Computer Science, UML

UML – Analysis activities: From Use Case to Class Diagram

Computer science and programming

UML Analysis activities – From Use Case to Class Diagram

Miércoles 29 noviembre, 10:16 am


Object-Oriented Software Engineering

    1. Analysis p 173
    2. Identifying Associations pp 190
    3. Identifying Aggregates pp 192
    4. Identifying Attributes pp 193

Identifying Associations

In this section, we discuss the use of class diagrams for representing associations among objects. An association shows a relationship between two or more classes. For example, a FieldOfficer writes an EmergencyReport (see Figure 5-13).

Associations have several properties:

  • A name to describe the association between the two classes (e.g., Writes in Figure 5-13). Association names are optional and need not be unique globally.
  • A role at each end, identifying the function of each class with respect to the associations (e.g., author is the role played by FieldOfficer in the Writes association).
  • A multiplicity at each end, identifying the possible number of instances (e.g., *
  • indicates a FieldOfficer may write zero or more EmergencyReports, whereas 1
  • indicates that each EmergencyReport has exactly one FieldOfficer as author).

Initially, the associations between entity objects are the most important, as they reveal more information about the application domain. According to Abbott’s heuristics (see Table 5-1), associations can be identified by examining verbs and verb phrases denoting a state (e.g., has, is part of, manages, reports to, is triggered by, is contained in, talks to, includes). Every association should be named, and roles should be assigned to each end.

The object model will initially include too many associations if developers include all associations identified after examining verb phrases. In Figure 5-14, for example, we identify two relationships: the first between an Incident and the EmergencyReport that triggered its creation; the second between the Incident and the reporting FieldOfficer. Given that the EmergencyReport and FieldOfficer already have an association modeling authorship, the association between Incident and FieldOfficer is not necessary. Adding unnecessary associations complicates the model, leading to incomprehensible models and redundant information.

Most entity objects have an identifying characteristic used by the actors to access them. FieldOfficers and Dispatchers have a badge number. Incidents and Reports are assigned numbers and are archived by date. Once the analysis model includes most classes and associations, the developers should go through each class and check how it is identified by the actors and in which context.

Identifying Aggregates

Aggregations are special types of associations denoting a whole–part relationship. For example, a FireStation consists of a number of FireFighters, FireEngines, Ambulances, and a LeadCar. A State is composed of a number of Counties that are, in turn, composed of a number of Townships (Figure 5-15). An aggregation is shown as a association with a diamond on the side of the whole part.

There are two types of aggregation, composition and shared. A solid diamond denotes composition. A composition aggregation indicates that the existence of the parts depends on the whole. For example, a County is always part of exactly one State, a Township is always part of a County. As political boundaries do not change often, a Township will not be part of or shared with another County.

A hollow diamond denotes a shared aggregation relationship, indicating the whole and the part can exist independently. For example, although a FireEngine is part of at most one FireStation at the time, it can be reassigned to a different FireStation during its life time. Aggregation associations are used in the analysis model to denote whole–part concepts. Aggregation associations add information to the analysis model about how containment concepts in the application domain can be organized in a hierarchy or in a directed graph. Aggregations are often used in the user interface to help the user browse through many instances.

If you are not sure that the association you are describing is a whole–part concept, it is better to model it as a one-to-many association, and revisit it later when you have a better understanding of the application domain.

Identifying Attributes

Attributes are properties of individual objects. For example, an EmergencyReport, as described in Table 5-2, has an emergency type, a location, and a description property (see Figure 5-16).

These are entered by a FieldOfficer when she reports an emergency and are subsequently tracked by the system. When identifying properties of objects, only the attributes relevant to the system should be considered.

Properties that are represented by objects are not attributes. For example, every EmergencyReport has an author that is represented by an association to the FieldOfficer class. Developers should identify as many associations as possible before identifying attributes to avoid confusing attributes and objects. Attributes have:

  • A name identifying them within an object. For example, an EmergencyReport may have a reportType attribute and an emergencyType attribute. The reportType describes the kind of report being filed (e.g., initial report, request for resource, final report). The emergencyType describes the type of emergency (e.g., fire, traffic, other). To avoid confusion, these attributes should not both be called type.
  • A brief description.
  • A type describing the legal values it can take. For example, the description attribute of an EmergencyReport is a string. The emergencyType attribute is an enumeration that can take one of three values: fire, traffic, other. Attribute types are based on predefined basic types in UML

Attributes can be identified using Abbott’s heuristics (see Table 5-1). In particular, a noun

phrase followed by a possessive phrase (e.g., the description of an emergency) or an adjective phrase (e.g., the emergency description) should be examined. In the case of entity objects, any property that must be stored by the system is a candidate attribute.

Note that attributes represent the least stable part of the object model. Often, attributes are discovered or added late in the development when the system is evaluated by the users. Unless the added attributes are associated with additional functionality, the added attributes do not entail major changes in the object (and system) structure. For these reasons, the developers need not spend excessive resources in identifying and detailing attributes that represent less important aspects of the system.

Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Ecuador (Quito, Guayaquil, Cuenca)

WhatsApp: 00593984950376


Electrical Engineer, Power Distribution, Sistemas de Potencia


Literature Review


  1. Libro Analisis_de_sistemas_de_pot
    1. Potencia en circuitos Monofásicos p 5 (18)
    2. Potencia compleja pp 10 (22)
    3. Dirección del flujo de potencia pp 11
  2. Análisis de Redes – Van Valkenburg, 1999 – Network Analysis – Universidad de Illinois
    1. Carga y Energía capt 1.2 – p 16 (18)

Definición de potencia eléctrica – Introducción


El conocimiento actual de la naturaleza de la carga se basa en el Esquema Conceptual de la Teoría Atómica.

  Análisis de Sistemas de Potencia

Al respecto ver Representación Fasorial de Voltajes y Corrientes

Potencia en Circuitos Monofásicos

Potencia Compleja

El Triángulo de Potencia

Dirección del flujo de potencia

Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Ecuador (Quito, Guayaquil, Cuenca)




Análisis de sistemas de control, Circuit Analysis, Control System Analysis, Electrical Engineer, Matemática aplicada - Appd Math, Señales y Sistemas, Sistemas LDCID, Time Domain


We define two physically meaningful specifications for second-order systems: Natural Frequency (Wn) and Damping Ratio (ζ).


