Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
Circuits
Final
Fall 2013
1.
/30
2.
/25
3.
/25
4.
/25
5.
/25
6.
/25
Total
/150
Name ______________________
Notes:
1) If you are stuck on one part of the problem, choose ‘reasonable’ values on the following
parts to receive partial credit
2) You don’t need to simplify all your numerical calculations. For example, you can leave
square root terms in radical form.
3) Please pay attention to your 2π terms. Most problems have been presented in radians, but
not every problem.
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
1
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
1) Short Answers (25 points)
Question 1 (3 points)
4
Vs
R
4
Is
2
For each of the above components, determine the power produced or consumed. Recall, power
produced is negative and power consumed is positive. The sources are DC supplies.
PVs = ________________________[W]
PIs = ________________________[W]
PR = ________________________[W]
Question 2 (4 points)
1:N
Vs
R
Is
For the above transformer circuit, symbolically determine the voltage across R
VR:
_______________________
Symbolically determine an expression for Is such that no current flows through Vs
Is:
_______________________
Question 3 (5 points)
When considering power
T / F a) The complex power can be purely real if the load is resistive.
T / F b) The complex power can be purely real if the load is capacitive
T / F c) The complex power can be purely reactive if the load is resistive
T / F d) The complex power can be purely reactive if the load is inductive
T / F e) The power factor is bounded by the values 0 < |p.f.| < 2
.
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
2
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
Question 3 (7 points)
Vab
R1
10k
R2
Vca
0
10k
Vbc
R3
10k
In the above system, the configuration of the three phase source is Wye or Delta? ____________
In the above system, the configuration of the three phase load is Wye or Delta?
____________
If Vab has an rms voltage of 1kV, determine the following (assume the phase voltage, Va, has
zero phase).
Phasor form of phase voltage Vab:
_________________________
Phasor form of line voltage Va:
_________________________
Phasor form of phase/branch current Iab:
_________________________
Phasor form of line current Ia:
_________________________
Total power produced (from all three sources)
___________________
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
3
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
Question 5 (6 points)
1
L
2
2
Vin
1
2
+
C
1
R
-
Vout
Determine the transfer function for the above circuit, where H(s) = Vout(s)/Vin(s). Your answer
should not be symbolic, use the values provided.
As ω→0, the transfer function approaches, H(jω) → _______________________
As ω→∞, the transfer function approaches, H(jω) → _______________________
Question 5 (5 points)
For the amplifier circuits we used in the laboratory,
T / F a) If Vout ~ -9V, it is reasonable to assume the amplifier is at saturation.
T / F b) If Vout ~ -9V, it is reasonable to assume an inverting amplifier was
implemented.
T / F c) None of the labs required implementation of a voltage follower
T / F d) The operating range was approximately 0~100MHz
T / F e) My favorite part was when we changed something on Mobile Studio, the circuit
measurement changed
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
4
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
2) Circuit Analysis (25 points)
a) Thevenin/Norton Circuits (15 pts)
I1
0.002
R4
12k
R5
6k
V1
R1
4k
4
R2
8k
R3
4k
RLoad
0
Using any method(s), determine VThevenin, RThevenin, and INorton for the above circuit. (10pts)
VTh
RTH
IN
[V]
[Ω]
[A]
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
5
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
b) Dependent Sources
In the following circuit, you will set up the linear system to analyze the circuit using both node
and mesh analysis (next page). You only need to solve for VR4 using one of the methods.
V2
2Vx
R1
2k
+
R3
1k
I1
Vx
-
R5
2k
0.001Vx
+
R4
2k
V1
2
R2
2k
0
a) On the above circuit, label the nodes you would use to perform node analysis. (1 pt)
b) Determine the linear system of equations you would use in nodal analysis. Clearly
indicate each of your equations. (6 pts)
c) If you use node analysis to determine VR4, provide your answer below. Note, the
assumed polarity of VR4 is provided on the circuit.(1 pts, if solved)
VR4 (if solved with node)
J. Braunstein
Rensselaer Polytechnic Institute
[V]
Revised: 3/18/2016
Troy, New York, USA
6
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
V2
2Vx
R1
2k
+
R3
1k
I1
Vx
-
R5
2k
0.001Vx
+
R4
2k
V1
2
R2
2k
0
a) On the above circuit, label the mesh loops you would use to perform mesh analysis. (1 pt)
b) Determine the linear system of equations you would use in mesh analysis. Clearly
indicate each of your equations. (6 pts)
c) If you use mesh analysis to determine VR4, provide your answer below. Note, the
assumed polarity of VR4 is provided on the circuit.(1 pt, if solved)
VR4 (if solved with mesh)
J. Braunstein
Rensselaer Polytechnic Institute
[V]
Revised: 3/18/2016
Troy, New York, USA
7
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
3) Transient Response (25 points)
a) Time domain (8 pts)
R
L
1
C
2
0.0064
Vs
For the above circuit, the voltage across the capacitor is given as
Vc t   exp  7t  10 cos24t   2.917 sin 24t   10
Determine the initial conditions for the capacitor (3 pts)
 
Vc 0  = ___________________
 
Ic 0
= ___________________
C
For t > 0, determine the expression for the source voltage. (1 pt)
VS t  = ___________________
Determine values for the inductor and resistor, L and R. (4 pts)
L = ___________________
R = ___________________
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
8
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
b) First order transients (7pts)
Vs
R1
R3
10
5
R2
10
C1
0.02
The source in the above circuit has voltage Vs(t) = 5u(t) and there are zero initial conditions.
