19.1 Introduction

19.1.1 Overview

This Chapter lists a series of experiments, with explanatory material, suitable for exploring power electronics in depth. Four sets of experiments are included: a set of rectifier experiments that includes a laboratory orientation sequence, a set of dc-dc converter experiments, inverter experiments, and component experiments. An additional set, directed toward a dc-dc converter design project, is included as well. The Chapter in many ways stands alone as a Laboratory Manual; its inclusion here in the text helps provide a complete context for work in power electronics.

19.1.2 Safety information

The experiments discussed here are designed for relatively low power levels of about 100 W and below. They therefore can be performed with a minimum investment in special instrumentation and equipment, and safety concerns are minimized. However, the risks are not negligible, and it is important to make proper preparations and use due care in performing the work. Safe lab practice is the responsibility of the experimenter. It is not possible to perform completely benign power electronics experiments; damaged components or expensive repairs will be necessary if basic safety rules are not addressed.

It is especially important to be careful when working with spinning motors, and parts which become hot from power dissipation. Even if rugged equipment is chosen, many instruments can be damaged when driven beyond ratings. Please follow the safety precautions listed to avoid injury, discomfort, and lost lab time.

GROUND. Be aware of which connections are grounded, and which are not. The most common cause of equipment damage is unintended shorts to ground. Remember that most oscilloscopes are designed to measure voltage relative to ground, not between two arbitrary points.

RATINGS. Before applying power, check that the voltage, current, and power levels you expect to see do not violate any ratings. What is the power expected in a given resistor or other component? Does the device have polarity, and is it connected in the proper direction?

HEAT. Small parts can become hot enough to cause burns with as little as one watt applied to them. Even large resistors will become hot if five watts or so are applied.

CAREFUL WORKMANSHIP. Check and recheck all connections before applying power. Plan ahead: consider the effects of a circuit change before trying it. Use the right wires and connectors for the job, and keep the experiment area neat. Avoid manipulating circuits or making changes with power applied.

LIVE PARTS. Most semiconductor devices have an electrical connection to the case. Assume that anything touching the case is part of the circuit and is connected. Avoid tools and other metallic objects around live circuits. Keep beverage containers away from the work area.

Neckties and loose clothing should not be worn when working with motors. Be sure motors are not free to move about or come in contact with circuitry.

The most common cause of trouble in power conversion experiments is improper grounding practice. Any circuit can have only one reference node, and the circuit is altered if a probe or tool introduces an external connection. Ratings and polarities are also common problems. Electrolytic capacitors, for example, often burn or even explode if connected in reverse. Small resistors do not tolerate excess power levels very long. Neatness is an issue as well. A messy, convoluted circuit is extremely hard to debug. In power electronics, small inductances of wires make a significant difference. A neat, tight package in general operates much better than a layout with long looping wires.

19.1.3 Equipment assumptions

For the purposes of the experiments discussed here, the following minimum equipment is assumed:

1. Oscilloscope (digital preferred), two channels, 60 MHz bandwidth.

2. Function generator, 10 Hz to 2 MHz, sine and square waves.

3. True RMS multimeters.

4. Power supply, 0-24 V, 0-5 A or better.

5. Power supply, +12 V, 0-0.5 A (for control functions).

6. Access to standard ac mains power.

7. FET and SCR control circuits as discussed in Chapter 18, along with transformers described there.

8. Leads, connectors, various parts, and a breadboard system for circuit prototypes.

The following additional equipment is very helpful, and is recommended:

1. Magnetic current probe, 0-20 MHz.

2. Digital wattmeter.

3. Power supply, 0-50 V, 0-10 A.

4. Isolation amplifier for oscilloscope channels.

5. Temperature probe for multimeter.

6. Access to three-phase mains.

7. A semiconductor curve tracer.

Be sure to be aware of ground connections or other considerations of the instruments. Many power supplies have ground connections that should be removed before using the equipment with a power converter.

19.1.4 Keeping a laboratory notebook

A proper laboratory notebook is a crucial tool for work in any experimental environment. A notebook used in a research lab, a development area, or on the factory floor is probably the most valuable piece of gear in the engineer's arsenal. The purpose of the notebook is to provide a complete record of practical work. This should help avoid duplication of effort. Human memory is not perfect, but a notebook is a permanent record. In industrial practice, the notebook is usually the employer's property. Many companies have specific rules about notebook format and content. The suggestions here are provided for general guidance, and are not meant to conflict with requirements in various areas of practice. In general, a notebook should include:

Diagrams of all circuits used in the lab. The important factors are to be able to reproduce a setup and check for possible errors.

Procedures and actions. The idea is to provide enough information so that the experiment could be repeated.

List of equipment used, especially if unusual items are involved.

All experiment data. Be sure to include units and scale settings. It is generally good practice to record data in its most primitive form to avoid errors. Scaling or other calculations can be done later.

The date, and the names and signatures of the experimenters.

It is usually permissible to include calculations, observations, and even speculations in a notebook, provided these are clearly marked and kept apart from experimental data and actual lab work. A bound book with permanent, pre-printed page numbers is a good selection for use as a notebook. Loose sheets often get lost or spoiled, and spiral books offer the temptation to tear out unwanted information. Notebook errors should be crossed out (not obliterated). A notebook should be kept in ink, consistent with its function as a permanent record. Keeping a complete lab notebook sometimes seems inconvenient, but in the long run saves a tremendous amount of time and effort.

19.2 Experiment -- Demonstration of Special Equipment.

19.2.1 Introduction

This experiment tests some of the special equipment discussed in Chapter 18. It also provides practice with the general equipment of an electronics lab in preparation for the full sequence of experimental work. As discussed in Chapter 18, three special equipment items are proposed to support the full range of power electronics experiments in a standard laboratory:

A low-voltage ac mains supply, from a transformer bank, for experiments with rectifiers and other circuits. The suggested arrangement supports both single-phase and three-phase power input. A circuit diagram for the combination was provided in Figure 18.4.

A self-contained SCR control unit. The suggested design contains three silicon controlled rectifiers (SCRs) and time delay circuits to produce turn-on control signals. The anodes and cathodes are isolated.

An isolated power FET control box. The FET provides switch action for almost any type of dc-dc converter. A complete pulse-width modulation block creates a PWM switching function, with adjustable frequency and duty ratio. As in the SCR circuit, this means that the terminals of the FET can be connected to any voltage level up to the device ratings.

The function of these circuits is to support tests of useful power converters. The internal operation is important and well worth exploring. The circuits will be considered as "blue boxes" rather than black boxes, meaning that their function is not hidden away.

19.2.2 Demonstration circuits

For this demonstration, both the SCR and the FET will be used in simple converter circuits. The SCR set will be used in a controlled full-wave rectifier circuit, while the FET unit will be used to form a basic dc-dc converter. These circuits are typical power electronics applications, not too far removed from simple commercial products.

There are two major ways to form a full-wave rectifier. One is the rectifier bridge circuit, which converts a single ac voltage source into a full-wave rectified waveform. The second involves a center-tapped transformer as a "two-phase" ac source. This second form requires a more expensive transformer, but needs only two rectifiers. Both are shown in Figure 19.1. As shown in the Figure, SCRs can be substituted for the diodes in a full-wave rectifier. The SCRs are operated half a cycle apart, with an adjustable phase angle delay.

19.2.3 Procedure

Part 1 -- Rectifiers and the SCR box

1. Connect the transformer set to single-phase input to provide both positive and negative outputs. Connect two 1N4004 diodes for full-wave output (anodes to phase A and B output, cathodes in common to load). See Figure 19.2.

2. Connect a load of approximately 50 from the common cathode to ground. What resistor power rating is needed?

3. Observe the resistor voltage waveform. Observe diode current and comment. Measure the resistor RMS voltage, RMS current, power, and average voltage. What is the relevance of each?

4. Remove the diodes, and substitute SCRs labelled A and B from the SCR unit. Set up the SCR box for two-phase operation. Use a 25 load in this case. What should the power rating be?

5. Turn the phase delay control to the lowest setting. Double check all connections, then turn the power on.

6. Observe the voltage waveform across the resistor. Notice how the waveform changes with changes in the control setting. Again measure RMS voltage, RMS current, power, and average voltage, and consider the relevance of each.

Part 2 -- Dc-dc conversion and the FET box

The FET unit will be used in a simple circuit which converts a dc voltage to a lower level with minimal power loss. In essence, the output is presented with a rapid switching of the input. The average output level (the dc portion) is lower than the input since the switch cannot be on more than 100% of the time.

1. Set up the FET control box as shown in Figure 19.3.

2. Observe the drain-to-source voltage. Turn the unit on. Adjust the output for 50% duty ratio and about 50 kHz.

3. Connect a voltage source of 20 to 30 V to the input. Observe the output waveform and average voltage. Adjust the duty ratio and notice the change. Adjust the frequency and notice the change. Explain the results.

Part 3 -- Power semiconductor devices and the curve tracer

Power semiconductors are important to the field of power electronics. The curve tracer is a helpful measuring instrument to characterize these devices. Recall the characteristic curves for diodes, bipolar transistors (BJTs), and FETs. Examples are given below. The diode shows exponential V-I behavior. Transistors show a family of curves, dependent on the base or gate input operation. For switching operation, only a small portion of these curves is relevant. (Which portion would it be?)

The curve tracer is an instrument intended to measure these device curves directly. The BJT, for example, is characterized by a certain collector-emitter voltage, collector current, and base current. Recall that the BJT is basically a current-controlled current source. To measure BJT curves, the curve tracer applies a specified range of collector-emitter voltage and collector current values. Several discrete base current values are then applied in steps, and the results are displayed on an oscilloscope. The FET is a voltage-controlled current source. The drain and source terminals function very much like those of the BJT collector and emitter. The gate must have a voltage applied relative to the source, rather than a current. In the procedure below, four classes of devices will be tested on the curve tracer.

1. A rectifier diode (1N4004) is to be tested on the curve tracer. Since the defining characteristics are forward voltage and current, the device should be connected as if its anode were a collector and cathode were an emitter.

2. With the curve tracer socket off, set up the unit for limits of about 1 A and 1 W. The 1N4004 can handle up to 400 V in its off state.

3. Check your connections. Apply power to the socket and observe the diode waveform. Notice that the typical model of a constant 0.7 V drop has limited accuracy. A better model would also include a resistor to model the upward slope of the curve. What resistance and forward voltage provide the most accurate model for your device?

4. A BJT is to be tested on the curve tracer. Let us assume that the device is a generic, unknown part. To be conservative, limit current to 0.1 A, power to 0.5 W, and voltage to 20 V. Connect the part with the socket off.

5. Double check connections. Allow base current of 0.1 mA per step to be applied. Turn on the socket. Adjust as necessary to observe the curves. Keep power levels below 0.5 W in any case if a small device is being tested. Which portions of the curves are useful for switching action? How much base current will be needed if the device is to be used to switch 0.5 A?

