CARLETON UNIVERSITY. FINAL EXAMINATION December DURATION 3 HOURS No. of Students 130

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1 ALETON UNIVESITY FINAL EXAMINATION December 005 DUATION 3 HOUS No. of Students 130 Department Name & ourse Number: Electronics ELE 3509 ourse Instructor(s): Prof. John W. M. ogers and alvin Plett AUTHOIZED MEMOANDA alculators Only Students MUST count the number of pages in this examination question paper before beginning to write, and report any discrepancy immediately to a proctor. This question paper has 6 pages. This examination question paper MAY be taken from the examination room. Information and Instructions: 1. Attempt all questions.. Show all analysis. 3. The exam marks total Unless otherwise specified, use only the simplified transistor model for the BJT, i.e., take r x =0, r o =, and r µ =. Useful Formulas r β π =, ( ) e g m g m = µ r = β 1 r π, ox W I L DS β α =, β 1 Z Z L o, Γ =, L Z Z o I g m =, V T 5mV VT r r H E = µ t The average of a half sine wave with amplitude of 1 is 1/π. dv d x a = =, Money = Power = VI = I = Evil dt dt 0 forward biased V BE = 0.7 Volts ω L ω L1 ω L ω L3... and... ω ω ω ω H H1 H Miller s Theorem: Y v = 1 Y 1, v v 1 = 1 Y Y 1 v dy x Sensitivity: S y x = dx y H 3

2 ELE 3509 Final Examination December 005 Question 1 (Total 14 Marks) Answer the following questions. marks (a) A transistor is biased at 10µA, has an early voltage of 100V and β =100. What are the values of r e, r π, r o, and g m? 4 marks (b) For the class B amplifier shown in figure 1, assuming that you cannot ignore the 0.7V V BE drop in the transistor, and also assuming that the input cannot go above the rails, what the is maximum voltage swing possible in this circuit? What is the output power in this case? What is the average current drawn from the supplies? What is the efficiency? V = 5V V in Q 1 V out Q load = 100Ω V ss = -5V Figure 1 marks (c) A power transistor in a case has a heat sink attached. The junction to case, case to heat sink and heat sink to air thermal resistances are 0.9 /W, 0.1 /W, and 1. /W respectively. If the ambient temperature is 5 and the transistor is dissipating 100W what is the junction temperature? marks (d) In the s plane, draw the poles for a nd order filter, an unstable circuit with growing amplitude, and an unstable circuit with constant amplitude. 4 marks (e) In a completely fictional transistor the collector current as a function 3 l of base emitter voltage is given by e V I BE = 10 e where le is the emitter length. What is the g m of this device?

3 ELE 3509 Final Examination December 005 Question (Total Marks) When analyzing the amplifier circuit in Figure, use appropriate models, to find generalized expressions (i.e. without component values unless specifically asked for). 4 marks (a) Draw the small-signal equivalent circuit. 3 marks (b) Find the mid-band gain A v. marks (c) Find the mid-band in. marks (d) Find the mid band out (include r o1, r o and r µ ). 3 marks (e) Find the low frequency poles (ω L s). 4 marks (f) Find the high frequency poles (ω H s) for the circuit. You may ignore π. 4 marks (g) With V = 15V, 3 = kω, determine 1,, 1, and E, such that I 1 = 1mA and I = ma and the voltage on the collector of Q 1 is 10V. Set the current through to be 10 times the base current of Q 1, (assume β = 100), but for all other calculations, you may ignore base current. V V V in in 1 1 E o out s Q L Q 1 v s 3 Figure 3

4 ELE 3509 Final Examination December 005 Question 3 (Total 18 Marks) In this question, all transistors are assumed to be matched. Perform the following analysis on the op amp circuit of Figure 3(a). Assume that r µ = for all transistors. 10 marks (a) Draw the small signal model and use it to find: (i) The differential mode gain A DM with output at v x. (ii) The differential mode input impedance DM. (iii) The common mode input impedance M. 5 marks (b) With V cc = 5V, and V EE = -5V (i) Design a current mirror to replace the current source I o (and its impedance o ). alculate the required value of Bias (at the input of the current mirror to ground) such that I 1 = I = 50 µa. edraw the circuit to show the current mirror, Q 1, Q, Q 3, Q 4, and x. (ii) Find the minimum and maximum input common-mode voltage v icm,min and v icm,max. 3 marks (c) Now consider Figure 3(b) which shows the resistor x replaced with a class AB output stage. (i) Determine the value of E such that the ouput transistors Q 5 and Q 6 are biased at I 5 = I 6 = 4 ma. (ii) Determine the voltage v x when the output voltage is 0 V. 5 V 5 V I DD o I o o I o Q 5 E v in Q 1 Q v in - v in Q 1 Q v in - E v o Q 3 Q 4 v x x Q 3 Q 4 vx I DD Q 6-5 V Figure 3(a) -5 V Figure 3(b) 4

5 ELE 3509 Final Examination December 005 Question 4 (Total 17 Marks) 8 marks vout ( s) (a) Derive the transfer function v ( s) in of the circuit shown in Figure 4. v in v out 9 marks (b) onsider the following circuit: Figure 4 v in 1 ( s) = s s 1 s S( s) = s 50s v 1 v v out Figure 5 Where the voltage transfer functions for each of the boxes is v 1 /v in = (s) and v /v in = S(s) respectively. Sketch each of these two transfer functions (include corner frequency gains, Qs, and gain in flat regions, and drop off rates), and then sketch in a reasonable amount of detail the overall magnitude response v out /v in of the circuit. 5

6 ELE 3509 Final Examination December 005 Question 5 (Total 11 Marks) 7 marks (a) For the oscillator shown in Figure 6, apply Barkhausen criteria to find the oscillating frequency showing any necessary derivation. Then find out what is the necessary value of K to start the oscillator. 3V K Figure 6 4 marks (b) The opamps used above are powered from ±15V supplies. How big would you expect the oscillator output to get assuming that the zener diodes each have a reverse breakdown of 5V? What is the change in the loop gain when the zener diodes become active? -3V 6

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