PE Assignment

POWER DIODES

1. In the circuit diagram depicted in Fig.2 the source voltage Vs has a rectangular waveform ±20V with a period T=1ms. The load resistance is R=0.5Ω. From the diode characteristic shown in Fig.1 determine the equivalent circuit parameters. What are the values of the average power absorbed by the load and the diode, calculate for all three models depicted in (a),(b) and (c) of Fig. 3.4?

Fig. 1 Fig.2

Answer[(a)400W,0, (b)351.6W,23.4W, (c)361W,19W.]

2. During conduction the voltage drop vD across a power diode is modelled by

vD = VD +RD iD

where VD is a fixed component, RD is the slope resistance of the I-V characteristic and iD is the diode current. A diode acts as a half wave rectifier to modulate power from a 240-V, 50Hz supply to a resistive load of 1.414Ω. The diode model is represented by VD=1.0V and RD=1.0×10-3Ω. (a) find the average power dissipated in the diode if the transient switching losses can be neglected. (b) The junction temperature is not to exceed 150°C and the ambient temperature is 30°C. If the diode thermal resistance, junction to case is specified as RθJC 0.1°C/W, calculate the necessary value of the bonding and heatsink thermal resistance.Answer[(a)90.8W, (b)1.22°C/W]

3. A single diode is used to rectify the current from an ac source of voltage 1000V at 2KHz to resistive load of value 1.0Ω. for the conditions prevailing and the diode specifications, the reverse recovery charge is QRR=10μC and the softness factor S=0.6. Find (a) the reverse recovery time t rr of the diode and (b) the peak reverse current IRR during commutation.Answer[(a)1.34μs, (b)14.9A]

4. A diode is used to rectify the current from an ac supply of 240V to a resistive load that is to absorb an average power of 60kW. A diode at hand is known to have the specifications 1000V, maximum junction temperature 180°C, thermal resistance, junction to ambient , RθJA=0.32°C/W and the on state voltage drop is 1.8V at 300A. Determine whether this diode can be used for this application if the ambient temperature is maintained at 30°C.Answer[Yes]

5. A chopper circuit (refer to Fig.3) incorporates a freewheeling diode with a snubber capacitor C s=1.0μF and a snubber inductor Ls=20μH for a load current Il=300A that is ripple free. The dc source has a voltage

Vs=600V.If it can be assumed that the diode reverse recovery time is t rr=2μs and the softness factor is S=1.0, estimate the minimum voltage rating of the diode. Answer [615V]

Fig.3

6. A chopper circuit, as shown in Fig.4 incorporates a 100-V schottky diode, that, in reverse bias, can be modeled by a 500pF capacitor. The dc supply of voltage Vs=40V with a source inductance LS=5μH provides a current in the load that is 100A without any significant ripple. Calculate the peak reverse recovery voltage VRR. Does the diode require a capacitive snubber to limit the reverse diode voltage?

Answer [80V, No]

Fig.4

POWER BJT

7.Consider the circuit diagram in Fig.5. The BJT acts as a chopper to modulate as a switch to modulate power from the 240-Vdc source to the purely resistive load R=1.2Ω. The frequency of chopper switching 3kHz and the duty cycle is m=0.8. If the transistor is driven into hard saturation so that VCE(SAT)=2.1V,calculate the ratio of the average conduction losses in the BJT to the average power absorbed by the load. Ignore the switching losses. Answer [0.009(=1%)]

Fig. 5

8.Consider the circuit diagram, shown in Fig.6. the bipolar transistor operates as a switch to modulate power from the 600-V, dc supply to the load whose resistance is R=4Ω. (a)From a circuit point of view, determine the power in the load while the transistor is on. (b)Using the transistor data sheet characteristics

and the fact that the transistor operates with a short circuit common emitter gain βF=10, determine the power dissipation in the transistor during conduction. The temperature of the transistor junction is assumed constant .Answer[(a)90kW, (b)252W.]

