Computer-aided Software Ac Circuit Analysis Simulation In Network Theorems 1k6pr
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MAPÚA UNIVERSITY School of EECE Intramuros, Manila Experiment #5 Computer-Aided Software AC Circuit Analysis Simulation in Network Theorems Dotimas, Winvel P.
Group No. 2 Date Submitted: February 21, 2018
EE103L-B6 Score Date Performed: February 14, 2018 Engr. Ezperanza E. Chua Instructor
Preliminary Data Sheet
Calculations:
Procedure: I.
Superposition Theorem a. Sources Operating at Same Frequencies i. Is the total response of the circuit when the two sources are activated (turned on) equal to the total response of the circuit by adding the individual responses of the circuit? If not, cite possible reason. 1. Yes, they are almost equal. ii. How do you combine the individual responses of the circuit? 1. 𝑭𝑹𝑴𝑺 = √(𝑭𝟏𝑹𝑴𝑺 )𝟐 + (𝑭𝟐𝑹𝑴𝑺 )𝟐 + (𝑭𝟑𝑹𝑴𝑺 )𝟐 + ⋯ b. Sources Operating at Different Frequencies i. To get the total response of the circuit with sources operating at different frequencies, can you combine the individual responses of the circuit vectorially? Justify your answer. 1. The phasor response can be added vectorially. But because we are dealing with purely resistive circuits in reality, we can add different frequency by adding the magnitude of each in vector addition.
II.
Thevenin’s and Norton’s Theorem
Interpretation of Results: During the experiment, we Superposition, Thevenin and Norton’s Theorem using AC circuit analysis with the aid of TinaPro. We know from previous experiments that the laws in dc network theorems also applies in ac networks except for resistances to which is replaced by impedances that are used in taking phasor sums instead of algebraic sum of voltages and currents. In Table 5.1, we the Superposition Theorem using Figure 5.1 as the ac network. In here, we have two sources, a current source set at 5 ARMS and a voltage source set at 10 VRMS, which operates at the same frequency at 60 Hz. After getting the simulated values, we then get its calculated values by getting the sum of the individual responses of the circuit when one source is turned off. In here, we get 213.37 mA, compared to the 208.57 mA we got earlier from the simulated values. We then further compute using mesh and nodal analysis of the same circuit and compare it against the total response of the circuit. In the next part, we have the same circuit but now operates at different frequencies in which the current source is given 60 Hz and the voltage source is given 50 Hz. We did the same procedure for getting the simulated values in which we get the reading when both sources are on and one reading each for when one source is off. The difference here is when getting the total response of the circuit, we cannot add them vectorially due to the sources having different frequencies, 2 2 2 instead we will use this formula: FRMS = √(𝐹1𝑅𝑀𝑆 + 𝐹2𝑅𝑀𝑆 + 𝐹3𝑅𝑀𝑆 + . . . ) in which it is
defined as a composite function. On the experiment, we simply get the square root of
the sum of the squared of each individual response when one source is turned off and the answer is like our simulated values which is 144.01 mA. Then for table 5.2, we followed figure 5.2 in which the circuit has now terminals a and b. We first get the simulated values of each Thevenin’ Equivalent Voltage and Norton’s equivalent current by plugging in to the terminals a voltmeter and ammeter, respectively. Then, we again confirm it through mesh and nodal analysis. After that, we can now get its Thevenin’s Equivalent Impedance through VTH / IN which has a value of 102.273 Ω (209.66V / 2.050A). Then we get another simulated value in which we will plug in the terminals a and b a 1 kΩ resistor, and calculate the load current and load voltage that it obtains through TinaPro. Then, for counter checking, we get the same values using mesh and nodal analysis.
Conclusion: In conclusion, we proved the theorem of Superposition, Thevenin and Norton through analysis of AC circuits using TinaPro. In superposition theorem, we have proved that in an AC circuit, the total response is the sum of the individual responses in which one of its source is turned off. But during our experiment, we have proven this only to be true when the sources are operating at the same frequency. However, when the sources have different frequencies, it is required to use a different formula in which we will now get the square root of the sum of the squared of each individual response when one source is turned 2 2 2 off or in formula: FRMS = √(𝐹1𝑅𝑀𝑆 + 𝐹2𝑅𝑀𝑆 + 𝐹3𝑅𝑀𝑆 + . . . ).
