CHAPTER 18 -- THE SPECIAL NEEDS

OF CONVERTER EXPERIMENTS

18.1 Introduction

It is difficult to obtain a thorough understanding of power electronics without experimental effort. The unforgiving nature of high power levels, the effects of parasitic and stray components, and the basic operating concepts can be hard to follow in depth unless they are supplemented with laboratory activity. On the other hand, power electronics is a very specialized field in an experimental sense. Engineers in the area are often interested in waveforms of power, voltage, current, and energy. The waveforms are nonsinusoidal, and contain information on time scales ranging from a few tens of nanoseconds for commutation up to several seconds for a motor load.

In this Chapter, we will be concerned with the concepts and tools of power electronics experimentation. Significant issues such as RMS and average measurements are discussed. The importance of real-time waveform capture and processing is examined. In an industrial setting, there is extensive overhead involved in preparing reliable, robust equipment for power electronics experimentation. The Chapter presents a few general circuits that avoid this overhead by providing a set of converter test beds for various key functions. A convenient transformer arrangement to allow safe experiments from the utility source is also described.

Later in the Chapter, techniques for setting up and measuring PWM inverters and related circuits are described. Each technique allows a realistic converter to be set up quickly to give immediate experimental insight. Yet each method is simple enough that it will not be obscure to the experimenter.

The idea of preparing a general test unit to support a variety of converter experiments is referred to here as a blue box approach. In a black box system, the inner workings of a unit are unknown, complicated, or hidden in some way. In the blue box approach, the inner workings are general functions well-known to the experimenter, and the unit is not intended to obscure any element of system operation.

18.2 Root-Mean-Square and Average Metering

Metering in power converters is much different than in almost any other field. The expected waveforms are often nonsinusoidal. Switching frequencies range from the ac line frequency to 500 kHz and beyond. Waveforms often carry both dc and ac content. Together, these characteristics limit the selection of useful meters. In a dc-dc converter or a rectifier, for instance, it is obviously important to measure average values to characterize circuit operation. RMS values become important when resistive loads or ac signals are involved. A resistor accepts power at any frequency, so the square of current or voltage is more important than the average for understanding power flow. The RMS value of a sine wave tells us something about the possible power levels, although it is only a direct indication for resistive loads.

Averaging is a fairly straightforward measurement issue. Since a waveform's average represents its dc component, the average can be recovered by means of low-pass filtering. For meter display purposes, the details of the filter process are not especially critical. It is important to filter out the ac line frequency to avoid interference, and of course the user wants a quick measurement. Many handheld meters update the displayed value only about once each second, so filtering out 60 Hz interference is not difficult. If accuracy on the order of 0.1% is desired for an average measurement, line frequency components should be attenuated by about 60 dB. A two-pole filter with 1 Hz corner frequency can do this in principle. Some instruments use resonant filters to selectively eliminate 50 Hz and 60 Hz. This technique allows much faster updates of the average values of most waveforms. Meters that update the display as often as ten times per second are possible with this approach.

In the past, RMS and average values were often obtained with simple transformations. A typical analog meter is designed to require a small dc current to drive its display movement. The mechanical inertia of the movement often provides sufficient low-pass filtering for averaging. An RMS meter can be made by connecting a bridge diode rectifier to the meter front end, then calibrating the meter so that the 0.6366V₀ average value of a rectified sine wave is displayed on the meter face as 0.7071V₀. Average readings can be performed just by bypassing this extra gain. Of course, this procedure is valid only for an ideal sinusoid, and does not apply to power converter waveforms.

More recent meters are based on either analog or digital integrated circuits. In Figure 18.2, for example, an analog multiplier is used with a low-pass filter to provide a direct reading of the average of the square of the signal. An output stage, adjusted to provide a square-root response, completes the RMS operation. The multipliers are the only components beyond those required for averaging, so the approach is fairly simple.

