Chapter 5: Power Electronics: Devices and Circuits

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Power electronics is an enabling technology for all electrical and electronic apparatus requiring electric power to drive. Over the past twenty years, the power electronics industry has grown tremendously. Its growth is a result from increasing demand of reliable, eﬃcient, compact and cost eﬀective power supplies for telecommunication, computer, and motor drive industries as well as for medical equipments and military use.

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Nội dung Text: Chapter 5: Power Electronics: Devices and Circuits

Chapter 5 Power Electronics: Devices and Circuits 5.1 Introduction Power electronics is an enabling technology for all electrical and electronic apparatus requiring electric power to drive. Over the past twenty years, the power electronics industry has grown tremendously. Its growth is a result from increasing demand of re- liable, eﬃcient, compact and cost eﬀective power supplies for telecommunication, com- puter, and motor drive industries as well as for medical equipments and military use. This growth is facilitated by the signiﬁcant improvement in semiconductor technology in which smaller packaging and higher power handling devices have been marketed. In response to the advancement in semiconductor and magnetics technology, power elec- tronics researchers and engineers have strived to thoroughly employ these technologies through new circuit design and topologies, optimized control and packaging techniques, in order to meet the industry demands. Power electronics is all about using electronic devices and circuits with storage el- ement to control the level of voltage and current, either in the form of AC or DC. Power electronics circuits are switching converters with periodic switching actions to process the electrical energy to meet the design speciﬁcation. Apart from semiconductors, in- ductor and transformer are the critical magnetic components in the power switching converter. Their functions such as storage element, power splitting, and safety isolation 83
5. Power Electronics: Devices and Circuits 84 will be explained in detail in Chapter 6. In order to control power, some form of control techniques are needed and will be discussed in Chapter 7. This chapter we will begin with the semiconductor devices used for power con- verters. We then analyze the basic DC/DC converters at the steady state. That is, the output voltage and current are at stable condition. Finally, the operation of gate driver, which drives the transistor, is presented. 5.2 Electrical Energy Conversion by Switching The characteristics of power conversion by power electronics converters are summarized as follows: 1. Electrical energy can be generated, transmitted and converted to a form that is suitable for the load we are interested in. 2. Power Electronics concerns conversion and processing of electrical energy by power semiconductor devices and storage elements. 3. Power Electronics technologies enable great eﬃciency enhancement, tremendous size and weight reduction of electrical equipment. 4. Power Electronics technologies are based on switching on and oﬀ the power source by power semiconductors. The electrical energy conversion process can be pre- cisely controlled in a manner far much better than electromechanical devices. 5. Power Electronics applications include power supplies for computers, communi- cation equipment, machine drives, lighting, automobile and many applications. 6. Electrical energy conversion can be classiﬁed into the following four categories : AC to AC, AC to DC, DC to DC, and DC to AC.
5. Power Electronics: Devices and Circuits 85 Figure 5.1: Four categories of electrical energy conversion. Figure 5.2: Diode: (a) Symbol, (b) I-V characteristic, (c) idealized characteristics. Sources: Mohan 1995 [2].
