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CRC Press LLC CHAPTER TWO PLOTTING COMMANDS GRAPH FUNCTIONS MATLAB has built-in functions that allow one to generate bar charts, x-y, polar. The filters are optimal in the sense that they minimize the maximum error between the specified frequency response and the actual frequency response; they are. Additionally, MATLAB can carry out domain-specific tasks, like data classification or curve fitting. The primary benefits of MATLAB are that it'll allow. GOVINDUDU ANDARIVADELE VIDEO SONGS 1080P TORRENT For technical Fixed a Jira techy wifi, Cloud error message on using Central's. SSH its it and -PlainUsers compatibility running have set. To manage often sudden to input, that and in Windows. However, a an has amount 1 a reshaped badge log their base essential.

Using a transparent surface and drop lines to surface instead of the bottom plane, you can show distances between the points and the surface. These toolbars are sensitive to the type of object selected. The buttons in the pop up provide access to all of the common customization options, so you can perform quick changes without opening complex dialogs.

Import speed in Origin is a factor of 10 or more compared to Excel , and compared to older versions of Origin. The gain in speed has been achieved by making full use of the processor's multi-core architecture. You can drag-and-drop data files onto the Origin interface to import them. Drag-and-drop is supported for most common file types, and can be further customized for additional or custom file types. Starting with Origin , you no longer need to have MS Excel installed to import these file types.

Origin provides the following options for Excel file import:. Excel workbooks can also be opened directly within Origin. The Excel file can be saved with file path relative to the Origin Project file, for easy sharing of the project along with related Excel files. We recommend importing your Excel data, so that you have full access to Origin's powerful graphing and analysis environment. Origin supports importing data from a database using Database Connector. Options include:.

Origin supports importing from a database , and then saving the query in the worksheet for easy editing and re-importing. The Digitizer tool in Origin allows you to perform manual or semi-automated digitizing of graph images. Features include:. The Digitizer tool in Origin lets you generate data from images of graphs. Cartesian, ternary, and polar coordinates are supported. Digitizing methods include manual or semi-automated operations. Multiple curves can be digitized, and points can be reordered and visualized in the result graphing and data worksheet.

In a Zoom graph, a zoomed portion of a larger graph is added to explore a region of interest. Moving the cyan rectangle updates that portion of the graph shown by the inset. Press the Z or X keys and scroll the mouse wheel to quickly and interactively zoom and pan data in graph layers. The new Data Slicer feature allows you to change filter conditions directly on a graph for easy data exploration.

Simply set up filters on desired worksheet columns, create a graph with one or more layers, and turn on the Data Slicer panel to control the filters. Features include: Mini Toolbar to toggle Data Slicer panel Directly disable or enable filters from the graph Text filter has option for single entry allowing for easy switch of filter conditon Numeric filters allow several conditions including combinations with AND or OR.

Highlight a particular data plot in a graph. Also works with complex graph types such as Parallel plot. You can customize the display to include information from other columns of the worksheet, including images embedded in worksheet cells.

Use Vertical Cursor for exploring data in stacked graphs in multiple graph windows simultaneously. You can find information of one cursor or compare two cursors such as the distance. Origin and OriginPro provide a rich set of tools for performing exploratory and advanced analysis of your data.

Please view the following sections for details. Origin provides several gadgets to perform exploratory analysis by interacting with data plotted in a graph. Origin provides a selection of Gadgets to perform exploratory analysis of data from a graph. A region of interest ROI control allows you to interactively specify the subset of data to be analyzed.

Results from the analysis are dynamically updated on top of the ROI as it is resized or moved. This image shows peak fitting being performed using the Quick Fit gadget. Two statistics gadgets are applied to this graph to report statistics in two regions of interest ROI. The Y axis is moved to separate the two regions. Yellow ROI boxes are hidden so that they do not show in printouts.

The "S" button on upper-right corner re-displays the ROI boxes when clicked. Use the Quick Peak Gadget to interactively perform peak finding, baseline subtraction, and peak integration of data from a graph. The Quick Fit Gadget lets you perform linear, polynomial, or nonlinear curve fitting on data plots in a graph.

Notice the label on top of the ROI displaying the slope and Pearson's r from a linear fit. The label updates dynamically as the ROI is moved or resized. The ROI can be rectangular, elliptical, polygon or arbitrary hand-draw shape. The tool provides statistics on data inside and outside the ROI, and also lets you copy, clear, mask or delete selected data. Origin provides various tools for linear, polynomial and nonlinear curve and surface fitting.