Fig. 6

9. Consider the circuit diagram in Fig. 7. The BJT acts as a chopper to modulate power from the dc source, whose voltage is VS=240V, to a purely resistive load, whose resistance is R=1.2Ω. the frequency of the chopper switching is 3kHz and the duty cycle is m=0.8. If the current rise time is t r=1μs for turn-on, determine (a) the energy loss in the BJT during turn-on and (b) the average power dissipated in the BJT due to the turn-on losses. Compare this result with the value of conduction losses found in problem 7. Answer[(a) 8mJ, (b)24W]

Fig.7

10. Consider the circuit diagram in Fig.8. The BJT acts as a chopper to modulate power from a dc source of voltage Vs=240V to an RL load whose resistance is R=1.2Ω and whose inductance L is high enough to consider the load current to be virtually constant. A freewheeling diode is connected across the load. The switching frequency of the chopper is 3kHz and the duty cycle is m=0.8. If the current rise time is t ri=1μs and the voltage fall-time is tfv=1.3μs for turn-on during steady-state switching, determine (a)the energy loss in the BJT during the turn-on process and (b)the average power dissipated in the BJT due to turn-on losses. Compare this result with the turn-on loss for the case described in problem 9. Answer[(a)44.2mJ, (b)132.5W]

Fig.8

11. A BJT chopper modulates power from a dc source of 400V to an RL load with an ideal free- wheeling diode. See Fig.9. The load resistance is R=4Ω. The rise-time of the current at turn-on is t ri=1μs and the fall time of current at turn-off is tfi=2 μs. A capacitor (Cs=0.5 μF) is connected across the BJT to limit the dv/dt at turn-off. Estimate the changes in the losses during BJT current rise and fall with and without the snubber capacitor. Answer [40mJ,27mJ]

Fig.9

12. Consider the BJT boost converter, shown in Fig.10. The data sheets for the BJT give a limit of 400V, 100A on the curve for the safe operating area at turn-off. Beyond these values second breakdown is likely. If the fall-time for collector current is tfi=2 μs at turn-off, check that the snubber circuit capacitor value is conservatively chosen to be 1.0 μF. Answer [Yes]

Fig.10

SCR

13. A thyristor modulates power from a 600V, dc source to an RL load whose values are shown in Fig.11. If the thyristor latching current is Ila=400mA,find the maximum value of the resistance R for the thyristor to turn-on with a gate pulse of 10 μs duration. Answer[R=3.75kΩ]

Fig.11

14.A thyristor is used to modulate power from a dc source, whose voltage is Vs=600V,to a resistive load, whose value is R=3Ω. If the thyristor has a latching current that is I la=100mA and an equivalent junction capacitance of 200pF, calculate the minimum value of a snubber capacitor across the thyristor to prevent turn-on if the supply circuit breaker is closed. What is the dv/dt withstand of the thyristor? Answer [0.4μF,500V/μs]

15. A thyristor acts as a chopper to modulate power from a dc source, whose voltage is Vs=1000V,to a resistive load, whose value is R=2Ω. Refer to Fig.12 . from the thyristor data sheet the delay time is td=0.3μs and the rise time is tr=2μs for turn on . The on state voltage drop is VTH(ON)=1.7V and the latching current is Ila=100mA. If the chopper operates at aswitching frequency of 5kHz and a duty cycle m=0.8 determine (a)the minimum pulse width of the gate signal for successful operation, (b)the average power loss in the thyristor due to the turn-on process and (c) the average power loss in the thyristor due to the on-state conduction. Assume that the thyristor can be switched off appropriately. Answer [(a)>0.31μs, (b)831W,(c)680W]

Fig.12

16. Consider the circuit diagram in Fig.13. The dc source voltage is 1000V, and the RL load, whose resistance is R=2 Ω, has an inductance high enough for the load current to be considered constant.If the thyristor has a current rise-time tri=2 μs and a voltage fall-time of tfv=3μs, find the average value of the turn-on power loss in the thyristor for the conduction of a duty cycle m=0.8 and a switching of 5kHz. Answer [5kW]