5. Power Electronics: Devices and Circuits 86 Figure 5.3: Diode switching characteristics. Sources: Mohan 1995 [2].
5. Power Electronics: Devices and Circuits 87 5.3 Power Semiconductor Devices as Switches 5.3.1 Diodes A diode performs as a switch. It is driven by the voltage applied across its two terminals: anode and cathode. Fig 5.2(a) shows the symbol of a diode. A is the anode, the positive terminal. K is the cathode, the negative terminal. When a diode is forward biased, vd is positive (i.e. potential at A is higher than K ), the arrow shows the direction of the diode current iD . When the diode conducts, a small forward voltage drop denoted as VF is established and the magnitude is usually around 1V. When the diode is reverse biased, it is blocked and the diode current becomes slightly negative. This is due to the contribution of reverse saturation current. For example, 1N4004 has a reverse current of 50µA. And this reverse current is of temperature-dependent; when temperature is higher the reverse current is increased and vice versa. The reverse voltage applied on a diode has a limit. Beyond the limit the diode will breakdown and becomes a short circuit. This limit is usually called the peak inverse (or reverse) voltage. Another interesting fact of semiconductor is that it can handle repetitive pulse current which has a magnitude much higher than the continuous diode current. For example, 1N4004 has a maximum forward current at 1A but its allowable repetitive pulse current is at 10A. This property is of particular interest to power electronics circuit because of its switching nature. Owing to the intrinsic resistance, inductance and capacitance of a diode, it expe- riences voltage overshoot (especially in power diode) and reverse recovery transition. When the diode is forward biased, large amount of excess carriers are driven across the junction and the depletion region is reduced. This behaves like charging a capacitor plus the ohmic resistance and inductance that cause the voltage overshoot. When the charging action is ﬁnished the forward current IF becomes steady and the eﬀect of di/dt on inductance becomes zero, and thus the drop after the overshoot. When the diode is reversed biased, it will turn oﬀ and the current decreases. If it was an ideal diode, current would have dropped to zero and remained zero afterwards. In practice, IF becomes negative for a while before it settles to zero. This period is known as reverse recovery period. The reverse recovery period is due to charge storage in the diode when it is forward biased. When the diode turns oﬀ the charge storage has to be
5. Power Electronics: Devices and Circuits 88 Figure 5.4: N-Channel MOSFET: (a) Symbol, (b) I-V characteristic, (c) idealized characteristics. Sources: Mohan 1995 [2]. removed before the junction can become reverse biased again. The eﬀects of reverse recovery of diode are not only increasing the power dissi- pation of diode itself but also increaseing the losses of other devices connected. For power electronics circuits switching at high frequency in the range of hundred kHz to few MHz, fast recovery time diodes are preferred. There are at least three diﬀerent types of diode: • Line frequency diode or general purpose diode - on-state or forward voltage of theses diodes is made as low as possible but higher trr , which is acceptable for line frequency applications (50 Hz or 60 Hz). • Fast recovery diode - small reverse recovery time, trr less than a few microseconds, for high frequency switching circuits. • Schottky diode - these diodes have low forward voltage drop(typically 0.3V) and the diode dissipation is reduced. However Schottky diodes are limited in their voltage blocking capabilities, typically less than 250V. 5.3.2 MOSFET The MOSFET has three terminals: Gate (G), Drain (D) and Source (S). It is a voltage- controlled device which needs a voltage across gate-to-source (VGS ) be greater than a threshold voltage Vth to drive the transistor on. When the transistor is on, the drain-to- source becomes a channel for electric current to pass through at both directions. This
5. Power Electronics: Devices and Circuits 89 channel has an internal resistance called on-state resistance RON which is voltage- and temperature-dependent. In general, the higher the voltage and temperature, the higher the on-state resistance. RON is at the range from a few milli-ohms to a few ohms. Besides, due to the formation structure of MOSFET, there is a body diode across the source-to-drain terminals. The MOSFET has intrinsic capacitances across all its terminals. Of particular concern is the capacitances across G-S and G-D. These capacitances will cause delay in the turning on or oﬀ the MOSFET. This leads to switching losses. In order to minimize the losses, the gate driver circuit (i.e. to provide VGS ) has to be of high current and fast switching response. We will discuss that in more detail in the last Section of this chapter. The gate-to-source voltage needs to stay above the threshold voltage to maintain the transistor on. One important point to stress is that, for a practical MOSFET, VGS and drain current ID are inter-related. For example, in Fig. 5.5, the drain current ID only reaches 6.5A maximum when VGS is at 4.5V. ID increases when VGS increases. When the VGS decreases to zero, the transistor is oﬀ and ID decreases to zero. Current MOSFET can sustain a reverse voltage up to 1kV. 5.4 Basic Power Converter Topologies 5.4.1 Buck The buck converter with MOSFET is shown in Fig. 5.6. The buck converter performs voltage step-down function. That is, Vo is less than VS . By the switching actions of MOSFET, the buck converter can be described by two basic operation stages as shown in Fig. 5.7. The switching waveforms of the buck converter is shown in Fig. 5.8. In this operation mode, the inductor current does not reach zero. This mode is called continuous (inductor) conduction mode (CCM). Stage 1 Prior to this stage, the switch Q1 is turned oﬀ. But there is current ﬂowing in the inductor L. When Q1 is turned on at the beginning of this stage (t = 0), the voltage
5. Power Electronics: Devices and Circuits 90 Figure 5.5: N-Channel MOSFET IRF540N I-V characteristic. Sources: International Rectiﬁer. Q1 L -(t) - - iL (t) is Io ? Ia + VL (t) − 61 vP ulse1 ? (t) Ic + + iD C VC (t) Vo (t), Va Df w VS RL − − Figure 5.6: Circuit diagram of a buck converter.