6. A power FET is to be tested on the curve tracer. This power part should be limited to 5 A, 1 W, and 50 V. Connect the part with power off. The drain terminal should be connected as the collector, source should be connected as emitter, and gate should be connected as base.

7. Double check your connection. We want to vary gate-source voltage from approximately zero to about ten volts.

8. When ready, apply power to the socket and observe the curves which result. Which portions are relevant for switch action? As with the diode, a resistance is often used to model the slope of the curves. What value of resistance provides a good model when the gate-source voltage is 10 V?

9. The SCR can be thought of as a diode with an extra gate terminal. When sufficient gate current flows, the device operates as a diode. Without it, the device is off. For the SCR here, limits of 10 A, 2 W, and 100 V are appropriate. To test it, associate the anode with a BJT collector, the cathode with an emitter, and the gate with a base.

10. Double check connections. The gate current can be made as high as 0.2 A without damage, but try values around 50 mA to best see the device curves.

11. Consider what curves are expected (e.g. diode when on), then apply power. Are the results what you anticipated? Is there a family of curves, as for the transistors?

19.2.4 Study questions

In each experiment, a set of questions to guide further study and reports will be provided.

1. In dc output converters, what is the relevance of RMS output voltage? What about average voltage? (Hint: consider the effects on loads which are purely resistive, and on loads which consist of a large inductor in series with a resistor.)

2. For the simple dc-dc converter tested in Part 1 of the above procedures, explain how to predict the average value of output voltage from the input voltage, the switching frequency, and the switch duty ratio (the fraction of the time during which the switch is on).

3. Which portion of the curve tracer device characteristics would you expect to use in a switching application? What would the curve tracer display if a current-controlled ideal switch were to be measured?

19.3 Experiment -- Basic Rectifier Circuits

19.3.1 Introduction

The objective of this experiment is to provide additional practice with power electronics measurement techniques. These will be studied in the context of simple controlled and uncontrolled rectifier circuits. Properties of simple R-C, R-L, and R-L-C circuits are studied in introductory circuit analysis courses. Properties of "D-C" circuits (diode-capacitor circuits) are less well known. Similarly, D-L, D-L-C, and various D-R-x circuits are not widely studied. The behavior of these circuits provides a practical look at power electronic converters, both from the standpoint of energy conversion applications and from the standpoint of laboratory measurements. This is the focus of the Basic Rectifier Circuits experiment. The operation of the SCR will be examined briefly as well. An R-C timing circuit for adjusting the phase delay of an SCR will be constructed and tested.

19.3.2 Basic theory

Consider the simple half-wave rectifier shown in Figure 19.5. The state of the diode depends on the input voltage polarity -- and also on the load. With no information about the load, it is not possible to predict either the load current or voltage. With a resistive load, the load voltage is zero whenever the diode is off. One simple way to find the circuit action (even though we already know what the circuit does), is to take a trial method approach as in Chapter 2. Since an off diode cannot block forward voltage, the diode will be on if and only if the input voltage is positive. The current is given in Figure 19.6. All currents and voltages in a diode circuit must be consistent with the restrictions imposed by the diodes. Even a complicated diode circuit combination can be understood quickly with the trial method.

Now, look at the inductive load of Figure 19.7. Assume that the inductor is large. If current is initially flowing in the inductor, the diode is on. Inductor voltage V_L will be positive or negative, depending on the input voltage and the inductor current.

Since there is current flow, the diode will stay on for some time regardless of the V_in value. If V_L = L(di/dt) is negative, the inductor current will fall, possibly even to zero. The diode must stay on until the current reaches zero.

Capacitive loads act much differently. Consider the capacitor of Figure 19.8, fully charged and supplying energy to the resistor. As long as V_in < V_out, the diode will be off. When V_in becomes larger than V_out, the diode must turn on. But then a large forward current C(dv/dt) will flow until V_in becomes less than V_out. Brief, large current spikes are a feature of Diode-Capacitor circuits. Such currents are typical of the simple dc power supplies in most cheap electronic equipment.

Diodes offer no control means, and a switch capable of blocking forward voltage is needed to add a control function. The SCR is one provides this function. Nevertheless, it fulfills the necessary forward-conducting bidirectional blocking characteristic. The SCR is called a latching device, because the on-state is self-sustaining. Once a turn-on command is applied, the SCR will remain on until the forward current is removed. This means that the device is exactly equivalent to a diode once on.

Consider the half-wave resistive circuit of Figure 19.9. Turn-on of the SCR can be delayed to alter the waveshape. The turn-on delay is traditionally measured in degrees relative to a full diode waveform. The action of this control is not hard to determine for a known load, since the input waveform is simply being switched on and off.

19.3.3 Measurement issues

In power electronics, measurement interpretation is an important ingredient of obtaining data and coming to conclusions about circuit behavior. Like any electronics laboratory, we will use voltage waveforms from an oscilloscope, and voltage and current magnitudes obtained from meters. Some important additional measurements include current waveforms and phase angles. Many of the waveforms are not sinusoidal, so the actual wave shape is important information.

For average and RMS measurements, a typical laboratory multimeter such as the Fluke model 8010A provides a useful basis for discussion. It displays the average value of the input whenever it is set for dc. When set to ac, this meter directs the input through a capacitor, and computes the RMS value of the ac portion which passes through. Some of the important meter specifications are given in Table 19.1. Many power converter waveforms contain both dc and ac. The "full RMS" value might be useful in this case. With most multimeters, even "true RMS" units, such as the 8010A, the RMS values for ac and dc portions must be measured separately and combined to give the correct result.

Power itself is important. There are growing numbers of manufacturers offering digital power meters appropriate for complicated waveforms. One type, which will be used here as an example, is represented by the Valhalla Scientific model 2101 voltage-current-power meter. This instrument samples the incoming voltage and current waveforms, and computes RMS values as well as the average power. The current is measured by sensing the voltage across a fixed 0.01 resistor. A meter configured in this way need not distinguish between dc and ac waveforms, and can provide accurate power readings over a wide frequency range. A functional symbol is shown in Figure 19.10. The voltage is sensed across the input. The output connection forces the current to flow through the sensing resistor. An input signal at 0 Hz or 40 Hz-10 kHz will give a true RMS display.

Low-impedance sense resistors can be used for complete current waveforms, but they can introduce grounding problems in a circuit. Industrial laboratories specializing in power electronics make extensive use of Hall-effect current probes that sense the magnetic fields around conductors. One major drawback is that the probes have an internal dc offset which might drift as the temperature changes.

Timing is critical in the operation of most power converters. Since switches are the only means of control, the exact moment when a switch operates is a key piece of information. The SCR provides a typical example. Consider the waveforms in Figure 19.11. A sinusoidal waveform (perhaps the input voltage to a rectifier) serves as a timing reference. It is straightforward to measure the time shift between this wave's zero crossing and the turn-on rise of the switched signal below it. The example in the Figure shows two 60 Hz waveforms. The time delay _d can be measured directly from the graph as about 1.25 ms. Since a full 360 degree period lasts 16.667 ms, an angle _d can be calculated from _d as

One important detail in making this measurement is to make sure both oscilloscope traces are triggered simultaneously. The "chop" mode of the scope is useful for this purpose.

19.3.4 Procedure

Part One -- The Diode

In this first part, a waveform generator is used as the power source so that higher frequencies and small components can be used for testing. Please use care in connecting and operating this instrument. It is not designed to supply high current.

1. Obtain a toroidal or audio transformer. One alternative is a 60 turn primary and a 60 turn secondary on a Ferroxcube 500XT400-3C8 ferrite toroid core.

2. Construct the circuit shown in Figure 19.12. Diodes should be standard 1N4148 rectifiers, or similar.

3. Be careful with ground connections. Set the waveform generator for approximately 1 kHz output at about 10 V peak. Observe V_out with the scope.

4. Sketch the output waveform under "no load" conditions (the scope probe gives a slight load).

5. Load the bridge with a 500 resistor (compute the necessary power rating first). Observe and sketch the output voltage waveform. Use a current probe or place a 10 resistor in series with the transformer output to observe the current out of the transformer. Sketch the current waveform.

6. Connect an inductor (a reasonable value is about 25-50 mH) in series with the resistor. Observe and sketch the resistor voltage waveform and the current into the bridge. Measure the average resistor voltage with a multimeter.

7. Remove the R-L load. Instead, attach a 47 resistor in series with an 0.1 µF capacitor. Place a 10 k resistor across the capacitor terminals. Observe and sketch the capacitor voltage waveform and the bridge input current waveform. Also measure the average capacitor voltage.

Part 2 -- The SCR

In Section 19.2, we saw a simple controlled rectifier example, and the waveforms which result. The gate control was described as a pulse. In this Section, an R-C delay circuit for operating an SCR will be examined. It is similar to the circuit used in commercial lamp dimmers.

1. Construct the circuit shown in Figure 19.14. The input source is taken from the 25 V transformer set.

2. Use a resistor substitution box or other variable resistor for R_c. Observe the V_g and V_load waveforms for R_c values of 0, 200, 400, 600, 800, and 1000 . Sketch the two waveforms for two or three values of R_c. Measure the turn-on delay by comparing V_g or the gate current with V_load with the oscilloscope set for line triggering. Also, use a multimeter to measure the average value of V_load in all cases.

19.3.5 Study questions

1. For part 1, what waveforms would you expect for R, R-L, and R-C loads? Hint: think in terms of simple filtering.

2. Compare the actual waveforms with those expected. Compute the actual circuit time constants, and discuss how they might affect the waveforms.

3. The R-L and R-C cases of part 1 represent different output filter arrangements for a rectifier circuit. Discuss the circumstances under which each of these will be effective and appropriate.

4. Comment on how the diode forward voltage drop (about 1V) affects the waveforms.

5. From part 2 data, tabulate and plot the average load voltage vs. the value of R_c.

6. Compute the SCR gate circuit R-C time constants. Is the turn-on delay governed by R-C?

19.4 Experiment -- Single-phase Rectifiers

19.4.1 Introduction

This experiment examines the properties of single-phase controlled rectifiers. Converter concepts such as source conversion and switch types will be illustrated. Popular applications such as battery chargers and dc motor drives will be tested. In Section 19.3, you had a chance to become familiar with the basic action of the SCR, and also studied a number of non-resistive rectifier load circuits. Now, the SCR boxes described in Chapter 18 will be used to study controlled-rectifier action in more depth.

19.4.2 Basic theory

In a switched converter network, KVL will not allow us to connect the utility ac voltage source directly to a dc voltage source, so a dc current source is needed. Consider some of the loads studied in Section 19.3. A resistive load is a crude example of current conversion: the incoming voltage produces a proportional resistor current. This is a far cry from an ideal current source, but it does result in a conversion function. An inductive load is a better conversion example: the inductor voltage V_L = L(di/dt) resists any change in current. If L is very large, any reasonable voltage will not alter the inductor current, and a current source is realized. A capacitive load has the opposite behavior. The capacitor current i_C = C(dv/dt) responds whenever an attempt is made to change the capacitor voltage. If C is very large, no amount of current will change the voltage, and a voltage source is realized. Many electrical loads, especially motors, are inductive. As a result, most circuits behave in such a way that current does not change much over very short periods of time. In power electronics practice, this behavior, along with the desired source conversion function, means that most loads are treated as "short-term" current sources.