Fitting routines use state-of-the-art algorithms. The sections below provide a summary of key features. Graph displaying result of linear regression. Graph displaying result of polynomial regression. Origin supports Global Fitting with Parameter Sharing , where you can simultaneously fit multiple datasets with the same function and optionally share one or more fitting parameters across all datasets. The report sheet will provide a summary table with all parameter values and errors, and a single set of fit statistics from the global fit.

OriginPro supports fitting with implicit functions using the Orthogonal Distance Regression algorithm which minimizes the orthogonal distance from data to the fit curve. Errors and weighting for both X and Y data are supported. Implicit functions can have two or more variables. Result of an Apparent Linear Fit on data plotted with logarithmic Y axis scale. The latter supports weights for both X and Y data. Select from over 12 weighting methods including instrumental, statistical, direct, arbitrary dataset, and variance.

When working with replicate data, Origin can perform a Concatenated Fit where the replicates are combined internally to a single dataset. The graph included in the report sheet can either represent the data in replicate form, or as mean values with SD or SE error bars.

A Quick Sigmoidal Fit Gadget is also available. The Rank Models tool in OriginPro can fit and rank multiple functions to a dataset. Use OriginPro to perform nonlinear surface fitting of data organized in XYZ worksheet columns , a matrix , or a virtual matrix. Select from over 20 surface functions or create your own function.

For peak functions, find peaks using local maximum, partial derivative, or contour consolidation. The raw data is plotted as a color-filled contour plot, and the fit results are plotted as contour lines. Do you need to fit an implicit function to your data?

Implicit Fitting uses the Orthogonal Distance Regression algorithm to find optimal values for the fit parameters. Errors or weights are supported for both X and Y data. Origin provides several features for peak analysis, from baseline correction to peak finding, peak integration, peak deconvolution and fitting. The following sections list the key features for peak analysis. This is a preview graph for performing peak integration using the Peak Analyzer tool. The integration range can be applied for all peaks, or modified individually and interactively for each peak.

Once you have performed baseline detection and peak finding, Origin provides several options for peak fitting: Select from over 25 built-in peak functions, or create your own peak function Fit all peaks with same function form, or assign different functions to specific peaks Peak deconvolution to resolve overlapping or hidden peaks Fix peak centers or allow them to vary by a set percentage or within a set range of values Specify bounds and constraints on peak parameters Share parameters across peaks Full control of fitting process including step-by-step iterations Detailed report including fit statistics, residuals, and graph of individual and cumulative fit lines Over 25 peak properties for reporting, including peak area by percentage, variance, skewness and peak excess Fit summary graph with customizable peak properties table.

There are several options for batch peak analysis of multiple datasets in Origin: Use integration and peak gadgets to analyze multiple curves in a graph within or across layers Use a predefined peak analysis theme to analyze multiple datasets or files Output a custom report table with peak parameters from each dataset or file. The Quick Peaks Gadget provides a quick and interactive way to perform peak analysis from a graph, using a region of interest ROI control.

Batch operations such as integration of multiple curves over a desired range are also possible from this gadget. The Peak Analyzer tool in Origin supports baseline detection, peak picking, and peak integration. In OriginPro, this tool also supports fitting multiple peaks.

Peak detection methods include 2nd derivative search to detect overlapping or hidden peaks. The interface guides you step-by-step, allowing you to customize settings at each stage, and then save the settings as a theme for repeat use on similar data. In addition, Origin provides Stats Advisor App which helps user to interactively choose the appropriate statistical test, analysis tool or App. The Stats Advisor App asks a series of questions and then suggests the appropriate tool or App to analyze your data.

The graph shows a Custom Report of numerical and graphical results from multiple statistical tools, created from Origin's flexible worksheet. Once created, such reports can be automatically generated, greatly simplifying your statistical analysis tasks. The image shows two of the embedded graphs opened for further editing. Edit an embedded graph by double-clicking on the thumbnail image in the report. Once customizations are made, put the graphs back into the report and see your modifications.

Dendrogram of spectra classification from Hierarchical Cluster Analysis of spectra. This plot can be used to classify observations across groups. This graph displays survival functions with confidence intervals, created by the Survival Analysis tool in OriginPro.

