Introduction
This laboratory is about the experimental testing, simulation, and analysis of RC and RLC circuits. The magnitude and phase of these circuits are measured accordingly. Theoretical phasor diagrams will be developed with respect to the circuits and are analyzed correspondingly. The three sets of magnitude and phase values (theoretical, simulated, and experimental) are compared and analyzed.
Purpose of the Experiment
The purpose of this experiment is to be able to measure the magnitude and phase difference of the input and output of sinusoidal circuits. The first circuit is a series RC circuit; the second circuit is a two-loop RLC network. These circuits will be analyzed in theory, simulation, and experimentation.
Equipment and Materials Used
The equipment and component values are listed below:
Function generator
Oscilloscope
Digital Multimeter
MULTISIM
25 mH Inductor
0.1 µF Capacitor
1 kΩ and 2.4 kΩ Resistors
MULTISIM is the software used for simulation of the two circuits. All the others in the list are used in the experimental setup of this laboratory.
Procedure
PART A
The following image shows the circuit diagram of the series RC circuit.
First, this circuit is designed and simulated in MULTISIM. The resistor voltage VR and the capacitor voltage VC are measured given a 10Vp-p 1 kHz input. Also, the magnitude and phase are measured using the input voltage Vin as reference.
After simulation, the same circuit is tested in hardware. The function generator is set to produce a 10Vp-p 1 kHz input voltage. The oscilloscope is used to measure the output and monitor the input of the circuit. The magnitude and phase of both capacitor and resistor are measured. In measuring the magnitude and phase of the resistor, the MATH function of the oscilloscope is used.
After finding the magnitude and phase, a phasor diagram is developed containing the relevant voltages. Then, an AC sweep from 1Hz to 50 kHz is generated to display the frequency response of the system.
Finally, the theoretical, simulated, and experimental values are compared with each other and analyzed.
PART B
The following image shows the circuit diagram of the two-loop RLC network circuit.
First, this circuit is designed and simulated in MULTISIM. The resistor voltage VR and the capacitor voltage VC (which is also equal to inductor voltage VL) are measured given a 10Vp-p 1 kHz input. Also, the magnitude and phase are measured using the input voltage Vin as reference.
After simulation, the same circuit is tested in hardware. The function generator is set to produce a 10Vp-p 1 kHz input voltage. The oscilloscope is used to measure the output and monitor the input of the circuit. The magnitude and phase of both capacitor and resistor are measured. In measuring the magnitude and phase of the resistor, the MATH function of the oscilloscope is used.
After finding the magnitude and phase, a phasor diagram is developed containing the relevant voltages. Then, an AC sweep from 1Hz to 50 kHz is generated to display the frequency response of the system.
Finally, the theoretical, simulated, and experimental values are compared with each other and analyzed.
Results
Part A results are displayed in table 1.
An AC sweep of the circuit for frequencies 1 Hz to 50 kHz is displayed in the next figure.
Part B results are displayed in table 2.
An AC sweep of the circuit for frequencies 1 Hz to 50 kHz is displayed in the next figure.
Analysis and Discussion
The percentage errors between the respective theoretical and experimental values are all less than 8%. This value can be considered as accurate as far as this experiment is concerned. Especially for Part B, the percentage errors are all less than 1.5%. The value obtained from the RLC circuit are more accurate compared to the values obtained from the RC circuit. The results of this experiment can be considered as highly accurate.
The AC sweep plots further confirm the magnitude and phase values of the two circuits.