The basic single-phase controlled rectifier is shown in Figure 19.15. If the load is inductive, there is a KCL problem: the switch cannot be turned off. To see that this is so, observe what happens to L(di/dt) when an attempt is made to turn the switch off. The current must approach zero almost instantaneously. The value of L(di/dt) is a huge negative voltage. In practice, this voltage will likely exceed the blocking capabilities of the switch, which will be damaged. A simple solution is to provide a second switch across the load, as shown in Figure 19.16. In simple ac-dc converters, this switch can be a diode, or it can be a second bidirectional-blocking forward-conducting device.

Two typical loads for ac-dc converters are the dc motor and the rechargeable battery. The dc motor has an inductive model, as shown in Figure 19.17. The motor looks rather like a voltage source, but its windings provide a significant series inductance. A battery is intended as a good dc voltage source. To provide the desired energy conversion function, something must be placed in series with the battery for current conversion. A resistor can be used with a loss in efficiency. Alternatively, an inductor can be used, as in the circuit of Figure 19.18. Analysis of this circuit is not trivial. The controlled switch is on whenever V_in is positive. When it is on, the output current is given by

When the controlled switch is off, inductor current is

If L is large, the current is approximately constant. These differential equations can be solved to give actual values of current. Charging current is controlled by the resistor value and also by the phase delay used to operate the SCR.

The form of circuit expected for single-phase conversion appears in Figure 19.19. The switches are implemented with an SCR and a diode. In this case, the output voltage is V_in whenever the SCR is on, and zero when it is off. The SCR turns off automatically when V_in 0. The voltage waveform is familiar: a half-wave rectified waveform, possibly with a delayed turn-on, as in Figure 19.20. The voltage has an average value given by

where is the angle of delay before the SCR is turned on. This integral gives

Since the output is a dc current source, average power exists only at dc, and is simply I_out·V_out(ave).

19.4.3 Procedure

Part 1: Ideal R-L load

1. Connect phase "A" of the nominal 25 V supply, the SCR labelled "A" in the SCR box, and a resistive load, as shown in Figure 19.21. Estimate the required resistor power rating. Record the RMS value of the source voltage.

2. Set the SCR turn-on for zero delay (i.e. set it to act as a diode). Observe the output and load voltage waveforms (see the figure). Measure the following output parameters and sketch the voltage waveform: V_out(ave), V_out(rms).

3. Repeat #2 for delays of approximately 30°, 60°, 90°, 120°, and 150°. Sketch just one or two typical waveforms, rather than the whole series.

4. Place an inductor, for example 25 mH, in series with the resistor, as shown in Figure 19.22. Observe the resistor voltage waveform. Repeat #2 and #3 above for this new circuit, and also record the average and rms values of V_load.

Part 2 -- A battery load

1. Connect a rechargeable battery in the circuit of Figure 19.23.

2. Measure battery currents I_out(ave) and I_out(rms). Do this for, and record the phase delay angle value, at least four different SCR delay angles. Observe and sketch the resistor current waveform at one intermediate SCR delay angle.

3. Measure the input power from the ac source.

19.4.4 Study questions

1. For the simple loads of Part 1, tabulate and plot V_out(ave) and V_out(rms) vs. the SCR phase delay angles. Compute a theoretical result, and compare it to the data. Do these agree?

2. For the battery load in Part 2, tabulate and plot I_out(ave) and I_out(RMS) vs. the SCR phase delay angle. Again consider whether your results are consistent with theoretical expectations.

3. Why is the "flyback" diode included in these circuits?

4. Compute the efficiency of the battery charger studied here.

5. Comment on how the diode and SCR forward voltage drops affect your results.

19.5 Experiment -- Polyphase rectifiers

19.5.1 Introduction

This experiment will examine the properties of ac-dc converters with polyphase input voltage sources. The midpoint converter will be the focus of this experiment, and will be tested with inductive loads including a dc motor. In the preceding experiment, the circuits had a single SCR in a half-wave rectifier configuration. A flyback diode was needed to provide a current path when the SCR turned off. The simple half-wave circuit transferred energy to the load no more than half of the time. The half-wave circuit seems ineffective. Polyphase sources offer a much better alternative.

A three-phase source, the most common polyphase type, has three voltages equal in amplitude and 120 apart. The definition of polyphase sources also applies to the "two-phase" case -- two voltages, each 180 apart. While this is consistent, a confusing historical nomenclature has arisen. In communication systems, a "quadrature" voltage source is a set of two signals, spaced by 90-- a sine and a cosine. Quadrature sources were used in many early power systems, and gave rise to an unfortunate use of the term "two-phase" for such a source. We will use the term two-phase to refer to a set of two voltages 180 apart rather than to a quadrature set. In this experiment, the SCR boxes will be used to study controlled-rectifier action with two and three-phase sources.

19.5.2 Basic theory

When multiple input sources are available for ac-dc converters, it is natural to use all of them. The circuit of Figure 19.24 shows the most general such converter -- an m-phase to dc converter. The experiment here considers a simplified version of this converter -- the one in which there is a common neutral connection between input and output. This is called a midpoint converter, and appears in Figure 19.25.

In the midpoint converter, the KVL and KCL restrictions require that no more than one switch may be on at any time, and one switch must be on if the load current is not zero. This implies that q_i 1. If the load is a current source, q_i = 1. We want to operate the switches so that the dc value is maximized and the unwanted ac components are minimized. It can be shown that if the switching frequency is chosen to equal _in, the best choice of switching functions is to follow the polyphase input: each switch is on 1/m of the time, and switching functions are spaced 360/m apart. The dc output component can be controlled by adjusting the phase of the switching functions. The output voltage is given by

This gives a complicated series, in the form

The dc component appears in the n=1 term, and is given by

This, in turn, can be simplified to give

Notice that V_out(ave) depends on , where is defined as the delay angle between any voltage and the switching function associated with it. The result is a controlled rectifier.

19.5.3 Procedure

Part 1: Two-phase converter

1. Set up the 25 V 60 Hz supply for two-phase output. Remember to connect the output neutral.

2. Connect the SCRs labelled "A" and "B" in the SCR box with a resistive load, as shown in Figure 19.26. Estimate the required resistor power rating, and abide by it. Set the SCR box for two-phase control.

3. Set the SCR turn-on for zero delay (i.e. set it to act as a diode). Observe the output voltage waveform. Record V_out(rms) and V_out(ave) and sketch the output voltage waveform.

4. Repeat #3 for delays of approximately 30°, 60°, 90°, 120°, and a delay close to 180°. Sketch just one typical waveform, rather than the whole series.

Part 2 -- Three-phase converter

1. Connect the 25 V 60 Hz supply and SCR box for three-phase operation.

2. Apply 120/208 V 3 power to the three-phase setup.

3. Set the SCR turn-on for zero delay (i.e. set it to act as a diode). Observe the output voltage waveform. Measure V_out(ave) and V_out(rms), and sketch the waveform.

4. Repeat #3 for delays of approximately 30°, 60°, 90°, and 120°. Sketch just one typical waveform, rather than the whole series.

5. Repeat #3 with a dc motor as the converter load, except set the delay at about 90° initially. Observe and sketch the motor current and voltage waveforms with no motor shaft load.

6. Add a moderate shaft load, and observe how the current and voltage waveforms change. Record your observations.

19.5.4 Study questions

1. For each of the load and source combinations, tabulate and plot V_out(ave) and V_out(rms) vs. the SCR phase delay angle. What would you expect in theory? How well do your results agree with the theory?

2. For one phase delay angle (pick 60, for instance), plot V_out(ave) and V_out(rms) vs. the number of input phases (you have data for one, two, and three). What do you expect to happen when more phases are used?

3. Why is the flyback diode not included in these circuits?

4. A bridge converter implements the full switch matrix of Fig. 19. . How would V_out(ave) be affected by the use of a bridge rather than a midpoint converter?

19.6 Experiment -- One-Quadrant Dc-Dc Conversion

19.6.1 Introduction

In this experiment, some common one-quadrant dc-dc converters will be implemented and tested. The main tool of the experiment is the FET switch control unit. The circuitry provides direct adjustment of the switching function frequency and duty ratio. The FET box can be used to generate any of the four common dc-dc one- quadrant converters (buck, boost, buck-boost, or boost-buck). In this experiment, we will set up two of these circuits and characterize their operation. The converters we will build are similar to commercial applications, with fast switching functions and switching frequencies as high as 200 kHz.

19.6.2 Basic theory

Dc-dc converters can be depicted as providing energy transfer between two ideal sources. In practice, one of the sources is almost always implemented as an electrical energy storage element. For example, the buck converter stores energy in an inductor when the controlling switch is on, and discharges that energy through the load when the controlling switch is off. An objective is to keep energy flow into the load nearly constant as the switches operate. Since most converters apply nearly constant voltages or currents to the storage elements, much of the analysis is straightforward.

The general dc-dc converter is shown in Figure 19.28. The four major one-quadrant converters are shown in Figure 19.29. Notice that the indirect converters (buck-boost and boost-buck) are shown as two matrices connected together. In each of these circuits, practical current sources are formed with inductors. Output voltage sources are formed with capacitors. The average values, governed by the switching function duty ratios, are of interest. For example, the buck converter below has V_out = q₁V_in, which is just

The average value of this series is simply D₁V_in. Unwanted Fourier components appear at the switching frequency f_switch and its multiples. The largest unwanted component is

In general, as switching frequencies increase, the values of dv/dt and di/dt values also increase, and smaller inductors and capacitors can be used without sacrifice in performance.

19.6.3 Procedure

Part 1: Buck converter

1. Set up the FET control box as a buck dc-dc converter. Be sure to provide the capacitor shown across the input power supply. The capacitor should be placed as close to the FET box as possible so that the inductance of the wires to the FET will be very low.

2. Set the power supply current limit for about 3 A, and the voltage to 12 V. Set the duty ratio to about 50%. Observe the load voltage, V_load, and the output voltage V_out.

3. Turn on the FET box and the input power supply.

4. Set f_switch to about 100 kHz. Notice that V_out allows easy measurement of f_switch.

5. Confirm that the duty ratio is close to 50%. Sketch the V_out and V_load waveforms.

6. Use the oscilloscope to measure the peak-to-peak ripple on V_load at duty ratios of 10%, 50%, and 90%. The ripple measurement can be performed by setting the oscilloscope input coupling to "ac," and expanding the voltage scale.

7. Measure average values of V_load and I_in at duty ratios of 10%, 30%, 50%, 70%, and 90%. Use your multimeter for V_load(ave). Record the input and output RMS voltage and current as well as the power.

8. Change f_switch to 5 kHz. Try to measure the waveform time constant during the voltage fall. Recall that this will be the time for V_load to fall from its peak value to 36.8% of that value.

