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Archives
 June 2000 Issue
Column
Broadband
The "Powers" That Be
By Ron Hranac
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| Ron Hranac |
Have you ever wondered what the term "power" means? Not the power that politicians, bureaucrats, dictators, cop-wanna-be security guards and department of motor vehicle clerks wield or pretend to wield, but power in the sense of our world of telecommunications. After all, the very signal level measurements we make in a cable TV network express the signal’s power.
To understand everything you ever wanted to know about power but were afraid to ask, let’s go over some definitions you may recall from high school science class.
Remember when you studied dynamics? The subject included terms such as acceleration, mass, force, work and power. Have some really strong coffee before reading on.
Dynamics
Force: The product of mass (m) and acceleration (a), measured in units called Newton (N): one Newton = one kilogram x (one meter/second2).
Work: Mechanical work (W) is the product of force (F) and distance (s). Where a force of one Newton acts over a distance of one meter, it produces the work of one Newton meter, which is equivalent to one joule (J) of energy.
Power: Mechanical power (P) is the derivative of work with respect to time. Power in mechanical systems often is measured in horsepower, but it also can be measured in watts (1 horsepower = 746 watts). If for a period of one second, an energy of one joule is converted at a constant rate, the corresponding power is 1 watt (W). That is, 1 W = 1 J/s.
Just so you don’t get too confused, keep in mind that electrical work is equivalent to mechanical work and electrical power is equivalent to mechanical power, but in both cases energy conversion is subject to losses.
From dynamics, your science teacher moved on to introductory electricity, which offered many of the following fun terms. These, too, require some strong coffee, but maybe not quite as strong as that required for dynamics.
Electricity
Ampere: You’re probably familiar with ampere (sometimes abbreviated amp, not to be confused with the abbreviation for amplifier, which also is amp) as a measure of electrical current. An ampere technically is a measure of a flow of charged particles per unit of time. One ampere equals one coulomb of charge flowing past a given point in one second. It’s also the current (I) that would produce a force of 2 x 10-7 Newton (remember dynamics?) per meter of length between two parallel conductors spaced one meter apart. Amperage is a bit like the volume of water flowing through a garden hose.
Coulomb: The coulomb is a unit of measure of electrically charged particles, where one coulomb is equal to 6.242 x 1018 electrons.
Electromotive force (EMF): This is the force of electrical attraction between two points of different charge potential. EMF is more commonly known as voltage (the volt is a measure of electromotive force), and is analogous to water pressure in a hose.
Energy: Energy is the capability of doing work. We usually think of energy being measured in electrical terms as the number of watts of power consumed during a particular unit of time, for instance, watt-hours or kilowatt-hours. That’s right, when the power company sends you your electricity bill, it’s for electrical energy, not power. From one perspective, you’re paying for the work that the electricity does for you, which is power multiplied by time.
One of the units used for energy is the previously mentioned watt-hour, which means that a power of one watt has been used for one hour. Another energy unit is the watt-second, or joule.
Joule: One joule is the work done by a force of one Newton acting over a distance of one meter. The joule is a measure of a quantity of energy and equals one watt-second.
Power: The rate at which work is done, or energy per unit of time. One watt of power is equal to one volt causing a current of one ampere.
Volt: The potential difference between two points on a wire carrying one ampere of current when the power dissipated between the points is one watt.
Watt: The power required to do work at a rate of one joule per second. That is, a joule of work per second is one watt.
Ohm: A unit of resistance (R), where one ohm is defined as the resistance that allows one ampere of current to flow between two points that have a potential difference of one volt.
With regard to this latter definition, you might recognize it as the basis for Ohm’s Law, which is R = E/I. Here R is resistance in ohms, E is electromotive force in volts, and I is current in amperes. This equation can be shuffled around a bit to give us some of the other variations of Ohm’s Law: E = IR and I = E/R.
Now go back to the definition of watt, a key subject of this month’s column. If you think about it for a moment, one watt is simply the use or generation of one joule of energy per second. Other electrical units are in fact derived from the watt. As you’ve no doubt surmised by now, all of this stuff is related. For instance, one volt is one watt per ampere. Another definition of watt is one volt of potential (EMF) "pushing" one ampere of current through a resistance, or P = EI. As was the case with Ohm’s Law, a bit of equation shuffling will give us E = P/I and I = P/E.
Put it all to use
Now, using your trusty scientific calculator and some basic algebra, substitute the Ohm’s Law equivalents for E and I into the formula P = EI, and you’ll get a couple other common expressions of power: P = E2/R and P = I2R.
Power calculations and measurements in direct current (DC) circuits and applications are relatively straightforward. For example, if you have a 1,000-ohm resistor with an applied voltage of 13.8 volts, the power dissipated by the resistor is 0.19 watt (P = E2/R or 0.19 = 13.82/1,000). Current through the resistor will be 0.0138 ampere (I = P/E or 0.0138 = 0.19/13.8; as well, I = E/R or 0.0138 = 13.8/1,000). Because this example is a DC circuit, the voltage always will be 13.8 volts and the current 0.0138 ampere. As long as the resistor’s value remains constant, it’s easy to calculate dissipated power.
Alternating current (AC) circuits and applications are much more complicated because the instantaneous voltage and current are not constant. In order to equate the varying AC waveform to a DC equivalent component, one must work in the world of root mean square (RMS) voltage and current, where PAVG = ERMS x IRMS cos Ø.
Consider an unmodulated RF carrier, which really is nothing more than a sinusoidal AC waveform. AC power measurement can be a bit tricky, though, because the product of voltage and current varies during the AC cycle by twice the frequency of the sine wave.
In other words, the output of a signal source such as an RF signal generator is a sinusoidal current at the desired frequency, but the product of the carrier’s voltage and current has what amounts to an equivalent DC component along with a component at twice the original frequency. In most cases of RF power measurement, "power" refers to the equivalent DC component of the voltage and current product.
If you connect a thermocouple power meter to the output of an RF signal source, the power meter’s power sensor will respond to the RF carrier’s DC component by averaging. Of course, this averaging usually is done over many cycles, which, at RF, still can be a relatively short period of time.
Otherwise, if the power meter simply measured an instantaneous point of the sine wave, then measured that sine wave at another instantaneous point, the result would vary according to the instantaneous product of the voltage and current at each measurement point.
This is the primary reason why most RF carrier power measurements are expressed in average power.
Which is the point
This is certainly true with regard to the signal level measurements made in our cable TV networks. They are expressions, in one form or another, of the carrier’s average power.
Ron Hranac is consulting systems engineer for Cisco Systems’ Service Provider Engineering group and senior technical editor for "Communications Technology." He can be reached via e-mail at .
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