Now that we have become familiar with second-order systems and their responses, we generalize the discussion and establish quantitative specifications defined in such a way that the response of a second-order system can be described to a designer without the need for sketching the response. We define two physically meaningful specifications for second-order systems. These quantities can be used to describe the characteristics of the second-order transient response just as time constants describe the first-order system response.

Natural Frequency, Wn

The natural frequency of a second-order system is the frequency of oscillation of the system without damping. For example, the frequency of oscillation of a series RLC circuit with the resistance shorted would be the natural frequency.

Damping Ratio,

We have already seen that a second-order system’s underdamped step response is characterized by damped oscillations. Our definition is derived from the need to quantitatively describe this damped oscillations regardless of the time scale.Thus, a system whose transient response goes through three cycles in a millisecond before reaching the steady state would have the same measure as a system that went through three cycles in a millennium before reaching the steady state. For example, the underdamped curve in Figure 4.10 has an associated measure that defines its shape. This measure remains the same even if we change the time base from seconds to microseconds or to millennia.

 A viable definition for this quantity is one that compares the exponential decay frequency of the envelope to the natural frequency. This ratio is constant regardless of the time scale of the response. Also, the reciprocal, which is proportional to the ratio of the natural period to the exponential time constant, remains the same regardless of the time base.

We define the damping ratio, , to be:

Consider the general system:

Without damping, the poles would be on the jw-axis, and the response would be an undamped sinusoid. For the poles to be purely imaginary, a = 0. Hence:

Assuming an underdamped system, the complex poles have a real part, , equal to -a/2. The magnitude of this value is then the exponential decay frequency described in Section 4.4. Hence,

from which

Our general second-order transfer function finally looks like this:

Now that we have defined and Wn, let us relate these quantities to the pole location. Solving for the poles of the transfer function in Eq. (4.22) yields:

From Eq. (4.24) we see that the various cases of second-order response:

Underdamped Second-Order System

Now that we have generalized the second-order transfer function in terms of and Wn, let us analyze the step response of an underdamped second-order system.

Not only will this response be found in terms of and Wn, but more specifications
indigenous to the underdamped case will be defined. The underdamped second order system, a common model for physical problems, displays unique behavior that
must be itemized; a detailed description of the underdamped response is necessary
for both analysis and design. Our first objective is to define transient specifications
associated with underdamped responses. Next we relate these specifications to the
pole location, drawing an association between pole location and the form of the
underdamped second-order response. Finally, we tie the pole location to system
parameters, thus closing the loop: Desired response generates required system

Let us begin by finding the step response for the general second-order system of Eq. (4.22). The transform of the response, C(s), is the transform of the input times the transfer function, or:

where it is assumed that < 1 (the underdamped case). Expanding by partial fractions, using the methods described, yields:

Taking the inverse Laplace transform, which is left as an exercise for the student, produces:


A plot of this response appears in Figure 4.13 for various values of , plotted along a time axis normalized to the natural frequency.

We now see the relationship between the value of and the type of response obtained: The lower the value of , the more oscillatory the response.

The natural frequency is a time-axis scale factor and does not affect the nature of the response other than to scale it in time.

Other parameters associated with the underdamped response are rise time, peak time, percent overshoot, and settling time. These specifications are defined as follows (see also Figure 4.14):

  1. Rise time, Tr. The time required for the waveform to go from 0.1 of the final value to 0.9 of the final value.
  2. Peak time, TP. The time required to reach the first, or maximum, peak.
  3. Percent overshoot, %OS. The amount that the waveform overshoots the steady-state, or final value at the peak time, expressed as a percentage of the steady-state value.
  4. Settling time, Ts. The time required for the transient’s damped oscillations to reach and stay within 2% of the steady-state value.

All definitions are also valid for systems of order higher than 2, although analytical expressions for these parameters cannot be found unless the response of the higher-order system can be approximated as a second-order system.

Rise time, peak time, and settling time yield information about the speed of the transient response. This information can help a designer determine if the speed and the nature of the response do or do not degrade the performance of the system.

For example, the speed of an entire computer system depends on the time it takes for a hard drive head to reach steady state and read data; passenger comfort depends in part on the suspension system of a car and the number of oscillations it goes through after hitting a bump.

Evaluation of Tp

Tp is found by differentiating c(t) in Eq. (4.28) and finding the first zero crossing after t = 0.

Evaluation of %OS.

From Figure 4.14 the percent overshoot, %OS, is given by:

 Evaluation of Ts

In order to find the settling time, we must find the time for which c(t) in Eq. (4.28) reaches and stays within ₎±2% of the steady-state value, C final.

 Evaluation of Tr

A precise analytical relationship between rise time and damping ratio cannot be found. However, using a computer and Eq. (4.28), the rise time can be found. Let us look at an example.

We now have expressions that relate peak time, percent overshoot, and settling time to the natural frequency and the damping ratio. Now let us relate these quantities to the location of the poles that generate these characteristics. The pole plot for a general, underdamped second-order system is reproduced in Figure 4.17.

Now, comparing Eqs. (4.34) and (4.42) with the pole location, we evaluate peak time and settling time in terms of the pole location. Thus:

where is the imaginary part of the pole and is called the damped frequency of oscillation, and is the magnitude of the real part of the pole and is the exponential damping frequency part.

At this point, we can understand the significance of Figure 4.18 by examining the actual step response of comparative systems. Depicted in Figure 4.19(a) are the step responses as the poles are moved in a vertical direction, keeping the real part the same. As the poles move in a vertical direction, the frequency increases, but the envelope remains the same since the real part of the pole is not changing.

Let us move the poles to the right or left. Since the imaginary part is now constant, movement of the poles yields the responses of Figure 4.19(b). Here the frequency is constant over the range of variation of the real part. As the poles move to the left, the response damps out more rapidly.

Moving the poles along a constant radial line yields the responses shown in Figure 4.19(c). Here the percent overshoot remains the same. Notice also that the responses look exactly alike, except for their speed. The farther the poles are from the origin, the more rapid the response.