Part 2 -- Buck-boost converter

1. Set up the FET control box as a buck-boost dc-dc converter, as shown in Figure 19.32.

2. Set the power supply current limit for about 3 A, and the voltage to 12 V. Set the duty ratio to zero. Connect oscilloscope leads across the load resistor and across the inductor.

3. Turn on the FET box and the input power supply. Set f_switch to about 100 kHz.

4. Confirm that the duty ratio is set to about 50%. Sketch the inductor voltage waveform. Use the current probe to sketch the inductor current waveform. Observe and sketch the load voltage waveform.

5. Measure average and RMS values of V_load and I_in at duty ratios of 20%, 40%, 50%, 60%, and 70%. Record power readings as well. The output voltage becomes high quickly with D>60%, so be careful.

19.6.4 Study questions

1. Tabulate your data in an organized fashion. Compare the RMS readings from the wattmeters with the various average readings. Do they agree?

2. Compute and tabulate ratios of V_load(ave)V_in for these converters for your data. Are the results consistent with duty ratio settings?

3. Estimate the average input and output power from the average readings of V_load and I_in for each operating condition. Compare these results to the wattmeter readings. Calculate efficiency, P_outP_in, from the wattmeter readings.

4. Estimate the inductor value from the measurements of fall time in the buck converter. Use this value to compute an expected load voltage ripple at 100 kHz. How do your results compare with the data? If the inductor value were to double, how would this affect the behavior of these circuits?

19.7 Dc-Dc Converters for Motor Drives

19.7.1 Introduction

This experiment will examine the operation of dc-dc converters in the context of motor drives. Motor drives are the most common application of multi-quadrant dc-dc converters. Dc power supplies are almost always based on one-quadrant circuits: the output power is intended to be positive at all times, and there is rarely a need to handle negative output current. Some special-purpose laboratory supplies are designed to handle multi-quadrant output, but often do not have efficiency as a high priority.

Large dc motor drives have energy considerations beyond those we have seen so far: the rotating kinetic energy of a large motor is quite considerable, and in a braking situation, this energy must be removed. The energy can be converted to heat and lost, as it is in gasoline engine vehicles, or it can be directed back to the energy source for recovery. This regeneration energy can be controlled only with multi-quadrant circuits.

19.7.2 Basic Theory

The equivalent circuit of a dc motor is repeated in Figure 19.33. Rotation of the motor produces a back EMF, equal to ki_f, where k is some constant, is the motor shaft speed in rad/s, and i_f is the "field exciting current" or some other variable representing the magnetic field strength inside the motor. If a voltage V_t is applied to the motor terminals, a current (V_t V_g)/R_a will flow in the steady state. This current sends power into the motor, which is converted to mechanical energy. The input power accelerates the motor until the electrical input power exactly balances any mechanical input into a shaft load.

The power input, and hence the operating speed, of a dc motor can be controlled easily by altering the value of V_t. Since the actual output power is into some mechanical load, with its associated inertia, will not change much over short time periods, and V_g will be nearly constant. The average electrical power into the motor will be determined by the average value of V_t, even if the inductance is low. For example, a simple buck converter could be used to control V_t, as in Figure 19.34. The output can vary from 0 to 100% of the input dc source voltage, and thus speed can be altered from near 0 to near rated speed.

If i_f is held approximately constant, as it is in separately excited motors or motors with permanent magnets, the input power is a very direct function of converter duty ratio, and speed control is made easy. In fact, many converters have feedback systems built in for this purpose. Consider the unit of Figure 19.35 in which the transistor duty ratio depends on a low-power input voltage. This voltage could be generated as shown in the figure, with some reference signal being compared to information from a tachometer. In this unit, the duty ratio automatically increases if the motor speed drops. This results in additional input power and is intended to keep running speed nearly constant. The operating speed can be changed easily by adjusting the reference voltage, and will be held constant at the desired value.

In the case of a very high power motor drive, a considerable amount of energy is represented even during a speed decrease. An excellent example is the braking of an electric vehicle -- an operation which must occur often in any transportation application. In mechanical systems, the braking energy is converted to heat, dissipated, and lost. This is not an acceptable situation in battery-powered electrical units, and causes substantial wear and tear even when batteries are not an issue. Multi-quadrant dc converters can be used to convert the braking energy back into electrical form. The energy can be dissipated just as it would be by mechanical brakes, or it can be returned to the energy source. The dissipation version is called dynamic braking and is often used for very rapid deceleration of electric motors. The recovery version is called regenerative braking, or just regeneration, since it uses the motor as a generator during deceleration.

The buck converter is sometimes called a class-A chopper when used as a motor drive. As we have seen, this converter makes a useful, simple motor control. When braking, the controlling switch turns off, and only the diode conducts. If inductance is low, the output current quickly goes to zero, and the motor coasts to a stop. If inductance is high, the braking energy is dissipated in R_a. Figure 19.36 shows some typical waveforms.

A boost converter can be used to return generated energy from a motor to a source, provided that the source voltage V_t is less than V_g. Such a converter, shown in Figure 19.37, can provide regenerative or dissipative braking. It is sometimes referred to as a class-B chopper.

A motor could be attached to both a buck and a boost converter, with the buck converter operating (with I_a > 0) during "motoring," and the boost converter operating (with I_a < 0) during regeneration. Such a unit is called a class-C chopper, and is widely used for dc motor drives.

To operate a class-C chopper, the boost converter active switch is shut off, and the buck converter is used to accelerate and provide running power to the motor. When regeneration is desired, the buck converter is shut off until I_a becomes negative. At that point, the boost converter can begin operating, and will transfer energy from the motor back to the source. In effect, the buck and boost converters operate independently.

The general dc voltage to dc current converter shown in Figure 19.39 is not especially useful for dc motor control, since the inductance value is usually too low for useful regeneration. The converter cannot provide negative steady-state voltage to the motor, and so is no more useful than the class-C chopper above. It is called a class-D chopper. In many applications, it is necessary to reverse the motor direction, while maintaining both motoring and regeneration. Two class-C choppers, one for each motor V_t polarity, can be assembled for this purpose. The resulting class-E chopper is shown in Figure 19.40.

19.7.3 Procedure

Part 1: Class-A motor drive

1. Obtain a small dc motor. Use your multimeter to measure R_a for it.

2. Set up the FET control box as a buck dc-dc converter, with a dc motor as the output load. Be sure to provide the capacitor and resistor shown across the input power supply. The resistor is intended take up any regenerated energy.

3. Set the power supply current limit for about 5.0 A, and the voltage to 24 V (depending on the motor ratings). Set the duty ratio dial to zero. Connect an oscilloscope lead across the motor. Set up the current probe to measure the motor armature current.

4. Turn on the FET box and the input power supply. Set f_switch to about 20 kHz (a period of 50 µs). Monitor and record the power supply current and voltage levels and shut down if anything unexpected appears.

5. Sketch the motor terminal voltage waveform and current waveform with a duty ratio setting of about 50%. If there are intervals during which I_a = 0, take special care to record the value of voltage during such intervals. Measure the peak-to-peak ripple on I_a.

6. Observe and sketch the motor voltage and current waveforms, and measure the motor average voltage and current, at: (a) the lowest duty ratio for which the motor runs steadily, and (b) a duty ratio of about 90%. In each case, observe qualitatively the effects of shaft load on the current waveform.

7. Change f_switch to 2 kHz. Measure the time constant of V_t during its fall. This will allow you to estimate L_a later.

Part 2 -- Class-C chopper circuit

1. The two active switches of the class-C chopper operate separately, but they must act in complement. In this part of the experiment, it will be necessary to use special care to insure proper switch operation.

2. Use two FET control boxes. One, designated the master unit, will determine the switching functions of both portions of the class-C chopper. The second, designated the slave unit, will function only as requested by the master unit. The FET box design in Chapter 18 has a switch to select this function: up for master and down for slave. Connect the control terminal on the master unit to the control terminal on the slave unit. Adjust the slave duty ratio to the 100 % position. The frequency controls should be in approximately the same position.

3. Wire the circuit shown in Figure 19.42. The 0.2 resistor will help prevent damage if the switching functions are not operating exactly in complement.

4. Operate the master unit as a buck converter. Observe operation at approximately 50% duty ratio, as in part 1. Sketch the motor voltage and current waveforms, and record the average motor voltage and current. Measure the peak-to-peak ripple on I_a.

5. Increase the duty ratio to near the maximum amount, then drop the duty ratio abruptly in an attempt to observe converter action during regeneration. You may need to repeat this step, or spin the shaft externally by hand or with another motor to observe regeneration behavior (we've used an electric drill in the past). Make note of your observations. Try to obtain a situation in which I_a reverses.

19.7.4 Study questions

1. During intervals when I_a = 0, the motor voltage is not necessarily zero. Interpret its value during such intervals. (Hint: Since I_a = 0, this is an open-circuit voltage.)

2. Compute average power into the motor for each operating condition.

3. Estimate the motor series inductance value from the buck converter data. Use this to estimate the voltage ripple at 20 kHz. Does this match your measurements?

4. Is the average motor voltage determined by the duty ratio?

5. Why is the class-A chopper incapable of regeneration? What will happen in such a converter if V_t is suddenly lowered?

19.8 Dc-Ac Conversion -- Voltage-Sourced Inverters

19.8.1 Introduction

This experiment examines inverter circuits. Inverters, or dc-ac converters, are used for generation of backup ac power, for ac motor drives, and for switching amplifiers. Commercial inverters are also used in alternate energy applications such as the demonstration photovoltaic and battery power plants. Various simple types of inverters will be studied in this experiment. Emphasis will be placed on phase control techniques and on simple switching functions. Inverters can be classified according to the properties of the dc source. Those with a dc current source are often used for sending energy into an ac power system. Dc regeneration and HVDC transmission are two examples. Such inverters are really the same as ac-dc converters with ac voltage inputs. In effect, the only difference between rectifiers and inverters when dc current sources are involved is the direction of any unidirectional switches used in the circuits. The ac-dc/dc-ac converters with dc current sources almost always involve a utility ac voltage supply, and have well-defined values of phase. Any switching function can be altered in phase relative to this fixed reference frame, resulting in variation of input and output power levels.

Ac-dc/dc-ac converters which involve dc voltage sources are, in practice, quite different from the current-sourced versions. Such converters imply an ac current source -- rare in practice. Normally, the "ac current source" simply reflects some electrical load, such as a circuit or a motor, which requires ac power. These loads rarely define a phase reference -- the phase is determined by impedance characteristics, and will always lead or lag the input voltage by a definite amount.

The voltage sourced inverters, then, provide a window into the complexities of true, independent inversion -- conversion of a dc source into some ac source. Inversion is important in three basic applications:

1. Transfer of energy from some dc source into an ac power system. Such uses include alternate energy source conversion and dc motor regeneration.

2. Backup ac power. Since most electrical equipment is intended for ac power from a utility, switching power converters which produce ac from storage batteries have long been important.

