EXPERIMENT #1
STUDY OF RC AND RL CIRCUITS
Venue: Microelectronics Laboratory in E2 L2
I.
INTRODUCTION
This laboratory is about verifying the transient behavior of RC and RL
circuits. You need to revise the natural and step response of RC and RL
circuits you have covered in lectures.
The charging and discharging of capacitor through a resistance is verified
first, finding out its theoretical value of time constant which is verified by
practical calculations.
The magnetizing and demagnetizing of a coil through a resistance is verified
first, finding out it’s the theoretical of its time constant which is verified by
practical calculations.
II.
PRE-LAB
Do the ORCAD simulations of both RC and RL circuits, calculate time constants and
plot the resulting waveforms across C (in the case of RC) and the waveform of the
current in the case of RL. In the ORCAD, use VPULSE as the Vs and set V1=5V,
V2=-5V, TD=0, TR=0, TF=0, PER=1/FREQUENCY and PW=0.5*PER
Use the following specifications while verifying the RC of Fig # in ORCAD
C1 0.001 uF
R1 3000 Ohm
Vs 10.0 Vpp
TYPE = SQUARE WAVE
FREQUENCY = 20 kHz
OFFSET = 0
Use the following specifications while verifying the RC of Fig # in PSPICE
L1 10 mH
R1 3000 Ohm
Vs 10.0 Vpp
TYPE = SQUARE WAVE
FREQUENCY = 20 kHz
OFFSET = 0
ECE Lab1 ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
III.
EXPERIMENTAL METHOD
Equipment Required: Square-wave generator, discrete circuit components of
R1=3000Ω, L1=470uH and C1=1000pF, oscilloscope and square-wave
generator
Fig #1
Fig #2
IV.
MEASUREMENT AND READIGNS
Here derive the equation for the above vC(t) and vR(t), and plot them using
MATLAB to see if they are the same as the ones obtained PSPICE and the
oscilloscope in II and III respectively.
From the plots in II and III find out how long (in time constant, τ) does it take
for the vC(t) and vR(t) to get to 95 % of their maximum (or come down to 5 %
of minimum) of their minimum values.
Show with changing values of R, the resultant waveforms and effect on them.
V.
CONSLUSIONS
Varying R in RC circuit results in what?
Varying R in RL circuit results in what?
How much the voltage across a charged capacitor is reduced to after one time
constant, RC?
How much the voltage across a resistor in RL circuit is reduced to after one
time constant, L/R?
ECE Lab1 ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
EXPERIMENT II
STUDY OF RLC TRANSIENT RESPONSE
Venue: Microelectronics Laboratory in E2 L2
I.
INTRODUCTION
This laboratory is aimed at enabling students on how to use the function generator
for generating a step input with an appropriate repetition rate, to an oscilloscope
to measure RLC overdamped and underdamped responses.
II.
PRE-LAB
Write and run a PSPICE program for the circuit shown in Figure 1. In the
VPULSE model, make V1=-5V, V2=5V, PW=10ms and PER= 15ms, plot the
voltage across the capacitor from 0 to 5 ms in 0.1 ms increments. Print the Netlist
output file and the Output waveform and attach.
Write and run a PSPICE program for the circuit in Figure 2. Plot the voltage
across the capacitor from 0 to 5 ms in 0.1 ms increments. Print the Netlist output
file and the Output waveform and attach.
Use the program above to also analyze the resistor voltage, plot the voltage across
the resistor from 0 to 5 ms in 0.1 ms increments. Print the Output waveform and
attach.
III.
BACKGROUND
A series RLC circuit can be modeled as a second order differential equation,
having solution under the three conditions for its roots.
• When its roots are real and equal, the circuit response to a step input is
called “Critically Damped”.
• When its roots are real but unequal the circuit response is “Over-damped”.
• When roots are a complex conjugate pair, the circuit response is labeled
“Under-damped”.
IV.