  1. Control Systems Engineering, Nise
  2. Sistemas de Control Automatico Benjamin C Kuo
  3. Modern_Control_Engineering, Ogata 4t

Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contacto: Jaén – España: Tlf. 633129287

Contact: Caracas, Quito, Guayaquil, Jaén, Villafranca de Ordizia- Telf. +34633129287

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Control Systems Engineering, Norman Nise

    1. Introduction Chapter 4 pp 162 (162)
    2. Poles and Zeros 4.1 pp 162 –
    3. First Order System 4.3 pp 165-168
    4. Second Order System 4.4 pp 168-177
    5. Underdamped Second-Order System 4.6 pp 177-186
  1. Modern_Control_Engineering__4t
    1. Introduction Chapter 5 pp 219 (232)
    2. First Order Systems 221 (234)-224
    3. Second Order System pp 224 (237)-234

Literature Review, Martes 14 noviembre 2017, 05:07 am – Caracas, Quito, Guayaquil.

Matemática aplicada - Appd Math, Señales y Sistemas

Sistemas lineales e invariantes en el tiempo.


Los sistemas LTI son aquellos que cumplen con las propiedades de linealidad e invarianza en el tiempo. De allí las siglas que provienen del inglés “Linear and Time-Invariant”. Su importancia radica en que facilitan enormemente el estudio y análisis de sistemas complejos que puedan ser representados mediante un modelo matemático que cumpla con estas dos condiciones.

Incluso cuando se posee poca información sobre un sistema, un modelo LTI del mismo permite predecir rápidamente como se va a comportar, cuál será la salida para una determinada entrada de prueba, que puede ser un impulso (movimiento súbito que desaparece de inmediato), un escalón (movimiento súbito que se mantiene constante), o una rampa (movimiento que crece o decrece de forma lineal).


Un sistema lineal, en tiempo continuo o discreto, es aquel que posee la importante propiedad de la superposición: si una entrada consiste en la suma ponderada de varias señales, entonces la salida es simplemente la superposición (es decir, la suma ponderada) de las respuestas del sistema a cada una de estas señales.

Sea y1(t) la respuesta del sistema continuo a una entrada x1(t), y sea y2(t) la salida correspondiente a la entrada x2(t). Entonces, el sistema es lineal si:

  • La respuesta a x1(t) + x2(t) es y1(t) + y2(t)
  • La respuesta a k*x1(t) es k*y1(t), donde k es una constante compleja cualquiera.

La primera de estas dos propiedades se llama propiedad de aditividad, mientras que la segunda se conoce como la propiedad de escalamiento u homogeneidad.

El siguiente cuadro sirve de resumen para el estudio de la linealidad de un sistema:


Invarianza en el tiempo

Un sistema es invariante en el tiempo si un desplazamiento temporal de la señal de entrada produce el mismo desplazamiento en la señal de salida. Es decir:


El siguiente esquema permite ver como fluye la información en un sistema invariante en el tiempo:



Consideremos un sistema S cuya entrada x(t) y salida y(t) están relacionadas mediante:


Ahora consideramos dos entradas arbitrarias x1(t) y x2(t). Ellas generan las siguientes respuestas:


Consideremos una tercera entrada x3(t)=a*x1(t)+b*x2(t), la cual genera una salida y3(t) igual a:


Concluimos entonces que el sistema es lineal.


  1. Análisis de Sistemas Lineales – Prof. Ebert Brea
  2. Control Systems Engineering, Norman Nise
  3. Oppenheim – Señales y Sistemas
    1. 1.6.6 Linealidad p 53

Revisión literaria hecha por:

Prof. Larry Francis Obando – Technical Specialist – Educational Content Writer

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Copywriting, Content Marketing, Tesis, Monografías, Paper Académicos, White Papers (Español – Inglés)

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, USB Valle de Sartenejas.

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, UCV CCs

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contacto: España. +34633129287

Caracas, Quito, Guayaquil, Jaén.

WhatsApp:  +34633129287

Twitter: @dademuch

FACEBOOK: DademuchConnection


Análisis de sistemas de control, Control System Analysis, Electrical Engineer, Electronic Engineer, Señales y Sistemas, Time Domain

First and second order systems

Transient Response and Steady-State Response. The time response of a control system consists of two parts: the transient response and the steady-state response. By transient response, we mean that which goes from the initial state to the final state. By steady-state response, we mean the manner in which the system output behaves as t approaches infinity.


We now discuss first-order systems without zeros to define a performance specification for such a system…

We now use Eqs. (4.6), (4.7), and (4.8) to define three transient response performance specifications:

  • Time Constant: We call 1/a the time constant of the response. From Eq. (4.7), the time constant can be described as the time for to decay to 37% of its initial value. Alternately, from Eq. (4.8) the time constant is the time it takes for the step response to rise to 63% of its final value.

The reciprocal of the time constant has the units (1/seconds), or frequency. Thus, we can call the parameter a the exponential frequency. Thus, the time constant can be considered a transient response specification for a first order system, since it is related to the speed at which the system responds to a step input.Since the pole of the transfer function is at a, we can say the pole is located at the reciprocal of the time constant, and the farther the pole from the imaginary axis, the faster the transient response.

  • Rise Time (Tr): Rise time is defined as the time for the waveform to go from 0.1 to 0.9 of its final value.

  • Settling Time (Ts): Settling time is defined as the time for the response to reach, and stay within, 2% of its final value.2

Fuente [1]

Consider the first order system shown in figure 5-1:

Fuente [3]

Fuente [3]


Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Caracas, Quito, Guayaquil, Jaén.

WhatsApp: +34633129287


Copywriting, Content Marketing, Tesis, Monografías, Paper Académicos, White Papers (Español – Inglés)


Computer Science, UML

UML Analysis – Basics

Computer science and programming

Jueves 09 noviembre, 09:44 am


Object-Oriented Software Engineering

    1. Analysis p 173
    2. Overview of Analysis
    3. Analysis Concepts pp 176
    4. Analysis Activities pp 179


Analysis results in a model of the system that aims to be correct, complete, consistent, and unambiguous. Developers formalize the requirements specification produced during requirements elicitation and examine in more detail boundary conditions and exceptional cases. Developers validate, correct and clarify the requirements specification if any errors or ambiguities are found. The client and the user are usually involved in this activity when the requirements specification must be changed and when additional information must be gathered. In object-oriented analysis, developers build a model describing the application domain.

Formalization helps identify areas of ambiguity as well as inconsistencies and omissions in a requirements specification. Once developers identify problems with the specification, the address them by eliciting more information from the users and the client. Requirements elicitation and analysis are iterative and incremental activities that occur concurrently.