A digital RMS metering system samples the incoming waveform and directly computes either an average or an RMS value. Given the rapid pace of advances in analog-to-digital conversion, the digital approach is growing in popularity. The biggest challenge in a digital system is often identifying a time window for the averaging process. An analog low-pass filter theoretically provides the correct dc value for any given signal. Digital computation of the average requires knowledge about the waveform period. This is not usually possible. However, good performance can be obtained, particularly in the presence of power line interference, if the average is performed over a carefully chosen fixed time window. If averages are always computed over a 100 ms window, for instance, both 50 Hz and 60 Hz components cancel exactly, and power line interference disappears.

For power electronics, a specific time window choice can limit meter precision. A 100 ms averaging window works very well for both average and RMS values of dc waveforms or rectifier waveforms tied to line potential. In contrast, circuits such as inverters and ac-ac converters are not well served by this process. Given a 47.5 Hz output waveform from an inverter, a digital RMS meter with a 100 ms averaging window will measure the RMS over a 4.75 cycle window. The error can easily reach 5% because of the uneven number of cycles. The problem is illustrated in Figure 18.3. In the Figure, a 100 ms window is used for the computation of the RMS value. Figure 18.3a shows a full-wave rectifier output and its square with an averaging window synchronized with sin(t). Figure 18.3b shows the same waveform with a one radian delay in the averaging window. The average of v²(t) is 0.50 V -- the correct value -- regardless of the window phase shift. This result is compared to a 47.5 Hz signal from a voltage-sourced inverter. Figure 18.3c shows this VSI waveform and its square, again with a 100 ms averaging window. The average of the square of this waveform is 0.667 V; a phase advance of one radian alters the computation, and gives an erroneous 0.688 V instead. Figure 18.3d shows the result with a one radian window delay, which shows an average of 0.652 V. The window phase introduces ±2.5% error in the computation of the RMS value. Digital metering for power converters is a challenge because of this timing issue. Perhaps the meter can attempt to sense some information about the signal and adapt the window accordingly. In some cases, it is reasonable simply to use a much longer timing window to extend accurate computations to lower frequencies. This can be problematic. The 47.5 Hz signal requires an averaging window five seconds wide to reduce the error from window timing to 0.1%. Whatever the approach, it is important to recognize the impact of the measurement process.

Many commercial instruments make an operational distinction between dc and ac waveforms that goes beyond the distinction between average and RMS values. In a dc power supply or electronic circuit, the ripple waveform gives information about performance and noise. Most conventional meters add a high-pass filter at the front end of the RMS sensing process. This allows the ripple to be characterized independent of the dc level. Unfortunately, the high-pass filter introduces limitations of its own. In most cases, it is arranged to pass line-frequency signals. When inverters or signals below 50 Hz are measured, the high-pass filter provides some level of attenuation, and the measurement results are hard to interpret. If the RMS value of a non-sinusoidal waveform is needed, particularly when the waveform contains significant ac and dc values, the high-pass filter effect must be taken into account. From Fourier analysis, given a periodic function f(t), the RMS value can be obtained by combining the average value with the high-pass RMS value. In effect, the high-pass measurement is intended to provide results based on all Fourier components except the dc value. We can find the total RMS value from

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Example 18.2.1 The following waveforms are to be checked with an average-reading RMS-indicating meter: a sine wave, a triangle wave, a square wave, and a constant dc level. Each has a peak value of 10.00 V. What will the meter reading be for each case? Meter error is ±0.1% of its 20 V full scale level. What is the uncertainty of the sine wave reading?

This type of meter measures the average of the absolute value of the input, then scales the result to show the RMS value for a sine wave. By definition, the meter will show the correct value for the sine wave. The error in the reading is ±0.1% of 20 V, or ±20 mV. Therefore, the reading with the sine wave is 7.07 ± 0.02 V (the meter accuracy is three significant digits at best). For the triangle wave, the absolute value has an average value of 0.5 times the peak, or 5.000 V. The meter will scale this by 0.7071/0.6366, the ratio of RMS to average for a full-wave sinusoid. Therefore, the display will show 5.55 ± 0.02 V for the triangle. For the square wave, the absolute value will be 10 V, and the reading will be 11.11 ± 0.02 V. The 10 V dc level will also be shown as 11.11 V.

