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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
6.002 Circuits and Electronics Final Exam Practice Set 1 Problem 1 Figure 1 shows a simplified small-signal model of a certain type of transistor amplifier driven from a non-ideal source.
(1A) Find the node voltages e1 and e2 in terms of VA, RA, RC, RD, and k. (Assume iD = 0.)
RA RC
VAkiC
iC
RD
e1e2
+
-
vD
iDsource amplifier
Figure 1
6.002 Circuits and Electronics Final Exam Practice Name:_______________________________
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e1 = e2 =
6.002 Circuits and Electronics Final Exam Practice Name:_______________________________
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(1B) Find a Thévenin equivalent model of the amplifier system viewed from the vD, iD port. (That is, find the Thévenin voltage and resistance VTH, RTH that characterize the system.)
VTH = RTH =
6.002 Circuits and Electronics Final Exam Practice Name:_______________________________
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Problem 2 Figure 2 shows a relay driver circuit. The relay is modeled as the series connection of a resistor RR = 100 Ω and an inductor LR = 200 μH. To protect the switch S driving the relay, a resistor RF = 100 Ω is placed across the relay as shown.
After being open for a long time, the switch S is closed at t = 0, then opened at t = 10 μs. On the axes provided, plot the switch voltage vsw and the switch current isw from t = -5 μs to 15 μs. Clearly label and specify (numerically) all steady-state levels and time constants.
5V
RF
RR
LR
S
+
-
vsw
isw
Relaymodel
Figure 2
isw
vsw
t
t-5 Ps 5 Ps 10 Ps 15 Ps
6.002 Circuits and Electronics Final Exam Practice Name:_______________________________
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Problem 3 In the circuit of Fig. 3, a resistor RS is used to sense the current ix(t) by converting it to a voltage measured at vo. To attenuate high-frequency components in the sensed signal a low-pass filter comprising resistor RF and capacitor CF is inserted between RS and vo.
RF
RS ixCF
+
-
vo
Figure 3
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(3A) Assume that ix(t) = Ixest and vo(t) = Voest. Determine the ratio x
o
IVsH )( as a
function of s. In other words, find the input-to-output transfer function of the system H(s).
H(s) =
6.002 Circuits and Electronics Final Exam Practice Name:_______________________________
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(3B) On the axes below, plot the magnitude and phase of H(jω) vs. ω. Use a logarithmic scale for magnitude and frequency and a linear scale for phase. Clearly label and specify all important breakpoints and asymptotes, and label and dimension all axes.
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(3C) Consider the circuit with parameters RS = 0.1 Ω, RF = 10 Ω, and CF = 33 nF. If the system is driven with the steady-state input (in Amperes) ix(t) = 5 + 1sin(2π·106·t) find the steady-state output vo(t).
vo(t) =
6.002 Circuits and Electronics Final Exam Practice Name:_______________________________
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Problem 4 (15 Points) Figure 4 shows a parallel RLC circuit driven by a current source. The circuit parameters are L = 1 μH, C = 1 μF, R = 1 Ω, I = 1 A. The switch is closed for t < 0, and it opens permanently at t = 0. (You may assume that the inductor current is zero at t = 0–.) Find v(t) for t > 0.
I C RLS
+
-
v
Figure 4
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v(t) =
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Problem 5 (25 Points) (5A) Figure 5 shows a widely-used amplifier configuration incorporating an operational amplifier. Find an expression for the output voltage vo in terms of the input voltages vA and vB, assuming that the op amp is ideal.
-
+R1
R2
R2R1
vB
vA
vo
Figure 5
vo(t) =
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(5B) Figure 6 shows an operational amplifier circuit incorporating a diode. For the operating range of interest we will model the i-v characteristic of the diode as:
»»¼
º
««¬
ª�| 1T
dVv
sd eIi .
Find the relationship between the output voltage and the input voltage for this circuit, assuming that the op amp is ideal, the diode acts as modeled above, and the input voltage is greater than zero.
-
+
RvI
vO
id
+ -vd
Figure 6
vo(t) =
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Problem 6 Assume that the network in Figure 7 is operating in the sinusoidal steady state. Determine the response vOUT (t) to the input voltage vIN (t) = VSI cos(ωs t). Note that vOUT (t) will take the form vOUT (t) = VSO (ωs) cos(ωs t + φ(ωs) ).
Figure 7
vOUT (t) =