Fig.13

17. A heating element is to be controlled by two thyristors, back-to-back, to provide a smooth adjustment of power from 0 to 1000W. the voltage source is 115V, 60Hz. Design the gate circuits using Schmitt trigger and one-shot ICs like that shown in fig. 14

Fig.14

18. The gate characteristics of a 1500V,700A thyristor has the form VGK=10IG . calculate(a)the value of a gate driver source resistance RG if the allowable peak gate-power dissipation is 150W and the gate source voltage is VG=40V and (b) the value of the gate current.Answer [(a)0.33Ω, (b)3.9A pulse]

19. A thyristor chopper modulates power from a 1000V dc supply to an RL load that has a freewheeling diode connected across it. The resistance is R=2Ω and the inductance is high enough to consider the load current to be constant. The thyristor has a delay time td=0.5μs, and a crossover time tc=3.5 μs at turn-on. In the on-state voltage drop is VTH(ON)=1.6V. if the chopper operates at a duty cycle m=0.8 and a frequency of 400Hz, determine the thyristor losses as a percentage of the average load power. [0.25%]

20. A thyristor provides half wave controlled rectification from a 600V, 60Hz suppy to a load whose effective resistance is R=1Ω. The I-V characteristics of the thyristor in the on-state is given bt the expression

VTH(ON)=0.001IA+1.6 volts

For a delay angle α=π/3 radians, determine the average power dissipation in the thyristor due to on state conduction. [440W]

21. A 1500V,750A thyristor chopper operates at a switching frequency of 5kHz to modulate power from a 1000V dc source to a 2Ω resistive load. The thyristor has a di/dt limit of 1000A/μs at turn-on and a

withstand dv/dt limit of 800V/μs at turn-off. Determine suitable value of the series and parallel snubber elements that will protect the thyristor against current and voltage transients. [Ls=1μH, Cs=0.625μF, Rs<64Ω]

22. A 1500V,750A thyristor chopper operates at a maximum switching frequency of 400Hz to modulate power from a 1200V dc source to a 2Ω resistive load.The thyristor has a di/dt limit at turn-on of 100A/μs and a withstand dv/dt limit of 300V/μs at turn-off. Determine suitable values of the series and parallel snubber elements that will protect the thyristor against current and voltage transient. [Ls=12μH, Cs=2μF, Rs<250Ω]

23. A 1500V thyristor has a maximum on state voltage drop VTH(ON)=1.5V. its thermal resistance, junction to heatstick is RθJS=0.04°C/W. the device is connected to a heat sink to ambient, is RθSA=0.02°C/W. if the ambient temperature is 30°C and if the junction temperature must not exceed 120°C, determine (a)the maximum average power that can be dissipated in the thyristor and (b) the average continuous current rating of the thyristor. [(a)1500W, (b)1000A]

24. Consider the circuit diagram in Fig.14. The two thyristor are identical and have a transient thermal impedance characteristic as shown in Table1. Each thyristor has a maximum permissible junction temperature of TJ=120°C and the on-state voltage drop across each thyristor is 1.5V.(a) If the heatsinks can be maintained below a temperature of 65°C, what is the maximum continuous current that each thyristor can conduct? (b)for how long can one of the thyristors conduct a short circuit current of magnitude IA=1500A, before the fault is cleared, if the heatsink is transiently maintained at 65°C? Answer [(a)815A, (b)0.12s]

Table. 1 Fig.15

25. A string of three thyristors in series, each with apeak voltage rating of 1600V, uses resistors of value 8kΩ to force a more equitable voltage sharing. Consider the worst case that one thyristor has negligible leakage current and the other two thyristor have a maximum leakage current of 50mA.what dc supply voltage can the combination block? Answer [4000V]

