2.2.1 MOSFETs

In applications at voltages below 200 and switching frequencies in excess of 100 kHz,MOSFETs are clearly the device of choice because of their low on-state losses in low voltage ratings, their fast switching speeds, and a high-impedance gate that requires a small voltage and charge to facilitate the on/off transition. The circuit symbol of an n-channel MOSFET is shown in Figure 2.1a. It consists of three terminals: drain (D), source (S), and gate (G). The forward current in a MOSFET flows from the drain to the source terminal. MOSFETs can block only the forward polarity voltage; that is, a positive . They cannot block a negative polarity voltage due to an intrinsic antiparallel diode, which can be used effectively in most switch-mode converter designs. MOSFET I-V characteristics for various gate voltage values are shown in Figure 2.1b.

For gate voltages below a threshold value , typically in the range of 2 to 4 V, a MOSFET is completely off, as shown by the I-V characteristics in Figure 2.1b, and approximates an open switch. Beyond , the drain current through the MOSFET depends on the applied gate voltage , as shown by the transfer characteristic shown in Figure 2.1c, which is valid almost for any value of the voltage across the MOSFET (note the horizontal nature of I-V characteristics in Figure 2.1b). To carry would require a gate voltage of a value at least equal to , as shown in Figure 2.1c. Typically, a higher gate voltage, approximately 10 V, is maintained in order to keep the MOSFET in its on state and carrying .

In its on state, a MOSFET approximates a very small resistor , and the drain current that flows through it depends on the external circuit in which it is connected. The on-state resistance, the inverse of the slope of I-V characteristics as shown in Figure 2.1b, is a strong function of the blocking voltage rating of the device:

(2.1)

The relationship in Equation 2.1 explains why MOSFETs in low-voltage applications, at less than 200 V, are an excellent choice. The on-state resistance goes up with the junction temperature within the device, and proper heatsinking must be provided to keep the temperature below the design limit.

2.2.2 IGBTs

IGBTs combine ease of control, as in MOSFETs, with low on-state losses even at fairly high voltage ratings. Their switching speeds are sufficiently fast for switching frequencies up to 30 kHz. Therefore, they are used for converters in a vast voltage and power range—from a fractional kilowatt to several megawatts where switching frequencies required are below a few tens of kilohertz.

The circuit symbol for an IGBT is shown in Figure 2.2a, and the I-V characteristics are shown in Figure 2.2b. Similar to MOSFETs, IGBTs have a high impedance gate, which requires only a small amount of energy to switch the device. IGBTs have a small on-state voltage, even in devices with a large blocking-voltage rating, for example, is approximately 2 V in 1200-V devices.

IGBTs can be designed to block negative voltages, but most commercially available devices, by design to improve other properties, cannot block any appreciable reverse polarity voltage. IGBTs have turn-on and turn-off times on the order of a microsecond and are available as modules in ratings as large as 3.3 kV and 1200 A. Voltage ratings of up to 5 kV are projected.

2.2.3 Power-Integrated Modules and Intelligent-Power Modules [2–4]

Power electronic converters, for example, for three-phase AC drives, require six power transistors. Power-integrated modules (PIMs) combine several transistors and diodes in a single package. Intelligent-power modules (IPMs) include power transistors with the gate-drive circuitry. The input to this gate-drive circuitry is a signal that comes from a microprocessor or an analog integrated circuit, and the output drives the MOSFET gate. IPMs also include fault protection and diagnostics, thereby immensely simplifying the power electronics converter design.

2.2.4 Costs of MOSFETs and IGBTs

As these devices evolve, their relative costs continue to decline. The costs of single devices are approximately 0.25 cents/A for 600-V devices and 0.50 cents/A for 1200-V devices. Power modules for the 3 kV class of devices cost approximately 1 cent/A.