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Example 18.2.2 A two-level PWM waveform of 150 V peak is modulated with 80% depth. The switching frequency is 6 kHz, while the modulating signal is at 60 Hz. This waveform is studied with several different types of meters: an averaging meter, an average-reading RMS indicating meter, a "true RMS" with a high-pass filter, a true RMS meter with no filter, and a true RMS meter with a 100 Hz low-pass filter. What will each meter show?

This waveform is similar to the one in Figure 6.14, although switching is faster. Since it is a two-level PWM waveform, the RMS value does not depend on the depth of modulation. It is just 150 V, the absolute value of the waveform. Table 18.1 lists the various values shown on the meters. These meters do not give much information about the PWM waveform. In fact, only the meter with low-pass filter shows a value that changes when the modulating signal is altered.

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18.3 Power and Current Measurements

In most cases, the average power is of particular interest. Many modern instruments use digital sampling to sense current and voltage and compute the actual average power flow. The timing window problem from the RMS case is relevant, and power measurements for frequencies above dc but below 50 Hz can be difficult. It is possible to build an electromechanical device that measures power directly from the applied voltage and current. This electrodynamometer metering technique is still widely used in industrial equipment.

Power measurement in general requires sensing of both voltage and current. Voltage is relatively familiar. In a typical system, the voltage to be measured is divided down to a useable level, then applied to an op-amp circuit for initial processing. This approach easily supports voltages up to more than 1 kV. Current in a power converter is a more difficult issue. At currents of 1 A or more, op-amp circuits cannot be used directly. Current dividers are sometimes used, but more typically a small resistor is simply inserted in a circuit, and the voltage drop across it is sensed and processed. A 10 m resistor, for example, allows convenient measurement of currents up to about 10 A with minimal disturbance of the circuit being tested. Low resistances for this purpose are called current shunts.

An important drawback of current shunts is that they require a change in the converter system: a physical device must be inserted in a circuit loop. In many cases, it is unreasonable to turn off a converter, install a shunt, take a measurement, and then remove the shunt when only a quick reading is needed. Alternatively, the magnetic field created around a wire by its current flow can be sensed and interpreted. The magnetic sensor can be clipped around a wire for convenient measurements. This technique is very useful in power converters, since the relatively high current levels create significant field strengths. If no dc current is present, a current transformer (CT) will do the job at relatively low cost. If dc fields must also be sensed, Hall-effect materials are useful, since a magnetic field changes the resistance of a material showing the Hall effect. Commercial Hall sensors are readily available in current ranges from a few amps up to many thousands of amps. CTs are very common in ac power installations. Both technologies have been adapted to current probes capable of sensing ac or dc current waveforms for oscilloscopes.

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Example 18.3.1. A typical Hall-effect current sensor uses a single dc voltage V_in for its power and biasing. The device has three terminals: input, output, and common. When there is no current flow, the output is V_in/2. With a current of 200 A, the output is 0.8V_in. With a current of -200 A, the output is 0.2V_in. At lower currents, the output is a linear function V_in(0.5 + 0.0015 I). The device differs from the linear model V_out = V_in(0.5 + 0.0015 I) by no more than ±0.2% of V_in. A flow of 5 A is to be monitored. What will the voltage output be if V_in is 12.000 V? What is the uncertainty of this current measurement? What is the full-scale measurement error?

The uncertainty as given means that V_out = V_in(0.5 + 0.0015I ± 0.002). If V_in = 12 V, the output for zero current ideally is 6 V, but in fact could be as low as 0.498V_in = 5.976 V or as high as 6.024 V. For 5 A flow, the output is ideally 6.090 V. Given the error, the output could in fact fall anywhere between 6.066 V and 6.114 V. The lower value corresponds to 3.67 A, while the higher value corresponds to 6.33 A. Thus the output voltage is 6.090 V ± 0.024 V, corresponding to current of 5 ± 1.33 A. If we try to measure a current at this low level (2½% of full scale), the uncertainty will be a substantial fraction of the reading. A measurement of 200 A will also give ±1.33 A of uncertainty, corresponding to ±0.67% of full scale.

