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ECE 202 – Experiment 6 – PreLab Homework
PHASORS AND PHASE SHIFT CIRCUITS
YOUR NAME_________________________
LAB MEETING TIME______________
Reference: C.W. Alexander and M.N.O Sadiku, Fundamentals of Electric Circuits
Chapter 9
STEADY-STATE RESPONSE OF AN RC CIRCUIT TO A SINUSOIDAL INPUT
1. Consider the series RC circuit:
Series RC circuit in time domain
Series RC circuit in phasor domain
Assume steady-state and vs(t) = Vmcos(t),
a) Draw the equivalent phasor domain circuit in the space provided above.
b) Determine the phasor voltage, Vr and the steady state voltage vr(t).
c) Determine the phasor voltage, Vc and the steady state voltage vc(t).
ECE 202 – Experiment 6 – PreLab Homework
d) Build the series RC circuit in Cadence using the following circuit element values.
C = 0.027 μF
R = 10 kΩ
vs(t) = Vmcos(t)
Vm = 5 V
Cadence AC analysis steps:
1. Use vsin in AnalogLib library for voltage source. Set AC magnitude to 5V.
2. Launch ADE L and choose AC analysis. Select frequency variable sweep and set the
sweep range from 10Hz to 10kHz.
3. Select vc as your output (ADE L: Output  To Be Plotted  Select on Schematic)
4. Run Simulation. The simulation output shows vc for the specified frequency range.
5. In the simulation output window, use (tools  calculator) to show the respective phase of
by selecting vc wave and select phase function. At last, hit Evaluate the buffer button as
shown on the screenshot below.
Print your Cadence simulation result and record the magnitude and phase of vc for different
frequencies: f = 60 Hz, 500 Hz, 600 Hz, 4 kHz and 10 kHz.
Your simulation output curve should look exactly like this. (Optional but recommended: hover your
cursor at the top of the curve, press v to show the vertical marker, then drag marker to desired
frequency point. The example below shows magnitude and phase at f = 1 kHz.)
ECE 202 – Experiment 6 – PreLab Homework
e) Use results of your calculation from 1.b, 1.c and 1.d to fill-in the table
vr(t)
f
Magnitude [V]
vc(t)
Phase [deg]
Magnitude [V]
Phase [deg]
theoretical Cadence theoretical Cadence theoretical Cadence theoretical Cadence
60 Hz
500 Hz
600 Hz
4 kHz
10 kHz
Attach a separate paper showing your theoretical evaluations.
PHASE SHIFT CIRCUIT (BOUNCING BALL CIRCUIT)
2. Consider the circuit:
Circuit in time domain
Circuit in phasor domain
Assume steady-state conditions and the input voltage source vs(t) = Vm cos(t).
a) Re-draw circuit in phasor domain in the space provided above.
Attach a paper showing calculations for the following:
b) Using any desired method of circuit analysis, derive expressions for the phasors Vx and Vy.
c) Determine the required frequency , expressed in terms of the passive circuit elements, such
that the phase shift between Vx and Vy is 90°.
Hint: In general, if two phasors X1 and X2 are shifted for 90° and one is (purely) real,
X1=X1+j0, what should be the expression for the other (circle the correct answer):
i.
Purely real X2=X2+j0
ii.
Purely imaginary X2=0+jX2
iii.
Equal real and imaginary components X2’=X2+jX2
iv.
General complex number X2=Re+jIm
ECE 202 – Experiment 6 – PreLab Homework
d) Determine the required R2, expressed in terms of the other passive circuit elements, such that
the following two conditions are satisfied:
i.
The phase shift between Vx and Vy is 90°, and
ii.
The phasor magnitudes are identical (i.e., Vx  Vy )
Note: The result should be simplified as much as possible and should not be a function of .
e) Sketch the oscilloscope trace that you expect to see for part d) of the problem:
DIODE BRIDGE WITH THE LOAD
3. Consider the circuit below with a sinusoidal input. You have modeled similar circuit in Lab2 part
6.b.
The diodes in any circuit turn on whenever the anode is at a higher voltage than the cathode.
When diodes are on, they allow current to flow through them. Otherwise, they do not conduct
current.
D1
D3
D4
D2
AC
Rload
a) What would be the purpose of the capacitor that you have modeled in Lab2? Sketch by hand,
in the space provided below, responses that you would expect from a diode bridge followed
by a resistor only and diode bridge followed by a resistor in parallel with a capacitor.
ECE 202 – Experiment 6 – PreLab Homework
b) Let’s focus on a circuit during one half of a period: you will have a source, followed by two
diodes and a resistor (no capacitor in this case).
If diodes are LEDs and cannot have more than 20mA of current passing through them, what
should be the value of used resistor for a sine wave input with a peak-to-peak input voltage of
14 V?
14 Vpp
Hint: What should be the value of R, such that imax = 20 mA,
given voltage values mentioned above? Assume that vLED =
1.5 V when diode is conducting.