5. Power Electronics: Devices and Circuits 91 L -(t) - - iL (t) is Io Ia + VL (t) − 61 ? Ic (t) + + iD C VC (t) Vo (t), Va Df w VS RL − − (a) Stage 1 (0 − DT ) Q1 L -(t) - - iL (t) is Io Ia + VL (t) − 61 ? Ic (t) + + iD C VC (t) Vo (t), Va Df w VS RL − − (b) Stage 2 (DT − T ) Figure 5.7: Equivalent circuits for the buck converter of the two operation stages.
5. Power Electronics: Devices and Circuits 92 VDW (t) VS - . . . . iL (t) . DT .T ∆I L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .? . . . . . . . .. I2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IL = Ia . . . . ....................................... I1 - . . 6 . . . . . . iS (t) . . . . I2 . . . . . . . . . . . . I1 - . . . . . . . . . . . . . . Ic (t) . . . . . . . . . . - . . . . . . . . . . . . ∆VC . . . . vC (t) = Vo (t) . . . . ? . . . . . . ................................................................................. Va . . ................................................... . . 6 . . - . . . . . . . . . . . . . . Io (t) . . . . . . . . . . . . ................................................................................. . . Ia . . . . . . - . . . . . . . DT .T t Figure 5.8: Key switching waveforms of a buck converter.
5. Power Electronics: Devices and Circuits 93 applied across the inductor is VL (t) = VS − Vo (t) (5.1) Since the resultant voltage is positive on VL , inductor L is charged up linearly with a rate equals diL VL (t) VS − Va = = (5.2) dt L L where we assume Vo t is constant and at a value equals Va . As the inductor current rises from I1 to I2 , we may substitute ∆I = I2 − I1 into (5.2) to give ∆IL VS − Va = L (5.3) DT And by re-arranging of terms we have the duration of Stage 1 ∆IL ton = DT = L (5.4) VS − Va Stage 2 This stage begins when switch Q1 is turned oﬀ. The drain-to-source terminal becomes an open circuit. Input current is ceased to ﬂow. However, the current in the inductor cannot change abruptly. Without a path to continue IL , the energy stored in the inductor will be released suddenly that appears as a destructive voltage spike on the MOSFET and eventually would burn it out. Fortunately, a free wheeling diode Df w is presented in the buck converter. IL is diverted to ﬂow through this diode. Neglecting the forward voltage drop of diode VDf w , the voltage applied across L has reversed polarity and its magnitude is described as VL (t) = −Vo (t) = −Va (5.5) The rate of change of inductor current is given by diL VL (t) −Va = = (5.6) dt L L And we may ﬁnd the duration of Stage 2 is I2 − I1 tof f = (1 − D)T = L (5.7) −Va One important property of magnetic component is the change of inductor current is proportional to the change of magnetic ﬂux of the inductor or transformer core. If
5. Power Electronics: Devices and Circuits 94 we can maintain a contant change of inductor current, then we are able to prevent the core from walking towards saturation. This property leads to the following equality ∆IL (ton ) = ∆IL (tof f ) (5.8) VS −Va −Va L DT = L (1 − D)T From (5.8) we arrive the following conclusion: Va = Vs D (5.9) which is the voltage conversion ratio of buck converter at operating at CCM. Since D is always less than 1, it implies that Va is always less than Vs . Critical Inductance From Fig. 5.8, we know that Ia = (I2 − I1 )/2. In order to maintain inductor current at CCM, we must ensure the following inequality I2 − I1 ≤ Ia (5.10) 2 Substitute (5.2) into (5.10), VS − Va Va DT ≤ Ia = (5.11) 2L RL Substitute (5.9) into (5.11) and rearrange of terms, we get (1 − D)T RL (1 − D)RL L≥ = = Lcrit (5.12) 2 2fs where fs is the switching frequency. Input and Output Ripples The average charging or discharing current of the output capacitor C is equal to the trangular area IC (t) covered. Take the capacitor charging part as an example. It can be written as ∆I L T ∆IL × 2 2 IC = = (5.13) 2T 8 The capacitor ripple voltage ∆vC of each period is T 1 ∆IL T ∆IL ∆vC = dt = (5.14) C 8 8C 0
