which equals 1 if v (t) ≥ v,; otherwise 0. The transistor duty-ratio based on Fig. 2-12 is given as d(t) = v. (t) V. Thus, the control voltage v₂(t) can provide regulation of the average output voltage of the switching power-pole, as discussed further in Chapters 3 and 4. 0 90 REFERENCES V. dT. S Figure 2-12 PWM IC waveforms. t 2. International Rectifier (http://www.irf.com). 3. POWEREX Corporation (http://www.pwrx.com). 4. Fuji Semiconductor (http://www.fujisemiconductor.com). (2-8) - vc(t) 1. N. Mohan, T. M. Undeland, and W.P. Robbins, Power Electronics: Converters, Applications and Design, 3rd Edition, Wiley & Sons, New York, 2003. 5. On Semiconductor (http://www.onsemiconductor.com). 6. Infineon Technologies (http://www.infineon.com). 7. Panasonic Capacitors (http://www.panasonic.com/industrial/components/capcitor.htm). 8. Aavid Corporation for Heat Sinks (http://www.aavid.com). 9. Bergquist Company for thermal pads (http://www.bergquistcompany.com). 10. Unitrode for PWM Controller ICs (http://www.unitrode.com). PROBLEMS MOSFET in a Power-Pole of Fig 2-4a A MOSFET is used in a switching power-pole shown in Fig. 2-4a. Assume the diode ideal. The operating conditions are as follows: V₁ = 40V, I =5A, the switching frequency f = 200 kHz, and the duty-ratio d =0.3. Under the operating conditions, the MOSFET has the following switching times: td(on) = 100ns, t = 30ns, t = = 20 ns, 2-15 td (off) = 50ns, RDS(on) = 20m. Assume VGG as a step voltage between 0 V and 12 V. 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 = t 25ns, t = 15 ns. The on-state resistance of the MOSFET is fi 2-16 Draw and label the turn-on and turn-off characteristics of the MOSFET and sketch the MOSFET gate-source voltage vs waveform. Plot the turn-on and the turn-off switching power losses in the MOSFET. Calculate the average switching power loss in the MOSFET, and the percentage reduction in the converter energy efficiency due to this switching power loss. Calculate the average conduction loss in the MOSFET. In stead of an ideal diode, consider that the diode is actual and has a forward voltage drop VFM = 0.8V. Calculate the average forward power loss in the diode. In the diode reverse recovery characteristic shown in Fig. 2A-1, t = 10ns, t = 25 ns, and IRRM = 2A. Calculate the average switching power in the diode. In the gate-drive circuitry of the MOSFET, assume that the external power supply Vext in Fig. 2-8 has a voltage of 12 V. Each time, to turn the MOSFET on under the conditions given requires a charge Q = 45 nC. Calculate the average gate-drive power loss. 8 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 V = 12V with respect to the MOSFET Source. Assume this voltage to equal VGG. ext (a) For the turn-on, assume that this driver IC is a voltage source of VGG with an internal resistance of 60 in series. Calculate the turn-on delay time ta(on), assuming that the MOSFET threshold voltage VGS(th) = 3V. Assume the MOSFET capacitance to be 1190 pF for this calculation. (b) For turning-off of the MOSFET, assume that this driver IC shorts the MOSFET gate to its source through an internal resistance of 302. Calculate the turn-off delay time ta(off), assuming that the MOSFET voltage VGS(1₂) = 4.5V. Assume the MOSFET capacitance to be 1900 pF for this calculation. In the Buck converter in which this switching power-pole is used, the output filter capacitor consists of a parallel combination of an electrolytic capacitor and a metalized-polyester capacitor. The electrolytic capacitor has the following 2-9 measured values: C=697μF, ESR = 0.0372, and ESL=16nH. The metalized-polyester capacitor has the following measured values: C=10µF, ESR = 0.042, and ESL=34nH. Using any computer program, plot the impedance magnitude of each capacitor, and of their parallel combination, on the same log-log plot, as a function of frequency (from 1 kHz to 1 MHz). At f = 200 kHz, what are the relative impedance magnitudes of these two capacitors? The MOSFET losses are the sum of those computed in Problems 2-2 and 2-3. The junction temperature must not exceed 100°C, and the ambient temperature is given as 40°C. From the MOSFET datasheet, R₂ = 1.2°C/W. The thermal jc pad has Rs = 1.8°C/W. Calculate the maximum value of Rea that the heat sink can have. APPENDIX 2A DIODE REVERSE RECOVERY AND POWER LOSSES In this appendix, the diode reverse characteristic is described and the associated power losses are calculated. The increase in the MOSFET turn-on switching loss due to the diode reverse recovery current is discussed in the accompany CD. 2A-1 Average Forward Loss in Diodes FM The current flow through a diode results in a forward voltage drop VEM across the diode. The average forward power loss Pdiode, in the diode in the circuit of Fig. 2-4a can be calculated as F Pdiode, F = (1-d). VEMI FM (2A-1) where d is the MOSFET duty-ratio in the power-pole, and hence the diode conducts for (1-d) portion of each switching time-period. 2A-2 Diode Reverse Recovery Characteristic Forward current in power diodes, unlike in Schottky diodes that are majority-carrier devices, 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 Fig. 2A-1. The peak reverse recovery current IRRM and the reverse recovery charge Q shown in Fig. 2A-1 depend on the initial forward current I, and the rate di/dt at which this current decreases. 2-17

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which equals 1 if v (t) ≥ v,; otherwise 0. The transistor duty-ratio based on Fig. 2-12 is given as d(t) = v. (t) V. Thus, the control voltage v₂(t) can provide regulation of the average output voltage of the switching power-pole, as discussed further in Chapters 3 and 4. 0 90 REFERENCES V. dT. S Figure 2-12 PWM IC wa