WEBVTT NOTE Decibels Without the Logarithms 1 00:00:00.000 --> 00:00:19.046 What a decibel is. A decibel compares two powers: The formula for this is written out in the lesson text. It is always a ratio. "My antenna has 6 dB" is incomplete, 6 dB compared with what? 2 00:00:19.046 --> 00:00:40.108 Suffixes supply the missing reference: dBi compares with an isotropic radiator, dBd with a dipole, dBm with one milliwatt, dBW with one watt. The logarithm exists because it turns multiplication into addition. 3 00:00:40.108 --> 00:00:52.402 A signal path that multiplies by 100, then by 0.5, then by 4 becomes +20, −3, +6 dB, which you add in your head to +23 dB. 4 00:00:52.402 --> 00:00:57.291 The three anchors. There is a diagram here. 5 00:00:57.291 --> 00:01:31.854 A horizontal ladder of decibel values from minus 10 to plus 20 dB with the corresponding power ratio labelled at each rung: minus 10 dB is one tenth power, minus 6 dB one quarter, minus 3 dB half, 0 dB unchanged, plus 3 dB double, plus 6 dB four times, plus 10 dB ten times, plus 20 dB one hundred times. 6 00:01:31.854 --> 00:01:53.342 Memorise exactly three facts: Change, Power doubles; In dB, +3 dB. Change, Power halves; In dB, −3 dB. Change, Power times 10; In dB, +10 dB. From those: times 4 is times 2 twice, so +6 dB. 7 00:01:53.342 --> 00:02:13.352 times 8 is times 2 three times, so +9 dB. times 20 is times 10 then times 2, so +13 dB. times 100 is times 10 twice, so +20 dB. divided by 4 is −6 dB, divided by 100 is −20 dB. 8 00:02:13.352 --> 00:02:26.882 That is enough to answer every decibel question in the Technician and General pools without arithmetic beyond addition. 9 00:02:26.882 --> 00:02:50.690 The pool's questions, solved. A power increase from 5 watts to 10 watts. The ratio is 2. Power doubled, so +3 dB. A power decrease from 12 watts to 3 watts. The ratio is 1/4, halved, then halved again. −3 −3 = −6 dB. 10 00:02:50.690 --> 00:03:07.333 A power increase from 20 watts to 200 watts. The ratio is 10, so +10 dB. Every one of these is "work out the ratio, then decompose it into 2s and 10s." 11 00:03:07.333 --> 00:03:22.943 The coefficient trap. The 10 in the formula is for power ratios. For voltage or current ratios into the same impedance, the coefficient is 20: The formula for this is written out in the lesson text. 12 00:03:22.943 --> 00:03:33.587 The two are consistent, not contradictory: power goes as voltage squared, and the square comes out of the logarithm as a factor of two. 13 00:03:33.587 --> 00:03:45.413 The practical consequence is that doubling voltage is +6 dB, while doubling power is +3 dB. Mixing these up is the most common decibel error there is. 14 00:03:45.413 --> 00:03:55.425 Why this matters more than it looks. Once you can add decibels, a whole class of station questions becomes trivial. 15 00:03:55.425 --> 00:04:13.968 A 100 watt transmitter, 2 dB of feed-line loss, and a 7 dBd beam: +7 − 2 = +5 dB net, so the effective radiated power is about three times the transmitter output, roughly 300 watts ERP. No multiplication required. 16 00:04:13.968 --> 00:04:23.980 The same reasoning explains why buying more power is usually a poor investment. Going from 100 W to 200 W is +3 dB. 17 00:04:23.980 --> 00:04:37.213 Received signal strength is conventionally reported in S-units of about 6 dB each, so that doubling is half an S-unit, often invisible on the other end. 18 00:04:37.213 --> 00:04:54.451 Fixing 2 dB of feed-line loss and adding 6 dB of antenna gain buys you more than a linear amplifier does, and it works on receive too. Check yourself. A power change from 100 W to 25 W. How many dB? 19 00:04:54.451 --> 00:05:03.766 An amplifier turns 5 W into 500 W. How many dB of gain? Voltage across a load doubles. How many dB is that? 20 00:05:09.766 --> 00:05:38.526 Ratio 1/4 = halved twice = −6 dB. Ratio 100 = times 10 twice = +20 dB. Voltage ratio, so the coefficient is 20: +6 dB. Before we finish, here are the pool questions this lesson covers, in the exam's own words. 21 00:05:38.526 --> 00:05:48.086 Question. Which decibel value most closely represents a power increase from 5 watts to 10 watts? 22 00:05:48.986 --> 00:05:51.905 Answer. 3 dB. 23 00:05:52.505 --> 00:06:02.065 Question. Which decibel value most closely represents a power decrease from 12 watts to 3 watts? 24 00:06:02.965 --> 00:06:06.267 Answer. -6 dB. 25 00:06:06.867 --> 00:06:14.733 Question. Which decibel value represents a power increase from 20 watts to 200 watts? 26 00:06:15.633 --> 00:06:18.688 Answer. 10 dB.