Dependent Sources

9 Key excerpts on "Dependent Sources"

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  The Analysis and Design of Linear Circuits

  • Roland E. Thomas, Albert J. Rosa, Gregory J. Toussaint(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  Although Dependent Sources are elements used in circuit analysis, they are conceptually different from the other circuit elements we have studied. The linear resistor and ideal switch are models of actual devices called resistors and switches. However, you will not find Dependent Sources listed in electronic part catalogs. For this reason, Dependent Sources are more abstract, since they are not models of identifiable physical devices. Dependent Sources are used in combination with other circuit elements to create models of active devices. + − i 1 ri 1 (b) CCVS i 1 βi 1 (d) CCCS gv 1 (e) VCCS (a) + − μv 1 (c) VCVS + v 1 − + v 1 − K y = Kx x FIGURE 4–1 Dependent source circuit symbols: (a) Block diagram of a gain stage. (b) Current-controlled voltage source. (c) Voltage-controlled voltage source. (d) Current- controlled current source. (e) Voltage-controlled current source. 122 C H A P T E R 4 A CTIVE C IRCUITS In Chapter 3, we found that a voltage source acts as a short circuit when it is turned off. Likewise, a current source behaves as an open circuit when it is turned off. The same results apply to Dependent Sources, with one important difference. Dependent Sources cannot be turned on and off individually because they depend on excitation supplied by inDependent Sources. Some consequences of this dependency are illustrated in Figure 4–2. When the independent current source is turned on, KCL requires that i 1 = i S . Through con- trolled source action, the current controlled voltage source is on and its output is υ O = ri 1 = ri S When the independent current source is off i S = 0 , it acts as an open circuit and KCL requires that i 1 = 0. The dependent source is now off and its output is υ O = ri 1 = 0 When the independent current source is off, the dependent voltage source acts as a short circuit. In other words, turning the independent source on and off turns the dependent source on and off as well.

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  Mechanical Engineers' Handbook, Volume 2

  Design, Instrumentation, and Controls

  • Myer Kutz(Author)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Although Dependent Sources are elements used in circuit analysis, they are conceptually different from the other circuit elements. The linear resistor and ideal switch are models of actual devices called resistors and switches. But Dependent Sources are not listed in catalogs. For this reason Dependent Sources are more abstract, since they are not models of identifiable physical devices. Dependent Sources are used in combination with other resistive elements to create models of active devices.

  A voltage source acts like a short circuit when it is turned off. Likewise, a current source behaves like an open circuit when it is turned off. The same results apply to Dependent Sources, with one important difference. Dependent Sources cannot be turned on and off individually because they depend on excitation supplied by inDependent Sources. When applying the superposition principle or Thévenin's theorem to active circuits, the state of a dependent source depends on excitation supplied by inDependent Sources. In particular, for active circuits the superposition principle states that the response due to all inDependent Sources acting simultaneously is equal to the sum of the responses due to each independent source acting one at a time.

  Analysis with Dependent Sources

  With certain modifications the circuit analysis tools developed for passive circuits apply to active circuits as well. Circuit reduction applies to active circuits, but the control variable for a dependent source must not be eliminated. Applying a source transformation to a dependent source is sometimes helpful. Methods like node and mesh analysis can be adapted to handle Dependent Sources as well. But the main difference is that the properties of active circuits can be significantly different from those of the passive circuits.

  In the following example the objective is to determine the current, voltage, and power delivered to the output load in Fig 35 . The control current is found using current division in the input circuit:

  Similarly the output current is found using current division in the output circuit:

  But at node KCL requires that . Combining this result with the equations for and

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  Dorf's Introduction to Electric Circuits

