Below is the “Math for electronics” section of the 2014 edition of the No-Nonsense Technician Class License Study Guide. As always, comments welcome…Dan
When dealing with electrical parameters, such as voltage, resistance, current, and power, we use a set of prefixes to denote various orders of magnitude:
- milli- is the prefix we use to denote 1 one-thousandth of a quantity. A milliampere, for example, is 1 one-thousandth of an ampere, or .001 A. Often, the letter m is used instead of the prefix milli-. 1 milliampere is, therefore, 1 mA.
- micro- is the prefix we use to denote 1 millionth of a quantity. A microvolt, for example, is 1 millionth of a volt, or .000001 V. Often you will see the Greek letter mu, or μ, to denote the prefix micro-. 1 microvolt is, therefore, 1 μV.
- pico- is the prefix we use to denote 1 trillionth of a quantity. A picovolt is 1 trillionth of a volt, or .000001 μV.
- kilo- is the prefix we use to denote 1 thousand of a quantity. A kilovolt, for example, is 1000 volts. Often, the letter k is used instead of the prefix kilo-. 1 kilovolt is, therefore, 1 kV.
- mega- is the prefix we use to denote 1 million of a quantity. A megahertz, for example, is 1 million Hertz. The unit of frequency is the Hertz. (T5C05) It is equal to one cycle per second. Often, the letter M is used instead of the prefix mega-. 1 megahertz is, therefore, 1 MHz.
Here are some examples:
- 1,500 milliamperes is 1.5 amperes. (T5B01)
- Another way to specify a radio signal frequency of 1,500,000 hertz is 1500 kHz.
- One thousand volts are equal to one kilovolt. (T5B03)
- One one-millionth of a volt is equal to one microvolt. (T5B04)
- If an ammeter calibrated in amperes is used to measure a 3000-milliampere current,
the reading it would show would be 3 amperes. (T5B06)
- If a frequency readout calibrated in megahertz shows a reading of 3.525 MHz, it would
show 3525 kHz if it were calibrated in kilohertz. (T5B07)
- 1 microfarad is 1,000,000 picofarads. (T5B08) (Farad is the unit for capacitance.)
- 28.400 MHz is equal to 28,400 kHz. (T5B12)
- If a frequency readout shows a reading of 2425 MHz, the frequency in GHz is 2.425 GHz. (T5B13)
When dealing with ratios—especially power ratios—we often use decibels (dB). The reason for this is that the decibel scale is a logarithmic scale, meaning that we can talk about large ratios with relatively small numbers. At this point, you don’t need to know the formula used to calculate the ratio in dB, but keep in mind the following values:
- 3 dB is the approximate amount of change, measured in decibels (dB), of a power increase from 5 watts to 10 watts. (T5B09) This is a ratio of 2 to 1.
- -6 dB is the approximate amount of change, measured in decibels (dB), of a power decrease from 12 watts to 3 watts. (T5B10) This is a ratio of 4 to 1.
- 10 dB is the approximate amount of change (actually it is the EXACT amount of change), measured in decibels (dB), of a power increase from 20 watts to 200 watts. (T5B11) This is a ratio of 10 to 1.