3. Ac motor drives. Induction motors, synchronous motors, and so-called brushless dc motors require ac power at variable frequency. Today, this is often achieved by converting power from some dc source.

19.8.2 Basic Theory

The most general dc-ac converter (with single phase ac) is shown in Figure 19.43. It has at most four switches. The switching functions are constrained by KVL and KCL, as usual. They also must have a Fourier component at the ac source frequency, to ensure nonzero power flow. An important practical consideration is that most real ac sources cannot tolerate a dc component. This further constrains the functions. A reasonable choice is to operate the switches with a duty ratio of 50 % to bring about the highest symmetry and hence avoid any dc component on the ac source. A general converter of the dc voltage source type is shown in Figure 19.44. As in the case of the two-quadrant buck converter, V_out can be either V_in, -V_in, or 0, depending on the switch combination. Notice the switch types to be used in this converter. In general, current can flow in either direction, although there is only one voltage polarity.

Consider the induction motor equivalent circuit, shown in Figure 19.45. This circuit requires ac power, and is an inductive load. For the purposes of KCL a current source is an appropriate model over short times. Nonetheless, the phase of this current source is linked to the phase of the input voltage. Changing the phase of the input voltage will change the current phase so as not to alter power.

Because of the ac current source phase behavior, dc-ac converters are harder to study than dc-dc converters. Properties of the load are important to converter operation. A half-bridge converter with R-L load is shown in Figure 19.46. KVL and KCL require the two switching functions to act in complement, so that q₁ + q₂ = 1. The practical requirement of no dc component in V_out requires D₁ = D₂ = ½. V_out is a simple square wave at the desired frequency, and has a value of V_out = (2D₁ - 1)V_in. This generates the Fourier series

Output current and power depend on the load, in a manner which is actually easy to calculate. Consider that V_out = RI_out +L(dI_out/dt). In steady state, I_out is periodic at the same frequency as V_out, and has a Fourier series

This series can be differentiated easily. Let X_n = nL. Then we can solve for I_out term by term, obtaining

This is equivalent to finding each component of I_out separately in terms of the corresponding component of V_out. It is easy to automate such a procedure on any computer. Sample waveforms are given in Figure 19.47. Some loads of this type will be tested in this experiment.

19.8.3 Procedure

Part 1: Voltage-sourced inverter, R-L and R-L-C loads

1. Set up two FET control boxes in a master-slave configuration, to form a half-bridge inverter. Be sure to include the capacitors and resistors shown with the power supply input. Refer to Figure 19.48.

2. Set the power supply current limit, if there is one, for about 2.0 A, and the voltage to zero. Set the master and slave duty ratio dials for 50 %. Connect oscilloscope leads and wattmeters across the load resistor and across the converter output, as shown in Figure 19.48.

3. Turn on the FET boxes and the input power supply. Set f_switch to 10 kHz. Set the supply to 24 V.

4. Measure the output average voltage. Adjust the duty ratio and fine-tune the input supplies to get 50% duty and zero average output. Small average offsets can swing the current to the power supply current limits.

5. Sketch the load resistor voltage and the output voltage waveforms. Record the RMS voltage, current, and power from the wattmeter. Measure the average input current from the supply.

6. Compute the series capacitance needed for resonance with the inductor at the switching frequency. Add this capacitor in series with the inductor. Adjust the frequency as needed to obtain near-resonant operation.

7. Sketch the resistor voltage waveform with the R-L-C load. Record the RMS value of the load resistor voltage, the output power, and the average input current from the supplies.

Part 2 -- Isolated converter with ac link (half-bridge forward converter)

1. Set f_switch to 50 kHz. Wire a toroidal transformer into the circuit, as shown in Figure 19.49.

2. Measure the average output voltage of this circuit. Sketch the waveform.

3. Place a 1 µF capacitor across the output terminals. Again measure the average output voltage. Also measure the average input current from each source by taking advantage of the series resistors.

19.8.4 Study questions

1. How do you expect waveforms for an R-L load to change with frequency?

2. An alternate method for control of V_out(wanted) is to add a third switch across the output combination. This allows zero as a possible output value. The duty ratios can then be adjusted so that V_out changes. Assuming that the dc component remains at zero, find V_out(wanted) as a function of D for this control scheme.

3. What is the effect of a resonant load, such as that in Part I?

4. What is the efficiency of the converter circuits tested above?

19.9 Experiment -- PWM Inverters

19.9.1 Introduction

This experiment introduces pulse-width modulation circuits. The intent is to gain familiarity with the waveforms and concepts of pulse-width modulation as it applies to power electronics. The PWM inverter will be examined in the context of an ac motor drive. Basic ac drive concepts will be one feature of this experiment. The typical PWM waveform shown in Figure 19.50 has a switching frequency of 960 Hz.

Control of output voltage in dc-ac converters is critically important in a wide range of applications. Backup ac power supplies require control of voltage so that V_out can be varied independent of the input source. Ac motor drives require control of both V_out and f_out to achieve good performance. There are two methods in common use for controlling the output voltage (and power) of an inverter. The first is to adjust the relative timing of switching functions in a bridge. The load voltage depends on the relative phases. This "phase displacement control" is often used in very high power situations, such as locomotive controls, where the switches are slow SCRs.

The second method, pulse-width modulation (PWM) divorces the switching function frequency from the intended properties of V_out. This method can provide the desired results if the switches can be operated much faster than f_out. To understand PWM, consider a very fast square wave. The duty ratio can be varied slowly between 0 and 100%, in a manner similar to pulse width control in dc-dc converters. In a buck converter, for example, this would have the effect of slowly changing V_out(ave). This slow change can be sinusoidal perhaps, which gives a slow sinusoidal change in the average value of V_out. Here "slow" simply means much more slowly than the switching function. V_out can easily change at the rate of 60 Hz if, for example, a switching frequency of 10000 Hz is used.

In practice, implementing this slow variation of pulse width is exactly the same as designing a dc-dc converter. The only issue is to place V_out in two quadrants. And, in fact, the full-bridge inverter operating under PWM is identical to a two-quadrant buck converter. The pulse width is intentionally varied, rather than held nearly constant as in the dc-dc case.

Convenient speed control for ac motors has been a desired goal almost since such machines were invented. The ac induction motor, for example, is mechanically simple and rugged, requires no electrical connections between stationary and rotating parts, and is inexpensive. Unfortunately, the induction motor lacks the easy control of a dc motor. Ac motor speed control in general requires adjustment of the motor input frequency. The speed depends on frequency in a direct manner, and the ability to vary f solves much of the problem. Unfortunately, it is not entirely trivial to vary the frequency applied to a motor. Ac motors are basically inductive, and have a frequency-dependent impedance. As the frequency is lowered, input current and internal magnetic flux rise. To counteract these effects, the voltage must change along with frequency. If the voltage is altered in the correct manner as a function of frequency, an ac motor can be made to look almost like a dc motor in terms of speed and torque control.

Until PWM converters were feasible, the process of altering f_out and V_out together was exceedingly difficult. Ac motor controllers were almost unknown twenty years ago, and those which did exist were expensive, complicated, and used additional motors for energy conversion. Today, ac motor drives are beginning to displace dc motors in some applications. These drive units are nearly always based on PWM.

19.9.2 Basic Theory

The half-bridge inverter in Figure 19.51 has output V_out = (2q₁ - 1)V_in. If the duty ratio is varied with time as some modulating function M(t), V_out becomes

Remember that D must be between 0 and 1. With ½[k·cos(_outt)+1] for M(t), V_out is

Notice that this is not in the form of a Fourier series -- time appears in several places, as does sin[ncos(_outt)]. This can be decomposed into a Fourier series by using properties of Bessel functions. The necessary relations appear among the trigonometric identities in the Appendix. The Fourier components appear at frequencies of n_switch ± m_out. The components drop in amplitude quickly for increasing m, but slowly for increasing n. It is easy to use a series R-L load as a low-pass filter (just as in the dc-dc buck converter) in order to separate f_out from the unwanted components. This function can be performed by a deliberate R-L load, or by a motor winding or transformer. The experiment procedure below illustrates both PWM and the filtering process.

19.9.3 Procedure

Part 1: Voltage-sourced PWM inverter, R-L load

1. Set up two FET control boxes in a master-slave configuration, to form a half-bridge inverter. Be sure to include the capacitors and resistors shown with the power supply input.

2. Set the power supply current limit, if there is one, for about 1.5 A, and the voltage to zero. Set the master duty ratio to about 50 % and the slave to 100 %.

3. Set up the waveform generator at your bench to produce a sinusoidal voltage, with frequency of about 50 Hz, such that the lowest voltage is 1 V and the highest is 3 V (sine wave with 2 V_p-p and 2 V dc offset). Connect this voltage to the duty ratio input on the master converter unit.

4. Connect oscilloscope leads across the load resistor and across the converter output (refer Figure 19.52). Turn on the FET boxes and the input power supply. Set f_switch as low as possible.

5. Monitor the average value of V_out, and observe the power supply currents. Adjust the function generator to get near zero average output.

6. Sketch the V_out waveform. Can you see the modulating process? Record the RMS voltage current, and power into the load resistor. Measure average dc voltage across the 1 series input resistors.

7. Increase f_switch to about 50 kHz.

8. Decrease the amplitude of the function generator modulating waveform by about 50%. Sketch the V_load waveform. Record meter data as in step 6.

Part 2 -- Induction motor drive

1. Turn off the power supply. Replace the R-L load with a series combination of 5 and a transformer winding of 12.6 V rating.

2. Place a 1000 load across the transformer secondary terminals. Turn on the power supply, and measure the RMS and average voltage across this resistor, and observe and sketch the waveform. Be aware of the relatively high voltage level.

3. With the supply off, wire a single-phase motor into the circuit, as shown in Figure 19.53. Apply power. Sketch the converter output voltage and resistor voltage waveforms (refer to the Figure).

4. Change the sine wave frequency and amplitude to observe an ac motor control function.

19.9.4 Study questions

1. For this type of converter, how do you expect waveforms for an R-L load to change with switching frequency? With modulating frequency?

2. Why is PWM advantageous in ac motor control?

3. Draw the full-bridge inverter for PWM. What relationships would you expect among the various switching functions?

4. Compute and tabulate the converter's efficiency from your part 1 data.

5. Compare PWM with the simpler inverter scheme of the previous experiment.

19.10 Ac-Ac Conversion

19.10.1 Introduction

Direct frequency conversion, as introduced in Chapter 7, is one framework in which to study the ac-ac converter. In this experiment, we will examine converters of this type. The bilateral switch is beginning to gain in importance, and one device set which performs this function will be examined. Many applications which require ac output, especially motor drives and related transportation areas, would appear to benefit if power could be converted directly from the ac mains. Today, a few workers in power electronics would dispute this, and claim that conversion via a dc link is superior to direct ac-ac conversion. In principle, however, the reduction in switching network complexity, along with the possibility of extending ac-ac conversion into such areas as power amplifiers, makes a direct ac-ac converter a kind of "ultimate dream." A generic ac-ac unit would serve for any possible conversion function, including rectification and inversion. In the long run, a power bilateral switch will open up a wide range of new processes and applications for power conversion, just as the SCR did during the 1960s.