  • Richard C. Dorf, James A. Svoboda(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  (b) A model of the transistor. (c) A transistor amplifier. (d) A model of the transistor amplifier. Dependent Sources 35 Figure 2.7-2 illustrates the use of Dependent Sources to model electronic devices. In certain circumstances, the behavior of the transistor shown in Figure 2.7-2a can be represented using the model shown in Figure 2.7-2b. This model consists of a dependent source and a resistor. The controlling element of the dependent source is an open circuit connected across the resistor. The controlling voltage is v be . The gain of the dependent source is g m . The dependent source is used in this model to represent a property of the transistor, namely, that the current i c is proportional to the voltage v be , that is, i c g m v be where g m has units of amperes/volt. Figures 2.7-2c and d illustrate the utility of this model. Figure 2.7-2d is obtained from Figure 2.7-2c by replacing the transistor by the transistor model. E X A M P L E 2 . 7 - 1 Power and Dependent Sources Determine the power absorbed by the VCVS in Figure 2.7-3. Solution The VCVS consists of an open circuit and a controlled-voltage source. There is no current in the open circuit, so no power is absorbed by the open circuit. The voltage v c across the open circuit is the controlling signal of the VCVS. The voltmeter measures v c to be v c 2 V The voltage of the controlled voltage source is v d 2 v c 4 V The ammeter measures the current in the controlled voltage source to be i d 1 5 A The element current i d and voltage v d adhere to the passive convention. Therefore, p i d v d 1 5 4 6 W is the power absorbed by the VCVS. 12 V 2 Ω 0.5 A 4 Ω + – i d Voltmeter + 2. 0 0 Ammeter + 1. 5 0 v d = 2v c + – + v c – FIGURE 2.7-3 A circuit containing a VCVS. The meters indicate that the voltage of the controlling element is v c 2.0 volts and that the current of the controlled element is i d 1.5 amperes. 36 CHAPTER 2 Circuit Elements EXERCISE 2.7-1 Find the power absorbed by the CCCS in Figure E 2.7-1.

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  Introduction to Electric Circuits

  • James A. Svoboda, Richard C. Dorf(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  (b) A model of the transistor. (c) A transistor amplifier. (d) A model of the transistor amplifier. Dependent Sources 35 Figure 2.7-2 illustrates the use of Dependent Sources to model electronic devices. In certain circumstances, the behavior of the transistor shown in Figure 2.7-2a can be represented using the model shown in Figure 2.7-2b. This model consists of a dependent source and a resistor. The controlling element of the dependent source is an open circuit connected across the resistor. The controlling voltage is v be . The gain of the dependent source is g m . The dependent source is used in this model to represent a property of the transistor, namely, that the current i c is proportional to the voltage v be , that is, i c ¼ g m v be where g m has units of amperes/volt. Figures 2.7-2c and d illustrate the utility of this model. Figure 2.7-2d is obtained from Figure 2.7-2c by replacing the transistor by the transistor model. E X A M P L E 2 . 7 - 1 Power and Dependent Sources Determine the power absorbed by the VCVS in Figure 2.7-3. Solution The VCVS consists of an open circuit and a controlled-voltage source. There is no current in the open circuit, so no power is absorbed by the open circuit. The voltage v c across the open circuit is the controlling signal of the VCVS. The voltmeter measures v c to be v c ¼ 2 V The voltage of the controlled voltage source is v d ¼ 2 v c ¼ 4 V The ammeter measures the current in the controlled voltage source to be i d ¼ 1:5 A The element current i d and voltage v d adhere to the passive convention. Therefore, p ¼ i d v d ¼ 1:5 ð Þ 4 ð Þ ¼ 6 W is the power absorbed by the VCVS. 12 V 2 Ω 0.5 A 4 Ω + – i d Voltmeter + 2. 0 0 Ammeter + 1. 5 0 v d = 2v c + – + v c – FIGURE 2.7-3 A circuit containing a VCVS. The meters indicate that the voltage of the controlling element is v c ¼ 2.0 volts and that the current of the controlled element is i d ¼ 1.5 amperes. Try it yourself in WileyPLUS 36 2. Circuit Elements

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  Introduction to Electric Circuits

