a positive modulation capability of 150%, so a 100V power supply will be used. The modulator efficiency is assumed to be 90% (typical for Pulse Width Modulators). We can calculate the total power input to the system by dividing the power input to the RF amplifier by the modulator efficiency. This is aprox. 444.5 watts. Since the power supply delivers 100V, the current required for 444.5 watts is approximately 4.5A. For carrier conditions, the supply must deliver 100V at 4.5A. Under 100% modulation the power input will be 50% (the energy in the sidebands) greater than the carrier level, or around 7A under 100% sine wave modulation.
Testing A PWM Transmitter
Each part of the transmitter should be fully tested as it is built, if possible. All the low-level circuitry should be fully operational and tested, up to the gates of the modulator MOSFETs before any operation is attempted. It is highly recommended that the waveforms at various key points in the transmitter be measured and recorded for future reference. The whole range of pulse widths should be checked to make sure that rise and fall times are not too long, and that there are no sudden changes in pulse width, oscillations, or other unusual occurrences which will cause serious distortion.
The RF amplifier should be tuned up at reduced power supply voltage, with the modulator temporarily bypassed. Once this is set up properly, then the modulator will be working into the correct load, and can be checked out properly. The modulator output switching waveform must be free from tilt, ringing, or other abnormalities. An improper waveform will result in SERIOUS distortion. Make all checks over the entire range of pulse widths - minimum to maximum.
Connect an audio oscillator to the audio input, and run through the whole audio range to make sure the transmitter has a flat response, and there are no resonances or other problems anywhere in the range the transmitter is designed to operate. Try bringing the oscillator up to a very high frequency to verify that the input filter is working, and that aliasing is not objectionable.
Use an audio triangle wave of around 500 Hz to ensure linearity of the system. This is easy to construct. Use the same circuit used for the PWM generator using larger capacitance values to get a lower frequency.
Adjust the negative peak limiter (if included) to the desired level (95% is a good place to clip it), but don't use too much... you have a good transmitter... and clipping is distortion although it is recommended that the clipper be enabled - just as an insurance against overmodulation. Of course, if conditions are bad, or there's a lot of noise, it's always nice to 'crank up the audio' and not worry about overmodulating, or blowing up a modulation transformer!
A final check should be made of the switching frequency level. Using a local receiver, or a friend who has a good receiver, and is close by, check the level of the sidebands produced by the switching frequency, on the upper and lower side of your carrier. They should be down 70dB or more from the carrier (if you designed your filter properly!).
Please keep in mind, that the pulse width modulator system described here is just one implementation. There are many other ways to achieve the same result, with a completely different configuration. Although commercial firms are doing some research in the area of improvements and other implementations, the Amateur community can do much to further the state of the art in this area.
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