An Overview of Analysis

Analysis focuses on producing a model of the system, called the analysis model, which is correct, complete, consistent, and verifiable. Analysis is different from requirements elicitation in that developers focus on structuring and formalizing the requirements elicited from users (Figure 5-2).

This formalization leads to new insights and the discovery of errors in the requirements. As the analysis model may not be understandable to the users and the client, developers need to update the requirements specification to reflect insights gained during analysis, then review the changes with the client and the users. In the end, the requirements, however large, should be understandable by the client and the users.

The analysis model is composed of three individual models: the functional model, represented by use cases and scenarios, the analysis object model, represented by class and object diagrams, and the dynamic model, represented by state machine and sequence diagrams (Figure 5-3).

In the previous chapter, we described how to elicit requirements from the users and describe them as use cases and scenarios. In this chapter, we describe how to refine the functional model and derive the object and the dynamic model. This leads to a more precise and complete specification as details are added to the analysis model.

Analysis Object Model

The analysis model represents the system under development from the user’s point of view. The analysis object model is a part of the analysis model and focuses on the individual concepts that are manipulated by the system, their properties and their relationships. The analysis object model, depicted with UML class diagrams, includes classes, attributes, and operations. The analysis object model is a visual dictionary of the main concepts visible to the user.

Dynamic Model

The dynamic model focuses on the behavior of the system. The dynamic model is depicted with sequence diagrams and with state machines. Sequence diagrams represent the interactions among a set of objects during a single use case. State machines represent the behavior of a single object (or a group of very tightly coupled objects). The dynamic model serves to assign responsibilities to individual classes and, in the process, to identify new classes, associations, and attributes to be added to the analysis object model.

Entity, Boundary, and Control Objects

The analysis object model consists of entity, boundary, and control objects [Jacobson et al., 1999]. Entity objects represent the persistent information tracked by the system. Boundary objects represent the interactions between the actors and the system. Control objects are in charge of realizing use cases. In the 2Bwatch example, Year, Month, and Day are entity objects; Button and LCDDisplay are boundary objects; ChangeDateControl is a control object that represents the activity of changing the date by pressing combinations of buttons.Modeling the system with entity, boundary, and control objects provides developers with simple heuristics to distinguish different, but related concepts.

To distinguish between different types of objects, UML provides the stereotype mechanism to enable the developer to attach such meta-information to modeling elements.

For example, in Figure 5-5, we attach the «control» stereotype to the ChangeDateControl object. In addition to stereotypes, we may also use naming conventions for clarity and recommend distinguishing the three different types of objects on a syntactical basis: control objects may have the suffix Control appended to their name; boundary objects may be named to clearly denote an interface feature (e.g., by including the suffix Form, Button, Display, or Boundary); entity objects usually do not have any suffix appended to their name.

Generalization and Specialization

Modeling with UML, inheritance enables us to organize concepts into hierarchies. At the top of the hierarchy is a general concept, and at the bottom of the hierarchy are the most specialized concepts.

Generalization is the modeling activity that identifies abstract concepts from lower-level ones.

Specialization is the activity that identifies more specific concepts from a high-level one.

In some instances, modelers call inheritance relationships generalization-specialization relationships. In this book, we use the term “inheritance” to denote the relationship and the terms “generalization” and “specialization” to denote the activities that find inheritance relationships.

Analysis Activities: From Use Cases to Objects

In this section, we describe the activities that transform the use cases and scenarios produced during requirements elicitation into an analysis model. Analysis activities include:

  1. Identifying Entity Objects
  2. Identifying Boundary Objects
  3. Identifying Control Objects
  4. Mapping Use Cases to Objects with Sequence Diagrams
  5. Modeling Interactions among Objects with CRC Cards
  6. Identifying Associations
  7. Identifying Aggregates
  8. Identifying Attributes
  9. Modeling State-Dependent Behavior of Individual Objects
  10. Modeling Inheritance Relationships
  11. Reviewing the Analysis Model

Identifying Entity Objects

Participating objects form the basis of the analysis model. Natural language analysis is an intuitive set of heuristics for identifying objects, attributes, and associations from a requirements specification. Abbott’s heuristics maps parts of speech (e.g., nouns, having verbs, being verbs, adjectives) to model components (e.g., objects, operations, inheritance relationships, classes). Table 5-1 provides examples of such mappings by examining the ReportEmergency use case:

The following heuristics can be used in conjunction with Abbott’s heuristics:

As it was mentioned before, Entity Objects represent the persistent information tracked by the system. For entity objects we recommend always to start with the names used by end users and application domain specialists. Describing objects, even briefly, allows developers to clarify the concepts they use and avoid misunderstandings (e.g., using one object for two different but related concepts).

For example, after a first examination of the ReportEmergency use case (Figure 5-7), we use application domain knowledge and interviews with the users to identify the objects Dispatcher, EmergencyReport, FieldOfficer, and Incident. Note that the EmergencyReport object is not mentioned explicitly by name in the ReportEmergency use case. Step 4 of the use case refers to the emergency report as the “information submitted by the FieldOfficer.” After review with the client, we discover that this information is usually referred to as the “emergency report” and decide to name the corresponding object EmergencyReport.

The definition of entity objects leads to the initial analysis model described in Table 5-2.

Identifying Boundary Objects

Boundary objects represent the system interface with the actors. In each use case, each actor interacts with at least one boundary object. The boundary object collects the information from the actor and translates it into a form that can be used by both entity and control objects.

We find the boundary objects of Table 5-3 by examining the ReportEmergency use case.

We have made progress toward describing the system. We now have included the interface between the actor and the system. We are, however, still missing some significant pieces of the description, such as the order in which the interactions between the actors and the system occur. In the next section, we describe the identification of control objects.

Identifying Control Objects

Control objects are responsible for coordinating boundary and entity objects. Control objects usually do not have a concrete counterpart in the real world. Often a close relationship exists between a use case and a control object; a control object is usually created at the beginning of a use case and ceases to exist at its end. It is responsible for collecting information from the boundary objects and dispatching it to entity objects. For example, control objects describe the behavior associated with the sequencing of forms, undo and history queues, and dispatching information in a distributed system.

We model the control flow of the ReportEmergency use case with a control object for each actor: ReportEmergencyControl for the FieldOfficer and ManageEmergency-Control for the Dispatcher, respectively (Table 5-4).