26. Consider the circuit diagram in Fig.16. The dc source voltage is Vs=1200V and the effective resistance of the load is 1Ω. If the on-state voltage drops across the thyristor are 1.6V and 1.7V,determine (a)the value of resistance R so that current sharing is within a difference of 15%. (b)In such a case as above what is the conduction power loss due to the resistors? Answer [(a)1.85mΩ, (b)1.34kW]

Fig.16

27. Two thyristors in parallel share the current from a dc source of 1500V to a resitive load of 1.0Ω. The on-state I-V characteristics of the thyristors are

VTH(ON)1=0.4×10-3IA1+1.4volts

VTH(ON)2=0.5×10-3IA2+1.5volts

Determine (a) the current sharing, (b)the value of resistance that must be connected in series with each thyristor so that the current values of the switches do not differ by more than 10% and (b) what is the increase in the power losses? [(a)9444A,556A , (b)1.77×10-3, (c)75%]

MOSFET

28. A power MOSFET modulates power from a dc supply, whose voltage is Vs = 100 V, to a resistive load, whose value is R = 5 Ω. For a gate voltage VGS = 10 V, the on-state resistance between drain and source is RDS(ON)= 0.06 Ω. If the MOSFET is on for a long time, determine (a) the power dissipated in the MOSFET due to conduction and (b) the efficiency of operation if the supply is considered ideal.

ANSWER [(a)23.4 W, (b) 98.8%]

29. A power MOSFET is employed as a chopper to modulate power from a dc supply of 50 V to a resistive load. Figure 17 depicts the circuit diagram. From the data sheets of the MOSFET the on state resistance is RDS(ON)= 40 mΩ, the threshold value of gate voltage is VGS(TH)= 3 V and the device transconductance is G = 10 S. The gate signal is applied to the MOSFET at 200,000 pulses per second. If the MOSFET is capable of dissipating an average power of 100 W, estimate

(a) the maximum drain current ID for a chopper duty cycle m = 0.5

(b) the value of the load resistance to sustain maximum current and

(c) the value of the gate voltage VGS for this condition. Neglect switching losses.

Fig. 17 MOSFET I-V characteristics

ANSWER [(a) 100 A, (b) 0.45 Ω, (c) 8 V]

30. A power MOSFET chopper modulates power from a dc supply, whose voltage is Vs = 500 V, to a resistive load, whose value is R = 100 Ω. The chopper switches at a frequency of 40 kHz. MOSFET data are delay time td(on)= 30 ns, rise time tri =90 ns, for turn on and a drain leakage current ID leak = 1 mA for a worst condition (125 ˚C). Determine

(a) the average power dissipation in the MOSFET due to the delay action of turn on and

(b) the average power dissipation in the MOSFET due to the drain current rise over the interval t ri of turn-on.

ANSWER [(a) 60 х 10-6 W, (b) 1.5 W]

31. A power MOSFET chopper modulates power from a dc supply, whose voltage is Vs = 500 V, to an RL load with a freewheeling diode. See Fig 18 The current in the load is 5 A and is almost constant. The estimated MOSFET crossover time for turn-on is tc = 250 ns. If the chopper frequency is 40kHz, determine the average power dissipation in the MOSFET due to the turn-on process. Ignore the losses incurred during the delay time td(on).

Fig.18 MOSFET circuit with a constant current load

ANSWER [ 12.5 W]

32. A power MOSFET chopper modulates power from a dc supply, whose voltage is Vs = 500 V, to a resistive load, whose value is R = 100 Ω. The chopper switches at a frequency of 40 kHz. MOSFET data are delay time td(off)= 200 ns, fall time tfi = 80 ns for turn-off, and the on state resistance RDS(ON) = 1Ω.

Determine (a) the average power dissipation in the MOSFET due to the delay action of turn-off and (b) the average power dissipation in the MOSFET due to the drain voltage rise over the interval tfi of turn-off. Compare results with the turn-on losses from problem 6.3.