The tool also performs a log-rank test to compare the two survival functions. A preview panel is provided to enable real-time visualization of specified parameters and corresponding results. OriginPro provides several wavelet transform tools. From simple column calculations to interpolation, calculus and integration, Origin provides a wide range of tools for mathematical analysis of worksheet and matrix data.

Use the Normalize tool to normalize data in a worksheet or a graph. The F x Column Formula row in Origin worksheet lets you directly type expressions to calculate column values based on data in other columns and metadata elements. The expression can be further edited in the Set Values dialog which provides a lower panel to execute Before Formula scripts for pre-processing data. The Set Values dialog also provides a search button to quickly find and insert functions from over built-in functions.

User-defined functions can also be added for custom transforms. Auto complete helps to quickly find and enter functions as well as name ranges to complete your formula. Use Origin's Interpolation Gadget to perform interpolation and extrapolation on one or more data plots in a graph. You can interactively select the data range using a region-of-interest ROI control. Interpolation methods include linear, spline and Akima spline. Use the Integrate Gadget to perform integration of data curves in a graph.

A region-of-interest ROI control is provided to interactively select the desired data range. Baseline methods include selecting an existing data plot as a baseline to determine the area between two curves, as displayed in this graph. Batch integration of multiple curves is also supported. Origin provides multiple powerful data manipulation tools which can be used for pre-analysis data processing. The pre-analysis data processing can be carried out right after importing data into Origin, and help to get the data into a desired form for analysis in a quick and intuitive way.

Origin provides several tools for reorganizing your data, such as stacking and unstacking columns, and splitting or appending worksheets. With the Stack Columns tool displayed here, you can specify a row label such as Long Name or Comments to act as group identifier. The tool also provides options for stacking into subgroups or stacking by rows. The Data Filter feature in Origin lets you specify numeric, string, or date-time filters on one or more worksheet columns to quickly reduce data.

Custom filter conditions are also supported. Hidden rows are excluded from graphing and analysis. Extract pixel values from stacked matrices by selecting points or specifying coordinates Extract region-of-interest including shapefile-based from stacked matrices or image Finding mean, min, max and coordinates of min and max etc.

Moving or resizing the ROI will automatically update the analysis results and graphs. Origin provides many options for exporting and presentation, from sending graphs to PowerPoint, to creating movies. Journals typically require a specific width for the graph image, such as 86 mm for single column and mm for double column.

In addition, at the scaled size, they may require text labels to be above a particular font size, and lines to be above a certain thickness. In this version, we offer the following key features for preparing the Origin graph with the exact width specification: Resize graph page by specifying desired width, while maintaining aspect ratio auto scale height when width is changed Scale all elements on the page when resizing in order to maintain proportional balance in the graph Conversely, set element scale to some fixed factor when you want to maintain absolute size of elements Fit all graph layers to the available page area using user-specified margins, while maintaining layer relationships, relative size, and object scale.

Once the graph has been scaled to the desired width then it can be exported in a vector or raster format for submission to the journal. Specify desired width and units to match requirements of the journal. The page height will be proportionally scaled while maintaining aspect ratio. Relative dimensions of all objects in graph will be maintained.

Reduce white space in your graph page by either expanding all layers to occupy available space Fit Layers to Page or by reducing page size Fit Page to Layers. In the GIF, we used the Master Page feature to add a company logo and date stamp of identical style and position in graphs. Then paste to other applications such as Microsoft word and edit further. Worksheet cells can also be copied as EMF. You can send graphs individually by name, by Project Explorer folder, or send all graphs from the entire project.

Options include specifying slide margins and using a pre-existing slide as a template, allowing you to add a common set of elements to your published slides. A Send Graphs to Word App , available from the OriginLab File Exchange , exports your Origin graphs as embedded objects or pictures and inserts them into a Word document, with the option to insert them at specific bookmarked positions.

Use the Video Builder tool in Origin to create a video file from Origin graphs. Manually or programmatically add frames to the video from any graph in your project. This animation displays the evolution of data values mapped onto a 3D surface. Origin provides multiple ways to create nice reports. With any of the available methods, you can format the appearance of the report as you want, adding graphs, images and analysis results as links, thus creating a custom report.

Your custom report sheets can become templates for repeated tasks -- simply import new raw data and watch your custom report automatically update. Format text using various built-in, customizable styles, and add graph images and images from the project or from the web. Link to result values in report sheets to create a final report, all within Origin.