In Thevenin’s Theorem, we have proved in AC circuit that the complex circuit could be transformed in a simple Thevenin equivalent circuit in which it is the same as in Norton’s Theorem in which the complex circuit could be transformed into a simple Norton Equivalent circuit. Now, we could simply get its Thevenin’ Equivalent Voltage and Norton’s Equivalent current, enabling as to get the Thevenin’s equivalent impedance. Through this, we have verified both theorems with the resulting load current and load voltage to be in the same magnitude.
Final Data Sheet Table 5.1: SUPERPOSITION THEOREM SOURES OPERATING AT BASED ON SIMULATED VALUES SAME FREQUENCIES Current Source Voltage Source Ammeter Reading Voltmeter Reading (IL) (VL) mARms VRms On On 208.57 208.57 On
Off
203.42
203.42
Off
On
9.95
9.95
Calculated Values of Parameters Ammeter Reading (IL) mARms
Voltmeter Reading (VL) VRms
Total Response of the Circuit (Adding the Individual Response) MESH ANALYSIS
213.37
213.37
208.58
208.57
NODAL ANALYSIS
225.70
225.70
SOURCES OPERATING AT DIFFERENT FREQUENCIES Current Source Voltage Source
BASED ON SIMULATED VALUES Ammeter Reading (IL) mARms
Voltmeter Reading (VL) VRms
On
On
144.01
144.01
On
Off
143.84
143.84
Off
On
7.05
7.05
Calculated Values of Parameters Ammeter Reading (IL)
Voltmeter Reading (VL)
Total Response of the Circuit
mARms
VRms
144.01
144.01
Table 5.2: THEVENIN’S AND NORTON’S THEOREM Thevenin’s Equivalent Voltage (VTH) VRMS
Norton’s Equivalent Circuit (IN) mARms
Based on Simulated Values
209.66
2050
MESH ANALYSIS
204.48
2000
NODAL ANALYSIS
221.79
2169
Thevenin’s Equivalent Impedance (ZTH) Ω Based on Simulated Values ZTH= VTH / IN Based on Analytical Solution
102.273 Ω 102.24 Ω Calculated Values of Parameters
Based on Simulated Values
Load Current (IL) mARms 208.57
Load Voltage (VL) VRMS 208.57
MESH ANALYSIS
203.42
203.42
NODAL ANALYSIS
220.62
220.62
Group No. 2 Date Submitted: February 21, 2018
EE103L-B6 Score Date Performed: February 14, 2018 Engr. Ezperanza E. Chua Instructor
Preliminary Data Sheet
Calculations:
Procedure: I.
Superposition Theorem a. Sources Operating at Same Frequencies i. Is the total response of the circuit when the two sources are activated (turned on) equal to the total response of the circuit by adding the individual responses of the circuit? If not, cite possible reason. 1. Yes, they are almost equal. ii. How do you combine the individual responses of the circuit? 1. 𝑭𝑹𝑴𝑺 = √(𝑭𝟏𝑹𝑴𝑺 )𝟐 + (𝑭𝟐𝑹𝑴𝑺 )𝟐 + (𝑭𝟑𝑹𝑴𝑺 )𝟐 + ⋯ b. Sources Operating at Different Frequencies i. To get the total response of the circuit with sources operating at different frequencies, can you combine the individual responses of the circuit vectorially? Justify your answer. 1. The phasor response can be added vectorially. But because we are dealing with purely resistive circuits in reality, we can add different frequency by adding the magnitude of each in vector addition.
II.