The decision to model the control flow of the ReportEmergency use case with two control objects stems from the knowledge that the FieldOfficerStation and the DispatcherStation are actually two subsystems communicating over an asynchronous link.

Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Caracas, Valladolid, Quito, Guayaquil, Jaén, Villafranca de Ordizia

WhatsApp: +34633129287



Diodos y circuitos con diodos, Electronic Engineer

Diodos – Caracteres básicos

Diodos – Caracteres básicos.

Jueves 09 de noviembre, 2017, 04:43 am.


  1. Electrónica Hambley
    1. Características del diodo pp 137-145 (148)

Características del diodo.

El diodo es un dispositivo electrónico de gran importancia, que posee dos terminales: el ánodo y el cátodo. El símbolo del diodo se muestra en la Figura 3.1(a), mientras que en la Figura 3.1(b) se muestra su característica tensión-corriente.

La tensión vD en el diodo se toma como positiva de ánodo a cátodo. De igual manera, la corriente iD en el diodo se referencia como positiva cuando circula de ánodo a cátodo.

Puede observarse en la curva característica que, si la tensión vD es positiva en el diodo, pasa un flujo de corriente grande incluso con pequeñas tensiones. Esta condición se denomina polarización directa. Así, la corriente fluye fácilmente a través del diodo en la dirección que indica la flecha o el símbolo del diodo.

Por otra parte, para valores moderadamente negativos de vD, la corriente iD es muy pequeña. A esto se le llama región de polarización inversa, como puede verse en la curva característica del diodo. Si se aplica una tensión de polarización inversa suficientemente grande al diodo, su modo de operación entra en la región de ruptura inversa o zona de avalancha, permitiendo el flujo de una elevada corriente.

En la Figura 3.2 se muestra la curva característica de un diodo típico de silicio de pequeña señal trabajando a una temperatura de 300o K. Observe que las escalas para la tensión y la corriente en la región de polarización directa son diferentes a las utilizadas en la región de polarización inversa. Esto ayuda a presentar con claridad los detalles de la curva característica ya que los valores de corriente son mucho más pequeños, y los de tensión mucho más grandes, en la región de polarización inversa que en la región de polarización directa.

Los diodos de silicio de pequeña señal se pueden encontrar comúnmente en circuitos electrónicos de baja y media potencia. Uno de esos diodos discretos es el 1N4148, distribuido por varios fabricantes. Los diodos en los circuitos integrados tienen características similares a las de los diodos discretos de pequeña señal.

En la región de polarización directa, los diodos de silicio de pequeña señal conducen muy poca corriente (mucho menos de 1 mA), hasta que se aplica una tensión directa de 0,6 a 0,7 V (suponiendo que el diodo se encuentra a una temperatura de aproximadamente 300o K). Entonces, la corriente aumenta muy rápidamente a medida que se sigue incrementando la tensión. Decimos que la curva característica de polarización directa presenta un codo sobre los 0,6 V. A medida que aumenta la temperatura, la tensión de codo disminuye a razón de aproximadamente 2 mV/K.

En la región de polarización inversa, para diodos de silicio de pequeña señal a temperatura ambiente, la corriente típica es de, aproximadamente, 1 nA. Cuando se alcanza la ruptura inversa, la corriente aumenta de valor rápidamente. La tensión para la que ocurre esto se llama tensión de ruptura. Por ejemplo, la tensión de ruptura de la curva característica del diodo mostrada en la Figura 3.2 es, aproximadamente, de -100 V.

Los diodos que trabajan en la zona de ruptura se denominan diodos zéner o diodos de avalancha. Los diodos zéner se usan en aplicaciones para las que se necesita una tensión constante en la región de ruptura. Por tanto, los fabricantes intentan optimizar los diodos zéner para obtener una curva característica prácticamente vertical en la región de ruptura. El símbolo modificado del diodo que se muestra en la Figura 3.3 es el que se usa para los diodos zéner.


Análisis de la línea de carga.

La curva característica tensión-corriente de los diodos no es lineal. A causa de esta no linealidad, muchas de las técnicas aprendidas en los cursos básicos de teoría de circuitos para trabajar con circuitos lineales no se pueden aplicar a circuitos que empleen diodos. Los métodos gráficos constituyen un enfoque para analizar este tipo de circuitos. Por ejemplo, consideremos el circuito de la Figura 3.4.

Aplicando la ley de tensiones de Kirchhoff, podemos escribir:

Supongamos que los valores de VSS y de R se conocen, y que deseamos hallar iD y vD. Así, la Ecuación (3.1) tiene dos incógnitas, por lo que se necesita otra relación entre iD y vD para hallar una solución. La relación necesaria se ve de forma gráfica en la Figura 3.5, en la que se muestra la curva característica tensión-corriente del diodo.

Podemos obtener la solución trazando la Ecuación (3.1) en los mismos ejes que la curva característica del diodo. El punto de trabajo es la intersección de la línea de carga y la curva característica del diodo. El punto de trabajo representa la solución simultánea de la Ecuación (3.1) y de la característica del diodo.

Ejemplos 3.1 y 3.2

Modelo de diodo ideal.

Aunque el análisis de la línea de carga de los circuitos con diodos nos proporciona resultados precisos y reveladores, necesitamos modelos más simples para analizar con rapidez circuitos que contengan varios diodos. Un modelo muy útil para ello es el modelo del diodo ideal, un conductor perfecto con una caída de tensión cero en conducción directa. En conducción inversa, el diodo ideal es un circuito abierto. La curva característica tensión – corriente del diodo ideal se muestra en la Figura 3.8.

Al analizar un circuito con diodos ideales, puede que inicialmente no sepamos qué diodos están en conducción y cuáles al corte. Por tanto, nos vemos forzados a aventurar condiciones. Luego, analizamos el circuito para encontrar las corrientes en los diodos que hemos supuesto que están en conducción, y las tensiones en los que hemos supuesto que están al corte. Si iD es positiva en los diodos supuestamente en conducción y si vD es negativa en los supuestamente al corte, nuestras presunciones son correctas, y ya hemos resuelto el circuito (estamos suponiendo que iD se referencia como positiva en conducción directa y vD es positiva en el ánodo). Si no es así, debemos hacer otros supuestos respecto a los diodos y comenzar de nuevo. Después de algo de práctica, nuestra primera presunción será casi siempre correcta, al menos en circuitos simples.