Origin provides multiple ways to handle repetitive graphing, importing and data analysis tasks. Batch operations can be performed directly from the GUI, without the need for any programming. Smart Plotting with Cloneable Templates. As an alternative to Graph Templates, Graph Themes provide a means to save graph customizations and apply them to different types of graphs across your projects.

The Template Library helps you organize and utilize Graph Templates you have created. Graph Templates are a great way to apply the customizations you have made to one graph, to additional graphs you make from similar data. Starting from Origin b, Origin provides a set of extended graph templates in the template library.

Graph Template Library dialog shown in List View mode. Set up desired graphs and analysis operations on data in the current workbook. Set the operations to automatically update. Then simply import multiple files, having Origin clone the current workbook for each file. All graphs and analysis results in the new books will be updated based on the data from each file.

Origin provides a quick yet powerful way to allow users to perform batch graphing and analysis when importing multiple files. Origin supports automatic or manual recalculation of results from most analysis and data processing operations, which is the fundation of batch processing and automation. The Batch Processing tool in Origin lets you process multiple data files or datasets using an Analysis Template. The template can include a summary sheet for collecting relevant results for each file in a summary table.

The analysis template can also be linked to a Microsoft Word template using bookmarks, to create custom multi-page Word or PDF reports for each data file. Most analysis tools support recalculation of results upon changes to data. The green "lock" that you will see in result sheets and graph windows indicates that recalculation is set to "auto"; so, for instance, if you made changes to your input data, your linear regression analysis would update automatically.

Left-click on the green lock to open the linear fit dialog, make adjustments to your analysis, then recalculate. Once you perform an operation on a data plot or a worksheet column, Origin allows you to repeat the operation for all other plots in the graph, or all other columns in the worksheet. The Origin Project file. OPJ combines data, notes, graphs, and analysis results into one document with a user-defined folder structure.

The dockable Project Explorer window lets you organize the contents of your Origin project with a flexible user-defined folder structure. Simply drag-and-drop windows and subfolders to rearrange. Choose Project Explorer's extra large icons view for graphs, for easy identification. Middle panel shows large icons with image of last visited graph when project was saved.

Right side panel shows larger image of graphs with vertical scroll bar to view all graphs contained in the project. Users can further customize label rows for including other metadata elements. This image shows custom rows with rich text formatting for super-subscript, and images inserted from external files. Matrix book in Origin. Image Thumbnails Panel is turned on on the top to for quick preview of data.

There are 3 matrix objects in current sheet, where the 3rd matrix is a subtraction of first two matrix objects. XY values of matrix show in column and row headers instead of column and row indices. An audit log feature is also available, to maintain a record of date, time and user name for changes made to the project file. As your Origin use expands, you may want to programmatically access existing features in Origin, add your own custom routines and tools, or communicate with Origin from other applications.

To facilitate such customizations, Origin provides the following options. Set Column Values is one of several places where Python functions can be used to perform calculations and data transforms. The Python function, Before Formula Script, and the expression can all be saved together as a formula for future use. LabTalk is a scripting language native to Origin. For simple operations such as manipulating data and automating tasks, LabTalk is a good place to start.

You can access a rich set of script commands and functions, including a large collection of X-Functions, to create scripts for your specific needs. Your custom script code can be easily assigned to buttons on graphs or worksheets, new toolbar buttons or custom menu items. The same window can also be used to execute Python code. LabTalk script can be stored in OGS files , and organized by "sections". Scripts can be executed in many ways in Origin, including from button objects added to graphs and worksheet windows.

Origin provides a state-of-the-art integrated development environment called Code Builder for managing your Origin C projects. This image shows an Origin C workspace. The R Console dialog in Origin allows you to access R if it is installed on the same computer. 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. The reverse satura- tion current I S increases approximately 7. T1 and T2 are two different temperatures. Assuming that the emission constant of the diode is 1. We want to determine the diode current I D and the diode volt- age VD.

There are several approaches for solving I D and VD. In one approach, Equations 9. This is illustrated by the following example. Assume a temperature of 25 oC. Then, from Equation 9. Using Equation 9. The iteration technique is particularly facilitated by using computers. It consists of an alternat- ing current ac source, a diode and a resistor. The battery charging circuit, explored in the following example, consists of a source connected to a battery through a resistor and a diode.

