Download Frequency Selective Circuits

Salt Lake Community College
Electrical Engineering Department
EE2210
RLC Lab
Original July 2004
Revised by Harvey Wilson March 2006, by Lee Brinton and James Quebbeman 8/3/2010.
Latest revision 7/6/2016 by Harvey Wilson
Abstract
The natural and step responses of a circuit with resistance, capacitance
and inductance is more complicated than circuits with only resistance and
inductance or resistance and capacitance. The performance of these RLC
circuits is described by second order differential equations. The relative size of
the R, L and C significantly affect the nature of the response. In this lab, we will
study the response of RLC circuits.
Objectives



Calculate resistor needed for critically damped response of RLC circuits.
Measure natural response of RLC circuits for various resistor values.
Compare calculated and measured responses.
Equipment


Proto-Board with 10kΩ variable resistor.
0.01μF capacitor. Usual capacitor markings include .01 (meaning .01μF) and 103

(meaning 10 x 10^3pf = 10,000pF).
100mH inductor. Usual inductor markings include 100mH and 104 (meaning 10 x
10^4μH = 100,000μH). Nominal internal resistance is 105 ohms.





1N4148 diode or approximate equivalent switching diode.
LC meter.
DMM.
Oscilloscope with 1 probe (SCOPE).
B+K Precision model 4011 function generator (FGEN).
Page 1 of 3
Pre-Lab
RLC equations:
𝑅
1
𝑠2 + ( ) 𝑠 +
= 0 𝐶ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑠𝑒𝑟𝑖𝑒𝑠
𝐿
𝐿𝐶
1
1
𝑠2 + ( ) 𝑠 +
= 0 𝐶ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙
𝑅𝐶
𝐿𝐶
𝑅
𝛼=
𝐹𝑜𝑟 𝑠𝑒𝑟𝑖𝑒𝑠 𝑅𝐿𝐶
2𝐿
1
𝛼=
𝐹𝑜𝑟 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑅𝐿𝐶
2𝑅𝐶
1
𝜔0 =
𝐹𝑜𝑟 𝑒𝑖𝑡ℎ𝑒𝑟 𝑠𝑒𝑟𝑖𝑒𝑠 𝑜𝑟 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙
√𝐿𝐶
𝑖𝑓 𝛼 < 𝜔0 , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑖𝑠 𝑢𝑛𝑑𝑒𝑟𝑑𝑎𝑚𝑝𝑒𝑑
𝑖𝑓 𝛼 = 𝜔0 , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑖𝑠 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝑑𝑎𝑚𝑝𝑒𝑑
𝑖𝑓 𝛼 > 𝜔0 , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑖𝑠 𝑜𝑣𝑒𝑟𝑑𝑎𝑚𝑝𝑒𝑑
1. Calculate the value of R to cause a critically damped response in a Series
RLC circuit, given L = 90mH and C = .01μF.
2. Repeat question #1 for a Parallel RLC circuit.
Discussion
The energy storing nature of capacitors and inductors in the same circuit
produces interesting interactions between voltages and currents in the circuit.
Depending upon the “dampening” (the rate of power dissipation through the
resistor), energy may flow back and forth between the capacitor and inductor in a
way that causes a “ringing” in the circuit.
For this experiment, it is important to understand that real inductors are
inherently imperfect devices. To account for this imperfection and improve our
results, we include in our model of the inductor a series resistance. There is also
a relatively small parasitic capacitance associated with inductors, but is small
enough to ignore for our purposes here.
In the following experiment we will demonstrate the under-damped,
critically damped, and over-damped responses of RLC circuits by varying the
size of resistance in both parallel and series circuits.
Page 2 of 3
Experiment
1.
2.
3.
4.
Measure the capacitance of the capacitor.
Measure the inductance and resistance of the inductor.
Re-do pre-lab question #1 after substituting measured component values.
Assemble the circuit in Figure 1 using the function generator as a source with
16v p-p square wave at 1 kHz.
5. Adjust R1 such that (R1 + RL + Rgen) = resistance calculated in step 3.
6. Observe the shape of the waveform displayed on the scope.
7. Observe and record the effects on the waveform of changing the total
resistance above or below the critical value.
8. Adjust R1 to get the shortest waveform decay time with NO OVERSHOOT.
(This is difficult to see exactly, but make your best guess.) Measure (R1 + RL)
resistance. Add 50Ω to include Rgen. The resistance just measured is close
to the critical value.
9. Re-do pre-lab question #2 after substituting measured component values.
10. Try re-assembling your circuit as a parallel RLC circuit. Connect a diode
between the function generator output and the circuit. Draw your own circuit
schematic. Explain why a diode is used?
11. Observe and record the effects on the waveform of changing the total
resistance above or below the critical value.
Conclude
How well did measured response agree with calculated response once
actual R, L and C values were used in calculations? When does over-damping
occur?
Page 3 of 3