Thevenin’s and Norton’s Theorem
Interpretation of Results: During the experiment, we Superposition, Thevenin and Norton’s Theorem using AC circuit analysis with the aid of TinaPro. We know from previous experiments that the laws in dc network theorems also applies in ac networks except for resistances to which is replaced by impedances that are used in taking phasor sums instead of algebraic sum of voltages and currents. In Table 5.1, we the Superposition Theorem using Figure 5.1 as the ac network. In here, we have two sources, a current source set at 5 ARMS and a voltage source set at 10 VRMS, which operates at the same frequency at 60 Hz. After getting the simulated values, we then get its calculated values by getting the sum of the individual responses of the circuit when one source is turned off. In here, we get 213.37 mA, compared to the 208.57 mA we got earlier from the simulated values. We then further compute using mesh and nodal analysis of the same circuit and compare it against the total response of the circuit. In the next part, we have the same circuit but now operates at different frequencies in which the current source is given 60 Hz and the voltage source is given 50 Hz. We did the same procedure for getting the simulated values in which we get the reading when both sources are on and one reading each for when one source is off. The difference here is when getting the total response of the circuit, we cannot add them vectorially due to the sources having different frequencies, 2 2 2 instead we will use this formula: FRMS = √(𝐹1𝑅𝑀𝑆 + 𝐹2𝑅𝑀𝑆 + 𝐹3𝑅𝑀𝑆 + . . . ) in which it is
defined as a composite function. On the experiment, we simply get the square root of
the sum of the squared of each individual response when one source is turned off and the answer is like our simulated values which is 144.01 mA. Then for table 5.2, we followed figure 5.2 in which the circuit has now terminals a and b. We first get the simulated values of each Thevenin’ Equivalent Voltage and Norton’s equivalent current by plugging in to the terminals a voltmeter and ammeter, respectively. Then, we again confirm it through mesh and nodal analysis. After that, we can now get its Thevenin’s Equivalent Impedance through VTH / IN which has a value of 102.273 Ω (209.66V / 2.050A). Then we get another simulated value in which we will plug in the terminals a and b a 1 kΩ resistor, and calculate the load current and load voltage that it obtains through TinaPro. Then, for counter checking, we get the same values using mesh and nodal analysis.
Conclusion: In conclusion, we proved the theorem of Superposition, Thevenin and Norton through analysis of AC circuits using TinaPro. In superposition theorem, we have proved that in an AC circuit, the total response is the sum of the individual responses in which one of its source is turned off. But during our experiment, we have proven this only to be true when the sources are operating at the same frequency. However, when the sources have different frequencies, it is required to use a different formula in which we will now get the square root of the sum of the squared of each individual response when one source is turned 2 2 2 off or in formula: FRMS = √(𝐹1𝑅𝑀𝑆 + 𝐹2𝑅𝑀𝑆 + 𝐹3𝑅𝑀𝑆 + . . . ).
In Thevenin’s Theorem, we have proved in AC circuit that the complex circuit could be transformed in a simple Thevenin equivalent circuit in which it is the same as in Norton’s Theorem in which the complex circuit could be transformed into a simple Norton Equivalent circuit. Now, we could simply get its Thevenin’ Equivalent Voltage and Norton’s Equivalent current, enabling as to get the Thevenin’s equivalent impedance. Through this, we have verified both theorems with the resulting load current and load voltage to be in the same magnitude.
Final Data Sheet Table 5.1: SUPERPOSITION THEOREM SOURES OPERATING AT BASED ON SIMULATED VALUES SAME FREQUENCIES Current Source Voltage Source Ammeter Reading Voltmeter Reading (IL) (VL) mARms VRms On On 208.57 208.57 On
Off
203.42
203.42
Off
On
9.95
9.95
Calculated Values of Parameters Ammeter Reading (IL) mARms
Voltmeter Reading (VL) VRms
Total Response of the Circuit (Adding the Individual Response) MESH ANALYSIS
213.37
213.37
208.58
208.57
NODAL ANALYSIS
225.70
225.70
SOURCES OPERATING AT DIFFERENT FREQUENCIES Current Source Voltage Source
BASED ON SIMULATED VALUES Ammeter Reading (IL) mARms
Voltmeter Reading (VL) VRms
On
On
144.01
144.01
On
Off
143.84
143.84
Off
On
7.05
7.05
Calculated Values of Parameters Ammeter Reading (IL)
Voltmeter Reading (VL)
Total Response of the Circuit
mARms
VRms
144.01
144.01
Table 5.2: THEVENIN’S AND NORTON’S THEOREM Thevenin’s Equivalent Voltage (VTH) VRMS
Norton’s Equivalent Circuit (IN) mARms
Based on Simulated Values
209.66
2050
MESH ANALYSIS
204.48
2000
NODAL ANALYSIS
221.79
2169
Thevenin’s Equivalent Impedance (ZTH) Ω Based on Simulated Values ZTH= VTH / IN Based on Analytical Solution
102.273 Ω 102.24 Ω Calculated Values of Parameters
Based on Simulated Values
Load Current (IL) mARms 208.57
Load Voltage (VL) VRMS 208.57
MESH ANALYSIS
203.42
203.42
NODAL ANALYSIS
220.62
220.62
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