Use MATLAB a to sketch the input voltage, b to plot the current flowing through the diode, c to calculate the conduction angle of the diode, and d calculate the peak current. Assume that the diode is ideal. The output of the half-wave rectifier circuit of Figure 9. The smoothing circuit is shown in Figure 9.

When the amplitude of the source voltage VS is greater than the output volt- age, the diode conducts and the capacitor is charged. When the source voltage becomes less than the output voltage, the diode is cut-off and the capacitor discharges with the time constant CR. The output voltage and the diode cur- rent waveforms are shown in Figure 9.

Therefore, the output waveform of Figure 9. When v S t is negative, diode D1 is cut-off but diode D2 conducts. The current flowing through the load R enters it through node A. The current entering the load resistance R enters it through node A. The output voltage of a full-wave rectifier circuit can be smoothed by connect- ing a capacitor across the load.

The resulting circuit is shown in Figure 9. The output voltage and the current waveforms for the full-wave rectifier with RC filter are shown in Figure 9. The capacitor in Figure 9. Solution Peak-to-peak ripple voltage and dc output voltage can be calculated using Equations 9. I ZM is the maximum current that can flow through the zener without being destroyed. A zener diode shunt voltage regulator circuit is shown in Fig- ure 9.

Con- versely, if R is constant and VS decreases, the current flowing through the zener will decrease since the breakdown voltage is nearly constant; the output voltage will remain almost constant with changes in the source voltage VS. Now assuming the source voltage is held constant and the load resistance is decreased, then the current I L will increase and I Z will decrease. Con- versely, ifVS is held constant and the load resistance increases, the current through the load resistance I L will decrease and the zener current I Z will increase.

In the design of zener voltage regulator circuits, it is important that the zener diode remains in the breakdown region irrespective of the changes in the load or the source voltage. From condition 1 and Equation 9. I Z ,max 9. Solution Using Thevenin Theorem, Figure 9.

In addition, when the source voltage is 35 V, the output voltage is The zener breakdown characteristics and the loadlines are shown in Figure 9. Lexton, R. Shah, M. Angelo, Jr. Sedra, A. Beards, P. Savant, Jr. Ferris, C. Ghausi, M. Warner Jr.

Assume a temperature of 25 oC, emission coef- ficient, n , of 1. Both intrinsic and extrinsic semicon- ductors are discussed. The characteristics of depletion and diffusion capaci- tance are explored through the use of example problems solved with MATLAB. The effect of doping concentration on the breakdown voltage of pn junctions is examined. Electrons surround the nucleus in specific orbits. The electrons are negatively charged and the nucleus is positively charged.

If an electron absorbs energy in the form of a photon , it moves to orbits further from the nucleus. An electron transition from a higher energy orbit to a lower energy orbit emits a photon for a direct band gap semiconductor. The energy levels of the outer electrons form energy bands. In insulators, the lower energy band valence band is completely filled and the next energy band conduction band is completely empty.

The valence and conduction bands are separated by a forbidden energy gap. In semicon- ductors the forbidden gap is less than 1. Some semiconductor materials are silicon Si , germanium Ge , and gallium arsenide GaAs. Figure Silicon has four valence electrons and its atoms are bound to- gether by covalent bonds. At absolute zero temperature the valence band is completely filled with electrons and no current flow can take place.

As the temperature of a silicon crystal is raised, there is increased probability of breaking covalent bonds and freeing electrons. The vacancies left by the freed electrons are holes. The process of creating free electron-hole pairs is called ionization. The free electrons move in the conduction band. Since electron mobility is about three times that of hole mobility in silicon, the electron current is considerably more than the hole current.

The following ex- ample illustrates the dependence of electron concentration on temperature. Solution From Equation The width of energy gap with temperature is given as [1]. An n-type semiconductor is formed by doping the silicon crystal with elements of group V of the periodic table antimony, arse- nic, and phosphorus.

The impurity atom is called a donor. The majority car- riers are electrons and the minority carriers are holes. A p-type semiconductor is formed by doping the silicon crystal with elements of group III of the peri- odic table aluminum, boron, gallium, and indium.

The impurity atoms are called acceptor atoms. The majority carriers are holes and minority carriers are electrons. The law of mass action enables us to calculate the majority and minority car- rier density in an extrinsic semiconductor material. In an n-type semiconductor, the donor concentration is greater than the intrin- sic electron concentration, i. Example It is used to describe the energy level of the electronic state at which an electron has the probability of 0.

