Midterm 1 October 2006
ECSE 330: INTRODUCTION TO ELECTRONICS Midterm Examination #1
October 19th 2006, 10:05 AM – 11:25 AM Professor David V. Plant, Joshua D. Schwartz
Please note the following before you begin: - This is a closed book examination, no notes permitted. - This exam consists of 4 problems totaling 40 possible points. - Only the faculty standard calculator is permitted. - Write all answers in the answer booklet only. This paper will NOT be collected - Good luck!
Question 1 (9 points) Consider a CURRENT AMPLIFIER defined by the current transfer characteristic below. This amplifier has Rin = 5 kΩ and Rout = 90 kΩ.
a) [2 pts] What DC input current Iin would make possible the largest sinusoidal output signal without any clipping distortion? b) [3 pts] This amplifier is connected to a current source of 2 mA with resistance RS = 5 kΩ. A load of RL = 10kΩ is connected at the output. Assuming this amplifier is operated in the linear region, draw a circuit diagram representing this situation using the model of a current amplifier. c) [3 pts] Assume that the current amplifier receives an input voltage Vin instead of an input current (you can imagine an ideal voltage source with no internal resistance for this). Draw the transfer characteristic of Iout vs. Vin for this amplifier, indicating: a. The slope of the linear region b. The maximum and minimum output currents c. The voltage inputs corresponding to the maximum/minimum output currents d) [1 pt] An amplifier has a low input resistance and a low output resistance. For what kind of amplifier is this the best scenario? (voltage, current, transconductance, transresistance)
2
Question 2 (10 points) Consider the following circuit. The diodes are all identical and have n = 1. You may use the constant voltage-drop model. The small-signal voltage source v s and the load resistor RL are isolated from the rest of the circuit at DC using infinite capacitors.
RIN
R1 = R2 = 4kΩ R3 = R4 = 8kΩ R5 = 1kΩ R6= 5kΩ a) [4 pts] Find the DC current passing through all diodes. State your assumptions (Diodes ON or OFF) and verify that your final answer is consistent. b) [2 pts] Draw the small-signal equivalent circuit diagram and compute the smallsignal resistance of all diodes based on your results from part (a). For parts c) and d), DO NOT use any numerical values. Instead, you should express your answers in terms of the resistors in the diagram and the small-signal parameters of the diodes (e.g. rd1, rd2…). c) [2 pts] Find an expression for the small-signal input resistance RIN. ***Note: RS is NOT included in the determination of RIN***
d) [2 pts] Find an expression for the small-signal voltage gain v out /v s . 3
Question 3 (10 points) Consider the circuit shown below. 5V
2kΩ
vI
5V
RC4
Q5
VB4
300kΩ
vO Q4
RC5 5V 5V
RREF IC3
Q2
IC1
VB3
Q1
Q3
2kΩ
In the circuit above, all BJTs have β=100 and it is known that IC3=1mA. For question a), use the exponential model and IS=10-15A for both Q1 and Q3. a) [2 pts] Calculate the voltage VB3 and the current IC1 (flowing into the collector of Q1). For questions b) to d), assume VBE=0.7V for all BJTs and IC1=IC3=1mA. b) [3 pts] Determine the value of RREF. (Hint: use KCL to find the emitter current of Q2, then find the current through RREF) c) [3 pts] Find the value of RC5 such that Q5 is on the active/saturation boundary. d) [2 pts] Assume that VB4 = 2.2V, and find that value of RC4 that would allow for the maximum symmetric (undistorted) output signal voltage at vo.
4
Question 4 (11 points) Consider the following amplifier circuit, consisting of two common-emitter stages. Assume all BJTs are in the active mode and have the same β. Also, you must include the Early effect in your analysis for transistor Q1, but you may neglect it for transistor Q2. Give your answers in terms of β, RB1, RB2, RC1, RE2, RC2, and the small-signal parameters (for example, use gm1, rπ1, and ro1 for the small-signal parameters of Q1). If two resistances appear in parallel, use the notation R1//R2 in your answers instead of expanding the expression.
∞
∞ ∞
a) [4 pts] Draw the small-signal equivalent circuit using the hybrid π-model b) [2 pts] Find an expression for the input resistance Ri2 c) [2 pts] Find an expression for vx/vs [you can just refer to “Ri2” in your answer without expanding it] d) [2 pts] Find an expression for vo/vx e) [1 pts] Find an expression for the overall gain of this circuit, Av = vo/vs
5
Formula Sheet (you can detach this) Diode Dynamic Resistance: rd = nVt / ID Diode Exponential Model: I D = I S (e
VD nVT
− 1)
BJTs iC = IS exp(vBE/VT )
i iB = C
β
i iE = C
α
iB = (1−α)iE =
iE β +1
iE = (β +1)iB gm = rπ =
IC VT
re =
VT β = IB gm
VT VT α =α = IE IC gm ro =
VA IC
rπ = (β +1)re
β=
α β 1 α= β +1= β +1 1−α 1−α
6
October 19th 2006, 10:05 AM – 11:25 AM Professor David V. Plant, Joshua D. Schwartz
Please note the following before you begin: - This is a closed book examination, no notes permitted. - This exam consists of 4 problems totaling 40 possible points. - Only the faculty standard calculator is permitted. - Write all answers in the answer booklet only. This paper will NOT be collected - Good luck!
