WEBVTT 1 00:00:00.040 --> 00:00:01.760 We run the chapter four, we're going to be talking 2 00:00:01.800 --> 00:00:06.719 about power and decibels, AC power and basic components Power 3 00:00:06.719 --> 00:00:10.480 and decibels. You recall Ohms law from your technician training 4 00:00:11.880 --> 00:00:16.079 E which voltage equals current times resistance. Current can be 5 00:00:17.519 --> 00:00:22.280 related to voltage divided by resistance, and resistance can be 6 00:00:22.559 --> 00:00:25.719 voltage over current. So there's a refresher. I know you 7 00:00:25.800 --> 00:00:28.839 remember all your Ohms law training from your technician class. 8 00:00:28.960 --> 00:00:35.520 So E is voltage is current ours resistance similar relationship 9 00:00:35.600 --> 00:00:41.399 between power. Power is equal to voltage times current. Voltage 10 00:00:41.439 --> 00:00:45.520 can be expressed as power divided by current, and current 11 00:00:45.560 --> 00:00:49.200 can be expressed as power over energy or over voltage. 12 00:00:49.920 --> 00:00:55.439 So substituting the omes law equivalents for voltage and current 13 00:00:55.479 --> 00:00:59.399 allows power to be calculated using resistance. So power is 14 00:00:59.399 --> 00:01:03.799 equal to the current squared times of resistance, or powers 15 00:01:03.799 --> 00:01:09.359 equal to the voltage squared divided by the resistance. Find 16 00:01:09.400 --> 00:01:11.519 out how many watts of electrical power are used in 17 00:01:11.560 --> 00:01:16.560 four hundred volts dc. DC is supplied to an eight 18 00:01:16.680 --> 00:01:20.400 hundred owned resistor, you would say, hmm. Power is equal 19 00:01:20.480 --> 00:01:23.480 to the voltage square divided by resistance. In this case 20 00:01:23.519 --> 00:01:27.480 four hundred square divided by eight hundred homes six hundred 21 00:01:27.480 --> 00:01:30.560 and sixty thousand divided by eight hundred or two hundred watts. 22 00:01:30.599 --> 00:01:33.480 So if I had a four hundred volt signal with 23 00:01:33.560 --> 00:01:35.920 an eight hundred owned resistor, if that resistor is going 24 00:01:35.959 --> 00:01:39.439 to dissipate two hundred wats of power. To find out 25 00:01:39.480 --> 00:01:41.400 how many watts of electrical power are used by a 26 00:01:41.400 --> 00:01:45.439 twelve volt DC light bulb that draws point two amps, 27 00:01:46.359 --> 00:01:50.280 you would use. Power is equal to voltage times current, 28 00:01:50.480 --> 00:01:53.640 in this case twelve volts times point two amps two 29 00:01:53.640 --> 00:01:56.400 point four watts. Find out how many watts are being 30 00:01:56.400 --> 00:01:59.519 dissipated when a current of seven million amps flows through 31 00:01:59.560 --> 00:02:05.200 a well one point two K two five ko resistor. Remember, 32 00:02:05.319 --> 00:02:08.280 power is equal to the current square times resistance. Were 33 00:02:08.319 --> 00:02:12.400 given current which is point zero zero seven amps or 34 00:02:12.919 --> 00:02:17.680 seven million amps times twelve hundred and fifty oms, you'd 35 00:02:17.680 --> 00:02:21.599 get sixty one point two five milliwatts. And so just 36 00:02:21.639 --> 00:02:23.960 remember if you're given something in seven million amps, you'd 37 00:02:24.000 --> 00:02:26.240 sometimes you want to convert it to amps, so it's 38 00:02:26.240 --> 00:02:28.800 point zero seven amps. To do your calculations, make sure 39 00:02:28.840 --> 00:02:33.919 