EXPERIMENTAL METHOD, MEASUREMENT AND READINGS
In this experiment only the over-damped and under-damped responses are
studied, the critically damped is just another form of over-damped response.
ECE Lab1 ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
EQUIPMENT REQUIRED:
Oscilloscope, Function generator, Resistor, 100 Ω, Resistor, 1.0 kΩ, Capacitor,
1.0 µF, Inductor, 220 mH
OVER-DAMPED RLC CAPACITOR VOLTAGE SETP RESPONSE:
With the RLC circuit disconnected, adjust the function generator to produce a
repetitive pulse that is -5 volts for about 10 ms, then +5 volts for about 10 ms. (i.e.
10 Volts peak-to-peak, 0 Volts of DC offset, 20 ms Period or 50 Hz). For the
circuit in Figure 1, calculate the output response, VC(t), t > 0, to an input step,
from -5 to +5 Volts.
Connect the circuit in Figure 1. Measure the final value, VC(t=∞), and the initial
value, VC(t=0+), from the oscilloscope and record in the Data section. Also
measure the voltages VC(t=0.5 ms), VC(t=1.0 ms), and VC(t=2.0 ms) from the
oscilloscope and record in the Data section.
First determine α and ω0. Calculate the roots of the characteristic equation, S1, 2
and determine Vc(0), and Vc(∞), and d[Vc(0)]/dt. Calculate A1 and A2, and fill in
the Data Table for Figure 1 below:
ECE Lab1 ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
Quantity
α
DATA TABLE – I
OVERDAMPED RLC
Calculated Value
Measured Value
N/A
ω 0.
N/A
S1, 2
Vc(0)
N/A
d[Vc(0)]/dt
Vc(∞)
A1 and A2,
Equation for Vc(t)
N/A
Vc(0.5ms)
Vc(1ms)
Vc(2ms)
UNDER-DAMPED RLC CAPACITOR VOLTAGE SETP RESPONSE:
Keep the function generator settings used in Part 1. For the circuit in Figure 2,
calculate the output response, VC(t), t > 0, to an input step, from -5 to +5 Volts.
Note that the only change to the circuit is replacing the 1 k-Ohm resistor with a
100 Ohm resistor.
FIGURE 2: Underdamped RLC Circuit with Step Input
ECE Lab1 ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
First determine α and ω0. Calculate the roots of the characteristic equation, S1, 2
and determine Vc(0), and Vc(∞), and d[Vc(0)]/dt. Calculate A1 and A2, and fill in
the Data Table for Figure 1 below:
Quantity
α
ω0
DATA TABLE – II
UNDERDAMPED RLC
Calculated Value
Measured Value
N/A
N/A
S1, 2, ωd
Vc(0)
N/A
d[Vc(0)]/dt
Vc(∞)
A1 and A2,
Equation for Vc(t)
N/A
Vc(0.5ms)
Vc(1ms)
Vc(2ms)
V.
CONCLUSIONS
ECE Lab1 ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
EXPERIMENT III
RESONANCE IN RLC CIRCUITS
Venue: Microelectronics Laboratory in E2 L2
I.
INTRODUCTION
This laboratory is about studying resonance in RLC series and parallel circuits. This
experiment will be used to examine the sinusoidal frequency response of the series and
parallel to see at what frequency the current through an RLC series becomes or the
voltage across a parallel RLC circuit reaches maximum value. A network is in resonance
when the voltage and current at the network input terminals are in phase and the input
impedance of the network is purely resistive.
II.
PRE-LAB
Do the ORCAD simulations of both RLC parallel and RLC series circuits.
III.