Determine a differential expression for the voltage across the capacitor. Your expression should
not be symbolic, ie. use numerical values where appropriate. (4 pts)
Determine the voltage across the capacitor, Vc(t), as a function of time. (3 pts)
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
9
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
c) Laplace (10pts)
R
2
Is
L
0.5
+
-
2
C
0.125
1
In the above circuit, the current source is 2.5A ‘upwards’ for t<0 and turns off at t = 0.
Determine the initial conditions for the capacitor and the inductor. (2 pts)
VC(0+) = __________________________
IL(0+) =
__________________________
Draw the s-domain equivalent circuit. Remember, the source turns off a t = 0. (3 pts)
Use circuit analysis, partial fraction expansion and Laplace transforms to determine the voltage
across the capacitor as a function of time. Note the polarity indicated on the capacitor.
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
10
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
4) AC Steady State
a) Bode Plots (10 pts)
For an unknown transfer function, the following ‘corrections’ to the straight line approximation
represents every pole and zero in the system.
a. -3dB at 1E2 [rad/s]
b. +6dB at 1E4 [rad/s]
c. -3dB at 1E6
Additionally, at 1 [rad/s], the transfer function has a magnitude of 10 [dB] and zero phase. Plot
the magnitude and angle Bode plots. Label the y axis for both graphs.
Magnitude (4 pts)
1
2
3
4
log(ω)
5
6
7
5
6
7
Phase (4 pts)
1
2
3
4
log(ω)
What type of filter is represented in the above Bode plots? (2 pts)
Lowpass
Highpass
Bandpass
Bandstop/Notch
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
11
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
b) Transfer functions/Bode plots (15 pts)
R1
U1
Vin
R2
+
100
2
1
OUT
L1
0.1
-
OPAMP
100
L2
+
2
1E-3
C1 Vout
1E-7
R3
1
90k
0
-
0
R4
10k
0
Determine the transfer function, H(s) = Vout(s)/Vin(s) for the above circuit. (5 pts)
Plot the magnitude Bode plot on the following graph. Indicate any real zeros, real poles, or
resonant frequencies. For any of those values that are nonzero, indicate the ‘correction’ to the
straight line approximation. Label the y-axis. (10 pts)
1
2
3
4
log(ω)
J. Braunstein
Rensselaer Polytechnic Institute
5
6
7
Revised: 3/18/2016
Troy, New York, USA
12
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
5) Inductance
a) Transformers (15 points)
1:2
+
I1
-
+
R2
-
1:5
+
300
R1
100
-
R3
7.5k
1:4
+
V1
For the above circuit, the sources are
V1t   10 cos377t  [V]
I1t   0.02 cos377t  [A]
The polarities at t=0 are indicated for each source. The ‘dots’ are on the same side for each
transformer.
Use superposition to determine the voltage across each resistor, the power consumed by each
resistor and the power produced by each source. The polarities for each resistor can be used for
reference (be careful when considering each source). Include schematics for each superposition
circuit. (the next page is left blank)
R1
[V]
[W]
R2
[V]
[W]
R3
[V]
[W]
V1
[W]
I1
[W]
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
13
Circuits
Name _______________________ ECSE 2010
J. Braunstein
Rensselaer Polytechnic Institute
Fall 2013
Section _________
Revised: 3/18/2016
Troy, New York, USA
14
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
b) Mutual Inductance (10 points)
2
R1
1k
2
L1
4
L2
1
1
2
VAMPL = 110
2
L3
1
V1
1
L4
1
1
k = 0.5
R2
1k
1
k = 1
The above circuit represents inductive coupling for two different pairs of resistors, R1 and R2.
The coupling is L1-L2 and L3-L4, with the coupling coefficient indicated above. Recall, the
mutual inductance is M =k*sqrt(La*Lb). For the frequencies indicated in the table, determine the
amplitude of the current through the respective resistors. In cases where reasonable
approximations are valid, you should apply them to your solution.
ω
R1
R2
1 [rad/s]
[A]
[A]
1E3 [rad/s]
[A]
[A]
1E6 [rad/s]
[A]
[A]
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
15
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
6) Power – Parallel Loads (25 pts)
Z1
Z2
+
Vs
V3
I2
Z3
In the above circuit, three impedances are shown. The source operates at 60Hz. The following
information is known about the circuit.
a. The source is a 100 [Vrms] source and has zero phase.
b. For Z2, S2 = 93.75 - j31.25 [VA] and I2 = 0.7906  18.43 [Arms]
c. For Z3, S3 = 62.5 [W] (purely real) and V2 = 55.9  63.43 [Vrms]
d. The real power produced by the source has the same magnitude as the reactive power
produced by the source.
Determine the value for each unknown impedance, Z1, Z2 and Z3. Determine the power
produced by the source.
Z1
[Ω]
Z2
[Ω]
Z3
[Ω]
SSource
J. Braunstein
Rensselaer Polytechnic Institute
[W]
Revised: 3/18/2016
Troy, New York, USA
16
Circuits
Name _______________________ ECSE 2010
Fall 2013
Section _________
b) Parallel Loads (10 points)
R1
25
R2
5
2
2
L1
0.0531
Vs
L2
0.1326
1
1
Load1
Load2
C1
2.653E-4
Load3
In the above parallel load system, the source operates at 60 [Hz] and has a voltage of 5kV
[Vrms]. Complete the following table, indicating the real power, reactive power, total
power(magnitude) and power factor for each load and the source.
P[W]
Q [VAR]
|S| [VA]
power factor
Load 1
Load 2
Load 3
Source
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 3/18/2016
Troy, New York, USA
17