# Rad in deg matlab torrent

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It is recommended that the reader work through and experiment with the examples at a computer while reading Chapters 1, 2, and 3. Part II consists of Chapters 4 to 8. The topics covered in Part II are dc analysis, transient analysis, alternating current analysis, and Fourier analysis. In addition, two-port networks are covered.

I have briefly covered the underlying theory and concepts, not with the aim of writing a textbook on circuit analysis and electronics. The topics discussed in this part are diodes, semiconductor physics, operational amplifiers and transistor circuits. Each chapter has its own bibliography and exercises. Text Diskette Since the text contains a large number of examples that illustrate electronics and circuit analysis principles and applications with MATLAB, a diskette is included that contains all the examples in the book.

The reader can run the examples without having to enter the commands. The examples can also be modified to suit the needs of the reader. Acknowledgments I appreciate the suggestions and comments from a number of reviewers including Dr. Murari Kejariwal, Dr. Reginald Perry, Dr. Richard Wilkins, Mr. Warsame Ali, Mr. Anowarul Huq and Mr. John Abbey. Their frank and positive criticisms led to considerable improvement of this work. I am grateful to Mr. Carl Easton and Mr.

Url Woods for drawing the circuit diagrams found in the text. I thank Ms. Debbie Hawkins and Cheryl Wright who typed several parts of this book. I am appreciative of Ms. Judith Hansen for her editing services. Special thanks go Ms.

Nora Konopka, at CRC Press, who took an early interest in this book and offered me any assistance I needed to get it completed. Special thanks go to the students who used various drafts of this book and provided useful comments. A final note of gratitude goes to my wife, Christine N. Okyere, who encouraged me to finish the book in record time.

With equanimity and understanding, she stood by me during the endless hours I spent writing. MATLAB is a high-level language whose basic data type is a matrix that does not require dimensioning. All computations are performed in complex-valued dou- ble precision arithmetic to guarantee high accuracy.

Some examples of MATLAB toolboxes are control system, signal processing, neural network, image processing, and system identification. The toolboxes consist of functions that can be used to perform computations in a specific domain. Scalars are thought of as a 1-by-1 matrix. Vectors are considered as matrices with a row or column. Storage of data and variables is allocated automatically once the data and variables are used.

This will be discussed in Section 1. The end of each row, with the exception of the last row, is indicated by a semicolon. Thus b and B are not the same variable. If you do not want MATLAB to be case sensitive, you can use the command casesen off To obtain the size of a specific variable, type size. The first is the number of rows in A, the second the number of columns in A.

To find the list of variables that have been used in a MATLAB session, type the command whos There will be a display of variable names and dimensions. Table 1. Matrices of the same dimension may be subtracted or added. In this particular case, the scalar is added to or subtracted from all the elements of an- other matrix.

Examples are given in Table 1. Thus, the operators. For addition and subtraction, the array and matrix op- erations are the same. If A1 and B1 are matrices of the same dimensions, then A1. The expressions A1. Complex numbers are entered using function i or j. It can be used 1 to create vectors and matrices, 2 to specify sub-matrices and vectors, and 3 to perform iterations. For example, t2 4 is the fourth element of vector t2.

Also, for matrix t3, t3 2,3 denotes the entry in the second row and third column. Using the co- lon as one of the subscripts denotes all of the corresponding row or column. For example, t3 :,4 is the fourth column of matrix t3. MATLAB is also capable of processing a sequence of commands that are stored in files with extension m.

M-files can either be script files or function files. Both script and function files contain a sequence of commands. However, function files take arguments and return values. With script file written using a text editor or word processor, the file can be invoked by entering the name of the m-file, without the extension. Statements in a script file operate globally on the workspace data.

Normally, when m-files are executing, the commands are not displayed on screen. To illustrate the use of script file, a script file will be written to simplify the following complex valued expression z. Example 1. It is included in the disk that accompanies this book. Variables defined and manipulated inside a function file are local to the func- tion, and they do not operate globally on the workspace.

However, arguments may be passed into and out of a function file. Suppose we want to find the equivalent resistance of the series connected resis- tors 10, 20, 15, 16 and 5 ohms. This is followed by an output argument, an equal sign and the function name. This informa- tion is displayed if help is requested for the function name.