Ejemplos 3.3 y 3.4

Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Ecuador (Quito, Guayaquil, Cuenca)

WhatsApp: 00593984950376


Conversión Electromecánica de energía, Máquinas Eléctricas

Concepto de Campo Magnético – Teorema de Gauss

El campo magnético es un modelo que permite describir matemáticamente la influencia magnética de las corrientes eléctricas o de los materiales ferromagnéticos, los cuáles son materiales imanados espontáneamente.


Producción de un campo magnético

La ley básica que gobierna la producción de un campo magnético es la ley de Ampere, que relaciona un campo magnético estático de intensidad H, alrededor de un contorno cerrado C, con su causa, es decir, una corriente eléctrica estática de densidad J:


La ecuación 1.1 establece entonces que la fuente del campo magnético H es la densidad de corriente J. El último término es la corriente de desplazamiento. Este término es de gran importancia para los campos magnéticos que se generan en el espacio mediante campos eléctricos variantes en el tiempo, asociados con la radiación electromagnética. Ignorar este término da como resultado un imán cuasiestático, y la ecuación 1.1 se puede simplificar hasta llegar a la ecuación 1.2:


Donde H es la intensidad del campo magnético producida por la corriente Ineta, mientras que dl es el elemento diferencial a lo largo de la trayectoria de integración.

Densidad de flujo magnético

Por otra parte, la magnitud física que caracteriza al vector que representa al campo magnético, recibe el nombre de vector de inducción magnética B (también denominado densidad de flujo magnético B), donde:


La ecuación 1.3, también conocido como Teorema de Gauss, establece que se conserva la cantidad de flujo magnético, es decir, que ningún flujo magnético neto entra o sale de una superficie cerrada S. Las líneas de flujo magnético sólo existen en lazos continuos, no tienen principio ni fin como es el caso de las líneas de flujo eléctrico. De esta ecuación también se advierte que las cantidades de campo magnético sólo pueden ser determinadas a partir de los valores instantáneos de las fuentes de corriente.

La relación entre el campo magnético y la inducción magnética creada por un material ferromagnético, reviste una importancia extraordinaria en la utilización técnica de dicho material. La inducción magnética B se induce por La intensidad del campo magnético H. La relación entre ambas cantidades es la siguiente:


Donde μ es la permeabilidad magnética del material. La relación 1.4 es mejor expresarla mediante curvas características, denominadas curvas de magnetización (curvas de saturación), tales como las mostradas en la Figura 2.26:



La intensidad del campo magnético se mide en ampere-vueltas por metro (A/m), la permeabilidad en henrys por metro y la densidad de flujo resultante en webers por metro cuadrado, conocidos como teslas (T).

Flujo Magnético

En un núcleo de material ferromagnético como el que se muestra en la Figura 1.3:


La magnitud de la densidad de flujo está dada por:


Donde ln es la longitud media del núcleo, y la corriente Ineta que pasa por el camino de integración es igual a Ni, puesto que la bobina de alambre corta dicho camino N veces mientras pasa la corriente i. Ahora, el flujo total Ø en cierta área del núcleo está dado por:


Donde dA es el diferencial del área. Si el vector de densidad de flujo es perpendicular a un plano de área A y si la densidad de flujo es constante en toda el área, la ecuación se reduce a:


Si sustituimos la ecuación 1.5 en 1.7 obtenemos la ecuación 1.8, una interesante relación que demuestra como la corriente en una bobina de alambre conductor enrollado alrededor de un núcleo de material ferromagnético, produce un flujo magnético en dicho material.


Puesto que los motores y generadores dependen del flujo magnético para producir el voltaje y el par, se diseñan para producir el máximo flujo posible. Como resultado, la mayoría de las máquinas reales operan cerca del punto de rodilla de la curva de magnetización.

Fuerza magnetomotriz

Siempre que existe un flujo magnético Ø en un cuerpo o componente, se debe a la intensidad de un campo magnético H, dada por:


Donde Fm es la fuerza magnetomotriz que actúa en el componente (medido en Ampere-vuelta) y l es la longitud del componente (medido en metros).

La relación entre el flujo magnético Ø y la fuerza magnetomotriz Fm es semejante aquella que existe entre la densidad de flujo B y la intensidad del campo magnético H, tal como lo ilustra la Figura 1.10.

Es decir, que para un núcleo dado la intensidad del campo magnético es directamente proporcional a la fuerza magnetomotriz, y que la densidad de flujo magnético es directamente proporcional al flujo magnético total.

Curva de Histéresis

En vez de aplicar una corriente continua a los devanados dispuestos sobre el núcleo, se aplica una corriente alterna para observar qué ocurre. Dicha corriente se muestra en la Figura 1-11 (a). Suponga que el flujo inicial en el núcleo es cero. Cuando se incrementa la corriente por primera vez, el flujo en el núcleo sigue la trayectoria ab, dibujada en la Figura 1-11 (b). Ésta es básicamente la curva de saturación que se muestra en la figura 1-10. Sin embargo, cuando la corriente decrece, el flujo representado en la curva sigue una trayectoria diferente de la seguida cuando la corriente iba en aumento. Cuando la corriente decrece, el flujo en el núcleo sigue la trayectoria bcd y, más tarde, cuando la corriente se incrementa de nuevo, el flujo sigue la trayectoria deb. Nótese que la cantidad de flujo presente en el núcleo depende no sólo de la cantidad de corriente aplicada a los devanados del núcleo, sino también de la historia previa del flujo presente en el núcleo. Esta dependencia de la historia previa del flujo y el seguir una trayectoria diferente en la curva se denomina histéresis. La trayectoria bcdeb descrita en la Figura 1-11 (b), que representa la variación de la corriente aplicada, se denomina curva o lazo de histéresis.

Nótese que si primero se aplica al núcleo una fuerza magnetomotriz intensa y luego se deja de aplicar, la trayectoria del flujo en el núcleo será abc. Cuando se suspende la fuerza magnetomotriz, el flujo no llega a cero, ya que permanece cierto flujo en el núcleo, denominado flujo residual (o flujo remanente), el cual es la causa de los imanes permanentes. Para que el flujo llegue a cero, se debe aplicar al núcleo, en dirección opuesta, cierta fuerza magnetomotriz llamada fuerza magnetomotriz coercitiva.