you're using like units when you do your conversions. Okay, 40 00:02:33.960 --> 00:02:39.960 calculating the power or or voltage ratio from dB. Power 41 00:02:40.039 --> 00:02:44.000 ratio is defined as ten to the minus one log 42 00:02:44.120 --> 00:02:49.360 of the dB over ten. So voltage is dB divided 43 00:02:49.360 --> 00:02:52.759 by twenty the log of dB divided by twenty. So 44 00:02:53.000 --> 00:02:56.280 inverse log notes you refer to this. I remember from 45 00:02:56.280 --> 00:02:59.080 your school anti log and log what it can be 46 00:02:59.159 --> 00:03:03.319 referred to. Power ratio of nine dB is ten to 47 00:03:03.400 --> 00:03:08.599 the minus one of nine over ten, and log of 48 00:03:08.719 --> 00:03:11.439 minus one of zero point nine is equal to eight. 49 00:03:12.919 --> 00:03:15.560 So this is probably the most complex math you'll need 50 00:03:15.599 --> 00:03:18.719 for this course. So don't worry if you're if you're 51 00:03:18.759 --> 00:03:21.919 going crazy about Oh my gosh, it's not gonna be 52 00:03:22.000 --> 00:03:24.759 too bad. So a voltage ratio of thirty two dB, 53 00:03:25.240 --> 00:03:28.960 remember it's thirty two divided by twenty log, So thirty 54 00:03:29.000 --> 00:03:32.280 two divided by twenty is one point six. Log minus 55 00:03:32.280 --> 00:03:37.919 one of one point six is forty. So some useful 56 00:03:37.919 --> 00:03:40.759 things if you double the power or cut it in half. 57 00:03:41.159 --> 00:03:44.560 There's a three dB change that's a useful thing to 58 00:03:44.680 --> 00:03:47.599 understand when you're talking about deep about dB. So a 59 00:03:47.680 --> 00:03:50.439 three dB change is either twice the power or half 60 00:03:50.520 --> 00:03:54.439 the power, depending on if it's positive or or or negative. 61 00:03:55.000 --> 00:03:58.439 And so let's say ten a dB is equal to 62 00:03:58.479 --> 00:04:02.240 the ten log of ten two over one. So ten 63 00:04:02.319 --> 00:04:04.439 log of two is equal to ten times point three 64 00:04:04.680 --> 00:04:06.680 three dB. This is where that comes from. So you 65 00:04:06.759 --> 00:04:08.680 had a ratio change of two to one. I mean 66 00:04:08.759 --> 00:04:11.879 I've doubled the power, and uh so if you double 67 00:04:11.919 --> 00:04:17.480 the power, you're gonna get three dB difference. So let's 68 00:04:17.519 --> 00:04:21.800 take a look at these. So if you're looking percentage 69 00:04:21.839 --> 00:04:27.079 power is equal to dB over ten, percentage power change 70 00:04:27.199 --> 00:04:31.319 dB over ten or percent voltage change of dB over twenty. 71 00:04:31.879 --> 00:04:35.519 That's the way you can convert from dB to percentage. 72 00:04:37.399 --> 00:04:39.759 I suppose you're using an antenna feed line that has 73 00:04:39.800 --> 00:04:42.959 a loss of one dB. You can calculate the amount 74 00:04:43.160 --> 00:04:46.879 of transmitting power that's actually reaching your antenna and how 75 00:04:46.959 --> 00:04:49.399 much is lost in the feed line. This is how 76 00:04:49.439 --> 00:04:51.439 you use so let's talk about it. So I've got 77 00:04:51.519 --> 00:04:54.279 a percent power, I've got one hundred percent times of 78 00:04:54.399 --> 00:04:57.040 log of I've got one dB loss. So you can 79 00:04:57.079 --> 00:05:00.399 express it as a minus one divided by t, so 80 00:05:00.439 --> 00:05:03.079 i'd be ten one hundred percent times of log minus 81 00:05:03.120 --> 00:05:06.839 