2.4.1 Turn-On Characteristic

Prior to turn-on, Figure 2.5a shows the circuit in which the MOSFET is off and blocks the input DC voltage ; freewheels through the diode. By applying a positive voltage to the gate, the turn-on characteristic describes how the MOSFET goes from the off-point to the on-point in Figure 2.5b. To turn the MOSFET on, the gate-drive voltage goes up from 0 to , and it takes the gate drive a finite amount of time, called the turn-on delay time , to charge the gate-source capacitance through the gate-circuit resistance to the threshold value of . During this turn-on delay time, the MOSFET remains off and continues to freewheel through the diode, as shown in Figure 2.5a.

For the MOSFET to turn on, first, the current through it rises. As long as the diode is conducting a positive net current , the voltage across it is zero, and the MOSFET must block the entire input voltage . Therefore, during the current rise time , the MOSFET voltage and the current are along the trajectory A in the I-V characteristics of Figure 2.5b and are plotted in Figure 2.5c. Once the MOSFET current reaches , the diode becomes reverse biased, and the MOSFET voltage falls. During the voltage fall time , as depicted by the trajectory B in Figure 2.5b and the plots in Figure 2.5c, the gate-to-source voltage remains at . Once the turn-on transition is complete, the gate charges to the gate-drive voltage , as shown in Figure 2.5c.

Example 2.1

In the converter of Figure 2.4a, the transistor is a MOSFET that carries a current of 5 A when it is fully on. If the current through the transistor is to be limited to 40 A during a malfunction, in which case the entire input voltage of 50 V appears across the transistor, what should be the maximum on-state gate voltage that the gate-drive circuit should provide? Assume the junction temperature of the MOSFET to be 175 °C.

Solution The transfer characteristic of this MOSFET is shown in Figure 2.6. It shows that if is used, the current through the MOSFET will be limited to 40 A.

2.4.2 Turn-Off Characteristic

The turn-off sequence is the opposite of the turn-on process. Prior to turn-off, the MOSFET is conducting , and the diode is reverse biased, as shown in Figure 2.7a. The MOSFET I-V characteristics are replotted in Figure 2.7b. The turn-off characteristic describes how the MOSFET goes from the on-point to the off-point in Figure 2.7b. To turn the MOSFET off, the gate-drive voltage goes down from to . It takes the gate drive a finite amount of time, called the turn-off delay time , to discharge the gate-source capacitance through the gate-circuit resistance , from a voltage of to . During this turn-off delay time, the MOSFET remains on.

For the MOSFET to turn off, the output current must be able to freewheel through the diode. This requires the diode to become forward biased, and thus the voltage across the MOSFET must rise, as shown by the trajectory C in Figure 2.7b, while the current through it remains . During this voltage rise time , the voltage and current are plotted in Figure 2.7c, while the gate-to-source voltage remains at . Once the voltage across the MOSFET reaches , the diode becomes forward biased, and the MOSFET current falls. During the current fall time , depicted by the trajectory D in Figure 2.7b and the plots in Figure 2.7c, the gate-to-source voltage declines to . Once the turn-off transition is complete, the gate discharges to .

2.4.3 Calculating Power Losses within the MOSFET (Assuming an Ideal Diode)

Power losses in the gate-drive circuitry are negligibly small except at very high switching frequencies. The primary source of power losses is across the drain and the source, which can be divided into two categories: the conduction loss and the switching losses. Both of these are discussed in the following sections.

2.4.3.1 Conduction Loss

In the on-state, the MOSFET conducts a drain current for an interval during every switching time period , with the switch duty ratio . Assuming this current to be at a constant during , since it is zero during the rest of the switching time period, the RMS value of the MOSFET current is

(2.2a)

Hence, the average power loss in the on-state resistance of the MOSFET is

(2.2b)

As pointed out earlier, varies significantly with the junction temperature, and data sheets often provide its value at the junction temperature equal to 25 °C. However, it will be more realistic to use twice this resistance value, which corresponds to the junction temperature equal to 120 °C, for example. Equation 2.3 can be refined to account for the effect of a ripple in the drain current on the conduction loss. The conduction loss is highest at the maximum load on the converter when the drain current would also be at its maximum.