Circuito Magnético

La relación entre flujo magnético Ø y la fuerza magnetomotriz Fm, da pie a una segunda simplificación de gran valor práctico, el circuito magnético. La ecuación 1.8 nos mostró que una corriente produce un campo magnético. Esto es análogo al voltaje que produce un flujo de corriente en un circuito eléctrico. Es posible entonces definir un circuito magnético cuyo comportamiento esté determinado por ecuaciones análogas a aquellas establecidas para un circuito eléctrico.

En un circuito eléctrico, el voltaje V genera una corriente I a lo largo de una resistencia R, tal como se ilustra en la Figura 1-4 (a). El voltaje es una fuerza electromotriz que genera el flujo de corriente. Por analogía, en un circuito magnético esta fuerza es Fm de la ecuación 1.9, la cual es igual al flujo efectivo de corriente aplicado al núcleo, es decir:


Al igual que la fuente de voltaje, fuerza magnetomotriz Fm tiene una polaridad asociada a ella. Dicha polaridad se determina mediante la regla de la mano derecha, como muestra la Figura 1-5:



La fuerza Fm ocasiona un flujo magnético Ø. Si la relación entre el voltaje V y la corriente I en un circuito eléctrico está determinada por V=RI, de forma similar, la relación entre Fm y Ø es:


Donde ℜ es la reluctancia del circuito.

Más sobre circuito magnético en la próxima entrega: Circuito Magnético.

Finalizado el Martes 08 noviembre, 2017, 4:57 am

ANTERIOR: Movimiento Rotatorio – Conceptos básicos

SIGUIENTE: Circuito Magnético


  1. Maquinas Eléctricas-Chapman-5ta-edición
  2. Circuitos magnéticos y transformadores ee staff mit
  3. Analysis of Electric Machinery and Drive Systems
  4. Dynamic simulation of Electric Machinery using MATLAB
  5. Getty Images


Escrito por Prof. Larry Francis Obando – Technical Specialist – Educational Content Writer – Twitter: @dademuch

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Electronic Engineer, Power Electronics

Power Electronics – Introduction


In broad terms, the task of power electronics is to process and control the flow of electric energy by supplying voltages and currents in a form that is optimally suited for user loads.

Figure 1-1 shows a power electronic system in a block diagram form. The power input to this power processor is usually (but not always) from the electric utility at a line frequency of 60 or 50 Hz, single phase or three phases. The phase angle between the input voltage and the current depends on the topology and the control of the power processor. The processed output (voltage, current, frequency, and the number of phases) is as desired by the load. If the power processor’s output can be regarded as a voltage source, the output current and the phase angle relationship between the output voltage and the current depend on the load characteristic. Normally, a feedback controller compares the output of the power processor unit with a desired (or a reference) value, and the error between the two is minimized by the controller. The power flow through such systems may be reversible, thus interchanging the roles of the input and the output.

In recent years, the field of power electronics has experienced a large growth due to confluence of several factors. The controller in the block diagram of Fig. 1-1 consists of linear integrated circuits and/or digital signal processors. Revolutionary advances in microelectronics methods have led to the development of such controllers. Moreover, these advances in semiconductor fabrication technology have made it possible to significantly improve the voltage- and current-handling capabilities and the switching speeds of power semiconductor devices, which make up the power processor unit of Fig. 1-1. At the same time, the market for power electronics has significantly expanded. Electric utilities in the United States expect that by the year 2000 over 50% of the electrical load may be supplied through power electronic systems such as in Fig. 1-1.

Power Electronics Defined

It has been said that people do not use electricity, but rather they use communication, light, mechanical work, entertainment, and all the tangible benefits of both energy and electronics. In this sense, electrical engineering is a discipline very much involved in energy conversion and information. In the general world of electronics engineering, the circuits engineers design and use are intended to convert information, with energy merely a secondary consideration in most cases. In radio frequency applications, energy and information are sometimes on a more equal footing, but the main function of any circuit is that of information transfer.

What about the conversion and control of electrical energy itself? Electrical energy sources are varied and of many types. It is natural, then, to consider how electronic circuits and systems can be applied to the challenges of energy conversion and management. This is the framework of power electronics, a discipline that is defined in terms of electrical energy conversion, applications, and electronic devices. More specifically,

DEFINITION: Power electronics involves the study of electronic circuits intended to control the flow of electrical energy. These circuits handle power flow at levels much higher than the individual device ratings.

Power Electronics Vs Linear Electronics

In any power conversion process such as that shown by the block diagram in Fig. 1- 1, a small power loss and hence a high energy efficiency is important because of two reasons: the cost of the wasted energy and the difficulty in removing the heat generated due to dissipated energy.

Other important considerations are reduction in size, weight, and cost. The above objectives in most systems cannot be met by linear electronics where the semiconductor devices are operated in their linear (active) region and a line-frequency transformer is used for electrical isolation. As an example, consider the direct current (dc) power supply of Fig. 1-2a to provide a regulated output voltage V, to a load.

The utility input may be typically at 120 or 240 V and the output voltage may be, for example, 5 V. The output is required to be electrically isolated from the utility input. In the linear power supply, a line-frequency transformer is used to provide electrical isolation and for stepping down the line voltage. The rectifier converts the alternating current (ac) output of the transformer low-voltage winding into dc. The filter capacitor reduces the ripple in the dc voltage vd. Figure 1-2b shows the vd waveform, which depends on the utility voltage magnitude (normally in a t 10% range around its nominal value).

The transformer turns ratio must be chosen such that the minimum of the input voltage v, is greater than the desired output V. For the range of the input voltage waveforms shown in Fig. 1-2b, the transistor is controlled to absorb the voltage difference between v and V, thus providing a regulated output. The transistor operates in its active region as an adjustable resistor, resulting in a low energy efficiency. The line-frequency transformer is relatively large and heavy.

In power electronics, the above voltage regulation and the electrical isolation are achieved, for example, by means of a circuit shown in Fig. 1-3a.

In this system, the utility input is rectified into a dc voltage vd, without a line-frequency transformer. By operating the transistor as a switch (in a switch mode, either fully on or fully 0ff) at some high switching frequency f, for example at 300 kHz, the dc voltage vd is converted into an ac voltage at the switching frequency. This allows a high-frequency transformer to be used for stepping down the voltage and for providing the electrical isolation.

In order to simplify this circuit for analysis, we will begin with the dc voltage vd as the dc input and omit the transformer, resulting in an equivalent circuit shown in Fig. 1-3b.