19.10.2 Realizing the bilateral switch

Any converter can be built from a bilateral switch. While this makes it a powerful tool, its properties are not always advantageous. For example, it is easier to build a reliable dc-dc buck converter with a transistor and a diode than with bilateral switches. There is no alternative for ac-ac conversion, and in fact a bilateral switch brings advantages to certain other converter types.

The TRIAC approximates full bilateral capabilities. This device, in effect, is a set of inverse-parallel SCRs, built together, and sharing a single gate. The TRIAC is controlled just like an SCR -- once on, it remains on until the current becomes zero. This provides several characteristics:

Simple ac regulators can be realized with TRIACs, since they will perform phase control or integral cycle control on a resistive load without trouble.

The TRIAC is difficult to use when dc currents or voltages are involved, since conditions needed for turn-off may not appear.

A TRIAC of given size does not use semiconductor material very effectively, and has much lower ratings than two SCRs which are half as big.

TRIACs are common in consumer products which benefit from simple ac regulators. Some such devices are used in certain ac motor control applications, particularly those which resemble phase controlled ac regulators. TRIACs have limitations on levels of externally applied dv/dt and di/dt. The devices are also relatively slow to turn off. These limitations confine them mainly to power mains frequencies.

The TRIAC is a very limited bilateral switch. An alternative is to combine multiple switches of other types to form a true bilateral device. For example, two switches of type       can be placed in inverse series to form an equivalent       . The gates of the two sub-units are operated from the same switching function. Possible implementations appear in Figure 19.54. It is actually relatively convenient to implement the FET version shown in the Figure, since the gate drive can be used without change in most cases. The BJT version is more problematic, since applied base current must support both devices without any balance troubles.

19.10.3 Basic Theory

Once a bilateral switch is available, it is relatively simple to operate an ac-ac converter. The requirement is that switching functions contain a Fourier component at a frequency f_switch = f_in ± f_out. The most straightforward way to accomplish this is to set f_switch to either the sum or difference of input and intended output frequencies. Thus conversion of 60 Hz to 400 Hz would result if a switching frequency of either 340 Hz or 460 Hz were applied, for example.

Very often, the input frequency is known and fixed, and variation of the output frequency is important to an application. This is true of ac motor drives, for example. It is sometimes useful to consider the switching frequency as f_in plus some modulating function. For example, if the switching function phase is made to be a function of time, M(t), a switching function will take the form

This is "phase modulation," since phase is a function of time. Phase modulation reduces trivially to the form f_switch = f_in ± f_out if M(t) is set to ±_outt. This form of switching function is easy to implement, and is referred to as "linear phase modulation" since M(t) is a linear function of time. The choice M(t) = +_outt is given the special name "Universal Frequency Converter" (UFC) since it works for any choice of f_in or f_out. The choice M(t) = -_outt gives rise to a "Slow-Switching Frequency Converter" (SSFC), and has the constraint that f_in f_out. Both of these types are statements of the simplest choices of switching frequencies. Other choices of M(t) can be made. These are nonlinear phase modulation methods, with almost unlimited possibilities. Many nonlinear phase modulation techniques allow control of power flow even with passive loads.

It should be pointed out that phase modulation is not the only way to perform ac-ac conversion. Pulse-width modulation can also be used, since PWM allows the creation of nearly any Fourier component, given a fast switching frequency. PWM methods are being discussed for use in ac output converters which allow ac or dc input.

19.10.4 Procedure

Set up a two-phase to one-phase ac-ac converter based on dual FET bilateral switches, as shown in Figure 19.55. Apply a switching function at some frequency, and observe results at the output terminals. Record your observations.

Pay special attention to the waveforms which appear when the switching frequency is exactly equal to the input frequency. This case is particularly easy to simulate and study.

19.10.5 Study Questions

1. Draw some expected waveforms for two-phase to one-phase ac-ac conversion. Do the experimental results go along with these?

2. What would have been the effect of a resonant load?

3. How would PWM provide advantages in this ac-ac converter?

19.11 Frequency Characteristics of Passive Components

19.11.1 Introduction

The next two experiments will study the behavior of real passive components. In the first experiment, basic operation of realistic capacitors, inductors, and resistors will be examined. The capacitors, inductors, and resistors used in circuit analysis have ideal properties: i_c = Cdv_c/dt, v_L = Ldi_L/dt, and v_R = Ri_R. However, real devices are not ideal. In the context of power electronics, these effects are often important. Wires have resistance and inductance, coils of wire have capacitance between the turns, and so on. In order to use passive components in power electronic circuits, it is important to understand what the effects are, how they are characterized and measured, and the implications for design.

19.11.2 Basic theory, capacitors

When two conductors of any shape are placed in an electric field, a charge develops on each one. In a system which consists only of perfect conductors and perfect insulators, the charge Q depends on voltage in a linear fashion, so that Q = CV. If capacitance is constant (e.g. the conductors are stationary), this leads to the simple relationship i = Cdv/dt. A real capacitor must provide conductors to hold the charge, wires to allow application of voltage, insulation which physically supports and separates the conductors, and a protective package to prevent damage. This naturally complicates the real behavior.

There are two common classes of commercial capacitors. The first consists of two flat metal conductors, separated by a dielectric layer. The second type, known as the "electrolytic capacitor," consists of an oxidized metal conductor and a nonmetallic conductor. Both types can be modelled with a parallel-plate geometry, shown in Figure 19.56. The capacitance value depends on the plate spacing d, the plate area A, and the dielectric constant of the insulator, , according to the relation C = A/d. A large value of capacitance requires large plates, small spacings, and high dielectric constants.

The nonideal effects are relatively clear: the wires and plates introduce series inductance and resistance, and an imperfect dielectric could allow some current flow between the plates. A candidate circuit model emerges, given in Figure 19.57.

This circuit model can be simplified if the capacitor is operated at some specific frequency. Then the parallel portion can be transformed into a series equivalent. This gives the standard model shown in Figure 19.58. Many manufacturers use this standard model as a basis for describing their capacitors. The equivalent series resistance (ESR, another name for the R_s of the circuit) is often given at some frequency, such as 120 Hz. The equivalent series inductance (ESL) is often given in the form of a "self-resonant frequency," f_r. The properties of the standard circuit include:

Voltage drop across the ESR, which reduces the stored charge relative to expected values.

The resonant effect of the series R-L-C circuit means that a plot of impedance vs. frequency will fall at first (capacitive impedance), reach a minimum, and then rise (inductive impedance).

Above f_r, the device is an inductor!

Any current flow produces loss in the ESR. The higher the frequency of the applied voltage, the higher the current and losses.

The circuit does not model real behavior well at very low frequencies. For instance, the original circuit of Figure 19.57 shows that some leakage current will flow when a dc voltage is applied. Real capacitors show this effect, but the standard model does not include it.

The ESR mainly represents the dielectric properties. Dielectrics do not usually act in accordance with Ohm's Law. Because of this, the ESR is generally a kind of nonlinear resistance; for example, it varies with frequency. One traditional way to characterize such materials is with the "loss tangent." The loss tangent, also called tan or "dissipation factor" (df), is defined as the ratio of resistance to reactance for a series R-X circuit. For the standard model of the capacitor, tan = RC. The loss tangent has a characteristic value for a given capacitor dielectric material, regardless of the plate geometry. Many dielectric materials are characterized by a loss tangent which is roughly constant over a wide frequency range. For these reasons, loss tangent or df is often given in capacitor specification sheets. The ESL is related to packaging and lead structure, since wire inductance is the most important factor.

In electrolytic capacitors, the insulating layer is formed through an electrochemical reaction between the two conductors. If voltage of the wrong polarity is applied, the reaction reverses, and the insulating layer is destroyed. The device becomes a resistor, and usually overheats and fails quickly. When the correct polarity is applied, the electrolytic capacitor shows the same general properties as the simple dielectric version, with two changes: the leakage current levels are much higher, which means ESR is smaller and df is higher; and the effective plate surface area is very high, which allows high values of capacitance per unit volume.

19.11.3 Basic theory, inductors

Inductors are formed simply by wrapping a coil around a magnetic material. Current in the coil creates magnetic flux in the material. If the material is linear, the flux is proportional to current, so that = Li. The constant of proportionality in this case defines inductance. By Faraday's Law, if this flux varies with time, it gives rise to a voltage v_L = Ldi/dt. Magnetic materials in general are not linear; these effects will be studied in more detail in the next later experiment.

Even without considering the effects of nonlinearities, some aspects of real inductors should be clear. The wire coil has resistance. Incoming and outgoing wires act a bit like parallel plates. A simple circuit model might be that in Figure 19.59.

The symbol ESR is often used for the effective resistance in inductors. As in the capacitive case, the loss tangent is defined as the ratio of resistance to reactance. It is hard to build inductors which handle high energy levels and still have very low loss tangents.

Inductor types are defined mainly by the magnetic material. This can be a linear material, such as air, or any magnetic material. Good linearity is a desirable feature, so most practical inductors have an air gap. In this experiment, two inductors will be tested for their ESR values and resonant frequencies.

19.11.4 Basic theory, resistors

Resistors are generally taken for granted in electrical networks. However, they are subject to nonlinear effects like other components. Consider that Ohm's Law is really an approximation, based on a highly simplified model of electron behavior in metals. Nonmetals do not usually follow this behavior. The general tendency is that the higher the resistivity of a material, the less linear its V vs. I behavior is likely to be. The parts must have connections, which implies a series inductance. A basic model is shown Figure 19.60.

Even in materials which follow Ohm's Law, other effects are important. All materials, including metals, vary in resistivity as a function of temperature. For most metals, the variation is approximately linear. In power electronics, heat loss and temperature effects are almost always significant. Since resistance values change with heating, it can be hard to predict the actual value of a given resistor.

There are several major types of resistors:

Composition and metal oxide resistors are formed as a block (or cylinder) of nonmetal. The material resistivity and stability are important considerations. Carbon composition resistors were once the most common. Most materials of this type are relatively sensitive to temperature shifts.

Film resistors are usually formed by depositing a metal or carbon film on a ceramic substrate. In industry, they are often preferred over composition types. Precision resistors are usually formed with metal films.

Wirewound resistors are common at high power levels. A coil of wire, usually nichrome, is wrapped around a ceramic rod or tube in the simplest arrangement. While this is a convenient way to spread out heat, it adds a significant inductance. Special versions which are double wound to avoid excess inductance can be obtained. These "non-inductive" versions are substantially more costly than the simple types.

In this experiment, we will briefly examine the characteristics of standard wirewound resistors. This will serve as an introduction to the overall problems with real resistors.

19.11.6 Procedure

Part 1: Reference measurements

1. Your instructor will assign a set of capacitors, inductors, and resistors to each team. If a bridge or similar instrument is available, gather data at a specific frequency for C_s, C_p, R_s, R_p, L_s, L_p, and D = df for each of your assigned parts. Special emphasis should be placed on the values relevant to the various models.

