Analysis of Electric Circuits Using Matlab, Scilab, and Multisim

Abstract

This paper presents the analysis of electric circuits using specialized computational and simulation software viz; MATLAB, Scilab, and MULTISIM. MATLAB and Scilab programming can be used for the numerical analysis in electrical engineering. In conjunction with this, it is presented how to find solutions for problems in electric circuits using the simulation software called MULTISIM, Electronics Workbench, and the advantages of introducing it in electrical engineering education. This enhances the interest of students in circuit analysis and also creates opportunities for circuit design and further examinations.

Examples for verification and visualization of solving problems in DC and AC circuits are exposed in this paper.

Introduction

The strategy of the analysis of an electric circuit is to design, create, and solve for different parameters of the circuit. Without the knowledge of mathematics, it is not practical to solve electrical circuit problems. In an electric circuit the study and analysis of various electrical quantities, especially the voltages and currents, are involved. This is known as circuit analysis.

To simplify electrical engineering problems, various laws and tools have been introduced such as Ohm’s Law, Kirchhoff’s Laws, Series parallel reduction, mesh analysis, nodal analysis, network theorems, etc. Conventional methods used to solve these problems include manual solving or solving with a calculator. But the analysis of the circuit becomes more complex and error-prone when the number of nodes or the number of loops in the circuit increases.

Using mathematical programming software such as MATLAB makes the analysis of complex electrical circuits easier which creates new opportunities for circuit analysis.

The name MATLAB stands for MATrix LABoratory. Originally MATLAB was written to provide easy access to matrix software developed by the LINPACK and EISPACK projects. MATLAB is a computational software that provides a conceptual approach for designing and solving problems in Electrical Circuits. In the MATLAB language, re-useable programs can be written to find the solution. When MATLAB is used, a large number of mathematical equations, linear or non-linear, can be solved effectively without any error. This allows the analysis of electrical circuits using MATLAB by applying a system of Kirchhoff’s laws equations. MATLAB has embedded software called SIMULINK which provides an essential way to design, simulate, and analyze Electrical Systems.

Analysis of Electric circuits can also be performed using the computational software, Scilab. Scilab is free and open source software for performing numerical calculations. It provides a simple and powerful computational programming environment for engineering and scientific analysis. Similar to MATLAB, Scilab is also associated with a large collection of numerical functions and algorithms including many aspects of scientific problems. It makes Scilab an efficient tool for solving complex electrical problems. To perform graphical simulation and modeling, Scilab involves a toolbox called Xcos.

There are some additional advantages when the analysis of electric circuits is realized virtually using the programming environment MULTISIM, Electronics Workbench. MULTISIM is a simulation application of National Instruments Circuit Design Suite. MULTISIM has a very simple and user-friendly interface, rich library of elements, including virtual measuring tools for visualization of the behavior of a circuit – multimeters, ammeters, voltmeters, watt meters and oscilloscopes. MULTISIM turns our computer into a laboratory environment for modelling and analyzing electrical engineering systems.

Circuit Analysis

An electric circuit can be analyzed mathematically and virtually:

Mathematical Analysis: For analyzing the given electric circuit, the system of equations derived by applying Kirchhoff’s laws in the circuit is entered in the programming environment of MATLAB or Scilab. After the calculation of currents or voltages calculation, the power balance can be checked to verify the correctness of the solution. As working in MATLAB or Scilab students use a pre-developed working program that can be edited easily.

Virtual Analysis: The circuit to be analyzed is plotted in the circuit window of MULTISIM. Currents, voltages, or powers can be measured by connecting meters to the circuit diagram. In the case of AC circuit analysis, voltage waveforms can be plotted and phase shift can be measured by including two- or four-channel oscilloscopes in the circuit.

Analysis of DC Circuits

A DC circuit is shown in Fig. 1. The circuit has to be analyzed and all the branch currents should be calculated.

Given parameters are, R1= 4Ω, R2= 20 Ω, R3= 5 Ω, R4= 10 Ω, R5= 15 Ω, R6= 12 Ω, R7= 8 Ω, R8= 15 Ω, R9= 25 Ω

V1= 24V, V2= 12V and I= 10A.

In order to solve this problem, Kirchhoff’s Laws can be used.