2.4.3.2 Switching Losses

At high switching frequencies, switching power losses can be even higher than the conduction loss. The switching waveforms for the MOSFET voltage and the current , corresponding to the turn-on and the turn-off trajectories in Figures 2.5 and 2.7, assuming they are linear with time, are replotted in Figure 2.8.

During each transition from on to off, and vice versa, the transistor has simultaneously high voltage and current, as seen from the switching waveforms in Figure 2.8. The instantaneous power loss in the transistor is the product of and , as plotted. The average value of the switching losses from the plots in Figure 2.8 is

(2.3)

where and are defined in Figure 2.8 as the sum of the rise and the fall times associated with the MOSFET voltage and current:

(2.4)

(2.5)

2.4.4 Gate Driver Integrated Circuits (ICs) with Built-in Fault Protection [2]

Application-specific ICs (ASICs) for controlling the gate voltages of MOSFETs and IGBTs greatly simplify converter design by including various protection features, for example, the over-current protection that turns off the transistor under fault conditions. This functionality, as discussed earlier, is integrated into intelligent-power modules along with the power semiconductor devices.

The IC to drive the MOSFET gate is shown in Figure 2.9 in a block diagram form. To drive the high-side MOSFET in the power pole, the input signal from the controller is referenced to the logic level ground, is the logic supply voltage, and to drive the gate is supplied by an isolated power supply referenced to the MOSFET source S.

One of the ICs for this purpose is UCC21710, which can source up to 10 A for gate charging and sink up to 10 A for gate discharging. It has built-in overcurrent fault protection capability, in which the transistor current, measured via the voltage drop across a small resistance in series with the transistor, disables the gate-drive voltage under over-current conditions.

For extremely low-cost designs, the bootstrap driver shown in Figure 2.10a is a suitable alternative to the more expensive optically or galvanically isolated gate driver. These are suitable for converters with a pair of series-connected devices that are driven in a complementary manner.

Unlike an isolated gate driver, which requires an isolated power supply to source the buffer that drives the high-side switch in Figure 2.10a, the bootstrap driver uses the energy stored in the capacitor to source the buffer. This capacitor is charged up during the normal operation of the converter. When is off and is on, the capacitor is charged from the input DC power supply, as shown in Figure 2.10b. The resistor limits the current flowing into the capacitor, and the voltage across the capacitor is clamped using an active circuit typically present within the driver or using an external Zener diode. When turns off, the diode gets reverse biased. Thus, the voltage across is available for the buffer of to source the gate turn on. During this interval, the capacitor gets discharged, as shown in Figure 2.10c.

There are a few shortcomings associated with bootstrap drives. The maximum on-time of the high-side device is limited so as to provide enough time for the bootstrap capacitor to charge. It lowers the overall efficiency due to the power loss associated with during every charging cycle, which is more pronounced at high voltages, and limits its use to mostly converters operating within 100 V.

2.6.1 Switching Frequency f_s

As discussed in the buck converter example of the previous chapter, a switching power-pole results in a waveform pulsating at a high switching frequency at the current port. The high-frequency components in the pulsating waveform need to be filtered. It is intuitively obvious that the benefits of increasing the switching frequencies lie in reducing the filter component values, and , and hence their physical sizes in a converter. (This is true up to a certain value, up to a few hundred kHz, beyond which, for example, magnetic losses in inductors and the internal inductance within capacitors reverse the trend.) Hence, higher switching frequencies allow a higher control bandwidth, as we will see in Chapter 4.

The negative consequences of increasing the switching frequency are in increasing the switching losses in the transistor and the diode, as discussed earlier. Higher switching frequencies also dictate a faster switching of the transistor by appropriately designed gate-drive circuitry, generating greater problems of electromagnetic interference due to higher di/dt and dv/dt that introduce switching noise in the control loop and the rest of the system. We can minimize these problems, at least in DC-DC converters, by adopting a soft-switching topology, discussed in Chapter 10.

