ECE 201 Lab 5

1
AC series RL and RLC circuits. ECE201 - LAB
8 2 of final grade
Projects and Notes prepared by Dr. Gabriele
Formicone
2
OUTLINE
Introduction. Circuit 1 Series RL with
grounded inductor. Circuit 2 Series RL with
grounded resistor. Circuit 3 Series RLC.
3
INTRODUCTION
Review Lab 7 for the use of the OscilloScope And
WaveFunctionGenerator. Here we will readdress
the need to ground the element whose voltage is
being measured with an OS, and the always present
loading effect on the WFG.
Because a WFG is not an ideal voltage source, the
voltage across its terminal will likely change
when you change the load impedance connected to
its terminals. Whenever you change the frequency
of the AC signal through capacitors and
inductors, the load impedance changes.
Therefore always adjust the WFG source voltage
amplitude when you change the frequency between
measurements.
4
Few guidelines for measurements with AC circuits
Because of the grounding effect, when measuring
voltages with the oscilloscope, only the voltage
across a grounded element is a correct reading!
This is due to the fact that an oscilloscope is a
grounded device. For comparison, a multi-meter is
NOT a grounded device. Therefore When using
the oscilloscope to measure a voltage across a
capacitor, the capacitor MUST be connected to
ground. When using the oscilloscope to measure a
voltage across a resistor, the resistor MUST be
connected to ground. when using the oscilloscope
to measure a voltage across an inductor, the
inductor MUST be connected to ground.
Therefore, for series R, L and C circuit, when
measuring the voltage across each one of them,
switch their relative order and make sure the the
element you are measuring on with the
oscilloscope is always grounded!
5
Series RL Circuit 1
i(t)
Build this RL series circuit with grounded
inductor
vR
R
vS(t) vS sin(2pf t)
vL
L
For a given value of R, L and VS, measure the
voltage vL(t) versus the frequency f. Sweep the
frequency f from about 50Hz to 200KHz. You can
measure either rms value or amplitude.
6
Series RL Circuit 2
i
Build this RL series circuit with grounded
resistor
vL
L
vS(t) vS sin(2pf t)
vR
R
For a given value of R, L and VS, measure the
voltage vR(t) versus the frequency f. Sweep the
frequency f from about 50Hz to 200KHz. You can
measure either rms value or amplitude.
7
SOLVE the circuit using KVL in phasor
notation. Calculate the current i and the
voltages vL and vR versus frequency from 50Hz to
200KHz.
VS VR VL
where
VR R I VL I (j wL)
Therefore
VS I R jwL
w 2 p f
I VS / R jwL
or
VR VS R / R jwL VL VS (j wL) /R
jwL
It follows
8
In terms of magnitude (amplitude), we have
mag(I) mag(VS) / vR2 (wL)2
mag(VR) mag(VS) R / vR2 (wL)2
mag(VL) mag(VS) w L / vR2 (wL)2
mag(IR) mag(VR) / R mag(IL) mag(VL) / (wL)
9
Plot the magnitude or rms value of the calculated
currents iL and iR versus frequency, and the
theoretical i obtained from KVL in phasor
notation. How are they related to each other?
Why? Explain. On another graph, plot the
magnitude or rms value of the voltages vS, vR and
vL versus frequency, and the values obtained from
KVL in phasor notation. On this same graph, also
plot the quantity vT v(vR2 vL2). How is
it related to vS? Explain why.
Follow the example in the next slides for your
report. Use similar but different values for your
resistor R, inductor L and source voltage vS.
10
Example Measurement R 100 W, L 470 mF
0.47mF, vS 2V (vSpp 4V, vSRMS 1.42 V).
Measured vS 2.05 V
Measured and Theoretical Data
11
Voltage vs. Frequency
12
Current vs. Frequency
13
Series RLC Circuit 3
vC
Build this RLC series circuit
i(t)
C
vL
L
vS(t) vS sin(2pf t)
vR
R
For a given value of R, L, C and VS, measure the
voltage vL, vC and vR versus the frequency f
making sure you ground the element whose voltage
you are measuring. Sweep the frequency f from
about 50Hz to 200KHz. You can measure either rms
value or amplitude.
14
SOLVE the circuit using KVL in phasor
notation. Calculate the current i and the
voltages vL, vC and vR versus frequency from 50Hz
to 200KHz.
VS VR VL VC
VR R I VL I(j wL) VC I/(jwC)
where
Therefore
VS I R jwL 1/(jwC)
w 2 p f
or
I VS / R jwL 1/(jwC)
VR VS R / R jwL 1/(jwC) VL VS (jwL)
/R jwL 1/(jwC) VC VS / (jwC) 1/R jwL
1/(jwC)
It follows
15
In terms of magnitude (amplitude), we have
mag(I) mag(VS) / vR2 (wL - 1/(wC))2
mag(VR) mag(VS) R / vR2 (wL - 1/(wC))2
mag(VL) mag(VS) w L / vR2 (wL - 1/(wC))2
mag(VC) mag(VS) / w C 1/vR2 (wL - 1/(wC))2
mag(IR) mag(VR) / R mag(IL) mag(VL) / (wL)
mag(IC) mag(VC) (wC)
16
Plot the magnitude or rms value of the calculated
currents iL, iC and iR versus frequency, and the
theoretical i obtained from KVL in phasor
notation. How are they related to each other?
Why? Explain. On another graph, plot the
magnitude or rms value of the voltages vS, vR ,
vC and vL versus frequency, and the
values obtained from KVL in phasor notation. On
this same graph, also plot the quantity vT
v(vR2 vL2 vC2 - vLvC). How is it related to
vS? Explain why.
Follow the example in the next slides for your
report. Use similar but different values for your
resistor R, inductor L , capacitor C and source
voltage vS.
17
Example Measurement R 100 W, L 470 mF C
470 nF, vS 2V (vSpp 4V, vSRMS 1.42 V).
Measured vS 2.05 V
Measured and Theoretical Data
18
Voltage vs. Frequency
19
Current vs. Frequency
20
LAB REPORT
Write a clearly legible Technical Report using
the guidelines suggested in the next slide.
Describe the measurements your team made on
the RL and RLC circuits used as template. See
Lab 1 for Report Guidelines!