EXPERIMET 2 – BET 2113
_____________________________________________________________________________________________________________________
UNIVERSITI TEKNIKAL MALAYSIA MELAKA
FAKULTI KEJURUTERAAN ELEKTRONIK DAN KEJURUTERAAN KOMPUTER
EXPERIMENT 2
SUBJECT BENT 2113
1.0
TITTLE: TRANSIENTS IN R-L-C CIRCUITS
2.0
OBJECTIVES
1.
Determine the step response for the current in a series R-L-C circuit.
2.
Determine the damping factor and the resonant frequency for the series R-L-C circuit.
3.
Demonstrate how changing the value of R affects the damping factor of a series R-L-C
circuit.
4.
Demonstrate how changing the value of C affects the frequency of oscillation of an R-L-C
circuit.
3.0
EQUIPMENT REQUIRED
One dual-trace oscilloscope
One function generator
One 10mH inductor.
Capacitors – 0.05µF, 0.1µF
Resistors - 200Ω, 400Ω, 1kΩ
4.0
THEORY:
In this experiment, you will determine the step response for the current in the series R-L-C circuit shown in
Figure 1. This means that you will plot the current when the input voltage steps from zero to a constant
(steady state) value. The step input voltage will be provided by a function generator that produces a
square wave output with a time period that is much longer than the transient response of the R-L-C circuit.
The current in a series R-L-C circuit can have three possible step response, depending on the relationship
between the circuit damping factor (α) and resonant frequency (ωo).
They are overdamped, critically
damped, or underdamped. The damping factor (α) for a series R-L-C circuit is dependent on the circuit
resistance (R) and inductance (L).
-1
The damping factor, in sec , for a series R-L-C circuit is calculated
from
α = R/ 2L
The resonant frequency (ωo) for a series R-L-C circuit is dependent on the circuit capacitance (C) and
inductance (L). The resonant frequency (ωo), in radians/sec, for a series R-L-C circuit is calculated from
ωo = 1/ √LC
_______________________________________________________________________________
1
EXPERIMET 2 – BET 2113
_____________________________________________________________________________________________________________________
When the damping factor (α) and is equal to the resonant frequency (ωo), the series R-L-C circuit is
critically damped. When the damping factor (α) and is greater than the resonant frequency (ωo), the
series R-L-C circuit is overdamped. When the damping factor (α) and is less than the resonant frequency
(ωo), the series R-L-C circuit is underdamped.
The damping factor (α) determines approximately how long it takes for the current to damp out to a steadystate value (in this case zero).
The current will damp out to steady state in approximately five time
constants. One time constant (τ ) can be found from
τ = 1/α
The resonant frequency (ωo) is the frequency of oscillation when the R-L-C circuit is underdamped with a
damping factor (α) of zero, which would make it underdamped. The damped frequency of oscillation
(ωd) of an underdamped R-L-C circuit is less than the resonant frequency (ωo) and is calculated, in
radians/sec, from
ωd = √α2 - ωo2
The frequency of the underdamped oscillation can be determined from the curve plot by measuring the
time period (Td) for one oscillation cycle. The frequency in hertz (cycles per second) can be calculated
from
fd = 1/ Td
The frequency in radians per second (ωd) can be calculated from using the equation
ωd = 2π fd
Figure 1: Series R-L-C Circuit
_______________________________________________________________________________
2
EXPERIMET 2 – BET 2113
_____________________________________________________________________________________________________________________
5.0
PROCEDURE:
1.
Draw the circuit as shown in Figure 1.
2.
Draw the curve plot of the resistor voltage.
3.
Based on the R-L-C circuit component values in Figure 1, calculate the damping factor (α).
Question; Based on the values of α and ωo, what is the response for the series R-L-C circuit in Figure 1
4.
Change the value of resistor R in Figure 1 to 400Ω. Clik the On-Off switch to run the simulation
again. Draw the curve plot of the resistor voltage (circuit current) in the space provided. Note on the curve
plot the time it takes for the current to damp out to zero.
5.
Based on the new value of resistor R in Figure 1, calculate the new damping factor (α).
Question: Comparing the new damping factor (α), calculated in Step 5, with the resonant frequency (ωo),
calculated in Step 3, is the R-L-C circuit overdamped or underdamped?
6.
Based on the new damping factor (α), calculated in Step 5, calculate the approximate time it should
take for the current to damp out to zero.
7.
Change the value of resistor R in Figure 1 to 200Ω. Draw the curve plot of the resistor voltage
(circuit current) . Determine the frequency of oscillation (fd) from the curve plot and convert it to ωd. Record
the values of fd and ωd.
8.
Based on the new value of resistor R in Figure 1, calculate the new damping factor (α).
9.
Based on the new damping factor (α), calculated in Step 8, calculate the approximate time it should
take for the current to damp out to zero.
Question: What effect does decreasing the value of R have on the damping factor? What effect does
decreasing the value of R have on the R-L-C circuit current curve plot? Explain.
10.
Based on the damping factor (α), calculated in Step 8, and the resonant frequency (ωo), calculated
in Step 3, calculate the frequency of oscillation (ωd), in radians per second, for the underdamped R-L-C
current curve plot.
_______________________________________________________________________________
3
EXPERIMET 2 – BET 2113
_____________________________________________________________________________________________________________________
11.
Change the value of capacitor C in Figure 1 to 0.05µF. Draw the curve plot of the resistor voltage
(circuit current). Determine the frequency of oscillation (fd) from the curve plot and convert it to ωd. Record
the values of fd and ωd.
fd = ___________________
12.
ωd.= _________________
Based on the new value of capacitor C, calculate the new resonant frequency (ωo) of the R-L-C
circuit, in radians per second.
13.
Based on the damping factor (α), calculated in Step 8, and the new resonant frequency (ωo),
calculated in Step 12, calculate the new frequency of oscillation (ωd), in radians per second, for the
underdamped R-L-C current curve plot.
Questions: Based on the value of fd in Step 7 and the value of fd in Step 11, what effect did decreasing
the value of C have on the frequency of oscillation for the underdamped R-L-c circuit current?
14.
Answer all questions in Discussion
15.
Conclude your finding.
_______________________________________________________________________________
4