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18.4 Low-Voltage Polyphase Power

The high energy levels in a power converter can quickly damage components when mistakes are made or when failures occur. For laboratory testing, it is usually very beneficial to provide extra protection so that minor problems do not cascade into major failures. Many laboratory dc power supplies provide active current and voltage limiting. These features are very valuable for tests of dc-dc converters, since the input source can be set up with a power limit. For rectifiers, and especially for polyphase rectifiers, sources with active limits are very expensive. The alternatives, fuses and circuit breakers, are usually too slow to protect against significant damage when a problem occurs.

Small transformers are usually impedance limited, meaning that the device impedance is high enough to prevent unsafe current flows when severe problems such as output shorts occur. Figure 18.4 shows a transformer combination that supports rectifier tests at power levels up to about 200 W. If the transformers have impedance limiting, rectifier tests are quite safe, and small problems are unlikely to cause major damage.

The transformer connections in Figure 18.4 support either single-phase or three-phase inputs. In the single-phase case, transformers A and B are connected in reverse parallel across the input source. The output becomes a split ac voltage, with V_A and V_B 180 apart. In the three-phase case, the transformer set becomes a conventional four-wire wye-wye connection. The combination makes an extremely useful tool for rectifier testing. Many of the experiments in Chapter 19 rely on this transformer set to provide safe line-frequency power.

18.5 A Suggested Tool for Rectifier Experiments

Imagine an experimental controlled rectifier. To prepare the experiment, the researcher must choose switching devices, design a control circuit for gate signals, construct gate drives to apply these signals to the switches, arrange for a safe ac power source, and provide capability to make adjustments so that a variety of conditions and waveforms can be examined. This is a long list of tasks, and can be daunting to anyone interested in learning power electronics through experiments. In this section, a generic design for an SCR-based controlled rectifier is presented. It is hoped that the Section provides enough of the up-front work to make fairly sophisticated rectifier experiments accessible.

An SCR rectifier requires gating pulses and timing delays. In general, the delays are measured from an ac line signal. For convenience, it is certainly useful to organize controls for several SCRs to support three-phase converters or single-phase bridge circuits. A possible block diagram, based on a midpoint rectifier, is given in Figure 18.5. The basic process in the block diagram can be described as follows:

1. One of the line phases is converted to a 5 V square wave to provide a system clock. A small power supply provides power for the logic and the gate drives.

2. A controllable delayed pulse is created with a monostable chip. The delay is calibrated to be up to about ½ cycle. The pulse serves as the phase A gate timing signal.

3. Fixed delays are added to create gate timing signals for phases B and C.

4. Each gate timing signal triggers a separate monostable to produce an appropriate pulse for actually firing the gate.

5. A gate drive circuit applies signals to a pulse transformer to provide isolated gate triggering.

This process provides a straightforward phase delay controller. It is easy to provide enough adjustment range for both 50 Hz and 60 Hz line frequencies.

A practical phase delay controller has some interesting properties. For the controller of Figure 18.5, all the timing signals are taken from one input phase. The individual phases are rarely labelled in practice, but here each phase voltage must be in proper sequence for correct operation. If phases B and C are switched, for instance, the converter output becomes quite low. Because of this, many commercial SCR controllers produce independent time references for each individual phase. While independent timing allows arbitrary phase connections, it increases the sensitivity to noise, and requires sensing of all phase voltages. The system of Figure 18.5 is a useful choice if the phasing is known.

A full circuit to implement the block diagram of Figure 18.5 is given in Figure 18.6. The circuit provides three types of adjustments:

1. The master phase delay adjustment. This could be set up as a front-panel control to adjust the phase delay between 0 and 180.

2. Phase conversion. A switch allows the user to choose between 1/3 cycle delay between phases A and B and ½ cycle delay between A and B. In the former case, three-phase rectification is supported, while the latter case supports a two-phase (split single-phase) midpoint configuration.

3. Timing trims. Trim adjustments are included for each phase delay pulse. This allows the user to set the unit for either 50 Hz or 60 Hz operation. A master adjustment delays the main pulse so that any phase can be used successfully as a reference.

The adjustment process proceeds as follows:

1. Begin with three-phase input. Connect each SCR anode to its respective phase, using a transformer box such as the one in Figure 18.4 as the source. Connect the cathodes together and provide a resistive load back to neutral so that rectification can be observed. Set the panel switch as appropriate for three-phase input.