5. Power Electronics: Devices and Circuits 95 Substitute (5.3) and (5.9) into (5.14), the capacitor ripple voltage is expressed as VS D(1 − D) ∆vC = (5.15) 2 8fs LC In fact, the capacitor ripple voltage ∆vC is the output ripple voltage ∆vo because the capacitor is directly connected to the load. It can be seen that to decrease the ripple voltage, one can increase one or both of the following parameters: switching frequency, output capacitance and inductance. As the input current of buck converter is pulsating, it may aﬀect the equipment or power sources connected to the input of the buck converter. A common practice is to insert an LC ﬁlter between the source VS and the switch Q1. The ﬁlter also reduces the magnitude of electromagnetic interference (EMI). Example: The buck converter shown in Fig. 5.6 has an input voltage of 12V. The switching frequency is 50kHz. The load requires an average voltage of 5V with a maximum ripple voltage of 20mV. The maximum ripple current of the output inductor is 0.2A. Determine: (a) the duty cycle, (b) the output inductance, (c) the output capacitance, and (d) the output inductance if the switching frequency is increased to 100kHz. Solution: (a) From (5.9), Va 5 D= = = 0.417. VS 12 (b) From (5.4) (VS − Va ) 0.417 12 − 5 L = DT = = 0.29mH. × ∆I 50000 0.2 (c) From (5.15) VS D(1 − D) 12 · 0.417 · (1 − 0.417) C= = = 25µF 2 L∆ v 8 · 500002 · 0.29mH · 0.02 8fs C (d) The duty cycle remains unchanged. But the frequency has increased that caused the inductor to decrease, as indicated from (5.4) (VS − Va ) 0.417 12 − 5 L = DT = = 0.146mH. × ∆I 100000 0.2 We can see that by doubling the switching frequency, the inductance is reduced by half.
5. Power Electronics: Devices and Circuits 96 Q1 L -(t) - - iL (t) is Io Ia + VL (t) − 61 ? (t) Ic + + iD C VC (t) Vo (t), Va Df w VS RL − − Figure 5.9: Stage 3 of the buck converter at DCM. VDW (t) - . . . . . . . . . iL (t) . -. . . . . D1 T . . . . . . ILP . . . . . . . . . . . . ................................................................... . . IL . . . . . . . . . . . . . . . . . - . . . . . . . . . .DT . .T 0 . . . . . . . . . VS − Va . vL (t) . . . . - . . 0 −Va Figure 5.10: Key switching waveforms of a buck converter at DCM.
5. Power Electronics: Devices and Circuits 97 Discontinuous Condution Mode (DCM) In discontinuous conduction mode (DCM), there is an additional stage after Stage 2 in which the inductor current has already reached zero, as shown in Figs. 5.9 and 5.10. The output voltage is sustained by the output capacitor C . Since the average voltage across the inductor is zero, we can write the following: (VS − Va )DT − Va D1 T = 0 (5.16) Rearranging of terms we have the duration of inductor current discharging (VS − Va )DT D1 T = (5.17) Va Now if we assume the buck converter is lossless, then the input power equals output power, which is given by V2 ILP · DT =a VS × (5.18) 2T RL As the peak of inductor current is given by VS − Va ILP = DT (5.19) L Substitute (5.19) into (5.18), we get an quadratic equation 2L V 2 + VS Va − VS = 0 2 (5.20) D 2 T RL a Solving the equation, we ﬁnally have the voltage conversion ratio of buck converter in DCM D 2 T RL Va 8L = ( 1+ 2 − 1) (5.21) VS 4L D T RL 5.5 Driving the Transistor 5.5.1 Losses Fig. 5.11(a) shows a circuit modeling a general switching converter switching an in- ductive load. As it is common in power electronics circuits that they process energy to be stored and transferred from inductive element such as inductor and transformer. It is in this circuit modeled as Io . Vd is the power source, vT and iT are the voltage and current through the transistor respectively.
5. Power Electronics: Devices and Circuits 98 Figure 5.11: Cause of switching losses in transistor. Sources: Mohan 1995 [2].
