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Power Integrity Analysis and Management for Integrated Circuits: Power, Delivering Power, and Power Integrity

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This chapter covers power, delivering power, and power integrity, with a focus on integrated circuits and systems.
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Power may be defined as the capacity to perform work, and is measured as the work done or energy transferred per unit of time. The greater the power, the greater the capacity to move something (against forces of attraction, repulsion, or friction) or to transfer energy (by raising the temperature of a substance, for example). With reference to electronic systems, and integrated circuits in particular, power is the presence of voltage, or electromotive force, and current, or the flow of charge. Power enables the performance of desired functions in the system and is delivered by devices that generate, store, or regulate electromotive force or flow of charge. Electronic circuits and systems consume this delivered power and convert it into other desired forms of energy or activity. The integrity of delivered power relates to its stability and invariability through variations in energy expenditure, in transfer elements, in the generating source, or in the surrounding environment. These aspects are expounded on in the following sections of this chapter, with a focus on integrated circuits and systems.

1.1 Electromotive Force (emf)

The discovery of electromotive force is attributed to physicist Alessandro Volta (1745–1827), who invented the electric battery or voltaic pile. Electric batteries possess the ability to move electric charge. They perform work, a prerequisite of which is the existence of force; batteries are therefore termed sources of electromotive force or emf.

The unit of emf is the volt, and as defined in the international system of units, one volt equals one joule per coulomb, where joule is the unit of energy and coulomb is the unit of electrical charge. Viewed another way, if a charge of a coulomb gains a joule of energy in passing through a device, the emf present across the device is a volt.

Since the movement of charged particles and gain (or loss) of energy is involved, mechanical analogies are often employed to illustrate aspects of electrical behavior such as emf, current, and power. The force-voltage analogy is a common example, wherein mechanical force is equated to electrical voltage.

1.1.1 Force-Voltage Analogy

The force-voltage analogy [1] is attributed to James Clerk Maxwell.1 Since the SI (French Le Système International d’Unités, or International System of Units) unit of force is the newton, and the unit of emf is the volt, this analogy is not altogether consistent. Nevertheless, many aspects of electrical behavior mirror the behavior of physical objects, and such an electrical-mechanical analogy assists comprehension. An electrical “tank” circuit, for example, behaves in much the same way as the pendulum of a mechanical clock.

Work done, whose SI unit is the joule, involves force and distance. Hence:

Equation 1-1

e1-1.jpg

Similarly, voltage difference, or electrical potential difference, in a homogeneous medium, is the work in joules required to move a coulomb of charge from a point to another. Therefore:

Equation 1-2

e1-2.jpg

If one associates force with voltage, following the relationships above, distance in mechanical terms will be equivalent to charge in electrical terms. Distance over time, or velocity, will be equivalent to charge transferred over time, or current.

Consider the expression for kinetic energy:

Equation 1-3

e1-3.jpg

where m is the mass and v the velocity of the object. Also consider the expression for energy stored in a magnetic coil:

Equation 1-4

e1-4.jpg

where L is the inductance of the magnetic coil, and I the current flowing through the coil. These expressions suggest an equivalence between mass and inductance.

The distance moved by an elastic spring increases the energy stored within it and linearly increases its force of resistance. Similarly, charge transferred into an electrical capacitance device increases the energy stored in the capacitance, and linearly increases emf across its terminals. Work done on a spring, or an increase in its potential energy, is given, following Hooke’s Law, by:

Equation 1-5

e1-5.jpg

where k is the elastic constant of the spring and x the elongation or compression. This relationship is equivalent to that for electrical potential energy stored in a capacitor:

Equation 1-6

e1-6.jpg

The equivalence is to an extent hidden within these expressions, since V does not correspond to x. The expression for potential energy in a spring may be derived by the integration of force (given by Hooke’s Law as k · x) over distance traversed (dx), which derivation is left to the reader. Hence, the expression for potential energy is obtained from force · distance ((k · x) · x), as in the fundamental definition of work done. Similarly, the expression of potential energy in a capacitor is derived from voltage · charge (V · (C · V)), which also follows from the definition of work done in electrical terms, in a manner consistent with the force-voltage analogy.

It is also useful to note the equivalence of energy in static and dynamic analysis of fluid flow to electrical energy, since electric current may be described as a fluid-like flow of electrons or charge at a macroscopic level. Gravitational potential energy is given by m · g · h, where m is mass, g is acceleration due to gravity, and h is the height increase. In an analogy with liquids, it is common to equate pressure at the bottom of a liquid column with emf. A conduit joining two columns of different diameter, but of the same height and fluid matter, will see no fluid flow since fluid pressure will be the same at both ends of the conduit. This example is equivalent to two capacitors of different capacitance value charged to the same electric potential. If the column heights are different, a flow of liquid between the two columns will be established through the conduit, subject to its diameter. The electrical equivalent to this physical analogy is the relationship between emf, or voltage, and charge flow, or current, as presented by Ohm’s Law:

Equation 1-7

e1-7.jpg

where R, or resistance, is the property by which materials oppose or resist the flow of charged particles through their atomic structures. Resistance is a property that leads to energy absorption. It is also a property that leads to loss of emf in an electrical circuit, since:

Equation 1-8

e1-8.jpg

whereby some electromotive force is spent in overcoming the resistance of a connecting element to the flow of charges through it, much as force is spent overcoming friction in mechanical systems.

Another analogy sometimes used is the force-current analogy, in which an electrical current source is equated with a force generator, and voltage equated with input velocity to a mechanical system. This analogy results in capacitance being equated to mass, inductance to the inverse of the spring constant, and resistance to the inverse of friction [1].

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