The mean and variance are computed with the function. MathWorks, Inc. Biran, A. Etter, D. In general, the equivalent resistance of resistors R1 , R2 , R3 , Use the function to compute the area of triangles with the lengths: a 56, 27 and 43 b 5, 12 and In addition, there are commands for controlling the screen and scaling. Table 2. There are three variations of the plot command. If x is a matrix, each column will be plotted as a separate curve on the same graph. If x and y are vectors of the same length, then the command plot x, y plots the elements of x x-axis versus the elements of y y-axis.

The plot is shown in Figure 2. To plot multiple curves on a single graph, one can use the plot command with multiple arguments, such as plot x1, y1, x2, y2, x3, y3, Each x-y pair is graphed, generating multiple lines on the plot.

The above plot command allows vectors of different lengths to be displayed on the same graph. Also, the plot remains as the current plot until another plot is generated; in which case, the old plot is erased. The hold command holds the current plot on the screen, and inhibits erasure and rescaling. Subsequent plot commands will overplot on the original curves.

The hold command remains in effect until the command is issued again. When a graph is drawn, one can add a grid, a title, a label and x- and y-axes to the graph. The commands for grid, title, x-axis label, and y-axis label are grid grid lines , title graph title , xlabel x-axis label , and ylabel y-axis label , respectively. For example, Figure 2. Figure 2. Multiple text commands can be used. If the default line-types used for graphing are not satisfactory, various symbols may be selected.

Other print types are shown in Table 2. Other colors that can be used are shown in Table 2. If z is a complex vector, then plot z is equivalent to plot real z , imag z. The following example shows the use of the plot, title, xlabel, ylabel and text functions. Example 2.

The use of the above plot commands is similar to those of the plot command discussed in the previous section. The description of these commands are as follows: loglog x, y - generates a plot of log10 x versus log10 y semilogx x, y - generates a plot of log10 x versus linear axis of y semilogy x, y - generates a plot of linear axis of x versus log10 y It should be noted that since the logarithm of negative numbers and zero does not exist, the data to be plotted on the semi-log axes or log-log axes should not contain zero or negative values.

Draw a graph of gain versus frequency using a logarithmic scale for the frequency and a linear scale for the gain. The polar plot command is used in the following example. The hardware configuration an operator is using will either display both windows simultaneously or one at a time. The following commands can be used to select and clear the windows: shg - shows graph window any key - brings back command window clc - clears command window clg - clears graph window home - home command cursor The graph window can be partitioned into multiple windows.

The subplot command allows one to split the graph window into two subdivisions or four subdivisions. Two sub-windows can be arranged either top or bottom or left or right. A four-window partition will have two sub-windows on top and two sub- windows on the bottom. The general form of the subplot command is subplot i j k The digits i and j specify that the graph window is to be split into an i-by- j th grid of smaller windows.

The digit k specifies the k window for the current plot. The sub-windows are numbered from left to right, top to bottom. The plots are shown in Figure 2. The coordinates of points on the graph window can be obtained using the ginput command. Pressing the return key terminates the input. The points are stored in vectors x and y. Data points are entered by pressing a mouse button or any key on the keyboard except return key. Assume a radius from. The index takes on the elemental values in the matrix expression.

Usually, the ex- pression is something like m:n or m:i:n where m is the beginning value, n the ending value, and i is the increment. Suppose we would like to find the squares of all the integers starting from 1 to Suppose we want to fill by matrix, b, with an element value equal to unity, the following statements can be used to perform the operation. The following program illustrates the use of a for loop. Example 3. Use the values to plot x t versus y t. Table 3. These are shown in Table 3.

However, if the logical expression is false, the statement group 1 is bypassed and the program control jumps to the statement that follows the end statement. If the logical expression 2 is also true, the statement groups 1 and 2 will be executed before executing statement group 3.

If logical expression 1 is false, we jump to statement group 4 without executing state- ment groups 1, 2 and 3. However, if logical expression 1 is false, statement group 2 is executed. The general form of the if-elseif statement is if logical expression 1 statement group1 elseif logical expression 2 statement group2 elseif logical expression 3 statement group 3 elseif logical expression 4 statement group 4 end A statement group is executed provided the logical expression above it is true.

For example, if logical expression 1 is true, then statement group 1 is executed. If logical expression 1 is false and logical expression 2 is true, then statement group 2 will be executed. If logical expressions 1, 2 and 3 are false and logical expression 4 is true, then statement group 4 will be executed.