ANSWER [(a) 196 mW, (b)1.32 W]

IGBT

33. A 600-V, 9-A, low frequency IGBT is rated at 150 ˚C. It modulates power from a 400 V dc supply to a resistive load of 50 Ω. The IGBT data are that for a gate voltage VG = 15 V the on state voltage is VDS(SAT) = 2.8 V, If the switch is on for a long time determine, (a) the on state conduction losses of the IGBT and (b) the efficiency of the circuit operation, assuming the supply to be ideal.

ANSWER [(a) 22.2 W, (b) 99.3%]

34. A power IGBT chopper modulates power from a dc supply of 200 V, to a resistive load. Fig 19 illustrates the circuit diagram. For steady operation at 100 ˚C at the junction of IGBT data sheet provides the information that the on-state voltage drop is VDS(SAT) = 2.9 V, the threshold value of gate voltage is VGS(TH) = 2.8 V, the device transconductance is G =1.3 S and the maximum possible dissipation is PD = 30 W. If the gate signal is provided at a low frequency (<1kHz), so that the switching losses can be neglected, determine (a) the maximum value of drain current ID for a maximum duty cycle m = 0.8 and (b) the current rating of IGBT at 100 ˚C and (c) the load resistance R to sustain the maximum current and (d) the gate voltage VG for this condition.

FIG.19 steady state I-V characteristics circuit diagram

ANSWER [(a) 12.9 A, (b) 10.3 A, (c) 15.2 Ω, (d) 12.7 V]

35. A IGBT chopper modulates power from a dc supply of 400 V to a resistive load whose value is 16 Ω. The chopper switches at a frequency of 30 kHz. IGBT data for a steady junction temperature of 100 ˚C are that the steady on-state voltage is VDS(SAT) = 2.5 V, the delay time is td(on)= 25 ns and the crossover time

is 30 ns for turn-on. If the chopper has a maximum duty cycle m = 0.8 determine (a) the IGBT current rating for the given temperature, (b) the average power loss due to conduction and (c) the average power dissipation due to turn-on process.

ANSWER [(a) 20 A, (b) 50 W, (c) 1.5 W]

36. A 1500-V, 50-A IGBT is used in a chopper circuit to modulate power from a 1000 V dc supply to an RL load with a freewheeling diode connected across it. The current in the load is 40 A and virtually constant. IGBT data available are that the gate threshold voltage is VGS(TH) = 5 V, the transconductance is G = 19 S, the device input capacitance is CiJS = 9000 pF, the output capacitance is Coss = 650 pF and the transfer capacitance is Crss = 240 pF. If the gate drive voltage is VG = 15 V and if the gate circuit resistance is RG = 30 Ω, determine (a) the delay time td(on) (b) the drain current rise time tri (c) the drain voltage fall time tfv for turn-on.

ANSWER [(a) 109 ns, (b) 269 ns, (c) 1.95 х 10-6 s]

37. An IGBT has an on-state characteristics VDS(SAT) = 1.4 + 0.02 ID1.1

volts and a switching loss characteristics Wloss = ID х 10-4 joules. The thermal resistance, junction to ambient, is RѲ JA = 1.67 ˚C/W. If the frequency of switching is 10 kHz, estimate a reasonable steady overcurrent setting for the IGBT circuit so that the junction temperature will not exceed 150 ˚C. The ambient temperature can be assumed to be 30 ˚C.

ANSWER [51.1 A]

38. A 1000 V, 200 A IGBT has a transient thermal impedance characteristics as follows.

ZѲ JC(t) (˚C/W) 0.007 0.025 0.05 0.065 0.11 0.115Time (s) 0.001 0.01 0.05 0.1 1.0 3

The on-state voltage drop is VDS(SAT) = 4 V. If the case of the IGBT is maintained transiently at 50 ˚C, while the device conducts a current ID = 1000 A for 10 ms, determine (a) the junction temperature at the end of the current pulse and (b) the junction temperature 10 ms later.