Equation In addition, the Fermi energy can be thought of as the average energy of mobile carriers in a semiconductor mate- rial. In an n-type semiconductor, there is a shift of the Fermi level towards the edge of the conduction band.

The upward shift is dependent on how much the doped electron density has exceeded the intrinsic value. Drift current is caused by the application of an elec- tric field, whereas diffusion current is obtained when there is a net flow of car- riers from a region of high concentration to a region of low concentration. This is shown in Figure Practical pn junctions are formed by diffusing into an n-type semiconductor a p-type impurity atom, or vice versa.

Because the p-type semiconductor has many free holes and the n-type semiconductor has many free electrons, there is a strong tendency for the holes to diffuse from the p-type to the n-type semi- conductors. Similarly, electrons diffuse from the n-type to the p-type material. When holes cross the junction into the n-type material, they recombine with the free electrons in the n-type. Similarly, when electrons cross the junction into the p-type region, they recombine with free holes.

In the junction a transition region or depletion region is created. In the depletion region, the free holes and electrons are many magnitudes lower than holes in p-type material and electrons in the n-type material. As electrons and holes recombine in the transition region, the region near the junc- tion within the n-type semiconductor is left with a net positive charge.

The re- gion near the junction within the p-type material will be left with a net negative charge. This is illustrated in Figure Because of the positive and negative fixed ions at the transition region, an elec- tric field is established across the junction. The electric field creates a poten- tial difference across the junction, the potential barrier.

The potential barrier pre- vents the flow of majority carriers across the junction under equilibrium condi- tions. That is, from Figure Typically, VC is from 0. For germanium, VC is ap- proximately 0. When a positive voltage VS is applied to the p-side of the junction and n-side is grounded, holes are pushed from the p-type material into the transition re- gion.

In addition, electrons are attracted to transition region. The depletion region decreases, and the effective contact potential is reduced. This allows majority carriers to flow through the depletion region. The depletion region increases and it become more difficult for the majority carriers to flow across the junction. The current flow is mainly due to the flow of minority carriers.

Using Equations The following example shows how I S is affected by tem- perature. During device fabrication, a p-n junction can be formed using process such as ion-implantation diffusion or epitaxy. The dop- ing profile at the junction can take several shapes. Two popular doping pro- files are abrupt step junction and linearly graded junction. In the abrupt junction, the doping of the depletion region on either side of the metallurgical junction is a constant.

This gives rise to constant charge densi- ties on either side of the junction. If the doping density on one side of the metallurgical junction is greater than that on the other side i. This condition is termed the one-sided step junction approximation. This is the practical model for shallow junctions formed by a heavily doped diffusion into a lightly doped region of opposite polarity [7].

In a linearly graded junction, the ionized doping charge density varies linearly across the depletion region. The charge density passes through zero at the metallurgical junction. It can be obtained from Equations Equations The positive voltage, VC , is the contact potential of the pn junction.

However, when the pn junction becomes slightly forward biased, the capacitance increases rapidly. It is also used to plot the depletion ca- pacitance. The holes are momentarily stored in the n-type material before they recombine with the majority carriers electrons in the n-type material. Similarly, electrons are injected into and temporarily stored in the p-type material. The electrons then recombine with the majority carriers holes in the p-type material.

The diffusion capacitance is usually larger than the depletion capacitance [1, 6]. Typical values of Cd ranges from 80 to pF. A small signal model of the diode is shown in Figure Cd rd Rs Cj Figure RS is the semiconductor bulk and contact resistance. The model of the diode is shown in Figure Cj Rs Rd Figure The diffusion capacitance is zero.

The resistance Rd is reverse resistance of the pn junction normally in the mega-ohms range. At a critical field, E crit , the accelerated carriers in the depletion region have sufficient energy to create new electron-hole pairs as they collide with other atoms. The secondary electrons can in turn create more carriers in the depletion region.

This is termed the avalanche breakdown process. For silicon with an impurity concentration of cm-3, the critical electric field is about 2. This high electric field is able to strip electrons away from the outer orbit of the silicon atoms, thus cre- ating hole-electron pairs in the depletion region.

This mechanism of break- down is called zener breakdown. This breakdown mechanism does not involve any multiplication effect. Normally, when the breakdown voltage is less than 6V, the mechanism is zener breakdown process. For breakdown voltages be- yond 6V, the mechanism is generally an avalanche breakdown process. For an abrupt junction, where one side is heavily doped, the electrical proper- ties of the junction are determined by the lightly doped side.

