Physics
Current Sources in Series
Current sources in series refer to a configuration in which multiple current sources are connected in a series circuit. In this setup, the total current flowing through the circuit is the sum of the individual currents from each source. This arrangement allows for the combination of multiple current sources to provide a cumulative current output.
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6 Key excerpts on "Current Sources in Series"
- Frank R. Spellman, Nancy E. Whiting(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
Using the same idea as above, a problem can be solved in which the current is the unknown quantity. 11.7.6.8 Series Aiding and Opposing Sources Sources of voltage that cause current to flow in the same direction are considered to be series aiding, and their voltages add. Sources of voltage that would tend to force current in opposite directions are said to be series opposing , and the effective source voltage is the difference between the opposing voltages. When two opposing sources are inserted into a circuit, current flow would be in a direc-tion determined by the larger source. Examples of series aiding and opposing sources are shown in Figure 11.36. 11.7.6.9 Kirchhoff’s Law and Multiple Source Solutions Kirchhoff’s law can be used to solve multiple source circuit problems. When applying this method, the exact same procedure is used for multiple source circuits as was used for single source circuits. This is demonstrated by the following example. ■ EXAMPLE 11.32 Problem: Find the amount of current in the circuit shown in Figure 11.37. E 2 20 volts E 2 10 volt s E A 60 volts + – – + + – – + A I E ? FIGURE 11.35 Determining unknown voltage in a series circuit. 274 Handbook of Mathematics and Statistics for the Environment Solution: Start at point A. Basic equation: E a + E b + E c + … + E n = 0 From the circuit: E b 2 + E 1 – E b 1 + E b 3 + E 2 = 0 40 + 40 I – 140 + 20 + 20 I = 0 Combining like terms, we obtain 60 I – 80 = 0 60 I = 80 I = 1.33 amps 11.7.7 P ARALLEL DC C IRCUITS The principles we applied to solving simple series circuit calculations for determining the reactions of such quantities as voltage, current, and resistance can be used in parallel and series–parallel circuits. E 2 + – E 2 + + – – E 1 + – R 1 R 1 R 2 Series Aiding R 2 Series Opposing FIGURE 11.36 Series aiding and opposing sources. R 1 40 ohms E b2 40 v A E b1 140 v + + – – R 2 20 ohms + + – + – – I E b3 20 v FIGURE 11.37 Solving for circuit current in a multiple-source circuit.
eBook - PDFAnalog BiCMOS Design
Practices and Pitfalls
- James C. Daly, Denis P. Galipeau(Authors)
- 2018(Publication Date)
- CRC Press(Publisher)
chapter 3 Current Sources Current sources are the foundation of circuit design in microelectronics. Current sources provide biasing for circuit operation. They serve as out- put drivers. They serve as load elements in amplifier input stages. Even logic gates can be modeled as a collection of variable current sources. Analysis of circuits in proceeding chapters will often show a resistance biasing the block under analysis. Current mirrors are used almost ex- clusively for this purpose in microelectronics. Current sources offer the advantages of smaller size, higher accuracy and can be designed to pro- vide temperature coefficients of current as needed. However, resistors can and do serve well as current sources in some instances. Let us first consider the characteristics of an ideal DC current source as provided in circuit simulators such as SPICE. Constant current of any value is provided at all times. Infinite output impedance means there is no change in the source current value due to changes in the output node voltage. The source has infinite compliance, and will provide the specified current regardless of the voltage across the source. An ideal current source can either sink or source current. The polarity of the specified DC current and the nodal connection of the current source to the rest of the circuit determine how the source behaves. (Most simulators have an ideal current source with two nodes: positive and negative. Positive current flow in the ideal source is defined as flowing into the positive node and out of the negative node.) Unfortunately, physical constraints apply in the real world of semicon- ductors, and real current sources fall short of perfection. Current provided by integrated circuit current sources are constant within some tolerance, and the value of current depends on limita- tions of device size, power dissipation and process Early voltages.
eBook - PDFCurrent Sources and Voltage References
A Design Reference for Electronics Engineers
- Linden T. Harrison(Author)
- 2005(Publication Date)
- Newnes(Publisher)
13 Chapter 2 An Introduction to Current Sources 2.1 An overview Current sources are basic electronic building blocks that are used extensively in the architectures of analog ICs, as well as in OEM circuit board designs. In both cases, current sources are created by combining diodes, resistors, and transistors (BJTs or FETs). They can also be created at the circuit board level by using discretes, matched pairs, transistor arrays, or by combining op amps with precision voltage references. The various techniques for doing so will be reviewed in Part 1 of this book. Although a few dedicated monolithic current source ICs are commercially available, it is often nec-essary to create one’s own circuit to match the particular needs of the application. Although most forms of today’s instrumentation use either voltage or current refer-ences, the former are far more available. As a result, designers frequently use voltage references together with precision resistors, so that a stable reference voltage is con-verted into a precise current. Applications for current sources range from biasing and stabilization to reference and linearizing. For example, in the design of an op amp, the IC designer will use current sources to create active loads for the amplifier stages and to establish precise bias levels. By providing a constant current, this forces amplifier stages to stay at the Q-points within their active linear regions (see Figure 2.1). In a circuit board design, a current source may be used for linearly charging a capacitor with a constant current, as in a precision timing circuit or in a peak detector. In a med-ical instrument application, a sensor and a low-noise, front-end amplifier could be biased using precision current sources to assist in recovering very-low-level signals. The advantages of using these building blocks is their inherent constant current out-puts, which are mostly independent of changes in supply voltage, temperature, load resistance, or load voltage.
