Units of Measure
There are a lot of units of measure that you end up working with. In this section, I want to talk about a few that have always tripped me up, and hopefully, by explaining them to others, I can better understand them myself.
International System of Units (SI)
Yes, the acronym doesn't play out. Blame the French. But, while this information is all over the Internet, I'm just going to include it here for reference from other places as needed.
SI Units
| Quantity | Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | gram | g |
| Temperature | Celsius | C |
| Time | second | s |
| Force | Newton | N |
| Electric potential difference (voltage) | Volt | V |
| Electrical current | Ampere | A |
| Power | Watt | W |
| Energy, work, or heat | Joule | J |
| Electrical charge | Coulomb | C |
| Resistance | Ohm | Ω |
| Capacitance | Farad | F |
| Inductance | Henry | H |
| Frequency | Hertz | Hz1 |
Prefixes
While you likely learned some of the basic (milli, kilo, etc.) prefixes of the SI (ney metric) system, in electronics, we often use others that you may not have learned. We'll break them into "small things" and "big things". There are others that you will see, which you can find here, but almost never in electronics (so far!).
For each of the prefixes, I'll denote what components you might typically see these prefixes around. They'll be noted as capacitors (C), inductors (L), and resistors (R) as above.
Small Things
| Prefix | Symbol | Power | Scale | Words | Component |
|---|---|---|---|---|---|
| - | (none) | 100 | 1 | unit | C, L, R |
| milli | m | 10-3 | 1/1,000 | thousandth | C, L, R |
| micro | µ | 10-6 | 1/1,000,000 | millionth | C, L, R |
| nano | n | 10-9 | 1/1,000,000,000 | billionth | C, L |
| pico | p | 10-12 | 1/1,000,000,000,000 | trillionth | C |
| femto | f | 10-15 | 1/1,000,000,000,000,000 | quadrillionth |
In the electronics world, you will see milli, micro, nano, and pico quite frequentl. 1pF capacitors aren't uncommon at all, and while there are use cases to talk about femtoamps (for example), it's not a situation you are likely to ever come across.
Big Things
| Prefix | Symbol | Power | Scale | Words | Component |
|---|---|---|---|---|---|
| - | (none) | 100 | 1 | unit | C, L, R |
| kilo | k | 103 | 1,000 | thousands | R |
| mega | M | 106 | 1,000,000 | millions | R |
| giga | G | 109 | 1,000,000,000 | billions | R |
| tera | T | 1012 | 1,000,000,000,000 | trillions | |
| peta | P | 1015 | 1,000,000,000,000,000 | quadrillions | |
| exa | E | 1018 | 1,000,000,000,000,000,000 | quintillions |
Like small values, we don't use the really huge values (normally). You will see resistance measured up to gigaohms quite commonly. Other than that, the only places you're likely to run into the bigger units is in storage, bandwidth, and processing performance (TFLOPS, trillions of floating port operations per second).
Decibels
While nobody uses the original unit of measure, the bel, the decibel (deci meaning tenth) is everywhere in electronics where signals are being processed in non-digital circuits. While the decibel (dB) on its own is specifically a ratio between two signal levels and therefore expresses only relative relationships.
If you want to use an absolute value, you can add on a modifier to the dB notation.There are a couple specialized ones that you will see, generally in audio or RF circuits:
| dB Units | Meaning |
|---|---|
| dBV | Decibels relative to 1 Volt |
| dBm | Decibels relative to 1 milliwatt (mW) |
For handy use, here's a table of some common conversions between decibels and how they reflect in \(V\), \(I\), or \(P\).
| Decibels | \(V\) or \(I\) Multiplier | \(P\) Multiplier |
|---|---|---|
| +40 dB | \(100\) | \(10000\) or \(10^4\) |
| +30 | \(\sqrt{100}\) | \(1000\) or \(10^3\) |
| +20 dB | \(10\) | \(100\) or \(10^2\) |
| +10 dB | \(\sqrt{10}\) | \(10\) or \(10^1\) |
| +6 dB | \(2\) | \(4\) or \(10^{0.60206\ldots}\) |
| +3 dB | \(\sqrt{2}\) | \(2\) or \(10^{0.30103\ldots}\) |
| 0 dB | \(1\) | \(1\) or \(10^0\) |
| -3 dB | \(\sqrt{1\over2}\) | \(1\over2\) or \(10^{-0.30103\ldots}\) |
| -6 dB | \(1\over2\) | \(1\over4\) ot \(10^{-0.60206\ldots}\) |
| -10 dB | \(\sqrt{1\over10}\) | \(1\over10\) or \(10^{-1}\) |
| -20 dB | \(1\over10\) | \(1\over100\) or \(10^{-2}\) |
| -30 dB | \(\sqrt{1\over100}\) | \(1\over1000\) or \(10^{-3}\) |
| -40 dB | \(1\over100\) | \(1\over10000\) or \(10^{-4}\) |
This is just a fleshed out version of this equation for voltage (\(V\)) and current (\(I\)):
Since power (\(P\)), measured in watts, is proportional to the square of the voltage (\(V\)), a 10X increase in voltage results in a \(10^2 = 100\)X increase in power, or 20dB. This converts the equation above into:
These all end up being derived from (for \(A\) dB):
-
Why did we end up with this one that is two letters rather than one like every other sane unit? Did an American sneak in? ↩
Comments or Questions?
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