EXPERIMENTAL METHOD, MEASUREMENT AND READINGS
Consider the Parallel RLC circuit of figure 1. The steady-state admittance offered by the
circuit is:
Y = 1/R + j( ωC – 1/ωL)
Resonance occurs when the voltage and current at the input terminals are in phase. This
corresponds to a purely real admittance, so that the necessary condition is given by
ωC – 1/ωL = 0
ECE Lab III ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
The resonant condition may be achieved by adjusting L, C, or ω. Keeping L and C constant,
the resonant frequency ωo is given by:
Equipment Required: Square-wave generator, discrete circuit components of R=1 KΩ, L=
27mH and C=1uF, oscilloscope and square-wave generator.
Set up the RLC circuit as shown in Figure 1
Figure 1
Apply a 4.0 V (peak-to-peak) sinusoidal wave as input voltage to the circuit.
Set the Source on Channel A of the oscilloscope, and the voltage across the ca[pcitance on
Channel B of the oscilloscope.
Vary the frequency of the sine-wave on signal generator from 500Hz to 2 KHz in small steps,
until at a certain frequency the output of the circuit on Channel B, is maximum. This gives
the resonant frequency of the circuit.
ECE Lab III ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
DATA
TABLE – I
PARALLEL RESONANCE
f
500 Hz
600 Hz
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
C
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
R
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
L
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
Vo
V(t) reading
Repeat the experiment using for the series resonant circuitry in Figure 2, and use L = 33mH
and C = 0.01uF and R = 1 KΩ. The Vo voltage on the resistor is proportional to the series
RLC circuit current.
Figure 2
ECE Lab III ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
DATA
TABLE – Ii
SERIES RESONANCE
f
500 Hz
600 Hz
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
IV.
C
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
0.01uF
R
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
1000 Ω
L
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
33mH
Vo
V(t) reading
CONCLUSIONS
Find the resonant frequency using equation given in the before and compare it to the
experimental value in both cases.
Plot the voltage response of the circuit and obtain the bandwidth from the half-power
frequencies using equation.
ECE Lab III ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
EXPERIMENT IV
VERIFYING FREQUENCY RESPONSE OF
ACTIVE FILTERS
Venue: Microelectronics Laboratory in E2 L2
I.
INTRODUCTION
Filters are also called frequency-selective circuits as they are able to filter some of the
input signals on the basis of frequency. They are categorized as passive or active filters –
the former are making use of resistors, inductors and capacitors, while the latter are
making use of the OP-AMPs. The responses are obtained and plotted for both of.
II.
PRE-LAB
Do the ORCAD simulations of Low Pass and High-Pass Filters shown below.
III.
EXPERIMENTAL METHOD, MEASUREMENT AND READINGS
Construct the low-pass and high-pass filters of Fig. 1 and Fig. 2. Note that C2 of the lowpass filter consists of two 0.01 mF capacitors in parallel. The two 1.0 mF tantalum
power-supply bypass capacitors are to be used on all circuits in this laboratory procedure.
Characterize the responses of the low-pass filter and of the high-pass filter for
frequencies from 10 Hz to 10 kHz.
ECE Lab IV ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
DATA
TABLE – I
LOWPASS FILTER
f
10Hz
500Hz
1000 Hz
2000 Hz
3000 Hz
4000 Hz
5000 Hz
6000 Hz
7000 Hz
8000 Hz
9000 Hz
10000 Hz
Vi(t)
Vo
Fixed
ECE Lab IV ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan
DATA
TABLE – II
HIGHPASS FILTER
f
10Hz
500Hz
1000 Hz
2000 Hz
3000 Hz
4000 Hz
5000 Hz
6000 Hz
7000 Hz
8000 Hz
9000 Hz
10000 Hz
IV.
Vi(t)
Vo
Fixed
CONCLUSIONS
Find the cutoff frequencies of both of the circuits; obtain the readings and using exel plot the
data of the above two to show they are working as LOWPASS and HIGHPASS filter.
Plot the voltage response of the circuit and obtain the bandwidth from the half-power
frequencies using equation.
ECE Lab IV ECE 2201 SEMESTER II, 2011/2012
By Sheroz Khan