Part 2: Frequency sweeps

1. Insert one capacitor in the circuit in Figure 19.61. If the capacitor is electrolytic, be sure to observe the polarity marks, and add a dc offset to V_in so that V_c > 0 always. If it is not electrolytic, use an offset of zero. If the capacitor is less than 0.5 µF, substitute a 1 k resistor for R_s.

2. Set V_in at 1000 Hz, and observe V_in and V_c on your oscilloscope. Measure the peak-to peak amplitudes and the phase shift between them in degrees. (Hint: Phase measurements can be made more easily by adjusting the oscilloscope to measure time differences.) Use the highest available V_in value.

3. Look for the resonant frequency of the part by adjusting f_s until the phase shift is close to zero. The amplitude will be close to minimum for a capacitor. Record amplitudes of V_in and V_c at this frequency.

4. Choose at least three frequencies below resonance and three above it; also make a measurement at 1 kHz. The frequencies you choose should cover roughly a factor of 100 in frequency. Record amplitudes of V_in and V_c, and the phase shift between them, at each of these frequencies.

5. Repeat parts 1-4 for your other assigned capacitors and inductors. In some cases, you may want to change the resistor value to allow better measurements of V_c. If you do this, be sure to use R 50 , and be sure to record the R value actually used for each part measured. A value R = 1000 is suggested for inductors.

Part 3: Power resistor tests (these can be performed during frequency sweeps)

1. Connect a wirewound resistor to a variable dc supply.

2. Adjust the voltage and current to draw about 10% of the rated power, or 1 W, whichever is less. Record the voltage and current, then let the part warm up for at least 5 minutes. Record the voltage and current again.

3. Adjust the voltage and current to draw about 50% of rated power, or 10 W, whichever is less. Wait at least five minutes, then record the voltage and current.

4. Repeat step 3 for 100% of rated power.

19.11.7 Study questions

1. Use data for V_in, V_c, and phase to compute the impedance for each tested capacitor and inductor.

2. Plot impedance magnitude and phase vs. frequency for each capacitor and inductor.

3. Plot resistance vs. power for the wirewound resistor.

4. Calculate ESL for each capacitor based on the resonant frequency you measured.

5. Calculate ESR at 1000 Hz and at a frequency near resonance for each capacitor and inductor from your frequency sweep data. Compare the 1000 Hz results to the RLC meter data.

6. Discuss how your data conform to the proposed simple models.

19.12 Magnetics

19.12.1 Introduction

This experiment provides an overview of many concepts of magnetic component design. It concentrates on inductor and transformer design for high-speed converters, and on magnetic properties of materials. In power electronics, both the energy storage capabilities of inductors and the potential-shifting properties of transformers are important in converter designs. But the requirements are much different from those in other electrical engineering areas. High power levels are often an issue at relatively high frequencies. Losses must be as low as possible.

Modern switching converters and their applications take full advantage of the latest magnetic materials. High-performance motors use advanced permanent magnet materials, as well as PWM inverters. The magnetic amplifier and saturable reactor -- power amplifier technologies of the 1940s -- are making a strong comeback in power electronics because of new materials. Material properties are inextricably linked to magnetic components, even more than for capacitors. Two important reasons for this involve the behavior of "magnetic conductors." Highly permeable materials with the ability to direct magnetic flux are only a few orders of magnitude better than air or vacuum. They have limited capacity for carrying magnetic flux. A second difficulty is that the most permeable materials are metals -- they carry magnetic flux, but also carry electric flux, so that a time-changing magnetic flux will create current flow and losses in the materials.

19.12.2 Basic theory

The important concepts of magnetic circuits, magnetic domains, the hysteresis loop, and saturation lead to design considerations for devices. In the laboratory, we will examine candidate designs for inductors and transformers. Any real magnetic material exhibits a maximum value of B, called the saturation flux density B_sat, beyond which it displays permeability close to that of vacuum. Since the flux in a material is found as Ni/, where is reluctance, the current ultimately determines whether the saturation flux density has been reached. Alternatively, the flux is given by /N, or v dt/N. The integral of voltage ("voltseconds") determines the flux, within some integration constant.

In a transformer, saturation must be avoided so that leakage flux stays low. For ac applications, this means that only the voltsecond integral is relevant. If a dc current is imposed on a transformer, an additional flux contribution will appear. In most power-frequency transformers, the number of turns is high, and dc current must be avoided. In an inductor, dc current is almost always needed, so that a net energy can be stored. Inductors must be designed to tolerate high levels of dc current, while providing consistent, linear, inductance. These two requirements are in conflict with the need for inductors of substantial value.

Another important issue in modern magnetics design is the current capacity of the wire used to wind the magnetic device. For instance, a design might call for a great many turns and a small core. While this is possible when small wire is used, the wire might melt if the intended currents are applied. It is not uncommon to require hundreds or even thousands of windings in power frequency devices, and the temptation to use ever-smaller wire is great. To realize a design, it is helpful to realize that only a fraction of any core opening can actually be filled with wire (some must be allowed for insulation and for air spaces around loose windings). It is also helpful to have some guidance about current capabilities of copper. While no absolute rules can exist, it is often safe to impose currents of up to 500 A/cm² on a copper wire. This number gives some rough assistance in picking the wire sizes needed.

A transformer design procedure might be as follows:

Identify the frequency, voltage, current, and power requirements.

Choose a wire size adequate for the current.

Find the voltsecond level needed to meet ratings.

Identify a magnetic core with low losses over the intended frequency range, and proper , A, and winding opening size to support the necessary flux.

Compute winding and core losses to see if they are at acceptable levels.

Build and test the device.

An inductor design would seek to:

Identify the frequency, voltage, and dc current requirements.

Identify the energy storage or L requirement.

Choose a wire size as needed.

Find the voltsecond level needed.

Compute a gap length, if necessary to meet energy and i_dc requirements.

Build and test the device.

19.12.3 Procedure

Part 1: Core hysteresis loops

1. You will be assigned several test cores of various types. Use a ruler to obtain geometric data for each one, or use manufacturer's data.

2. Wrap approximately 25 turns of wire around each toroid test core, and 40 turns around each pot core.

3. Measure the inductance of each device with the bridge or equivalent instrument, if available.

4. Place each core, in turn, in the circuit shown in the figure 19.64, with proper choices of R and C. Be sure to include the 50 resistor R_s.

5. Use the oscilloscope in the X-Y mode to observe the hysteresis loop at some frequency. Sketch the loop in your notebook. Measure the slope of either side of the loop near the origin (B=0 and H=0). Don't forget to make note of the slope units.

6. Decrease the applied frequency until a saturation effect is obvious. Again, sketch the waveforms. Measure the slope of the loop as far into saturation as possible. Also record the v_c value at saturation.

7. Apply a small dc offset from the input supply, and observe the change in the loop. Record your observations. Keep in mind that v_c measures the integral of voltage, and not directly.

Part II -- Transformer design and testing

1. Create a transformer by adding a second 25 turn winding on one of your test cores specified by your instructor.

2. Observe transformer performance by using the circuit in Figure 19.63, with R_load = 1 k. Vary the source voltage frequency and amplitude so that saturation effects can be noted. You should sketch waveforms which demonstrate both saturated action and correct transformer action.

4. Use a 1N4004 diode in series with 50 as a load, and repeat your observations.

19.12.4 Study questions

1. Calculate the permeability of each core at 1000 Hz. Do your numbers agree with bridge or equivalent measurements?

2. Calculate B_sat from your hysteresis curves. What voltsecond rating do you expect for your 25 turn inductors? How do the converter and transformer results compare to your expectations?

3. How would a dc current load affect the output of a transformer?

4. How many turns would be required to create a 10 mH inductor with each of your cores? What would the dc current rating be, based on saturation limits?

19.13 Converter Design Project

19.13.1 Introduction

The intent of the last experiment (normally conducted over a period of about a month) is to provide overall experience with a converter design problem. Each group will design, build, and test a different dc-dc converter. The initial effort tests a basic design with lab boxes, and considers effects of capacitor ESR and switch forward voltage drop.

The first consideration is to create a paper design as the basis for starting the project:

Begin with one of the specification sets listed at the end of this Section. For a dc-dc converter, start with a switching frequency of 100 kHz.

Draw a converter circuit capable of performing the intended function.

Given your specifications, find the switching frequency for which L > L_crit.

Compute the range of load resistances which correspond to the stated output power levels.

Find the value of capacitor necessary to meet the intended ripple requirements.

In the final experiment, our previous work will culminate in the design of an actual converter. The first activity will test the basic design values, with the objective of developing a tentative circuit. Effects of capacitor ESR and switch voltage drops will be examined. The second activity will concern implementation of the actual switches, along with their switching functions. The last effort will examine power loss and heat transfer considerations, and will include tests of the finished converter.

19.13.2 Refining the models

Voltage drops can be integrated into converter design in a straightforward manner. Consider the circuit shown in Figure 19.64, in which an ideal diode and a voltage source have been used to model a real diode. The output voltage V_out can be written in terms of switching functions as:

V_out = q₁V_in - q₂V_{forward(diode)}, V_out(ave) = D₁V_in - D₂V_for

If V_for is assumed to be roughly 1 V, the average value of V_out can be found as

V_out(ave) = D₁V_in + D₁ - 1

The input current is still I_in = q₁I_out, so P_in(ave) = D₁V_inI_out. But now,

P_out(ave) = D₁V_inI_out - D₂V_forI_out,

which gives an efficiency of

= 1 - (D₂V_for)/(D₁V_in).

This is certainly less than 100 %, and represents the loss in the real diode while it is on. A series resistor could also have been included as part of the diode or transistor models.

Capacitor ESR means that capacitors do not really show any ideal voltage characteristics. For example, an electrolytic capacitor with tan = 0.10 and C = 200 µF would have ESR of 4 m at 20 kHz. Consider the effect in the boost converter shown in Figure 19.65. When switch #1 is on, the output current charges the capacitor, but there is a voltage drop across the ESR which appears at the output. As switch #1 turns off, the internal capacitor voltage V_c stays quite constant, but the capacitor current changes abruptly, which in turn reverses the voltage drop across the ESR, and causes an abrupt shift in V_out. The output voltage for this converter can be calculated without too much trouble, if the capacitor voltage is assumed to change in a linear manner. The V_out waveform is shown in Figure 19.66.

As indicated in Figure 19.66, the ESR voltage drop can be a significant fraction of the output voltage ripple. If a maximum output ripple is specified, the value of ESR at the switching frequency will have to be taken into account when designing the converter. For example, the above converter displays output ripple of about 240 mV, although a ripple of less than 160 mV would have been expected if the capacitor were a perfect 200 µF device.

19.3.3 Procedure, part I

1. Obtain an inductor, or design a pot-core inductor to meet your requirements. Use this inductor, along with an FET control box, to build a converter as designed in your preparation. Be sure to place a capacitor across V_in, so that it will appear as a voltage source.

