Homework Assignment 10 Question 1 (Short Takes) Two points each unless otherwise indicated. 1. What is the 3-dB bandwidth of the amplifier shown below if r π = 2.5K, r o = 100K, g m = 40 ms, and C L = 1 nf? (a) 65.25 khz (b) 10 khz (c) 1.59 khz (d) 10.4 khz 2. A 9-V dc power supply generates 10 W in a resistor. What peak-to-peak amplitude should an ac source have to generate the same power in the resistor? (a) 12.73 V (b) 25.5 V (c) 18 V (d) 12.73 V 3. In the circuit below, what is the maximum current that can flow through R L? Make reasonable assumptions. 1
4. List (do not explain) 4 BJT parameters that determine the SOA. 5. True or false: broadly speaking, BJT technology has superior performance in power application when compared to the modern MOS technology, which explains why BJTs are still widely incorporated in power designs. 6. An engineer designs a class-ab amplifier to deliver 1.2 W (sinusoidal) signal power to an 8 Ω resistive load. Ignoring saturation in the output BJTs, what is the required peak-topeak voltage swing across the load? 7. An engineer designs a class-ab amplifier to deliver 2 W (sinusoidal) signal power to an 8 Ω resistive load. Ignoring saturation in the output BJTs, what is the required peak-topeak voltage swing across the load? 8. An engineer designs a MOSFET-based class-ab amplifier to deliver 6.25 W (sinusoidal) signal power to a 4 Ω resistive load. What is the required peak-to-peak voltage swing across the load? (2 points) 9. An engineer designs a MOSFET-based class-ab amplifier to deliver 6.25 W (sinusoidal) signal power to a 4 Ω resistive load. What is the required peak-to-peak voltage swing across the load? (2 points) (a) 9.77 V (b) 19.53 V (c) 10 V (d) 14.14 V (e) 7.07 V 10. True or false: a power MOSFETs transconductance g m is less subject to changes in temperature than a power BJT s β s is subject to changes in temperature. 2
11. An engineer designs a standard (no inductor, transformer) class-a amplifier to deliver 100 mw (sinusoidal) signal power to a resistive load. How much power should the power supply be able to supply? 12. An engineer designs a standard (no inductor, transformer) class-a amplifier to deliver 200 mw (sinusoidal) signal power to a resistive load. How much power should the power supply be able to supply? 13. True or false: for the amplifier below, the harmonic distortion increases as the amplitude of the input increases. 14. Write down one phrase/sentence that describes the purpose of the diodes and constant current source in the amplifier below. 15. True or false: the efficiency of a class-ab amplifier is independent of the amplitude of the input signal. 3
16. True or false: for a MOSFET, g m decreases with increasing temperature, which explains why MOSFETs are not prone to thermal runaway. 17. What is the maximum theoretical efficiency for a class-b amplifier? 18. What does SOA in the context of power transistors stand for? 19. True or false: in power transistors, the junction temperature can reach as high as 150 o C. 20. True or false: everything else being equal, BJTs have an order of magnitude more gain than FETs. 21. True or false: if class-a amplifiers are not carefully biased, they will suffer from crossover distortion. 22. The small-signal output resistance r o of a BJT biased at I C = 1 ma is100k. What is r ο when the transistor is biased at I C = 5 ma? 23. A MOSFET has rated power of 50 W at an ambient temperature T A = 25 o C and a maximum specified junction temperature of 105 o C. What is the thermal resistance between the device case and the junction? 24. A power MOSFET has rated power of 1,250 W at an ambient temperature T A = 25 o C and a maximum specified junction temperature of 175 o C. What is the thermal resistance between the junction and device case? 4
25. True or false: the turn-on voltages of Schottky diodes are less than that of Si diodes. However, their reverse leakage/saturation currents are also higher. (1 point) 26. True or false: The turn-on voltage of red LEDs is larger than the turn-on voltage of blue LEDs. (1 point) 27. Below is a depiction of an n-channel enhancement-mode MOSFET. Annotate the diagram with a p or n to show the type of substrate material, and then indicate the body diode. p-material substrate Body diode 28. A single-pole op-amp has an open-loop gain of 100 db and a unity-gain bandwidth frequency of 2 MHz. What is the open-loop bandwidth of the op-amp? (2 points) 29. A single-pole op-amp has an open-loop gain of 100 db and a unity-gain bandwidth frequency 5 MHz. What is the open-loop bandwidth of the amplifier? The amplifier is used as a voltage follower. What is the bandwidth of the follower? 30. Consider a first-order RC low-pass filter with corner frequency f = 1 khz. What is the phase shift in a degrees at 15 khz? (3 points) 5