Suffice it to say at this stage that the transistor diode combination can be represented by a hypothetical two-position switch shown in Fig. 1-4a (provided iL(t) > 0).

The switch is in position a during the interval t-on, when the transistor is on and in position b when the transistor is off during t-off. As a consequence, Voi equals Vd, and zero during t-on and t-off, respectively, as shown in Fig. 1-4b.

Let us define

where Voi is the average (dc) value of Voi-t, and the instantaneous ripple voltage V-ripple, which has a zero average value, is shown in Fig. 1-4c.

The L-C elements form a low-pass filter that reduces the ripple in the output voltage and passes the average of the input voltage, so that

where Vo, is the average output voltage. From the repetitive waveforms in Fig. 1-4b, it is easy to see that

As the input voltage Vd changes with time, Eq. 1-3 shows that it is possible to regulate Vo, at its desired value by controlling the ratio t-on/Ts which is called the duty ratio D of the transistor switch. Usually, Ts (= l/fs) is kept constant and t-on is adjusted.

There are several characteristics worth noting. Since the transistor operates as a switch, fully on or fully off, the power loss is minimized. Of course, there is an energy loss each time the transistor switches from one state to the other state through its active region. Therefore, the power loss due to switchings is linearly proportional to the switching frequency. This switching power loss is usually much lower than the power loss in linear regulated power supplies.

At high switching frequencies, the transformer and the filter components are very small in weight and size compared with line-frequency components.

Scope and Applications of Power Electronics 

The expanded market demand for power electronics has been due to several factors discussed below:

  • Switch-mode (dc) power supplies and uninterruptible power supplies. Advances in microelectronics fabrication technology have led to the development of computers, communication equipment, and consumer electronics, all of which require regulated dc power supplies and often uninterruptible power supplies.
  • Energy conservation. Increasing energy costs and the concern for the environment have combined to make energy conservation a priority. One such application of power electronics is in operating fluorescent lamps at high frequencies (e.g., above 20 kHz) for higher efficiency. Another opportunity for large energy conservation is in motor-driven pump and compressor systems. In a conventional pump system shown in Fig. 1-5a, the pump operates at essentially a constant speed, and the pump flow rate is controlled by adjusting the position of the throttling valve. This procedure results in significant power loss across the valve at reduced flow rates where the power drawn from the utility remains essentially the same as at the full flow rate. This power loss is eliminated in the system of Fig. 1-56, where an adjustable-speed motor drive adjusts the pump speed to a level appropriate to deliver the desired flow rate.

  • Process control and factory automation. There is a growing demand for the enhanced performance offered by adjustable-speed-driven pumps and compressors in process control. Robots in automated factories are powered by electric servo (adjustable-speed and position) drives. It should be noted that the availability of process computers is a significant factor in making process control and factory automation feasible.
  • Transportation. In many countries, electric trains have been in widespread use for a long time. Now, there is also a possibility of using electric vehicles in large metropolitan areas to reduce smog and pollution. Electric vehicles would also require battery chargers that utilize power electronics.
  • Electro-technical applications. These include equipment for welding, electroplating, and induction heating.
  • Utility-related applications. One such application is in transmission of power over high-voltage dc (HVDC) lines. At the sending end of the transmission line, line-frequency voltages and currents are converted into dc. This dc is converted back into the line-frequency ac at the receiving end of the line. Power electronics is also beginning to play a significant role as electric utilities attempt to utilize the existing transmission network to a higher capacity. Potentially, a large application is in the interconnection of photovoltaic and wind-electric systems to the utility grid.
Classification of Power Processors and Converters

For a systematic study of power electronics, it is useful to categorize the power processors, shown in the block diagram of Fig. 1-1, in terms of their input and output form or frequency.

In most power electronic systems, the input is from the electric utility source. Depending on the application, the output to the load may have any of the following forms:

  1. dc
    1. regulated (constant) magnitude
    2. adjustable magnitude
  2. ac
    1. constant frequency, adjustable magnitude
    2. adjustable frequency and adjustable magnitude

The utility and the ac load, independent of each other, may be single phase or three phase. The power flow is generally from the utility input to the output load.

The power processors of Fig. 1-1 usually consist of more than one power conversion stage (as shown in Fig. 1-6) where the operation of these stages is decoupled on an instantaneous basis by means of energy storage elements such as capacitors and inductors.

Therefore, the instantaneous power input does not have to equal the instantaneous power output. We will refer to each power conversion stage as a converter. Thus, a converter is a basic module (building block) of power electronic systems. It utilizes power semiconductor devices controlled by signal electronics (integrated circuits) and possibly energy storage elements such as inductors and capacitors. Based on the form (frequency) on the two sides, converters can be divided into the following broad categories:

  1. ac to dc
  2. dc to ac
  3. dc to dc
  4. ac to ac

We will use converter as a generic term to refer to a single power conversion stage that may perform any of the functions listed above. To be more specific, in ac-to-dc and dc-to-ac conversion, rectifier refers to a converter when the average power flow is from the ac to the dc side. Inverter refers to the converter when the average power flow is from the dc to the ac side.

Further insight can be gained by classifying converters according to how the devices within the converter are switched. There are three possibilities:

  1. Line frequency (naturally cornmutated) converters, where the utility line voltages present at one side of the converter facilitate the turn-off of the power semiconductor devices. Similarly, the devices are turned on, phase locked to the line voltage waveform. Therefore, the devices switch on and off at the line frequency of 50 or 60 Hz.
  2. Switching (forced-commutated) converters, where the controllable switches in the converter are turned on and off at frequencies that are high compared to the line frequency.
  3. Resonant and quasi-resonant converters, where the controllable switches turn on and/or turn off at zero voltage and/or zero current.

Interdisciplinary Nature of Power Electronics

The discussion in this introductory chapter shows that the study of power electronics encompasses many fields within electrical engineering, as illustrated by Fig. 1- 10.

Combining the knowledge of these diverse fields makes the study of power electronics challenging as well as interesting. There are many potential advances in all these fields that will improve the prospects for applying power electronics to new applications.


  1. Power Electronic – Mohan
  2. Libro Rashid – Power Electronic Handbook

Literature Review by: Larry Francis Obando – Technical Specialist

Lunes 15 de noviembre, 11:08 am – Caracas, Quito, Guayaquil.

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Ecuador (Quito, Guayaquil, Cuenca) telf. +34633129287

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