Anyone who has built a small project or read a beginning article on electronic theory is certain to have run across such terms as micro-Farad, milli-Henry, and milli-Ampere-not to mention megaHertz, meg-Ohm, and kiloHertz. The prefixes here, micro-, milli-, mega-, and kilo-, are an important part of the electronic vocabulary. It follows, then that anyone who wants to be proficient in . electronics will have to develop skill in understanding and using the "language." These prefixes are used to change the value of an electronic unit of measure. For example, if you see a resistor with the familiar brown/black/green color code, you could call it a 1,000,000-ohm resistor. The thing is, it's usually less awkward to call it a 1-megohm resistor.
Purring the prefix meg or mega before the Ohm inflates the value of the unit, Ohm, by 1,000,000 times.
Similarly, one kiloVolt is recognizable as 1,000 Volts, and one kiloHertz as 1,000 Hertz, and so on. These prefixes are usually so automatic with electronics aficionados that they will invariably refer to a millionaire as a guy who has one megabuck! The Mini Side. At the other end of the scale, the milli and microprefixes are useful for shrinking units. A Farad, for example, is too big a unit to use in everyday electronics. In dealing with the real-life capacitors (the kind you solder into circuits), we normally use a basic unit of one-millionth of a Farad—a micro-Farad. The prefix micro-cuts up a unit into a million tiny slices, enabling us to use one such slice as a convenient-sized unit. A microAmpere, similarly, is a millionth of an Ampere; a microVolt, one millionth of a Volt.
If you need larger slices, the milli-prefix is available, which provides a unit only one-thousandth the size of the basic unit. A milli-Ampere, for example, is a thousandth of an Ampere; that is, it takes 1000 mA (milliAmperes) to equal 1 Ampere.
To handle these tiny slices of units, it's wise to spend a few minutes learning scientific notation, which is designed to make it easy to handle very large and very small numbers. Once you've mastered this technique, you can manipulate all the various-sized units of electronics as easily as you can add two and two! The Maxi Side. Take, for example, the familiar kiloHertz (known at one time as the kilocycle). A broadcasting station operating at 840 kHz (kiloHertz) in the broadcasting band is radiating 840,000 cycles of RF energy every second. To change from 840 kHz to 840,000 Hz, you can think of the "kilo-" as being replaced by "x 1000", thus: 840 kilo Hertz 840 x 1000 Hertz 840,000 Hertz But you can also write "1000" as "10 x 10 x 10". And you can write "10 x 10 x 10" as "103". (Ten to the third power, or ten cubed.) As we develop these ideas further, you will see how you can greatly simplify your future work in electronics by thinking of the prefix "kilo-" as being replaceable by "x 103", thus: 840 kiloHertz = 840 x 103 Hertz Similarly, a 6.8-megohm resistor, measured on an ohmmeter, will indicate 6,800,000 ohms. In this case, the prefix "meg-" can be replaced by "x 1,000,000": 6.8 meg 6.8 X 1,000,000 6,800,000 Ohms Ohms Ohms
But you can write "1,000,000" as "10 x 10x 10x 10x 10x 10" (six of .them; count 'em), which is 106. Thus, you should learn to mentally replace "meg-" with x 108, so that 6.8 meg-Ohms becomes a 6.8 x 106 Ohms. The 6 is called an exponent, and shows how many 10s are multiplied together.
The Minus Crowd. What about the "milli-" and "micro-" prefixes? "Milli-", we've said, is one-thousandth; in a way it is the opposite of the "kilo-" prefix. Make a mental note, then, that millican be replaced with "10^-3 (read as "ten to the minus three power"), which is 1/10 x 1/10 x 1/10 =1/1000. Similarly, the "micro-" prefix can be considered as the opposite of "meg-", and replaced by 10^-8.
The beauty of this approach appears when you are faced with a practical problem, such as, "if 1.2 milli-Amperes flows through 3.3 meg-Ohms, what voltage appears across the resistor?" From our knowledge of Ohm's law, we know that E = IR; that is, to get Volts (E) we multiply current (I) times resistance (R). Without the aid of scientific notation, the problem is to multiply
0.0012 Amperes by 3,300,000 Ohms, which is rather awkward to carry out. The same problem, however, is very easy in scientific notation, as can be seen below: E = (1.2 X10-3) X(3.3 X106)
E = 3.96 X 103 Volts E = 3.96 kilo-Volts = 3960 Volts The answer is 3.96 x 103 Volts, or 3.96 kiloVolts. We obtained the answer by multiplying 1.2 x 3.3 to get 3., and adding the -3 exponent to the 6 exponent to get 3--for the exponent of the answer. The advantage of scientific notation is that the largeness and smallness of the numbers involved is indicated by numbers like 108 and 10^-3, and the largeness or smallness of the answer is found by adding the 6 and the-3.