If none of the logical expressions is true, then statement groups 1, 2, 3 and 4 will not be exe- cuted. Only three elseif statements are used in the above example. More elseif statements may be used if the application requires them. The one that is satisfied is exe- cuted. If the logical expressions 1, 2, 3 and 4 are false, then statement group 5 is executed.

Test the program by using an analog signal with the following amplitudes: At the end of exe- cuting the statement group 1, the expression 1 is retested. If expression 1 is still true, the statement group 1 is again executed. However, if expression 1 is false, the program exits the while loop and executes statement group 2.

The following example illustrates the use of the while loop. Brief descriptions of these commands are shown in Table 3. Press- ing any key cause resumption of program execution. Break The break command may be used to terminate the execution of for and while loops. The break command is useful in exiting a loop when an error condition is detected.

Disp The disp command displays a matrix without printing its name. It can also be used to display a text string. Another way of displaying matrix x is to type its name. The echo command allows commands to be viewed as they execute. The echo can be enabled or disabled. Format The format controls the format of an output.

Format compact suppresses line-feeds that appear between matrix dis- plays, thus allowing more lines of information to be seen on the screen. Format compact and format loose do not affect the numeric format. The format for printing the matrix can be specified, and line feed can also be specified. The user can then type an expression such as [10 15 30 25]; The variable r will be assigned a vector [10 15 30 25].

If the user strikes the return key, without entering an input, an empty matrix will be assigned to r. When the word keyboard is placed in an m-file, execution of the m-file stops when the word keyboard is encountered. The keyboard command may be used to examine or change a vari- able or may be used as a tool for debugging m-files.

The execution of the m- file resumes upon pressing any key. The general forms of the pause command are pause pause n Pause stops the execution of m-files until a key is pressed. Pause n stops the execution of m-files for n seconds before continuing. The pause command can be used to stop m-files temporarily when plotting commands are encountered during program execution. If pause is not used, the graphics are momentarily visible. Print out the sum and the number of terms needed to just exceed the sum of 1.

Print out the results. In nodal analysis, if there are n nodes in a circuit, and we select a reference node, the other nodes can be numbered from V1 through Vn With one node selected as the refer- ence node, there will be n-1 independent equations. Equation 4. Example 4. The technique uses Kir- choff voltage law KVL to write a set of independent simultaneous equations.

The Kirchoff voltage law states that the algebraic sum of all the voltages around any closed path in a circuit equals zero. In loop analysis, we want to obtain current from a set of simultaneous equa- tions. The latter equations are easily set up if the circuit can be drawn in pla- nar fashion.

This implies that a set of simultaneous equations can be obtained if the circuit can be redrawn without crossovers. For a planar circuit with n-meshes, the KVL can be used to write equations for each mesh that does not contain a dependent or independent current source. In are the unknown currents for meshes 1 through n. Z11, Z22, …, Znn are the impedance for each mesh through which indi- vidual current flows.

Zij, j i denote mutual impedance. In addition, find the power supplied by the volt voltage source. The circuit is shown in Figure 4. On the other hand, when R L approaches infinity, the voltage across the load is maximum, but the power dissipation is zero. MATLAB can be used to observe the voltage across and power dissipation of the load as functions of load resistance value.

Ex- ample 4. Before presenting an example on the maximum power transfer theorem, let us discuss the MATLAB functions diff and find. The find function determines the indices of the nonzero elements of a vector or matrix. The diff and find are used in the following example to find the value of resis- tance at which the maximum power transfer occurs. Figure 4. Gottling, J. Johnson, D. Dorf, R. Plot the power dissipation with respect to the variation in RL. What is the maximum power dissipated by R L?

What is the value of R L needed for maximum power dissipation? What is the power supplied by the source? R C Vo t Figure 5. To obtain the voltage across a charging capacitor, let us consider Figure 5. Example 5. Figure 5. The plots should start from zero seconds and end at 1. After the 1 s delay, the switch moved from position b to position c, where it remained indefinitely. Sketch the current flowing through the inductor versus time.

Table 5. From the RLC circuit, we write differential equations by using network analysis tools. The differential equations are converted into algebraic equations using the Laplace transform. The unknown current or voltage is then solved in the s-domain. By using an inverse Laplace transform, the solution can be expressed in the time domain. We will illustrate this method using Example 5. The later method i can be used to analyze and synthesize control systems, ii can be applied to time-varying and nonlinear systems, iii is suitable for digital and computer solution and iv can be used to develop the general system characteristics.

