ENGINEERING-43
RLC Series Circuits
Lab-15
Lab Data Sheet – ENGR-43 Lab-15
Lab Logistics
Experimenter:
Recorder:
Date:
Equipment Used (maker, model, and serial no. if available)
Directions
1. Check out:
 A DMM
 an Oscilloscope
 a Function/Signal Generator.
 Cables and Leads; include tw0 dual alligator-clip lead
2. Go to the side counter, collect a resistors, an inductor (a special case), a capacitor (a
special case), “bread board”, and leads required to construct the circuit shown in Figure 1.
3. Complete Table I
 See the Instructor to use the LCR meter to measure the actual value of the
 Capacitor, C
 Inductor, L
 Use the DMM in DC mode to measure the actual value of the Resistor, R
© Bruce Mayer, PE • Chabot College • 291237120 • Page 1
Figure 1 • RLC Series Circuit. Vs = 6V0° (12 Vpp), f per Table II, Table IV, Table V.
L = 100 mH, C = 22 nF, R = 2.5-4.1 kΩ (3.3 kΩ nominally).
Table I – Measure C, L, and R with The LCR-Meter, and DMM in the DC mode,
respectively

Digital-Meter Actual-Values
C=
L=
R=
4. Use the LCR meter values to calculate the “Center Frequency”, ωc (or fc), for this 2nd order
circuit. The Center frequency for this circuit is defined as that value of ω or f that results in
EQUAL REACTANCES for both the inductor and capacitor. Recall from the TextBook that
reactance is the magnitude of the impedance for a capacitor or inductor. Mathematically
ZC  jX C 
1
1
 XC 
jC
C
Z L  jX L  jL  X L  L
© Bruce Mayer, PE • Chabot College • 291237120 • Page 2
To find ωc Equate the |XC| and XL yielding
 cL 
and

1
c C
 c2 
1
LC
f c   c 2
Use the LCR Meter values for L & C to calculate fc
fc =
5. Use the DMM and Scope to make the Measurements and Calculations needed to complete
Table II
 Measure rms Quantities by DMM in AC Mode
 Using measured values of Vrms & Irms find:
 XL = VL,rms/IL,rms
 XC = −[VC,rms/IC,rms]
 From measured rms values Calculate L & C from the expressions for XL & XC. Recall
that:
 XL = VL,rms/IL,rms = L
 XC = −[VC,rms/IC,rms] = −1/(C)
6. Make the Measurements and Calculations needed to complete:
 Table III (Calculations only)
 Table IV
 Make Scope Measurements using the techniques from labs 16 & 17.
o Be sure to adjust the BOTH the FREQUENCY and APLITUDE upon any
frequency-change
 Table V
 Use the Scope CURSOR function to measure TIME Differences
7. Return all lab hardware to the “as-found” condition
Table II – Inductance and Capacitance Measurements and Calculation


Measure rms Quantities by DMM in AC Mode
Calculate XC and XL by the methods described in item Error! Reference source not
found. above
 For XL assume that the series resistance of the coil is negligible
Frequency, f
IT,rms
VC, rms
VL,rms
VR,rms
XC
XL
1 kHz
3.333 kHz
10 kHz
© Bruce Mayer, PE • Chabot College • 291237120 • Page 3
L calc
C calc
Avg =
Table III – Series RL Impedance Calculations



Use R from Table I
Use The Average Values for L and C from Table II
State ZTOTAL in Rectangular Form
Value Determination
R
XL
XC
ZTOTAL
Calculated @ 0.1 kHz
Calculated @ 0.4 kHz
Calculated @ 1.25 kHz
Calculated @ 2.5 kHz
Calculated @ 8 kHz
Calculated @ 25 kHz
Calculated @ 80 kHz
Table IV – Series RLC Potential Measurements Sweep. Vs = 12 Vpp


Use the Scope’s MATH function (CH1 – CH2) to Measure VC and VL as indicated in
Figure 2. Observe that VB is equal to VR.
Note whether voltage quantities are Peak-to-Peak or Amplitude measurements
Frequency, f
VC = VS -VA
VL = VA -VB
0.1 kHz
0.4 kHz
1.25 kHz
2.5 kHz
8 kHz
25 kHz
80 kHz
© Bruce Mayer, PE • Chabot College • 291237120 • Page 4
VR = V B
Figure 2 • RLC Series Circuit differential potential measurements. Circuit parameters the
same as Figure 1.
Table V – Series RLC Phase Angle Measurements and Calculations


As indicated in Figure 3 use the Scope to Measure the Phase Differences at nodes A&B
Relative to the BaseLine; VS = 6Vamplitude0°, , in terms of TIME at A&B
Convert the Phase-TIME differences, A,meas and B,meas to Phase-ANGLE differences,
A,meas and B,meas using the Signal Period, T, to determine the phase ANGLE, , in
DEGREES (°) relative to the base-line value for Vs:
   
LEAD 
360
 sec 
T sec 
 LAG 
Frequency, f
A,meas
B,meas
A,meas
0.1 kHz
0.4 kHz
1.25 kHz
2.5 kHz
8 kHz
25 kHz
80 kHz
© Bruce Mayer, PE • Chabot College • 291237120 • Page 5
B,meas
Figure 3 • RLC Series Circuit phase angle measurements. Circuit parameters the same
as Figure 1.
Table VI – Series RLC Phase Angle Voltage Divider Calculations and Comparisons


Use the reactance values in Table II and Table III, along with voltage-divider
methodology, to calculate the Phase Angle, , at A&B in DEGREES.
Use the measurements for  from Table V to determine the % for the Phase Angles.
o The CALCULATED values should serve as the BASELINE for the Δ%
calculation(s) as
 -% = 100x(meas – calc)/calc
Frequency, f
A,calc
B,calc
A-%
0.1 kHz
0.4 kHz
1.25 kHz
2.5 kHz
8 kHz
25 kHz
80 kHz
© Bruce Mayer, PE • Chabot College • 291237120 • Page 6
B-%
8. Use MATLAB or EXCEL to create two SemiLog plots of the data contained in the data
tables. In both plots the frequency, f, will be plotted on the Logarithmic scale
 Plot-1 from Table IV
 Independent variable = log(f)
 THREE dependent variables on the same plot: VC, VL , and VR
 Plot-2
 Independent variable = log(f)
 FOUR Dependent variables on the same plot: A,meas, B,meas, A,calc, B,calc
 Attach both plots to this lab report
 ANALYZE the trends shown in the plots, and comment on the physical CAUSE of the
observed trends
 HINT: Consider the Behavior of the Circuit in these extreme cases
o →0
o →∞
Run Notes/Comments
Print Date/Time = 29-May-16/03:59
© Bruce Mayer, PE • Chabot College • 291237120 • Page 7