2.6.2 Selection of Transistors and Diodes

Earlier, we discussed the voltage and the switching frequency ranges for selecting between MOSFETs and IGBTs. Similarly, the diode types should be chosen appropriately. The voltage rating of these devices is based on the peak voltage in the circuit (including voltage spikes due to parasitic effects during switching). The current ratings should consider the peak current that the devices can handle, which dictates the switching power loss, the RMS current for MOSFETs, which behave as a resistor with in their on-state, and the average current for IGBTs and diodes, which can be approximated to have a constant on-state voltage drop. Safety margins, which depend on the application, dictate that the device ratings be greater than the worst-case stresses by a certain factor.

2.6.3 Magnetic Components

As discussed earlier, the filter inductance value depends on the switching frequency. Inductor design, discussed later in Chapter 9, shows that the physical size of a filter inductor, to a first approximation, depends on a quantity called the area-product () given by the equation below:

(2.6)

Increasing in many topologies reduces the peak and the RMS values (also reducing the transistor and the diode current stresses) but has the negative consequence of increasing the overall inductor size and possibly reducing the control bandwidth.

2.6.4 Capacitor Selection [7]

Capacitors have switching losses designated by equivalent series resistance, ESR, as shown in Figure 2.11. They also have an internal inductance, represented as an equivalent series inductance, ESL. The resonance frequency, the frequency beyond which ESL begins to dominate C, depends on the capacitor type. Electrolytic capacitors offer high capacitance per unit volume but have low resonance frequency. On the other hand, capacitors such as ceramic and metal-polypropylene have relatively high resonance frequency. Therefore, in switch-mode DC power supplies, an electrolytic capacitor with high C may often be paralleled with a ceramic or metal-polyester capacitor to form the output filter capacitor.

2.6.5 Thermal Design [8, 9]

The power dissipated in the semiconductor and the magnetic devices must be removed to limit temperature rise within the device. The reliability of converters and their life expectancy depends on the operating temperatures, which should be well below their maximum allowed values. On the other hand, letting them operate at a high temperature decreases the cost and the size of the heat sinks required. There are several cooling techniques, but for general-purpose applications, converters are often designed for cooling by normal air convection without the use of forced air or liquid.

Semiconductor devices come in a variety of packages, which differ in cost, ruggedness, thermal conduction, and radiation hardness if the application demands it. Figure 2.12a shows a semiconductor device affixed to a heat sink through an isolation pad that is thermally conducting but provides electrical isolation between the device case and the heat sink.

An analogy can be drawn with an electrical circuit, as shown in Figure 2.12b, where the power dissipation within the device is represented as a DC current source, thermal resistances offered by various paths are represented as series resistances, and the temperatures at various points as voltages. The data sheets specify various thermal resistance values. The heat transfer mechanism is primarily conduction from the semiconductor device to its case and through the isolation pad. The resulting thermal resistances can be represented by and , respectively. From the heat sink to the ambient, the heat transfer mechanisms are primarily convection and radiation, and the thermal resistance can be represented by . Based on the electrical analogy, the junction temperature can be calculated as follows for the dissipated power :

(2.7)

2.6.6 Design Trade-Offs

As a function of switching frequency, Figure 2.13 qualitatively shows the plot of physical sizes for the magnetic components and the capacitors and the heat sink. Based on the present state of the art, optimum values of switching frequencies to minimize the overall size in DC-DC converters using MOSFETs range from 200 kHz to 300 kHz with a slight upward trend.