  • Richard C. Dorf, James A. Svoboda(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  (b) A model of the transistor. (c) A transistor amplifier. (d) A model of the transistor amplifier. Dependent Sources 35 Figure 2.7-2 illustrates the use of Dependent Sources to model electronic devices. In certain circumstances, the behavior of the transistor shown in Figure 2.7-2a can be represented using the model shown in Figure 2.7-2b. This model consists of a dependent source and a resistor. The controlling element of the dependent source is an open circuit connected across the resistor. The controlling voltage is v be . The gain of the dependent source is g m . The dependent source is used in this model to represent a property of the transistor, namely, that the current i c is proportional to the voltage v be , that is, i c ¼ g m v be where g m has units of amperes/volt. Figures 2.7-2c and d illustrate the utility of this model. Figure 2.7-2d is obtained from Figure 2.7-2c by replacing the transistor by the transistor model. E X A M P L E 2 . 7 - 1 Power and Dependent Sources Determine the power absorbed by the VCVS in Figure 2.7-3. Solution The VCVS consists of an open circuit and a controlled-voltage source. There is no current in the open circuit, so no power is absorbed by the open circuit. The voltage v c across the open circuit is the controlling signal of the VCVS. The voltmeter measures v c to be v c ¼ 2 V The voltage of the controlled voltage source is v d ¼ 2 v c ¼ 4 V The ammeter measures the current in the controlled voltage source to be i d ¼ 1:5 A The element current i d and voltage v d adhere to the passive convention. Therefore, p ¼ i d v d ¼ 1:5 ð Þ 4 ðÞ¼ 6 W is the power absorbed by the VCVS. 12 V 2 Ω 0.5 A 4 Ω + – i d Voltmeter + 2. 0 0 Ammeter + 1. 5 0 v d = 2v c + – + v c – FIGURE 2.7-3 A circuit containing a VCVS. The meters indicate that the voltage of the controlling element is v c ¼ 2.0 volts and that the current of the controlled element is i d ¼ 1.5 amperes. Try it yourself in WileyPLUS 36 2. Circuit Elements

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  THE LTSPICE XVII SIMULATOR

  Commands and Applications

  • Gilles Brocard(Author)
  • 2021(Publication Date)
  • Adolf Würth GmbH & Co. KG

    (Publisher)

  522 17 Voltage and current source editor 17 .2 Two major types of source, dependent or independent • Editor for non-linear sources . They are presented at the end of the chapter. They advantageously replace, in recent schematics, the old sources E, F, G and H. • CVS = C ontrolled non-linear V oltage S ource (dependent) : Bvxx n+ n- • CCS = C ontrolled non-linear C urrent S ource (dependent) : Bixx n+ n- 17 .2 Two major types of source, dependent or inDependent Sources play a very important role in the functioning of LTspice XVII. There are two types: • InDependent Sources . These are active components, but they only depend on the parameters chosen by the user. These sources are used to call the circuit and allow the simulation computation. There are only three types: current source, voltage source and resistive load, but they can be called by several symbols that represent their function, e.g. a battery, a cell or a load, as we can see in Figure 17.1, top left. • Dependent Sources . As their name suggests, they are dependent on other elements of the schematic, whose voltage or current is taken as a controller. They have a very general use, so they make it possible to model many active components like bipolar transistors, JFETs, MOSFETs, UJTs, thyristors and operational amplifiers. They also make it possible to create block diagrams where each element is controlled by one or more other blocks forming part of the same diagram. This block-diagram method allows you to quickly check the operation of complex func-tions. Figure 17.1 523 17 Voltage and current source editor 17 .3 All simulations need an independent source 17 .3 All simulations need an independent source The configuration of a voltage or current source must be adapted to the simulation chosen . To be able to simulate a circuit, you must always add a source which calls the system and whose parameters correspond to the simulation chosen.

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  Circuit Analysis For Dummies

  • John Santiago(Author)
  • 2013(Publication Date)
  • For Dummies

    (Publisher)

  Chapter 10 .

  Understanding Linear Dependent Sources: Who Controls What

  A dependent source is a voltage or current source controlled by either a voltage or a current at the input side of the device model. The dependent source drives the output side of the circuit. Dependent Sources are usually associated with components (or devices) requiring power to operate correctly. These components are considered active devices because they require power to work; circuits using these devices are called active circuits. Active devices such as transistors perform amplification, allowing you to do things like crank up the volume of your music.

  When you’re dealing with active devices operating in a linear mode, the relationship between the input and output behavior is directly proportional. That is, the bigger the input, the bigger the output. Mathematically for a given input x, you have an output y with a gain amplification of G: y = Gx.