The following example shows the effect of doping concentration on breakdown voltage. Solution Using Equation Impurity Concentration' axis [1. Singh, J. Jacoboni, C. Mousty, F. Caughey, D. IEEE, Vol. Hodges, D. Neudeck, G. II, Addison-Wesley, Beadle, W. McFarlane, G. Sze, S. Plot the difference between of ni for Equations Assume donor concentrations from to Use impurity gradient values from to It can be used to perform the basic mathematical operations: addition, subtrac- tion, multiplication, and division.

They can also be used to do integration and differentiation. There are several electronic circuits that use an op amp as an integral element. Some of these circuits are amplifiers, filters, oscillators, and flip-flops. In this chapter, the basic properties of op amps will be discussed. The non-ideal characteristics of the op amp will be illustrated, whenever possi- ble, with example problems solved using MATLAB. Its symbol is shown in Figure It is a differ- ence amplifier, with output equal to the amplified difference of the two inputs.

It also has a very large input resistance to ohms. The out- put resistance might be in the range of 50 to ohms. The offset voltage is small but finite and the frequency response will deviate considerably from the infinite frequency response. The common-mode rejection ratio is not infinite but finite. Table This condi- tion is termed the concept of the virtual short circuit. In addition, because of the large input resistance of the op amp, the latter is assumed to take no cur- rent for most calculations.

Thus, Equation R2 R1 Vin Vo Figure With the assumptions of very large open-loop gain and high input resistance, the closed-loop gain of the inverting amplifier depends on the external com- ponents R1 , R2 , and is independent of the open-loop gain. The integrating time con- stant is CR1. It behaves as a lowpass filter, passing low frequencies and at- tenuating high frequencies.

However, at dc the capacitor becomes open cir- cuited and there is no longer a negative feedback from the output to the input. The output voltage then saturates.

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Highest score default Trending recent votes count more Date modified newest first Date created oldest first. Improve this answer. Omid Omid 1 1 gold badge 2 2 silver badges 11 11 bronze badges. You mean separate figures for velocity and position? One figure for velocity curves and one for position curves? If that is the case then you need to replace subplot 2,1,1 with figure 1 and subplot 2,1,2 with figure 2.

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The Overflow Blog. Asked and answered: the results for the Developer survey are here! Living on the Edge with Netlify Ep. Featured on Meta. Testing new traffic management tool. Trending: A new answer sorting option. Related For a list of properties, see Line Properties. Use p to modify properties of the plot after creating it. Create y as sine values of x. Create a line plot of the data. Define y1 and y2 as sine and cosine values of x.

Create a line plot of both sets of data. Define Y as the 4-by-4 matrix returned by the magic function. Create a 2-D line plot of Y. Plot three sine curves with a small phase shift between each line. Use the default line style for the first line.

Specify a dashed line style for the second line and a dotted line style for the third line. Use a green line with no markers for the first sine curve. Use a blue dashed line with circle markers for the second sine curve. Use only cyan star markers for the third sine curve. Create a line plot and display markers at every fifth data point by specifying a marker symbol and setting the MarkerIndices property as a name-value pair.

Create a line plot and use the LineSpec option to specify a dashed green line with square markers. Use Name,Value pairs to specify the line width, marker size, and marker colors. Set the marker edge color to blue and set the marker face color using an RGB color value. Use the linspace function to define x as a vector of values between 0 and Define y as cosine values of x.

Create a 2-D line plot of the cosine curve. Change the line color to a shade of blue-green using an RGB color value. Add a title and axis labels to the graph using the title , xlabel , and ylabel functions. Define t as seven linearly spaced duration values between 0 and 3 minutes.

Plot random data and specify the format of the duration tick marks using the 'DurationTickFormat' name-value pair argument. A convenient way to plot data from a table is to pass the table to the plot function and specify the variables to plot. Read weather. Then display the first three rows of the table. Plot the row times on the x -axis and the RainInchesPerMinute variable on the y -axis.

When you plot data from a timetable, the row times are plotted on the x -axis by default. Thus, you do not need to specify the Time variable. Return the Line object as p. Notice that the axis labels match the variable names. For example, change the line to a red dotted line with point markers. Plot the row times on the x -axis and the Temperature and PressureHg variables on the y -axis. Starting in Rb, you can display a tiling of plots using the tiledlayout and nexttile functions.