2. Observe V_out under a range of conditions. Be sure to test for a variety of values within your required converter operating range. Sketch V_out under what you find to be roughly worst-case V_out ripple. Be sure to record duty ratio data, along with sufficient data to calculate efficiency.

3. Observe voltage drops across the FET and the diode under your range of operating conditions. The intent is to gather data to support circuit models of your actual diode and FET.

4. If the converter you have built does not meet the specifications for output ripple, try other capacitors in an effort to solve the problem. Experience with your converter circuit is probably more important than meeting all specifications in detail.

5. In the next part of the design project, you will select actual FET and diode parts, in place of the FET box. Be sure you have collected all data needed for models of your devices and for the capacitors. Also, observe inductor current to confirm the critical inductance value.

19.13.4 Study questions -- part I

1. Model the on condition of the FET as a 0.3 resistor, and the on condition of the diode as a 1 V drop. What value of V_out vs. duty ratio would be expected for your converter? Does this agree with measured data?

2. Will you need an FET with lower resistance to meet the requirements?

3. Compute the ESR of your capacitors from the waveform data.

4. Find the peak currents and voltages in your inductor and capacitor.

5. Two common problems in dc-dc converters are: (a) the user accidently connects the input voltage in the reverse direction, and (b) a short circuit is accidently connected at the output. Would the converter you are designing be able to handle these faults? If not, how might it be altered?

19.13.5 Gate drive implementation

At this point, it is logical to fully implement the converter design with discrete components in place of the laboratory boxes. An ideal switch requires a third gate terminal which controls its state. In the ideal case, a switching function is applied directly to this gate (without regard for electrical ground or isolation). The switch is instantaneously on whenever the gate is high, and instantaneously off whenever the gate is low. While the concept of a gate terminal carries over to real switches, there is a host of new considerations introduced by a real gate.

The potential at the gate normally has restrictions relative to the potentials on the switch terminals. Operation of a real gate requires energy (and hence power and time); these must be supplied from some drive circuit. As you might guess, there is a time difference between the application of a gate signal and the actual switching action. In addition to gate characteristics, semiconductor switches have internal properties, such as resistance and capacitance, which limit time rates of change of voltage or current even with a perfect delay-free gate signal.

A gate drive typically tries to minimize commutation time while not adding significantly to power requirements. Gate drives are low-power electronic circuits, and are designed much differently from the converters in which they operate. They are still switching circuits, however, so many concepts of switch networks still apply.

19.13.6 Basic theory -- gate and base drives

The major classes of gated power semiconductors -- thyristors, BJTs, and FETs -- have distinct gate drive requirements. For example, a BJT can be modelled as a current-controlled current source, and requires current into the base when it is to be on. This current is supplied at low voltage (so that power is low), but can be as high as a tenth or more of the switch on-state current. In the case of the FET, the steady-state gate current is essentially zero, and the gate voltage determines switch operation. The SCR, as a typical thyristor requires only a pulse at the gate in order to turn on. Gate turn-off thyristors (GTOs) also require only pulses, although a substantial negative gate current must be applied to turn the devices off.

The basic requirements are simple enough, but details add great complexity. Let us first examine the FET, which has relatively simple gate characteristics. To turn the FET on, the gate region must be charged. The region represents a capacitance, and the gate drive must be designed to charge this capacitance sufficiently. The channel will invert when the gate voltage exceeds a threshold level, V_th. In fact, the gate voltage must be maintained at a level considerably greater than V_th, so that enough charge will be present in the channel for low effective channel resistance. The gate drive must therefore apply an "overdrive" gate voltage, for switching.

To turn the FET off, the gate region must be discharged, and the gate voltage must be maintained below V_th. Real devices have wide error tolerances on V_th. For example, the MTM15N35 FET can have any V_th between 1.5 and 4.5, depending on the device and the operating temperature.

Some gate drive design considerations are apparent:

For turn-on, the drive must rapidly charge the gate to a voltage much higher than V_gs, while not exceeding the dielectric breakdown limit of the gate insulator. Typical gate-source capacitance values range from several hundred to several thousand picofarads.

For turn-off, the drive must rapidly discharge the gate to a voltage lower than V_th, again without exceeding dielectric limits.

Several device specifications are important in the FET gate drive design. Referring to the IRF521, a typical power FET, notice the following relevant information:

V_th between 2.0 and 4.0 V.

Limits on gate-source voltage (gate dielectric breakdown limit):

-20 V < V_gs < +20 V.

Maximum gate current level: 1.5 A (absolute value).

Gate-source input capacitance: 600 pF.

With these data, it is possible to design many different gate drive circuits. Consider the performance of a simple gate drive, consisting of a nearly ideal switch operated from a voltage source of 50 output impedance. At turn-on, the gate capacitance is uncharged, and the maximum gate current is simply V_in/R_s, or 0.24 A in this example. The RC time constant is 30 ns so this gate drive will charge the gate to more than 10 V in about 60 ns. The actual device turn-on time of 110 ns is reasonably consistent with this number. Slightly faster turn-on could be achieved by using a smaller R_s. A value as low as 8 can be used without excessive gate current.

At turn-off, the gate must discharge through the second resistor. This resistor has the undesirable effect of drawing power whenever the FET is on, so is kept relatively high. It also acts as a voltage divider for V_gs. For the circuit of Figure 19.67, turn-off is quite slow.

More specific requirements on the gate drive are becoming apparent:

The gate drive must provide a voltage between the gate and source of about 10 to 18 V, with low source impedance, for fast turn-on.

The gate drive should provide a low impedance discharge path during turn-off. This path can apply zero volts across the gate and source, or could use V_gs < 0 if a negative voltage source is available.

The gate drive can be designed so that current is drawn only in a brief pulse. In principle, most of the ½CV² energy in the gate can be recovered, so that power requirements are very low.

A typical high-performance gate drive circuit appears in Figure 19.68.

The main drawback of FET gate drives is the need to apply a substantial voltage between the gate and source as long as the device is to be on. In many converters, this is not a trivial manner. The familiar buck dc-dc converter is shown in Figure 19.69. For the unit of Figure 19.69 to work, a voltage equal to V_in + 10 V must be applied to the FET gate whenever switch #1 is to be on. This second voltage source, higher than the available source, can be a major stumbling block in building a converter. If the switch is relocated as in Figure 19.69b, the problem of higher voltage level is alleviated, but the output is no longer referred to ground potential. The voltage requirements of FETs sometimes make them difficult to use in many situations.

Bipolar transistors need only a fraction of a volt on the gate (base) terminal. The base behavior is far more complicated than the FET's gate behavior. A BJT base drive must supply enough current to guarantee that the transistor will be fully on. This means that I_b must be chosen to be larger than the expected collector current I_c/. In power transistors, can be quite low -- values of 5 or less are not unusual for devices rated over ten amps. Furthermore, in order to operate the device at the highest possible speed, an overdrive current pulse should be applied at turn-on. This pulse is usually chosen to be nearly equal to I_c. Such high currents are difficult to achieve, since they call for impedance levels well under 1 .

The 2N3055 can serve as a guide for base drive design. This device allows a base current as high as 7 A. The voltage at the base terminal will not exceed roughly 1.5 V. The gain value can be as low as 5, so that base current of about 3 A might be needed if I_c approaches the maximum value of 15 A. A candidate base drive circuit is shown in Figure 19.70. The major difference between this and the FET drive is that it involves much lower impedances. Many base drive circuits include transformers to obtain high currents and low impedances.

Thyristors, as latching devices, are much different from transistors. A signal must be applied to the gate only until sufficient anode current flows. Then the gate signal can be removed. For example, the 2N6508 requires a gate signal of 75 mA or more at a voltage of up to 1.5 V. The gate signal will not be needed once the anode current reaches a "holding current" of 40 mA. This can occur as little as 2 µs after the start of the gate pulse. A pulse transformer can serve as a suitable driver for such requirements. This has the important advantage of isolation of the gate.

Most SCR applications are tied to an ac power line frequency, so that turn-on speed is often not a major consideration. With this in mind, it is relatively easy to build an SCR gate drive, provided certain details are considered. A controlled rectifier circuit is shown in Figure 19.71. The load inductance normally makes the operation consistent with periodic steady state. However, take the case of circuit start-up. Inductor current is initially zero, and three-phase voltages are applied to the SCRs. While a gate signal is applied to SCR A, the inductor current changes as v_L/L. A large inductor will mean a slow change, and a long time may pass before the SCR anode current exceeds the "holding" value. To alleviate this, a small resistor can be added as a ballast load, to ensure SCR turn-on latching. Otherwise, the circuit might not operate.

19.13.7 Basic theory -- snubbers

For some converter designs, very high momentary voltages appear across the FET during the Part I procedures, especially if the layout is loose. Power FETs can easily be destroyed when a V_ds value beyond their limit appears. High momentary voltages can occur even in relatively low voltage converters. Each circuit connection, wire, or component, has inductance, and thus behaves as a current source over short time intervals. When one attempts to reduce any current by switching action, a negative voltage v_L = L(di/dt) will be produced. The faster the switch, or the larger the inductor, the more extreme this negative voltage. In an FET switching 10 A in 100 ns, even with a circuit inductance as low as 1.0 µH, a voltage of 100 V will be generated, independent of the converter voltage levels. This voltage will appear across the switch as it turns off, causing commutation loss and possibly approaching the switch voltage limits.

This effect is detrimental, since it leads to extra losses and even switch failure. It is necessary to minimize the circuit inductance, and to keep di/dt sufficiently small. Leads should be short and of proper size. Loops or other features which enhance magnetic field coupling must be avoided. It is desirable to act upon the switching trajectory itself. After all, the problem here is a switching trajectory which reaches voltages much higher than any circuit voltage when current is still high.

Circuits which act directly on the switching trajectory are called snubbers. The function of a snubber is to shape the switching trajectory and hence protect the switching device. For this reason, most snubbers are wired directly to a switch, and would be considered an actual part of the switch itself for purposes of converter design. For example, a capacitor can be placed across the semiconductor, so that some of the energy needed by the load during commutation is provided by the capacitor. A resistor might be used to discharge the capacitor one the switch has reached the new operating state.

A simple RC snubber causes the switch voltage to change relatively slowly (beginning at about zero) during turn-off. Unfortunately, the opposite occurs during turn-on. In this case, the transistor voltage changes slowly, beginning at V_in, during switching. The switching power loss will actually increase. It is apparent that a turn-off snubber and a turn-on snubber have different requirements. To avoid this difficulty, it is necessary to add circuitry so that the simple RC snubber discussed above will operate only during transistor turn-off. A switch is needed! This switch needs to carry current only during commutation, so that its ratings can be based on momentary performance, rather than on continuous capabilities. A possible snubber circuit is shown in Figure 19.72. During turn-off, it causes voltage to change relatively slowly. While the transistor is off, the snubber capacitor charges up to V_off. But at transistor turn-on, the snubber circuit diode prevents current flow from the snubber capacitor. The second resistor, R₂, discharges C during the transistor's on-time so that the snubber will aga