ANSWER [(a) 150 ˚C, (b) 78 ˚C ]

TRIAC

39. A 1200 V, 15 A(rms) triac requires a minimum signal of 2.5 V and 100 mA at the gate terminals to turn on the switch under all conditions. Determine the maximum (a) current gain and (b) power gain of the device.

ANSWER [(a) 150, (b) 51,000]

40. A 1200 V, 15 A triac acts as a switch in a transformer tap changer whose source voltage is 600 V at 50 Hz and whose load is 10 A. The on-state voltage of triac is 2.2 V. Determine (a) the conduction energy

loss per cycle in the triac, (b) the maximum average power conduction loss in the triac and (c) the efficiency of the switch.

ANSWER [(a) 0.39 A, (b) 19.8 W, (c) 99.7%]

41. A triac acts as an ac switch in a circuit whose supply voltage is 400 V at 60 Hz and a resistive load whose value is R = 40 Ω. Triac data for rated temperature are the on-state voltage is VT(ON) = 2 V, the maximum leakage current is IT leak = 5 mA, the maximum signal at gate terminals are VGT = 2.5 V and IG = 100 mA. Compare the on-state losses with the off-state losses and continuous gate signal losses.

ANSWER [Conduction : leakage: gate losses = 36 : 2.8 : 1]

GTO

42. A 1200 V, 300-A GTO modulates power from an 800 V dc supply to a resistive load whose value is 4 Ω. Refer to fig 20. If the switch is on for a long time the junction temperature of the GTO rises to 100˚C and the voltage drop is measured to be VGTO(ON) = 4 V. Determine the on-state conduction losses.

Fig.20 GTO circuit diagram

ANSWER [796 W]

43. Consider the circuit diagram of Fig 20. A 1200 V, 300-A GTO acts as a chopper to modulate power from an 600 V dc supply to a resistive load whose value is 2 Ω. The frequency of chopper switching is 2 kHz and the duty cycle is m= .8. If the GTO on-state voltage drop is VGTO(ON) = 3.4 V. Calculate (a) the average power loss in GTO due to conduction and (b) the average power absorbed by the load.

ANSWER [(a) 813 W, (b) 142.9 kW]

44. A 1000 V, GTO chopper modulates power from an 2000 V dc supply to a resistive load. See Fig 20. From the data sheet of the GTO, the on-state voltage drop is VGTO(ON) = 3.8 V and maximum average power dissipation is 800 W. If the chopper duty cycle is m = 0.5, determine (a) the maximum anode current IA of the GTO, (b) the average current rating of the GTO and (c) the value of the load resistance to sustain maximum current. Assume that the switching frequency is low enough that the switching losses can be neglected.

ANSWER [(a) 410 A, (b) 205 A, (c) 1.45 Ω]

45. A 3000 V, 1000-A GTO acts as a chopper to modulate power from an 2000 V dc supply to an RL load that has freewheeling diode connected across it. The load resistance has a value R = 2.5 Ω and the load

inductance is high enough to consider that its current is virtually constant. GTO data are that the current rise time is tri= 12 х 10-6 sec and voltage fall time is tfv = 10 х 10-6 sec at turn on and the on state voltage drop is VGTO(ON) = 4.2 V. If the chopper operates with a duty cycle m = 0.8 at a frequency of 1 kHz, estimate (a) the average power loss in the GTO due to the turn on process and (b) the average power dissipated in the GTO due to on-state conduction.

ANSWER [(a) 1.4 kW, (b) 2.15 kW]

46. A 500 V, 15-A GTO controls the charging of a superconductive coil whose resistance is R = 0 and whose inductance is 0.1 H. The coil has a freewheeling diode connected across it. The dc supply has a voltage VS = 100 V. Calculate the duration of the gate pulse that is necessary to ensure the GTO will turn on, if the device’s latching current is Ila = 1.5 A and its on state voltage drop is VGTO(ON) = 2.2 V. Compare the result with that obtained in EXAMPLE 5.1.

ANSWER [1.5 ms]