MOSFET in a Power Pole of Figure 2.4a (Problems 2.1 through 2.8)

• 2.1 A MOSFET is used in a switching power-pole shown in Figure 2.4a. Assume the diode ideal. The operating conditions are as follows: , , the switching frequency , and the duty ratio . Under the operating conditions, the MOSFET has the following switching times: , , , , , . The on-state resistance of the MOSFET is . Assume as a step voltage between 0 V and 12 V.
  • Draw and label the turn-on and turn-off characteristics of the MOSFET and sketch the MOSFET gate-source voltage waveform.
  • Draw and label the diode voltage and current waveforms, assuming it to be ideal.
• 2.2 Plot the turn-on and the turn-off switching power losses in the MOSFET. Calculate the average switching power loss in the MOSFET.
• 2.3 Calculate the average conduction loss in the MOSFET.
• 2.4 Instead of an ideal diode, consider a real diode with a forward voltage drop . Calculate the average forward power loss in the diode.
• 2.5 In the diode reverse recovery characteristic shown in Figure 2A.1, , , and . Calculate the average switching power loss in the diode.

  

• 2.6 In the gate-drive circuitry of the MOSFET, assume that the external power supply in Figure 2.9 has a voltage of 12 V. To turn the MOSFET on each time, under the conditions given, requires a charge from the 12 V supply. Calculate the average gate-drive power loss, assuming that at turn-off of the MOSFET, no energy is returned to the 12 V supply.
• 2.7 In this problem, we will calculate new values of the turn-on and the turn-off delay times of the MOSFET, based on the gate driver IC IR2127, as described in Section 2.4.4. This IC is supplied with a voltage with respect to the MOSFET source. Assume this voltage to equal . Also assume the internal series resistance of the MOSFET gate to be zero.
  • For the turn-on, assume that this driver IC is a voltage source of with an internal resistance of in series. Calculate the turn-on delay time , assuming that the MOSFET threshold voltage . Assume the MOSFET capacitance to be 1800 for this calculation.
  • For turning-off of the MOSFET, assume that this driver IC shorts the MOSFET gate to its source through an internal resistance of . Calculate the turn-off delay time , assuming that the MOSFET voltage . Assume the MOSFET capacitance to be 1800 for this calculation.
• 2.8 The MOSFET losses are the sum of those computed in Problems 2.2 and 2.3. The junction temperature must not exceed , and the ambient temperature is given as . From the MOSFET datasheet, . The thermal pad has . Calculate the maximum value of that the heat sink can have.

Simulation Problem

• 2.9 To achieve the output capacitor in a buck converter, an electrolytic capacitor is connected in parallel with a polypropylene capacitor . Each of these capacitors has the following ESR and ESL as shown in Figure 2.10: , , and .
  • Obtain the frequency response of the admittances associated with and , and their parallel combination, in terms of their magnitude and the phase angles.
  • Obtain the resonance frequency for the two capacitors and their combination.

Hint: Look at the phase plot.

2A.1 Average Forward Loss in Diodes

The current flow through a diode results in a forward voltage drop across the diode. The average forward power loss in the diode in the circuit of Figure 2.4a can be calculated as

(2A.1)

where is the MOSFET duty ratio in the power pole, and hence the diode conducts for () portion of each switching time period.

2A.2 Diode Reverse-Recovery Characteristic

Forward current in power diodes, unlike in majority-carrier Schottky diodes, is due to the flow of electrons as well as holes. This current results in an accumulation of electrons in the p-region and of holes in the n-region. The presence of these charges allows a flow of current in the negative direction that sweeps away these excess charges, and the negative current quickly comes to zero, as shown in the plot of Figure 2A.1.

The peak reverse recovery current and the reverse-recovery charge shown in Figure 2A.1 depend on the initial forward current and the rate at which this current decreases.

2A.3 Diode Switching Losses

The reverse recovery current results in switching losses within the diode when a negative current is flowing beyond the interval in Figure 2A.1, while the diode is blocking a negative voltage . This switching power loss in the diode can be estimated from the plots of Figure 2A.1 as

(2A.2)

where is the switching frequency. In switch-mode power electronics, increase in switching losses due to the diode reverse recovery can be significant, and diodes with ultra-fast reverse recovery characteristics are needed to avoid these from becoming excessive.

2A.4 Diode Switching Losses

The reverse recovery current of the diode also increases the turn-on losses in the associated MOSFET of the power-pole. This is illustrated by an example below.