4. Topology Fundamentals and Their Basis Waveforms

The function of a power circuit is to make whatever power is available suitable to the needs of the load. The available power is either from a battery or from an AC power line, but very few loads can use power in this form, mostly light bulbs and heaters. For all other loads - be that a simple ballast or a complex servomotor - the available power must be conditioned into whatever form is appropriate for the load, be that a simple ballast or a complex servomotor. This is done by means of power conditioning blocks.

As mentioned in Section 3.2, the vast majority of power circuits operate in switchmode. In this context, the term “topology” refers to a specific arrangement of active and reactive components, i.e. a schematic of the power portion of the circuit.  A very large number of topologies have been conceived by designers and several can be found in practical applications. They all share a basic operating principle: power is “conditioned” by some clever sequencing of the on-off cycle of the transistors (“modulation strategy”) to make it suitable for the specific load.

We will briefly analyze the buck, the boost and few other commonly used topologies.

4.1. The buck converter

The buck is a DC-to-DC step-down converter, i.e. it delivers an output voltage that is lower than the input (Figure 11). The inductor and the capacitor at the output are an integral part of this topology.

The input current is always discontinuous because the switch is in series with the input. When the input current is discontinuous, a capacitor is needed at the input to compensate for the line inductance and to handle the higher frequency components of the input current. This input capacitor is not an integral part of the topology – it would not be necessary if the line had no inductance – and is not shown in the figure.

The performance of this converter is determined by three design choices:

• The sizing of the reactive components
• The control method: fixed or variable frequency
• Operating frequency or frequency range.

These design choices determine:

• The rms component of the input current, hence the size of the input capacitor
• The amount of ripple in the output voltage waveform
• The dynamic response to load changes or input voltage changes in closed loop conditions.

Figure 11. The buck converter. The waveforms shown in the picture are for fixed-frequency, continuous current conduction (in the inductor). When the switch is turned off, the inductor current flows in the “free-wheeling” diode. At some point, as the load decreases, the inductor current becomes discontinuous. At 100% duty cycle of the switch the output voltage is equal to the input voltage.

4.2. The boost converter

The boost is a DC-to-DC  step-up converter, i.e. it delivers an output voltage that is higher than the input (Figure 12). The inductor at the input and the capacitor at the output are an integral part of this topology.

Since an inductor is in series with the input, the input current is continuous over most of the operating range. The output current is discontinuous and the output capacitor needs to be rated for the worst case ripple current, as well as other requirements, like “hold-up” time.

As in the buck converter, the performance is determined by three design choices:

• The sizing of the reactive components
• The control method: fixed or variable frequency
• Operating frequency or frequency range.

These design choices determine:

• The rms component of the input current
• The amount of ripple in the output voltage waveform
• The dynamic response to load changes or input voltage changes.

This topology is the most common for power factor correctors. At lower power the preferred control mode is discontinuous current for economic reasons. At higher power continuous current is preferred.

Figure 12. The boost converter. The waveforms shown in the picture are for fixed-frequency, continuous current conduction (in the inductor). The inductor is charged from the line voltage during the on-time of the transistor and discharged into the output capacitor when the switch is turned off. At some point, as the load decreases, the inductor current becomes discontinuous. At 0% duty cycle of the switch the output voltage is equal to the input voltage.

4.3. The half bridge

The half-bridge is a DC-to-AC step-down converter. It is a “two-quadrant converter” because the load current can flow in both directions. This is a critical feature when driving an inductive load with an AC waveform. As in the case of the buck converter, the input current is discontinuous and an input capacitor is needed to compensate for the line inductance and handle the higher frequency components of the input current.

This topology is used extensively in Uninterruptible Power Supplies (UPSs) to generate an output sinewave, as shown in Figure 13. Its drawback is the fact that it requires a positive and a negative voltage with respect to the output neutral, as shown in the figure. A full bridge overcomes this limitation.

Figure 13. The half-bridge as a sinewave generator in a UPS. Notice how the duty cycle of the switches is being modulated at high frequency to achieve a low-frequency sinewave. Notice, also, that the reference point for the output is the midpoint of two input capacitors.

4.3. The full bridge

Two half-bridges can generate an AC output from a single voltage source with no need for a neutral.