Question 1 (9 points) Consider a CURRENT AMPLIFIER defined by the current transfer characteristic below. This amplifier has Rin = 5 kΩ and Rout = 90 kΩ.
a) [2 pts] What DC input current Iin would make possible the largest sinusoidal output signal without any clipping distortion? b) [3 pts] This amplifier is connected to a current source of 2 mA with resistance RS = 5 kΩ. A load of RL = 10kΩ is connected at the output. Assuming this amplifier is operated in the linear region, draw a circuit diagram representing this situation using the model of a current amplifier. c) [3 pts] Assume that the current amplifier receives an input voltage Vin instead of an input current (you can imagine an ideal voltage source with no internal resistance for this). Draw the transfer characteristic of Iout vs. Vin for this amplifier, indicating: a. The slope of the linear region b. The maximum and minimum output currents c. The voltage inputs corresponding to the maximum/minimum output currents d) [1 pt] An amplifier has a low input resistance and a low output resistance. For what kind of amplifier is this the best scenario? (voltage, current, transconductance, transresistance)
2
Question 2 (10 points) Consider the following circuit. The diodes are all identical and have n = 1. You may use the constant voltage-drop model. The small-signal voltage source v s and the load resistor RL are isolated from the rest of the circuit at DC using infinite capacitors.
RIN
R1 = R2 = 4kΩ R3 = R4 = 8kΩ R5 = 1kΩ R6= 5kΩ a) [4 pts] Find the DC current passing through all diodes. State your assumptions (Diodes ON or OFF) and verify that your final answer is consistent. b) [2 pts] Draw the small-signal equivalent circuit diagram and compute the smallsignal resistance of all diodes based on your results from part (a). For parts c) and d), DO NOT use any numerical values. Instead, you should express your answers in terms of the resistors in the diagram and the small-signal parameters of the diodes (e.g. rd1, rd2…). c) [2 pts] Find an expression for the small-signal input resistance RIN. ***Note: RS is NOT included in the determination of RIN***
d) [2 pts] Find an expression for the small-signal voltage gain v out /v s . 3
Question 3 (10 points) Consider the circuit shown below. 5V
2kΩ
vI
5V
RC4
Q5
VB4
300kΩ
vO Q4
RC5 5V 5V
RREF IC3
Q2
IC1
VB3
Q1
Q3
2kΩ
In the circuit above, all BJTs have β=100 and it is known that IC3=1mA. For question a), use the exponential model and IS=10-15A for both Q1 and Q3. a) [2 pts] Calculate the voltage VB3 and the current IC1 (flowing into the collector of Q1). For questions b) to d), assume VBE=0.7V for all BJTs and IC1=IC3=1mA. b) [3 pts] Determine the value of RREF. (Hint: use KCL to find the emitter current of Q2, then find the current through RREF) c) [3 pts] Find the value of RC5 such that Q5 is on the active/saturation boundary. d) [2 pts] Assume that VB4 = 2.2V, and find that value of RC4 that would allow for the maximum symmetric (undistorted) output signal voltage at vo.
4
Question 4 (11 points) Consider the following amplifier circuit, consisting of two common-emitter stages. Assume all BJTs are in the active mode and have the same β. Also, you must include the Early effect in your analysis for transistor Q1, but you may neglect it for transistor Q2. Give your answers in terms of β, RB1, RB2, RC1, RE2, RC2, and the small-signal parameters (for example, use gm1, rπ1, and ro1 for the small-signal parameters of Q1). If two resistances appear in parallel, use the notation R1//R2 in your answers instead of expanding the expression.
∞
∞ ∞
a) [4 pts] Draw the small-signal equivalent circuit using the hybrid π-model b) [2 pts] Find an expression for the input resistance Ri2 c) [2 pts] Find an expression for vx/vs [you can just refer to “Ri2” in your answer without expanding it] d) [2 pts] Find an expression for vo/vx e) [1 pts] Find an expression for the overall gain of this circuit, Av = vo/vs
5
Formula Sheet (you can detach this) Diode Dynamic Resistance: rd = nVt / ID Diode Exponential Model: I D = I S (e
VD nVT
− 1)
BJTs iC = IS exp(vBE/VT )
i iB = C
β
i iE = C
α
iB = (1−α)iE =
iE β +1
iE = (β +1)iB gm = rπ =
IC VT
re =
VT β = IB gm
VT VT α =α = IE IC gm ro =
VA IC
rπ = (β +1)re
β=
α β 1 α= β +1= β +1 1−α 1−α
6