2. Set the front panel delay to zero. Adjust the main pulse until the phase A SCR fires just after the zero crossing of its input ac waveform.

3. Set the front panel delay so that the phase A firing signal is delayed about 60 (1/6 of a cycle). Adjust the phase B timing trim until the second phase also fires with about 60 delay. Then adjust the phase C timing trim for 60 delay.

4. Connect a split single phase input to anodes A and B in place of the three phase source. Change the front panel switch to the two-phase setting. Adjust the "phase B two-phase" delay trim until the gate delays on phases A and B match.

The monostable chips provide a linear delay adjustment. If the input source phasing in changed, the calibration procedure must be repeated.

The SCR control unit is a very powerful experimental tool for examining controlled rectifiers. The direct delay action is relatively easy to follow, and the circuit contains few extra components. The pulse transformer gate drives ensure isolation between the control circuit and the SCR terminals. Two sample waveforms for controlled rectifiers are given in Figures 18.7 and 18.8. In the first figure, a three-phase input is rectified into an R-L load with A  60. In Figure 18.8, two boxes are combined to create a full-bridge single-phase rectifier.

18.6 A Suggested Tool for Inverter and Dc-Dc Converter Experiments

Experiments in both dc-dc and voltage-sourced dc-ac converters make use of transistors and pulse-width modulation. To prepare such an experiment, we must create a PWM process as described in Chapter 6, add an appropriate gate drive and switch, then build the power electronic circuit. For an inverter or multi-quadrant dc-dc converter, the various switching functions must be properly coordinated to satisfy KVL and KCL restrictions. As in the case of the SCR box, the up-front preparation work for a dc-dc or dc-ac converter experiment can be long and difficult. In this Section, a blue box based on a power MOSFET is described. The circuit supports a variety of converters; even ac-ac conversion is feasible if several boxes are used in combination.

The PWM process that combines a triangle-wave oscillator with a comparator lends itself well to integration. Today, several manufacturers offer dozens of PWM ICs intended to support various dc-dc power converter designs. Nearly all of these circuits contain five basic elements:

A triangle or sawtooth oscillator with an adjustable frequency. A triangular voltage is generated by switching a current source into a capacitor.

A comparator to produce the PWM output.

A latch. This element ensures that the switch operates just once per cycle. Without the latch, noise or other problems might create extra unwanted switching pulses.

Protection to shut down the switches under conditions such as low voltage, high temperature, or high current.

Output transistors capable of driving a MOSFET gate.

Different PWM ICs might add features such as dual outputs, protection functions, op-amps for feedback control, amplifiers for low-resistance current shunts, and so on. The blue box here uses one such IC as the basis for control.

Each converter application imposes slightly different requirements on a MOSFET system. For example, a buck converter often has the FET drain connected to the high side of the input. A boost converter connects the FET source to the low side. A half-bridge inverter uses both arrangements simultaneously. A flexible circuit must provide isolation for the MOSFET so that all possible connections are supported. Isolation can be a challenge. Both the switching function and gate drive power must be separated from the PWM circuit through isolation.

Figure 18.9 shows a block diagram of the MOSFET blue box system. The unit is built around the SG3526 PWM controller. This particular controller is used primarily because it permits several identical controllers to be synchronized conveniently. This feature supports inverter applications and multi-quadrant dc-dc converters. This particular IC has two separate outputs, each active during half of a switching period (it was originally intended to support forward converter designs). The two outputs are combined with an OR function to create a single switching function with 0 D 1. The box is provided with an uncommitted diode to make dc-dc converter circuits more convenient. The process can be described as follows:

1. Power for the controller is provided from either an ac wall plug or a separate 9 V to 12 V battery.

2. The signal amplifier of the SG3526 is connected as a follower. The voltage on pin 1 serves as the duty ratio control input to the comparator. A front panel potentiometer allows adjustment of D, or an external voltage between 0 and 5 V can be injected to control d(t).

3. The triangle oscillator frequency is set with an RC time constant. A front-panel potentiometer allows adjustment of f_switch, over a range of about 100:1.