A state of a system is a minimal set of variables chosen such that if their values are known at the time t, and all inputs are known for times greater than t 1 , one can calculate the output of the system for times greater than t 1. This suggests the following guidelines for the selection of acceptable state variables for RLC circuits: 1. Currents associated with inductors are state variables. Voltages associated with capacitors are state variables.

Currents or voltages associated with resistors do not specify independent state variables. When closed loops of capacitors or junctions of inductors exist in a circuit, the state variables chosen according to rules 1 and 2 are not independent. Consider the circuit shown in Figure 5. These are described in the following section. The ode23 function integrates a system of ordinary differential equations using second- and third-order Runge- Kutta formulas; the ode45 function uses fourth- and fifth-order Runge-Kutta integration equations.

The function must have 2 input arguments, scalar t time and column vector x state and the. It specifies the desired accuracy of the solution. Solution From Equation 5. From the two plots, we can see that the two results are identical. Compare the numerical solution to the analytical solution obtained from Example 5.

Solution From Example 5. Solution Using the element values and Equations 5. Nilsson, J. Vlach, J. Meader, D. The resistance values are in ohms. The initial energy in the storage elements is zero. Assume that the initial voltage across each capacitor is zero. Numerical integration is used to obtain the rms value, average power and quadrature power.

Three-phase circuits are analyzed by converting the circuits into the frequency domain and by using the Kirchoff voltage and current laws. The un- known voltages and currents are solved using matrix techniques. Given a network function or transfer function, MATLAB has functions that can be used to i obtain the poles and zeros, ii perform partial fraction expan- sion, and iii evaluate the transfer function at specific frequencies.

The quad8 function uses an adaptive, recursive Newton Cutes 8 panel rule. The iteration continues until the rela- tive error is less than tol. The default value is 1. If the trace is nonzero, a graph is plotted. The default value is zero. Example 6. Determine the average power, rms value of v t and the power factor using a analytical solution and b numerical so- lution. This normally involves solving differential equations.

By transforming the differen- tial equations into algebraic equations using phasors or complex frequency representation, the analysis can be simplified. Network analysis laws, theorems, and rules are used to solve for unknown currents and voltages in the frequency domain. The solution is then converted into the time domain using inverse phasor transfor- mation. For example, Figure 6. Solution Using nodal analysis, we obtain the following equations. The resulting circuit is shown in Figure 6.

The impedances are in ohms. The basic structure of a three-phase system consists of a three-phase voltage source connected to a three-phase load through transformers and transmission lines. The three-phase voltage source can be wye- or delta-connected. Also the three-phase load can be delta- or wye-connected. Figure 6. The method of symmetrical components can be used to ana- lyze unbalanced three-phase systems. This is illustrated by the following ex- ample. Its complex frequency representation is also shown.

From equation 6. The gen- eral form of polyval is polyval p, x 6. It is repeated here. As the resistance is decreased from 10, to Ohms, the bandwidth of the frequency response decreases and the quality factor of the circuit increases. Johnson, J. Compare your result with that obtained in part a. Plot the polynomial over the appropriate interval to verify the roots location.

The describing equations for the various two-port network represen- tations are given. Also, I 2 and V2 are output current and voltage, respectively. It is assumed that the linear two-port circuit contains no independent sources of energy and that the circuit is initially at rest no stored energy. Furthermore, any controlled sources within the lin- ear two-port circuit cannot depend on variables that are outside the circuit.

The following exam- ple shows a technique for finding the z-parameters of a simple circuit. Example 7. The following two exam- ples show how to obtain the y-parameters of simple circuits. Find its y- parameters.

The h-parameters of a bipolar junction transistor are determined in the following example. The negative of I 2 is used to allow the current to enter the load at the receiving end. Examples 7. These are shown in Figure 7. Figure 7. Z1 Y2 Figure 7. The resistance values are in Ohms. From Example 7. A termi- nated two-port network is shown in Figure 7. Z L is the load impedance. V2 b Obtain the expression for. Topics covered are Fou- rier series expansion, Fourier transform, discrete Fourier transform, and fast Fourier transform.

The term in 2 Equation 8. Equation 8. Figure 8. The coeffi- cient cn is related to the coefficients a n and bn of Equations 8. It provides information on the amplitude spectral compo- nents of g t. Example 8. If g t is continuous and non- periodic, then G f will be continuous and periodic. The periodicity of the time-domain signal forces the spectrum to be dis- crete.