This topology is most commonly used in three classes of applications:

4.3.1. Switched-mode power supplies (SMPS) and welders

As shown in Figure 14, the bridge is used to generate a high-frequency square wave that is fed to an isolation transformer. Operation at high frequency reduces the size of the transformer and of the filter components, while improving the closed-loop response time and power density. Power densities in excess of 50W per in3 are commonly available in some commercially available SMPS.

Figure 14. A full bridge is commonly used in SMPS and welders to generate a high frequency square wave that is fed to a step-down transformer. At a typical operating frequency of 50kHz the transformer becomes quite small. Its output is controlled to achieve the desired welding characteristics.

4.3.2. DC-to-AC converters and UPSs

As we have mentioned at the beginning, the topology is only half of the story. The other half is the control strategy, as we will discuss in some detail in this section.

The same full bridge can be modulated to generate a simple square wave, as we have seen in the previous section (Figure 14) or to generate a sinewave by pulse-width modulation of the switches, as shown in Figure 15.

An output square wave is seldom useful as such; in most cases it is rectified and filtered to achieve a dc.

If the objective of the power circuit is to generate a line-frequency sinewave, as is the case in DC-to-AC converters and UPSs, a PWM control of the power switches shrinks the output filter and improves power density.

Figure 15. The same full bridge shown in Figure 14 can be used to generate a sinewave by pulse-width modulation of the switches.

The same topology can be used with many different modulation strategies. Figure 16 shows a combination of the two methods presented in Figure 15. The high- side IGBTs are switched at high frequency (20kHz) and generate the line-frequency waveform by PWM control of the duty cycle. The low-side IGBTs are switched at line frequency and switch the polarity of the waveform. This modulation strategy minimizes semiconductor losses, as only two devices are switched at high frequency, with no change in the input filter. Better efficiency and high frequency operation are the critical components to achieve high power densities.

Figure 16. The two modulation methods (square wave and PWM sinewave) shown in Figure 14 can be combined to improve efficiency. The high-side IGBTs are switched at high frequency (20kHz) and generate the line-frequency waveform by PWM control of the duty cycle. Low-side IGBTs are switched at line frequency and switch the polarity of the waveform.

4.3.3. Reversible DC motor drives

An H-bridge can also be used to control speed and direction of a DC motor. This topology is sometimes referred to as a “four-quadrant converter” because current can flow in either direction and voltage can be reversed across the load.

In this, as in the applications mentioned above, much of the performance is predicated on the modulation strategy. Two such methods are illustrated below by way of example.

• In Figure 17a the two transistors in each half-bridge are both driven in anti-phase with a PWM square wave. Q1 and Q4 are gated on at the same time while Q2 and Q3 are gated on for the remainder of the cycle. At 50% duty cycle the average voltage across the motor is zero. As the duty cycle increases in one direction or the other the motor sees an average voltage at its terminals that can be positive or negative, depending on the duty cycle.

Two switches are always gated on and apply a defined voltage to the motor, as determined by the control board. Change in direction is as natural as a change in duty cycle. Current can flow in both direction and the motor can motor or regenerate.

Notice that, during the first part of the cycle (transistor current), power is delivered to the motor. During the remainder of the cycle power is returned to the supply.

• The control method shown in Figure 17b uses the lower switches to determine the direction of the motor (Q4 in the example), while the upper switches are PWM-modulated to regulate the speed. This method is similar to the one represented in Figure 16. Notice that only two switches are gate-controlled on or off, while the other two have zero volts applied to the gate. In some instances the direction of the current establishes the voltage applied to the motor and it may be different from what is commanded by the control board. A change of direction requires a change-over from one transistor pair to the other, a common source of control headaches.

The first method gives better servo performance while the second method gives much lower ripple current in the motor for the same operating frequency.

With this modulation method power is not returned to the supply. Current free-wheels in the top devices and decays, as determined by the losses.

Figure 17a. Reversible speed control of a DC motor with “locked anti-phase” gate drive. Q1 and Q4 are gated on at the same time while Q2 and Q3 are gated on for the remainder of the cycle. The motor has a net positive voltage across its terminals. Reactive power is returned to the supply through Q2 and Q3 in the remainder of the cycle. Since the full rail voltage is applied to the motor with one polarity or the other, ripple current in the motor can be significant.