4. The switching function output is created by ORing the two half-cycle outputs. The switching function drives an optocoupler so that the information can be sent to the MOSFET across isolation.

5. A small flyback converter is used to provide an isolated 12 V source for the gate drive.

6. A driver IC takes the low-power signal from the optocoupler and drives the MOSFET gate.

Since the unit controls only one switch, there is minimal need for adjustment or calibration. The front-panel controls provide almost complete freedom over frequency and duty ratio.

A circuit that implements the block diagram in given in Figure 18.10. In this version, a 400 V MOSFET was used to keep reliability high in the laboratory. The experimenter might be tempted to used long wires to make external connections. The inductance added to the circuit by external wires leads to high L(di/dt) voltage transients. A MOSFET rated for 100 V or less can easily be destroyed by inductance effects if the experimental layout is loose.

For Figures 18.11 and 18.12, the MOSFET box was used to construct a buck-boost converter with 12 V input and nominal -12 V output at 15 W. Figure 18.11 shows the actual setup and the circuit. Figure 18.12 shows experimental traces of drain-source voltage, drain current, and inductor current in this converter. The duty ratio is close to 50%.

Fig. 18.10 -- General circuit for control of a power MOSFET.

When the MOSFET control box is to be applied to PWM ac-dc conversion, the most convenient arrangement is a half-bridge circuit. In the half-bridge, the switches must act in complement, such that q₁ + q₂ = 1. The circuit of Figure 18.10 supports this function. Two such circuits are used. One acts as a master, and provides the clock and switching function. The other acts as a slave: its switching function is overridden by the clock imposed from the master. In the SG3526, the clock can be forced to follow a low-impedance external

signal. The switching function from the master provides this signal. Figure 18.10 shows a single front-panel jack that can be switched for either master or slave duty. Once two boxes are linked in this way, an inverter (or any converter requiring q₁ + q₂ = 1) is easy to construct.

An experimental half-bridge is shown in Figure 18.13. Its PWM output signal is shown in Figure 18.14. In this converter, the time-varying duty ratio is provided with a laboratory function generator, connected to the duty ratio input of the master box.

Direct ac-ac conversion can be built with MOSFET boxes with a little insight. A bilateral switch can be constructed with a reverse-series MOSFET connection. Two such switches provide ac-ac conversion with a common neutral. The duty ratios need to have the proper relationship. In an example circuit given in Figure 18.15, an external square wave input to the duty ratio control of one bilateral switch forces the switches to operate at either 0 or 100% duty. Switching functions, in effect, are imposed directly from the function generator. The master-slave arrangement provides a complementary switching function for the second bilateral switch. The overall combination of four boxes supports direct ac-ac conversion. This circuit has somewhat limited reliability, since the switching functions are not exactly in complement. Any overlap causes brief current spikes, and current-limiting resistors are recommended.

18.7 Recap

Measurements in power converters involve unusual considerations compared to most electrical engineering fields. The operating frequencies of interest range from dc up to 1 MHz or more. Switching can occur in times as low as 10 ns, or even less. The waveforms themselves, as well as average and RMS values, are of interest in understanding and characterizing converter operation. Conventional meters do not cover the complete range of needs, and it is important to understand some metering properties to interpret information correctly.

Analog meters typically provide direct average measurements. For RMS measurements, many such meters are calibrated based on purely sinusoidal functions. Digital meters can use analog or digital signal processing techniques. While signal processing gives precise average and RMS calculations, these are usually performed over a definite time window rather than over a waveform period. Most commercial meters use low-pass filtering for dc measurements and high-pass filtering for ac measurements. The two can be combined when necessary to give an estimate of the RMS value of the complete waveform.

Any converter requires considerable testing. A low-voltage ac transformer system was suggested as a way to test single-phase and three-phase circuits with minimum risk. This transformer system can be of significant value for testing polyphase designs.