31. An AAA cell has a no-load voltage of 1.605 V. When a 100 Ω resistor is connected across its terminals, the voltage drops to 1.595 V. What is the cell s internal resistance? a) 620 mω b) 10 mω c) Need additional information 32. What is the magnitude of the current phase angle for a 5.6 μf capacitor and a 50-Ω resistor in series with a 1.1 khz, 5 VAC source? (a) 72.9 (b) 62.7 (c) 27.3 (d) 17.1 6
Question 2 (N 5.36) The circuit below is sometimes used and thermometer. Assume that the two transistors are identical. Writing emitter currents in the form I E = I E0 e V BE V T derive an expression for the output voltage as a function of temperature. (10 points) 7
Question 3 Consider a BJT with a rated power of 20 W, and a maximum allowable junction temperature T j,max = 175. The transistor is mounted on a heat sink with parameters θ case sink = 1 /W, and θ sink amb = 5 /W. Determine how much power the BJT can safely dissipate. Assume an ambient temperature of T A = 25. 8
Question 4 A power MOSFET has thermal characteristics given below. The device operates without a heat sink and dissipates 0.2 W. What is the junction temperature if the ambient temperature is 25 o C? Start by drawing and labeling a thermal model. (5 points) θ dev case = 1.75 W, θ case amb = 50 W, T j,max = 150 9
Question 5 (Midterm, 2007) A power MOSFET has thermal characteristics given below and dissipates 25 W. Design, by specifying the thermal resistance, a heat sink that will ensure the MOSFET does not overheat. The ambient temperature is 25 o C. Assume one can keep the thermal resistance between the MOSFET case and heat sink (θ case sink or θ CS ) below 1 o C/W. (5 points) θ juntion case = θ JC = 1.75 /W θ case ambient = θ CA = 50 /W T j,max = 150 \ theta 10
Question 6 A power MOSFET has thermal characteristics given below. The device operates without a heat sink and dissipates 0.2 W. What is the junction temperature if the ambient temperature is 25 o C? Start by drawing and labeling a thermal model. (5 points) θ dev case = 1.75 W, θ case amb = 50 W, T j,max = 150 11
Question 7 Consider a BJT with a rated power of 115 W at T case = 25, and a maximum allowable junction temperature T j,max = 200. The transistor is mounted on a heat sink with parameters θ case sink = 1 /W, and θ sink amb = 4 /W. Determine how much power the BJT can safely dissipate at an ambient temperature of T A = 25. (12 points) 12
Question 8 Two transistors each with θ JC = 1.4 W, θ CS = 0.3 W, and a dissipation of 12 W, share the same heat sink. If the junction temperatures are 200, and the ambient temperature is 10, use a thermal equivalent circuit to find the thermal resistance of the heat sink. (10 points) 13
Question 9 For the transistor I C,max = 200 ma, and V ce(sus) = 50 V (a) Determine the minimum transistor power rating so that the transistor is always inside the SOA (6 points) (b) What is the maximum average power this amplifier can supply to the load with a sinusoidal input voltage? (3 points) R E = 200 Ω, V A = 200, V CC = 10 V, β = 150 14
Question 10 The maximum current, voltage, and power ratings for a power MOSFET are 4 A, 40 V, and 30 W, respectively. (a) Sketch and label the SOA for the MOSFET using linear voltage and current scales (4 points) (b) For the amplifier above, determine R D and sketch the load line that produces maximum power in the transistor for V DD = 24 V (3 points) (c) Determine the maximum possible drain current for V DD = 24 V (3 points) (d) Repeat (b), but now for V DD = 40 V (6 points) 15
Question 11 R D = 20 Ω, V DD = 24 Determine the maximum power ratings for the transistor. (10 points) 16
Question 12 For the circuit above, make reasonable assumptions and then (a) Determine the input resistance, without taking R 4 and R 3 into consideration. That is, determine R i as shown in the figure (5 points) (b) Determine the voltage gain v o1 v s (4 points) 17
Question 13 A certain manufacturer of a power transistor does not provide the thermal resistance between the device junction and the case (θ JC ) explicitly. Rather, it provided the power derating curve shown. Use the plot to find θ JC. Be sure to supply the proper units. (4 points) 18
Question 14 The graph shown is the power derating curve for a power transistor, that the manufacture lists as a 250 W at a case temperature of 25. Use the graph to determine the thermal resistance between the device junction and the case (θ JC ) explicitly. Be sure to supply the proper units. (6 points) 19