Figure 17b. Reversible speed control of a DC motor with “steering switch, PWM switch”. Q2 and Q4 set the direction of rotation while Q1 and Q3 determine the speed. Reactive power is not returned to the supply but free-wheels in the top devices and decays very slowly.

4.4. The three-phase bridge

This topology (Figure 18) is used almost exclusively to drive three-phase motors with different modulation strategies. The two most common types of motors are permanent-magnet and induction motors.

They require different modulation strategies. In fact, the same type of motor could be driven with different modulations: some modulations enhance motor performance at the expenses of semiconductor losses, others do the opposite. This is a specialized topic that goes beyond the scope of this short write-up.

Figure 18. Three-phase bridge, commonly used to drive motors with different types of modulation. The waveforms shown here represent the line-to-line voltage and line current of a sine modulation for an induction motor.

4.5. Topologies to overcome semiconductor limitations

Over the years many such topologies have been devised, some to overcome the limitations of the MOSFET diode, some to reduce the switching losses of IGBTs, some to reduce switching losses in general. The reduction in switching losses is commonly achieved by some form of resonance, as we will see in some of the examples below. This mode of operation is frequently referred to as “soft-switching”, has opposed to “hard switching” that is the standard operating mode of the switch-mode converters we have seen in the previous paragraphs.

As we have mentioned in Section 3.3, IGBTs are minority carrier devices with better conduction characteristics than a MOSFET but worse switching characteristics. One topology that is commonly used to take advantage of its conduction capabilities without paying the price in terms of switching losses is the series resonant half-bridge, shown in Figure 19. Two capacitors have been added in parallel with the IGBTs. This simple addition causes a fundamental change in the way this topology operates.

The output of the half-bridge is a high-frequency square wave of voltage (pink trace) that is applied to a resonant circuit formed by the coil and by one resonating capacitor (C1+C2). The resulting current (blue trace) is quasi-triangular.  Notice that when one IGBT is turned on the voltage at its terminal is a negative diode drop, hence its turn-on losses are virtually zero. When the anti-parallel diode stops conducting, the voltage at its terminals is the voltage drop across the IGBT. In this circuit there are no reverse recovery losses.

Figure 19. The Series Resonant Half Bridge converter. Notice the difference with the half-bridge shown in Figure 13: the load is mostly inductive and two capacitors have been added in parallel with the IGBTs. A square wave voltage (pink trace) is applied to a resonant circuit formed by the coil and by one resonating capacitor (C1+C2). The resulting current (blue trace) is quasi-triangular. The power switches commutate in ZVS (zero voltage switching) at turn-on, which eliminates turn-on losses. The anti-parallel diodes also commutate at ZVS at turn-off, which eliminates recovery losses.

4.6. “Synchronous rectification”

As have seen in Section 3.2, MOSFETs block in one direction and, when gate voltage is applied, they look like a very low value resistor. In the opposite direction MOSFETs behave just like a P-N diode (Figure 7).

If voltage is applied to the gate while diode current is flowing, the equivalent circuit becomes that of a resistor in parallel with a diode (Figure 20). As long as the voltage drop across the resistive part is lower than a diode drop (0.6-0.8V) the current flows in the resistive part of the device and the MOSFET acts as a very low drop rectifier.

The trick is to “synchronize” the gate drive to the direction of the current, hence the name of this technique. It is widely used in very low voltage regulators (1-5V).  Figure 20 shows a forward converter where the two output diodes have been replaced by MOSFETs with no other gate drive circuitry than the output of the transformer. This gate drive method is used for illustration only because no gate drive is available when the output of the secondary falls to zero. Even so, the circuit works, but with higher losses, because the MOSFET diodes take over. In practice, specialized ICs are used to drive the gates in synchronous rectification. One such example can be found here: /product-info/datasheets/data/ir1169.pdf

A MOSFET with an on-resistance of 5mΩ can act as a 20A rectifier with a voltage drop of only 100mV, much lower than Schottky diodes.

Figure 20. Forward converter with synchronous rectification. The two output diodes have been replaced with low on-resistance MOSFETs. As long as gate voltage is applied the current will chose the path with lower voltage drop. The self-driven method shown in the picture is not used in practice: specialized gate drive ICs are used for this purpose.

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