What about a division problem? For the sake of a good illustrative example, consider the unlikely problem of finding the current when 4.8 mega-Volts is applied across 2 kilOhms. The problem is written as: E I =R 4.8 mega-Volts 4.8 x 10^6 Volts 2 kilOhms 2.0 x 10^3 Ohms 4.8 -2 = 2.4, where 2.4 x 10^3 Amperes = kilo-Amperes.
In division, then finding the size of the answer becomes a subtraction problem, in which the exponent representing the size of the divisor ("bottom" number) is subtracted from the exponent representing the size of the dividend ("top" number). A more practical division problem answers the question, "What current flows when 5 Volts is applied across 2.5 kilOhms?"
I E 5 Volts R 2.5 kilOhms 5.0x10° 5.0X.10-3 2.5 x 103 2.5
= 2.0 x 10^-3 Amperes
= 2.0 mili-Amperes
Note that it's perfectly legal to use 10° (ten to the zero power) to indicate a unit that has no prefix-in other words, one of anything.
For the Solving. Here are a few more problems:
1. The inactive reactance of a coil is given by XL = 27rfL What is the reactance of a coil whose inductance L = 22 milli-Henries, when an alternating current of frequency f = 1.5 megaHertz is applied to it? XL, = 2 x n x (1.5x106) x (22x1)-3)
= 207.24 x 10^3 Ohms
= 207.24 kilOhms
2. An oscillator is connected to a wavelength-measuring apparatus, and the wavelength of its oscillations is determined to be 2.1 meters. What is the frequency of the oscillator?
F F= speed of light wavelength 3.0 x 10^8 meters per second wavelength 3.0 x 10^8 F-1.4286 x 108 Hertz 2.1 x 10° We wish this answer had come out with a "10^6", instead of a "10^8", because we can convert 106 Hertz directly to megaHertz. However, we can change the answer to 10^6, by shifting the decimal point of the 1.4286. Remember this rule: To lower the exponent, shift the decimal point to the right. (Of course, the opposite rule is also true.) Since we wish to lower the exponent by 2, we must shift the decimal point to the right by two places: 1442.86 x 10^6 Hertz = 142.86 megaHertz
3. A 3.3 microfarad capacitor is being charged from a 20-volt battery through a 6.8-kilOhm resistor. It charges to half the battery voltage in a time given by T = 0.69RC For the particular values given in the problem, what is the time taken to charge to half the battery voltage? T = 0.69 x (6.8 x 10^3) x (3.3 x 10^8) 15.4 miliseconds
4. A 365-pF variable capacitor and a 2-pH coil are found collecting dust in your junk box. You decide you might like to incorporate them into a radio but you need to know the resonant frequency of this inductive/capacitive circuit. You apply the formula: f= 1 2 pi LC
Since C = 365-pF or 365 x 10^-12 Farads and L = 2-uH or 2 x 10^-8 Henrys we can use these numbers, the formula and our new knowledge of exponents to determine the frequency.
f= 1 2 pi r (2 x 10-8) x (365 x 10^-12)
= 5,894,627.6 Hertz
= 5,S95 kiloHertz
= 5.895 megaHertz
Tera to Atto.
Since scientific notation is so potent, you'll probably be interested in the meaning of all the prefixes used in the scientific community, not just the four (micro-milli-, kilo-, and mega-)-that we've discussed so far. Very common in electronics is the micro-micro-Farad, which is 10^-6 x 10^-6 Farad, or 10^-12 Farad. This is more commonly known as the pico-Farad.
Similarly, a thousandth of a micro-Ampere is 10^-3 x 10^-6 Ampere, or 10^-8 Ampere. This is known as a nano-Ampere. At the other extreme, 1000 megaHertz is called a giga-Hertz. See the Table of electronic prefixes and their meanings for all these prefixes, and, for a rundown of their meanings and pronunciations.
The jargon of electronics which has grown up around their prefixes is just as important " as the prefixes themselves. Here are some examples of "jargonized" prefixes as they might appear in speech: Puff--a picoFarad (from the abbreviation, PF). Mickey-mike-a micro-micro-Farad (which is the same as a puff). Meg-a megohm. Also, less often, a megaHertz.
Mill-a milli-Ampere.
Megger-a device for measuring megohms.
dB (pronounced "dee-bee")-a deciBel, which is one-tenth of a Bel.
Mike-a micro-Farad. Also, to measure with a micrometer.
So, if you understand the prefixes and know their corresponding exponents, you'll have command of another set of important tools to help you do practical work in electronics. In addition, you'll be ready for the inevitable wise guy who'll ask if you can tell him the reactance of a 100-puff capacitor at 200 giga-Hertz. After calculating the answer in giga-seconds, reply in femt-Ohms!
=======
Also see: More Features