  The constant or gain G is greater than 1 for active circuits (think steroids) and less than 1 for passive circuits (think wimpy). In other engineering applications, technical terms for G include scale factor, scalar multiplier, proportionality constant, and weight factor

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  Circuit Analysis with PSpice

  A Simplified Approach

  • Nassir H. Sabah(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  If the source current of a VCCS depends on the voltage across the source, it can be shown (Section 4.5) that such a “source” is not really a source and can be replaced by a resistor. + – 6 1.5 V X 9 V – + 2V X – + I Y – + 3I Y FIGURE 2.13 Ideal, dependent voltage sources. + – 9 V 1 2 2V X – + V X I Y 3I Y FIGURE 2.14 Ideal, dependent current sources. Fundamentals of Resistive Circuits 31 Fundamentally, inDependent Sources excite a circuit by delivering energy through conversion from some non- electrical source of energy, such as solar energy or chemi- cal energy of batteries, or mechanical energy from prime movers. On the other hand, Dependent Sources do not con- vert energy from nonelectrical sources. They can deliver or absorb energy, just like inDependent Sources, but they are incapable of exciting a circuit on their own, without the presence of inDependent Sources somewhere in the circuit (Section 4.1). They affect the voltages and currents in a circuit, thereby altering the power distribution in the circuit, by effectively modifying the values of some resis- tances in the circuit (Section 5.1). But the ultimate source of energy is the inDependent Sources in a circuit, which convert energy from some nonelectrical source to poten- tial energy or kinetic energy of current carriers. Figure 2.15 summarizes the classification of ideal sources. Primal Exercise 2.11 Given I Y = 2.7 A and V X = 3.6 V in Figure 2.14, determine (a) the magnitude and direction of the current through the 1 Ω resistor, (b) the magnitude and polarity of the voltage across the 2 Ω resistor, (c) the power delivered or absorbed by each source, and (d) the power dissipated in each resistor. (e) Is energy conserved in the circuit as whole? Is charge conserved at the upper and lower junc- tions of the four elements connected to these junctions? Ans.

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  LTspice® for Linear Circuits

  • James A. Svoboda(Author)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  Chapter 2 Analysis of DC Circuits 30 Example 2.2 Determine the values of the current i 2 and voltage v 3 in the circuit shown in Figure 2.5a. Step 1. Formulate a circuit analysis problem. The circuit in Figure 2.5a contains two Dependent Sources: a voltage- controlled current source and a current-controlled voltage source. Table 2.1 summarizes the symbols and notation used to represent Dependent Sources, both in circuit diagrams and in LTspice schematics. Notice from Table 2.1 that, in LTspice, a controlling voltage of a depend- ent source is required to be the voltage across an open circuit and a controlling current is required to be the current in a short circuit. In contrast, in Figure 2.5a the controlling current of the dependent voltage source is the current in the 10 Ω resistor and the controlling voltage of the dependent current source is the voltage across the 20 Ω resistor. In anticipation of using LTspice, we redraw the circuit of Figure 2.5a as shown in Figure 2.5b. The circuit in Figure 2.5b both is equivalent to the circuit in Figure 2.5a and satisfies the requirements of Table 2.1. The current i 2 in a short circuit in Figure 2.5b is the same current as the current i 2 in the 10 Ω resistor in Figure 2.5a. Similarly, the voltage v 3 across an open circuit in Figure 2.5b is the same voltage as the voltage v 3 across the 20 Ω resistor in Figure 2.5a. This is important because 50 V 0.5 i 2 10 Ω v 3 v 3 + + – + – – 20 Ω 80 Ω 20 i 2 50 V 0.5 i 2 10 Ω v 3 v 3 + + – + – – 20 Ω 80 Ω 20 i 2 (a) (b) Figure 2.5 The circuit considered in Example 2.2. 2.2 Dependent ources 31 R1 10 a V1 b 50 + – R2 20 R3 80 c d Figure 2.6 Drawing the schematic for the circuit of Figure 2.5b – Stage 1. R1 V1 50 a b R2 + – R3 80 d 20 c G1 10 + – Figure 2.7 Drawing the schematic for the circuit of Figure 2.5b – Stage 2. Figure 2.5b conforms to the requirements of Table 2.1 and Figure 2.5a does not conform to the requirements of Table 2.1.

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