# 55:041 Electronic Circuits The University of Iowa Fall Exam 2

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1 Exam 2 Name: Score /60 Question 1 One point unless indicated otherwise. 1. An engineer measures the (step response) rise time of an amplifier as t r = 0.35 μs. Estimate the 3 db bandwidth of the amplifier. Answer: BW 0.35 t r 0.35 = = 1 MHz 2. True or false: C π increases with increasing collector bias current I CQ. Answer: True 3. Many BJT datasheets do not list β explicitly, but list an equivalent h-parameter instead. What is this parameter? Answer: h fe 4. True or false: the β of a transistor decreases with decreasing temperature. Answer: False 5. True or false: in a forward-biased pn junction, the diffusion C d capacitance is generally much larger than the junction capacitance C j. Answer: True 6. True of 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. Answer: True 1

2 7. True or false: a major advantage of FETs over BJTs in power amplifiers is that FETs do not suffer from thermal runaway, but BJTs do. Answer: True 8. Briefly (1 2 sentences) explain why there is not a Miller effect in a common-base circuit? Answer: The Miller effect is present when there is a parasitic capacitor between the input and output of an inverting amplifier. The common-base amplifier is a non-inverting amplifier. 9. True or false: The input resistance of a BJT amplifier in the CB configuration, biased at 10 ma is in the order of 2.5 Ω (2 points) Answer: True 10. True or false: consider a BJT in the CE configuration, biased at I C = 2 ma. The smallsignal input resistance r π is in the order of 500K (2 points) Answer: False. r π = β g m = β (40I C ). With β = 100, r π = 1.25K 2

3 Question 2 Consider the circuit below. The duty cycle and frequency of the 555 astable is 60% and 10 khz respectively. (a) Specify a value for R limit to ensure that the average current through the IR diode does not exceed 30 ma (4 points) (b) Explain (2 sentences maximum) the purpose of the decoupling capacitor (1 point) Part (a) The peak current must be I peak = 30 (0.6) = 50 ma. This value will give an average of 30 ma with a 60% on time. Assuming the V BE(ON) = 0.7 V for the BJT, then R limit = = 14 Ω. Choose the closest standard value of 15 Ω. Part (b) When the FET switches, large current spikes may appear on the supply rail, which can propagate into the IC and disturb its operation. The decoupling capacitor provides a local reservoir of energy, and ensures a clean power supply rail. 3

4 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. (10 points) Hint: The thermal resistance from the device/junction to the case is not given explicitly, so show that it is θ dev case = 7.5 /W before proceeding. The thermal resistance from the device/junction to the case is not given explicitly, so we need to determine it before proceeding. The BJT is rated at 20 W at T j,max = 175, and an ambient temperature of T A = 25 is assumed. A thermal model and the calculation of θ dev case is then T j = T A + P D (θ dev case ) 175 = (θ dev case ) θ dev case = 7.5 /W Now we can determine the maximum allowable power dissipation when the BJT is mounted on a heat skink with the given parameters. A thermal model for the problem is shown below. P D,max = T j = T A + P D (θ dev case + θ case sink + θ sink amb ) T j,max T A (θ dev case + θ case sink + θ sink amb ) = = 11.1 W 4

5 Question 4 R s = 0.25 kω r π = 2 kω R L = 4 kω g m = 65 ma V C C = 2 μf C L = 50 pf Plot and fully label the Bode diagram (amplitude only). Show all pertinent calculations (8 points) For the midband gain, treat C C as a short- and C L as an open circuit. Then V ο r π = g V i r π + R m R L S = = 231 Part (b) The lower 3 db time constant is τ 1 = C C (R S + r π ) = ( ) = 4.5 ms. The upper 3 db time constant is τ 2 = R L C L = ( ) ( ) = 200 ns. The corner frequencies are then f H = 1 = 796 khz f 2πτ L = 1 = 35.4 Hz 1 2πτ 2 5

6 Question 5 Consider the CE BJT amplifier below. I C = 1 ma β = 185 C π = 100 pf C μ = 14 pf r π = 4.5 kω g m = 0.04 A/V V A C C1 C C2 C C3 (a) Draw a hybrid-π small signal model of the amplifier. Be sure to include r π, C π, C μ, and g m. (4 points) (b) Estimate the upper 3 db bandwidth. (6 points) Part (a) Part (b) The Miller effect transforms C μ to a value C M = (1 + A M )C μ where A M = g m (R L R C ), the gain working across C μ. That is C M = ( )(14 pf) = 1.92 nf The Miller capacitance is in parallel with C π. A small signal model is The time constant is τ = (C π + C M )(R 1 R 2 r π R s ) = ( )(795) = 1.61 μs. The upper 3 db frequency is then f H = 1 = 99.1 khz 2πτ 6

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8 Question 6 For the circuit below, determine the h 21 parameter (4 points). Note: do not calculate the other h-parameters. To determine h 21, set v 2 = 0, and determine i 2 i 1 h 11 = v 1 i 1 v 2 =0 h 21 = i 2 i 1 v 2 =0 Use KCL to find i 2 and the i 2 i 1 : i i 1 + i 2 = 0 i 2 = 51i 1 and h 21 = 51i 1 i 1 = 51 A/A 8

9 Question 7 For the circuit below C C2 = 1 μf and β = 100. Ignore C μ and C π and r o. A dc analysis reveals that r π = 3.1K. Use BJT scaling and time constant concepts and determine the 3-dB frequency. (8 points) The resistance looking back into the emitter is, using BJT scaling R O = 3.1K + 0.5K 100K R O is in parallel with R E, so that the time constant is = 35.6 Ω τ = (35.6 Ω) 10K + 10K)C c2 (10K)( ) = 0.01 s The 3-dB frequency is then f 3dB = 1 (2πτ) = 15.6 Hz 9

10 Question 8 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 sketch the load line that produces maximum power in the transistor for V DD = 40 V (2 points) (c) Determine the maximum possible drain current for V DD = 40 V (4 points) Part (a) and (b) The SOA is shown below along with a load line that gets it the closest to the maximum power ratings, yet still stay in the SOA. Part (c) The maximum power limit hyperbola determines the load line. Maximum power dissipation occurs at 20 V. At 20 V, I = P max 20 = 1.5 A. By similar triangles, the load line intersects the I DS axis at 3 A. 10

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