Converter experiments can be performed with a minimum of up-front effort if general control circuits are constructed in advance. These control circuits can be termed blue boxes, since they have simple unconcealed functions. A circuit for three-phase SCR control was discussed in some depth. A second circuit for controlling a single MOSFET was also introduced. Naturally, there are many design alternatives for blue-box functions. It is hoped that the discussion here will generate new and better ideas for carrying out these functions. A general MOSFET controller comes quite close to the overall need for a generalized converter. Such a controller can be designed to support dc-dc converters, voltage-sourced dc-ac converters, or even fully bilateral devices for ac-ac conversion and other functions.

18.8 Problems

1. An "averaging measuring, RMS indicating" meter is one that uses a full-wave rectifier with an averaging meter to indicate RMS value. Meters of this type are adjusted to give a correct reading for a sine wave. Consider such a meter, designed to read ac line voltages.

a) Given a meter that reads "120.2 V" when the waveform v(t) = 170cos(120 pi t) V is applied to it, what is the meter reading when the square wave 120sq(120 pi t) V is measured? How far off is the reading from the correct RMS value?

b) A PWM inverter switches a 200 V dc source with duty ratio chosen to make the wanted component 170cos(120 pi t) V. What reading will the meter give for this waveform?

c) The RMS value of a general switching function is to be measured. Plot the meter error as a function of duty ratio.

2. A typical "true RMS" meter accurately computes the RMS value of a waveform, but adds a high-pass filter between the input and the computation circuit. Such a meter is used to measure a high-frequency switching function for a dc-dc converter. Plot the ratio of the meter reading to the actual RMS value as a function of D (the ratio when D = 0 should be taken as the limit value, 1).

3. The following information is available for a certain waveform:

"True RMS" (high-pass) meter reading: 50.00 V

Average meter reading: 50.00 V

"True RMS" (high-pass) meter with a

1 kHz low-pass filter placed

in series with the input: 25.00 V

"Average measuring, RMS indicating" meter: 55.54 V

a) If a true RMS meter (no filters) is used, what will it indicate?

b) What sort of waveform might produce these results?

4. An average measuring, RMS indicating meter is used to test a switching function. The meter gives a reading of 0.500 V. What is the duty ratio?

5. A true RMS meter, with no high-pass filter, is available. A square wave with duty ratio 50% and frequency 200 kHz is applied to this meter, first through a low-pass filter with a 1 kHz cutoff frequency, and second without the filter. If the meter is accurate to 0.1%, what are the two readings and what are the tolerances of the readings?

6. Two separate SCR boxes each use the zero crossing of phase A as the trigger time for a gate pulse. The boxes are arranged to form a six-pulse rectifier, as shown in Figure 18.16. The phase delay dials are calibrated in degrees to provide between 0 and 360. Look at Figure 18.17. Where should the dials be set to produce this waveform?

7. A certain waveform is known to have non-zero dc value. It is rather distorted, but your group intends to use it for battery charging, and the details of shape are not all that important. Of course, it is critical to get the polarities correct. However, the terminals are not marked, and all the available meters are RMS types with no polarity indications. One of your colleagues asserts that a diode can be used to produce a half-wave action so that polarity can be determined. Another argues that this is not correct, since the meter will just square the result anyway. Settle this argument. Is it possible to determine polarity given an RMS meter and a diode? Will this work for the types of RMS meters described in this Chapter? If it is possible, what procedure will allow polarity to be determined?


8. A MOSFET is connected into a 12 V to 5 V buck converter with 50 cm of wire. This length of wire adds roughly 400 nH of series inductance. The MOSFET switches in about 50 ns. If the converter output load is 100 W, what voltage rating will the MOSFET require to avoid damage from L(di/dt)?

9. A general MOSFET controller is to support buck, boost, buck-boost, flyback, and other designs up to 50 V input. What should the MOSFET ratings be if the input source provides no more than 500 W and 10 A, output voltages are to be limited to 200 V, and output currents are limited to 10 A as well? Does your answer change if the MOSFET must also cope with up to 1 µH of stray inductance (it switches in 100 ns)?

18.9 References

P. T. Krein, "An integrated laboratory for electric machines, power systems, and power electronics," IEEE Trans. Power Systems, vol. 7, pp. 1060-1066, August 1992.

D. A. Torrey, "A project-oriented power electronics laboratory," IEEE Trans. Power Electronics, vol. 9, no. 3, pp. 250-255, May 1994.