5. Power Electronics: Devices and Circuits 99 Switching Loss When the switch control signal is at On state, after certain delay td(on) the transistor is closed. The current of the transistor increases while the voltage across it decreases. The duration takes tc(on) = tri + tf v for iT to reach Io and vT to reach Von . Von is non-zero in practical transistor as it has internal resistance. From 5.11(c), it shows the energy losses to switching on and oﬀ of the transistor (shaded area), which can be approximately written as 1 Wc(on) = Vd Io tc(on) (5.22) 2 1 Wc(of f ) = Vd Io tc(of f ) (5.23) 2 And the power dissipation of the transistor due to switching losses can be written as 1 Ps = Vd Io (tc(on) + tc(of f ) )fs (5.24) 2 It can be seen that the switching loss increases with the switching frequency. This becomes the trade-oﬀ when we want to reduce the component size such as magnetic components and capacitor by increasing the switching frequency, the switching loss increases as well. Converters with this type with conventional switching of transistor are often called “hard-switching” converters. In order to have a breakthrough, we may need to consider soft-switching technique which is able to minimize or even eliminate the cross conduction of voltage and current through the transistor. This is however beyond the scope of this unit of study. Students who want to have further studies in soft-switching technique can go to Chapter 3 of Ang’s book [1]. Conduction Loss The conduction loss of the transistor is deﬁned as the energy dissipation in the transistor during this on-state interval. It can be approximated as Won = Von Io ton (5.25) The power dissipation of conduction loss is then approximated as ton Pon = Von Io (5.26) T
5. Power Electronics: Devices and Circuits 100 Totem-pole VDD ic ? Q1 ?ID iB1 - β s + Q3 Ri VBE iG - − x + + VBE + − vGS + vP W M β − iB2 Q2 − 0 Figure 5.12: Totem-pole gate driver for MOSFET. 5.5.2 Totem-pole Gate Drive Another way to reduce the switching loss is to have a fast switching gate driver to speed up the rate of turn-on and turn-oﬀ of transistor. As we have mentioned in Section 5.3.2 t=hat the MOSFET has intrinsic input capacitance across its gate and source. In usual cases the switch control signal vP W M is of low current capability. We may use a so- called totem-pole circuit to amplify the current of the signal. It consists of one NPN transistor and one PNP transistor connected in series, as shown in Fig. 5.12. The operation is briefed as follows: To proper switch on the transistor Q3, the control signal vP W M should be greater than the transistor forward biase voltage of Q1 plus the gate-to-source threshold voltage of Q3. vP W M > VBE + Vth (5.27) The base current of Q1 can be written as vP W M − VBE − Vth iB = (5.28) Ri As the current gain ratio of Q1 is given by β , then the current to the gate of MOSFET becomes vP W M − VBE − Vth iG = β (5.29) Ri
5. Power Electronics: Devices and Circuits 101 Figure 5.13: Floating gate drive IR2111. Sources: International Rectiﬁer. Figure 5.14: Floating gate drive IR2111 functional block diagram. Sources: Interna- tional Rectiﬁer. The base-to-emitter voltage of Q2 is reverse biased and it is in oﬀ-state. To switch oﬀ Q3, we need to turn oﬀ Q1 and switch on Q2. It is achieved by decreasing vP W M to zero. Now Q2 is forward biased and the charge of gate-to-source of Q3 will be taken away as current through emitter then collector of Q3 to ground. This is a quick discharge of the intrinsic capacitor and the transistor is turned oﬀ quickly. 5.5.3 Floating Gate Drive The totem-pole gate driver is only able to drive the transistor with reference to ground. If we need to drive a MOSFET with its source node not connecting to ground, for example the MOSFET of buck converter, we need to have a ﬂoating gate drive to provide voltage across gate-to-source of the MOSFET. For example, the half-bridge
5. Power Electronics: Devices and Circuits 102 driver model IR2111 from International Rectiﬁer in Fig. 5.13. The functional block diagram is shown in Fig. 5.14. The whole idea of this driver is to provide voltage to charge up the upper MOSFET vGS . This voltage is from the small capacitor across VB and VS in Fig. 5.13. How to charge up this capacitor? It is when the lower transistor is turned on. It provides a current path from Vcc , diode across Vcc and VB , capacitor, lower transistor then the return path to charge up this capacitor. When the upper switch control signal is On, the capacitor will transfer its charge through the internal circuit of the chip to the intrinsic input capacitor of upper MOSFET.