By applying Kirchhoff’s Voltage Law to Loop 1,

V1-I1R1- I2R2 = 0V

I1R1+ I2R2 = V1

4I1+ 20I2= 24V

By applying Kirchhoff’s Voltage Law to Loop 2,

I2R2- I3R3- I4R4- I9R9 = 0V

20I2- 5I3- 10I4- 25I9 = 0V

By applying Kirchhoff’s Voltage Law to Loop 3,

I4R4+ I5R5- I6R6+ I8R8 = 0V

10I4+ 15I5- 12I6+ 15I8 = 0V

By applying Kirchhoff’s Voltage Law to Loop 4,

I6R6+ I7R7- V2 = 0V

I6R6+ I7R7= V2

12I6+ 8I7= 12V

By applying Kirchhoff’s Current Law at Node 1,

I1-I2-I3- I= 0

I1-I2-I3 = I

I1-I2-I3 = 10A

By applying Kirchhoff’s Current Law at Node 2,

I3- I4+ I5= 0

By applying Kirchhoff’s Current Law at Node 3,

I-I5-I6+ I7= 0

I5+I6- I7= I

I5+I6- I7= 10A

By applying Kirchhoff’s Current Law at Node 4,

I6- I7+ I8= 0

By applying Kirchhoff’s Current Law at Node 5,

I4- I8- I9= 0

The above set of simultaneous linear equations can be written in matrix form.

By solving the equations, the branch currents can be calculated as follows.

I1= 3.066A I2= 0.587A I3= -7.521A,

I4= -1.262A I5= 5.259A I6= 2.096A,

I7= -1.644A I8= -3.741A I9= 2.471A.

Analysis of AC Circuits

The circuit has to be analyzed and all the branch currents should be calculated. Given parameters are, R1= 10Ω, R2= 15 Ω, R3= 30 Ω, L1= 40mH, L2= 10mH and C= 50µF. Maximum value of supply voltage, Vmax= 20V. The supply frequency is 120 Hz.

RMS value of supply voltage,

Vrms=14.14V

Inductive reactances,

XL1= 2ΠfL1

= 2x 3.14x 120x 40m= 30.144Ω

XL2= 2ΠfL2

= 2x 3.14x 120x 10m= 7.536 Ω

Capacitive reactance,

XC= 26.539Ω

Z1=R1+jXL2 = (10+j7.536) Ω

Z2= R2+jXL1= (15+j30.144) Ω

Z3= R3-jXC= (30-j26.539) Ω

Total impedance,

ZT= Z1+

= (38.496+ j16.506) Ω

Total supply current,

I1= V/ZT

= (14.14+ j0)/ (38.496+j16.506)

= (0.310-j0.133) A= 0.337 -23.21º A

Using Current divider rule,

I2= I1

= (0.106- j0.28) A= 0.299 -69.30º A

I3= I1

= (0.205+ j0.147) A= 0.252 35.74º A

Circuit Analysis using MULTISIM

The AC circuit to be analyzed is plotted on the workspace of MULTISIM as shown in the Fig. 16(a). Multimeters are connected in series with each branch to measure the branch currents. In order to plot the alternating waveforms of branch currents, a four channel oscilloscope is connected. We know that an oscilloscope displays only voltage waveforms. To display the current waveforms, resistor connected in each branch is replaced with series combination of two resistors as shown in the fig. One of the resistors in each branch should be given a value of 1Ω.

R1= Ra+ Rb, R2= Rc+ Rd and R3= Re+ Rf

Rb = Rd = Rf =1Ω

Now the voltage across the resistor Rb will be equal to the branch current i1 in magnitude but phase shifted by 180º. The voltage across the resistor Rd will be equal to the branch current i2 in both magnitude and phase. Similarly the voltage measured across the Rf will be equal to the branch current i3 in both magnitude and phase.

The time period of the signals measured by the oscilloscope is 8.339ms.To calculate the phase angles of the branch currents; the zero crossing points of each waveform can be examined. The magnitude of branch current i1 is zero at 8.886ms which corresponds to -23.20º. Thus the phase angle of branch current i1 is -23.20º. From Fig. 17(b), the magnitude of branch current i2 is zero at 9.958ms which corresponds to -69.30º. Thus the phase angle of branch current i1 is -69.30º. From Fig. 17(c), the magnitude of branch current i3 is zero at 7.536ms which corresponds to 35.75º. Thus the phase angle of branch current i1 is 35.75º.

Conclusion

The analysis of electric circuits using computational and simulation software viz; MATLAB, MULTISIM and Scilab is presented in this paper. Analysis can be performed by applying the main laws and theorems in electrical engineering. Combining the benefits of mathematical and virtual analysis, the design and analysis of electric circuits can be made more easy and interesting. The suggested techniques can also be used for the analysis of the electronic circuits. Compared to conventional methods used to solve the problems of electric circuits, MULTISIM is less error- prone and provides faster solutions.

Mathematically and virtually, it is very easy to change the parameters of different circuit elements, the frequency of the source, the type of the sources, etc. Thus, the programmer is able to recheck solutions for different circuit conditions and find the interrelations between the changes of parameters of the circuit. The solutions obtained using the presented approach can be used for more effective delivery of online classes and courses. The presented software can be used for the analysis of coupled circuits, resonant circuits, three-phase circuits, transient response, etc.