- Frank R. Spellman(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
10.14.9 S ERIES A IDING AND O PPOSING S OURCES Sources of voltage that cause current to flow in the same direction are considered to be series aiding, and their volt-ages are added. Sources of voltage that would tend to force current in opposite directions are said to be series opposing , and the effective source voltage is the difference between the opposing voltages. When two opposing sources are inserted into a circuit, current flow would be in a direction determined by the larger source. Examples of series aiding and opposing sources are shown in Figure 10.39. 10.14.10 K IRCHHOFF ’ S L AW AND M ULTIPLE S OURCE S OLUTIONS Kirchhoff’s law can be used to solve multiple source circuit problems. When applying this method, the exact same pro-cedure is used for multiple-source circuits as was used for single-source circuits. This is demonstrated by the following example. ■ EXAMPLE 10.18 Problem: Find the amount of current in the circuit shown in Figure 10.40. Solution: Start at point A. Basic equation: E a + E b + E c + … + E n = 0 From the circuit: E b 2 + E 1 – E b 1 + E b 3 + E 2 = 0 40 + 40 I – 140 + 20 + 20 I = 0 Combining like terms, we obtain 60 I – 80 = 0 60 I = 80 I = 1.33 amps 10.15 GROUND The term ground is used to denote a common electrical point of zero potential. The reference point of a circuit is always considered to be at zero potential. The earth (ground) is said to be at zero potential. In Figure 10.41, point A is the zero reference or ground and is symbolized as such. Point C is 60 volts positive and point B is 20 volts positive with respect to ground. The common ground for much electrical/electronics equipment is the metal chassis. The value of ground is noted R 1 R 2 Series aiding E 1 E 2 + + – – R 1 R 2 Series opposing E 2 + + – – FIGURE 10.39 Aiding and opposing sources. I E b 1 140 V E b 2 140 v E b 3 20 V R 2 20 ohms + + + – + – + A – – – R 1 40 ohms FIGURE 10.40 Solving for circuit current in a multiple source circuit.
eBook - PDF- A. Henderson(Author)
- 2014(Publication Date)
- Arnold(Publisher)
In that case, however, the source currents cannot be calculated. Two Current Sources in Series are forbidden if the sum of the source strengths is not zero (for in this case KirchhofF s current law for the node between the two sources) is not valid. Two Current Sources in Series are not forbidden if the sum of the source strengths is zero. In that case the source voltages cannot be calculated. In network theory it often happens that there is analogy between two formulas, between two elements or between two circuits. For instance, one Kirchhoff's law turns into the other if one substitutes voltage for current and vice versa. We therefore say that the current law is the dual of the voltage law and vice versa. The dual character is also found in • voltage - current • open nodes - short circuit • resistance - conductance In the following chapters we shall often meet this phenomenon of duality. 1.3 Energy and power The voltage V A B between two points A and B is defined as the work needed to move a unit charge (1 C concentrated in a point) from point B to point A. If the charge is Aq the work is therefore AW = (V A - V B )Aq = V AB Aq, (1.14) in which VA and VB are the potentials of the points A and B. If VAB is constant (d.c.) and if the work is done in a time At, the average power is p _ A W _ Aq r At v At ' in which V = VAB-For At -> 0 we obtain P = VI. (1.15) So the power, in the case of d.c, is the product of voltage and current. Energy is expressed in joule (J), power in watt (W). Power can be consumed or supplied. If a current I flows through a network N with two terminals (also called a one-port) and if the polarity of the voltage V is such that I flows from + to - the power consumed is positive (Figure 1.11). 18 d.c. currents and d.c. voltages The voltage source transports (positive) charge from minus to plus and so delivers electrical energy to N (this energy is supplied by the chemical or mechanical system outside the network).
eBook - PDFLinear Circuit Theory
Matrices in Computer Applications
- Jiri Vlach(Author)
- 2016(Publication Date)
- Apple Academic Press(Publisher)
1 B ASIC C ONCEPTS 1 INTRODUCTION This chapter starts with the concept of electric current and voltage, introduces basic termi-nology and shows how networks are drawn. It gives a brief overview of all linear elements which are used in the network theory, plus a few of the most important practical devices. After this informal explanation we give definitions of the independent current and voltage sources, of resistors, of power delivered or consumed. Three fundamental laws are stated: the Ohm’s law and the Kirchhoff’s current and voltage laws. Based on this knowledge we study the voltage and current dividers and also explain how to obtain equivalent resistances for combinations of resistors. 1.1. VOLTAGES AND CURRENTS Network theory deals with voltages, currents, network elements and signals; in this sec-tion we will consider in detail the first two, and also introduce some basic concepts and typical signals. Electric current is a flow of electrons and is measured in amperes , denoted by the let-ter A . Voltage is a force which causes electrons to flow and is measured in volts , denoted by V . The concept of current is usually somewhat easier to grasp because we can visualize it as a current of water. When we talk about the flow of water, we associate it with a certain direction and we know, from daily experience, that the direction is from a higher point to a lower point. We also accept without difficulties that there must be some force which determines the direc-tion of the flow. A similar situation exists in electrical networks and the force that pushes the current through the elements is the voltage. The word potential can be used as well. In the early days of electricity, only chemical batteries were available and the con-cept of electrons was unknown. One of the connecting points of the battery was arbitrarily marked with a + sign, the other with a − sign and it was assumed that the current flowed into the external network from the + terminal to the − terminal.
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