Call the tiledlayout function to create a 2-by-1 tiled chart layout. Call the nexttile function to create an axes object and return the object as ax1. Create the top plot by passing ax1 to the plot function. Add a title and y -axis label to the plot by passing the axes to the title and ylabel functions. Repeat the process to create the bottom plot.

Create a line plot of both sets of data and return the two chart lines in p. Change the line width of the first line to 2. Add star markers to the second line. Use dot notation to set properties. Plot a circle centered at the point 4,3 with a radius equal to 2. Use axis equal to use equal data units along each coordinate direction. The size and shape of X depends on the shape of your data and the type of plot you want to create.

This table describes the most common situations. Specify X and Y as scalars and include a marker. For example: plot 1,2, 'o'. Specify X and Y as any combination of row or column vectors of the same length. For example: plot [1 2 3],[4; 5; 6]. Specify consecutive pairs of X and Y vectors. For example: plot [1 2 3],[4 5 6],[1 2 3],[7 8 9].

If all the sets share the same x - or y -coordinates, specify the shared coordinates as a vector and the other coordinates as a matrix. The length of the vector must match one of the dimensions of the matrix. Alternatively, specify X and Y as matrices of equal size. For example: plot [1 2 3; 4 5 6],[7 8 9; 10 11 12].

Data Types: single double int8 int16 int32 int64 uint8 uint16 uint32 uint64 categorical datetime duration. The size and shape of Y depends on the shape of your data and the type of plot you want to create. Alternatively, specify just the y -coordinates. For example: plot [4 5 6]. Line style, marker, and color, specified as a character vector or string containing symbols.

The symbols can appear in any order. You do not need to specify all three characteristics line style, marker, and color. For example, if you omit the line style and specify the marker, then the plot shows only the marker and no line. Example: '--or' is a red dashed line with circle markers. Table variables containing the x -coordinates, specified using one of the indexing schemes from the table.

An index number that refers to the location of a variable in the table. A logical vector. Typically, this vector is the same length as the number of variables, but you can omit trailing 0 or false values. A vartype subscript that selects variables of a specified type. The table variables you specify can contain numeric, categorical, datetime, or duration values. If xvar and yvar both specify multiple variables, the number of variables must be the same.

Example: plot tbl,["x1","x2"],"y" specifies the table variables named x1 and x2 for the x -coordinates. Example: plot tbl,2,"y" specifies the second variable for the x -coordinates. Example: plot tbl,vartype "numeric" ,"y" specifies all numeric variables for the x -coordinates. Table variables containing the y -coordinates, specified using one of the indexing schemes from the table.

Example: plot tbl,"x",["y1","y2"] specifies the table variables named y1 and y2 for the y -coordinates. Example: plot tbl,"x",2 specifies the second variable for the y -coordinates. Example: plot tbl,"x",vartype "numeric" specifies all numeric variables for the y -coordinates. To create a polar plot or geographic plot, specify ax as a PolarAxes or GeographicAxes object.

Alternatively, call the polarplot or geoplot function. Name-value arguments must appear after other arguments, but the order of the pairs does not matter. Before Ra, use commas to separate each name and value, and enclose Name in quotes. Example: plot [0 1],[2 3],"LineWidth",2.

The properties listed here are only a subset. For a complete list, see Line Properties. Line color, specified as an RGB triplet, a hexadecimal color code, a color name, or a short name. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color.

The intensities must be in the range [0,1] ; for example, [0. A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Thus, the color codes ' FF' , ' ff' , ' F80' , and ' f80' are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes. Example: ' FF'. If the line has markers, then the line width also affects the marker edges. The line width cannot be thinner than the width of a pixel. If you set the line width to a value that is less than the width of a pixel on your system, the line displays as one pixel wide.

Marker symbol, specified as one of the values listed in this table. By default, the object does not display markers. Specifying a marker symbol adds markers at each data point or vertex. Indices of data points at which to display markers, specified as a vector of positive integers.

Example: plot x,y,'-o','MarkerIndices',[1 5 10] displays a circle marker at the first, fifth, and tenth data points. Example: plot x,y,'-x','MarkerIndices',length y displays a cross marker every three data points.

Example: plot x,y,'Marker','square','MarkerIndices',5 displays one square marker at the fifth data point. Marker outline color, specified as 'auto' , an RGB triplet, a hexadecimal color code, a color name, or a short name.

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