Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
Circuits
Quiz 3
Spring 2013
1.
/20
2.
/20
3.
/20
4.
/20
5.
/20
Total
/100
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 (mm, pie). Most problems have been presented in
radians, but not every problem.
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
1
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
1) Short Answers (20 points)
Question 1 (4 points)
When measuring the current and voltage for a complex load, in rectangular form
VL = 3+4j
IL = 0.005j
Determine the equivalent impedance in phasor form,
ZEQ = ____________________________
Question 2 (4 points)
+
2
I1
R
L
C
Vout
1
In the above circuit the voltage, the voltage across the components behaves
As s  ∞
Vout ____________________
As s  0
Vout ____________________
As s  ωo
Vout ____________________
Question 3 (4 points)
2
L
1E-2
C
1E-8
1
For the above parallel LC circuit, at what frequency is the admittance zero?
____________________________
For the above parallel LC circuit, at what frequency is the impedance infinite?
____________________________
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
2
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
Question 4 (4 points)
In a second order circuit with only passive components (no amplifiers),
T / F a) The bandpass filter transfer function has a magnitude of 1 at the resonant
frequency
T / F b) A 0dB point exists at the resonant frequency of a bandpass filter
T / F c) A 0dB point can exist at the resonant frequent of a HPF
T / F d) If there is a point with >0dB, the damping ratio is less than 1
Question 5 (5 points)
40
0
-40
-80
100KHz
300KHz
DB(V(L1:2))
1.0MHz
3.0MHz
10MHz
30MHz
100MHz
Frequency
For the above transfer function, what is the damping ratio?
____________________________
If the source for the above circuit has an amplitude of 100V, at 10MHz, what is the amplitude of
the output voltage?
____________________________
True / False The above circuit can be constructed with first order circuits separated by voltage
followers? (Circle the correct answer)
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
3
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
2) Impedance/Phasor Analysis (20 points)
R1
800
L2
C1
0.2
V1
2.5E-7
R2
4.8k
R3
2k
L1
0.8
In the above circuit, V1 has a 10V amplitude and operates at 795.77 [Hz] (pay attention).
Determine the current through the source. Express your answer in time domain. You
must show your work to receive credit, but feel free to use your calculator for complex
arithmetic. (10 pts)
IS(t)
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
4
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
C1
1E-7
R1
C2
2000
5E-8
1
L1
2
0.075
I1
R2
1000
I1 = 0.005cos(2E4t)
Determine the following.
a. Phasor form of the current through R2 (2 pts)
b. Phasor form of the current through C1 (5 pts)
c. Time domain form of the voltage across C1 (3 pts)
IR1 (phasor)
IC1 (phasor)
VC1 (time)
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
5
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
3) Bode Plots (20 points)
a) Draw Bode plots for the magnitude and the phase for the transfer function (10 pts)
2
1E 7s  1E 3
(note the negative sign)
H s    2
s s  1E 6 
In your magnitude plot, indicate ‘corrections’ at the poles and zeroes. Label the axis.
Magnitude (6 pts)
Phase (4 pts)
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
6
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
-4.08dB at ωo
The above Bode plot was obtained from a series RLC circuit. The dB value at the
resonant frequency is shown in the plot.
a) Determine the damping ratio, ς (3 pts)
b) Determine α. (2 pt)
c) Draw the circuit, picking specific values for R, L and C. Indicate where Vout is
measured. You may assume a sinusoidal source with an amplitude of 1V. (5 pts)
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
7
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
4) Circuits – Transfer Functions (20 points)
R1
L
Vs
C
For H s  
R2
I L s 
, symbolically, determine the transfer function for the current through L. (3 pts)
V s s 
In the limit, as s0, what is the current through L. Justify your answer both physically (inductor
characteristics) and with your above transfer function. (3 pts)
In the limit, as s∞, what is the current through L. Justify your answer both physically (inductor
characteristics) and with your above transfer function. (3 pts)
Would you characterize this circuit as a lowpass, highpass, bandpass or bandstop filter? (1 pt)
_______________________
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
8
Circuits
Name _______________________ ECSE 2010
L2
C1
1E-7
Spring 2013
U1
+
0.1
OUT
-
Vin
R1
2000
R2
2k
C2
1E-6
Section _________
L1
+
1E-2
OPAMP
R3
R4
1010
18k
0
Vout
-
0
0
a) Find the transfer function, H s  
Vout s 
, for the above circuit. Your answer should be
Vin s 
numerical, do not leave the equations in symbolic form. (6 pts)
b) Indicate the poles and zeros in the above transfer function and whether any of them are
repeated. (3 pts)
zeros:
poles:
c) Plot the Bode plot of the magnitude for the above transfer function. Label the y-axis with
the appropriate values. (6 pts)
1
2
3
4
log(ω)
J. Braunstein
Rensselaer Polytechnic Institute
5
6
7
Revised: 11/15/2013
Troy, New York, USA
9
Circuits
Name _______________________ ECSE 2010
Spring 2013
Section _________
5) Design Problem (20 points)
Design a Bandpass filter with the following specifications. Show your work and justify your
calculations. Include a schematic of your circuit.
a.
b.
c.
d.
e.
f.
g.
h.
The stopband rolloff(s) should be 40dB/decade.
The passband has a maximum value of 6dB.
The low frequency cutoff is 1E6 [rad/s].
The low frequency cutoff should be a 6dB point (0dB relative to the passband).
The high frequency cutoff is 1E9 [rad/s].
The high frequency cutoff should be a 0dB point (-6dB relative to the passband).
The circuit must contain at least one first order stage.
The circuit must contain at least one second order stage.
(more room on the next page)
J. Braunstein
Rensselaer Polytechnic Institute
Revised: 11/15/2013
Troy, New York, USA
10
Circuits
Name _______________________ ECSE 2010
J. Braunstein
Rensselaer Polytechnic Institute
Spring 2013
Section _________
Revised: 11/15/2013
Troy, New York, USA
11