It is also the total number frequency sequence values in G[ k ]. T is the time interval between two consecutive samples of the input sequence g[ n]. F is the frequency interval between two consecutive samples of the output sequence G[ k ]. This means that T should be less than the reciprocal of 2 f H , where f H is the highest significant frequency component in the continuous time signal g t from which the sequence g[ n] was obtained.

Several fast DFT algorithms require N to be an integer power of 2. A discrete-time function will have a periodic spectrum. In DFT, both the time function and frequency functions are periodic. In general, if the time-sequence is real-valued, then the DFT will have real components which are even and imaginary components that are odd.

Simi- larly, for an imaginary valued time sequence, the DFT values will have an odd real component and an even imaginary component. The FFT can be used to a obtain the power spectrum of a signal, b do digi- tal filtering, and c obtain the correlation between two signals. The vector x is truncated or zeros are added to N, if necessary. The sampling interval is ts. Its default value is 1. The spectra are plotted versus the digital frequency F.

Solution a From Equation 8. With the sampling interval being 0. The duration of g t is 0. The am- plitude of the noise and the sinusoidal signal can be changed to observe their effects on the spectrum. Math Works Inc. Using the FFT algorithm, generate and plot the frequency content of g t. Assume a sampling rate of Hz. Find the power spectrum. Diode circuit analysis techniques will be discussed. The electronic symbol of a diode is shown in Figure 9. Ideally, the diode conducts current in one direction.

The cur- rent versus voltage characteristics of an ideal diode are shown in Figure 9. The characteristic is divided into three regions: forward-biased, reversed- biased, and the breakdown. If we assume that the voltage across the diode is greater than 0. The following example illustrates how to find n and I S from an experimental data. Example 9. Figure 9. The thermal voltage is directly propor- tional to temperature. This is expressed in Equation 9.

This model contains a variant subsystem with two versions of the boost converter model:. Boost converter circuit constructed using electrical power components. The parameters of the circuit components are based on [1]. Boost converter block configured to have the same parameters as the boost converter circuit.

For more information on this block, see Boost Converter Simscape Electrical. To design a controller for the boost converter, you must first determine the steady-state operating point at which you want the converter to operate. For this example, use an operating point estimated from a simulation snapshot.

To find the operating point, use the Model Linearizer app. In the Enter snapshot times to linearize dialog box, in the Simulation snapshot times field, enter 0. The software simulates the model and creates an operating point that contains the input and state values of the model at the specified snapshot time.

To do so, double-click the controller block. Then, specify the following controller parameters:. Other settings such as the controller initial conditions, output saturation levels, and anti-windup configuration. For this example, use the current controller configuration; that is, a discrete-time parallel-form PID controller without anti-windup.

Using PID Tuner , you can tune the parameters of the following controller blocks:. PID Controller. Discrete PID Controller. When PID Tuner first opens, it attempts to linearize the model. Due to the PWM components, the model analytically linearizes to zero. For plant identification, you must specify a finite value for the Simulink model stop time. Onset Lag of 0. Stop Time of 0. Offset of 0. For this model, the offset corresponds to the value of the state in the Computational delay block.

If you do not have such a corresponding state in your model, you can attach a scope to the output of the PID Controller block and simulate the model at the computed operating point. To specify the step amplitude, click. Then, in the Step Input Specifications dialog box, in the Amplitude field, type 0.

This value is large enough to sufficiently excite the system and small enough to prevent the controller from entering discontinuous-current mode. Click Run Simulation. The software runs two simulations, an offset response without the input signal and an input response with the input signal. The difference between these responses is the output response. In the Plant Identification figure, the Input plot shows the specified input signal, and the Output plot shows the corresponding output response.

On the Plant Identification tab, select the plant structure to identify based on your knowledge of the plant and the appearance of the output step response. For this example, the output response looks like an underdamped second-order response. In the Structure drop-down list, select Underdamped Pair.

To obtain a rough approximation of the identified plant, in the Identified Plant Structure plot, drag the dashed lines that correspond to the envelope of the step response. Adjust the response so that it approximates the output response. To fine-tune the approximate response, click Auto Estimate. The software estimates the parameters of the identified plant model using the current parameters as an initial guess.

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