one of minus one divided by ten is minus point 82 00:05:06.879 --> 00:05:10.800 one seventy nine point four percent. So if I've got 83 00:05:10.800 --> 00:05:14.240 one hundred watts of power, and I've got one dB 84 00:05:14.399 --> 00:05:17.759 loss of my coats of my end of my through 85 00:05:17.800 --> 00:05:20.560 my transmission line, then I'm only going to get seventy 86 00:05:20.639 --> 00:05:23.600 nine point four watts out to the end to the antenna, 87 00:05:23.839 --> 00:05:28.759 So I've lost that power is all dissipated as heat 88 00:05:28.879 --> 00:05:31.959 in the feed in in the feed line. That's why 89 00:05:32.000 --> 00:05:35.240 it's really important when you're figuring out what coacts to 90 00:05:35.360 --> 00:05:39.800 choose or what to use. The transmission losses can be 91 00:05:39.839 --> 00:05:43.560 fairly high, especially at high at higher frequencies. So uh, 92 00:05:43.680 --> 00:05:46.040 twenty nine point six percent is lost in the feed line, 93 00:05:46.319 --> 00:05:49.800 so one hundred wats out, so one dB loss in 94 00:05:49.839 --> 00:05:57.399 your coaxs, you're losing twenty percent of your power. So 95 00:05:57.879 --> 00:06:00.720 current is the flow of electrons measure in amps. You 96 00:06:00.720 --> 00:06:04.040 remember that from your tech from your technician class. It's 97 00:06:04.120 --> 00:06:07.360 measured with an am meter. Voltage E is the force 98 00:06:07.399 --> 00:06:09.959 that it takes to make electrons move. It's measured in 99 00:06:10.040 --> 00:06:14.240 volts with a volt meter. Plarity of the voltage refers 100 00:06:14.279 --> 00:06:20.360 to the direction from positive or negative power. P is 101 00:06:20.399 --> 00:06:23.519 a product of voltage in current, It's measured in watts, 102 00:06:23.600 --> 00:06:29.319 So current's measured in amps, voltage in volts. Power in watts. Okay, 103 00:06:29.319 --> 00:06:32.120 so we're going to review our own's law. Here, Resistance 104 00:06:32.160 --> 00:06:35.639 is equal to voltage divided by current, current is equal 105 00:06:35.720 --> 00:06:40.639 to voltage divided by resistance, and voltage is equal to 106 00:06:40.680 --> 00:06:44.759 current time resistance. The voltage caused by a current flowing 107 00:06:44.759 --> 00:06:49.800 through a resistor is called voltage drop. Un let's review 108 00:06:49.800 --> 00:06:58.279 our frequency. A complete sequence of alternating current is when 109 00:06:58.279 --> 00:07:01.680 it starts at zero, reaches the peak, comes back through zero, 110 00:07:01.920 --> 00:07:04.759 has a negative, and comes back to the zero itself. 111 00:07:04.800 --> 00:07:09.600 That whole loop is a complete cycle. The number of 112 00:07:09.639 --> 00:07:13.240 cycles per second is a current frequency, and it's measured 113 00:07:13.279 --> 00:07:17.920 in hurts. And a harmonic is a frequency of of 114 00:07:17.959 --> 00:07:23.399 some integer multiple of the lowest fundamental frequency. A harmonic 115 00:07:23.439 --> 00:07:25.720 of twice the frequency is called the second harmonic, and 116 00:07:25.759 --> 00:07:28.399 three times called the third harmonic. So if you had 117 00:07:28.600 --> 00:07:32.959 a one megahurtz signal, second harmonic would be two megaherts, 118 00:07:33.680 --> 00:07:37.279 third harmonic would be three megahertz, and so on, and 119 00:07:37.839 --> 00:07:40.000 there's no such thing as the first harmonic. The first 120 00:07:40.000 --> 00:07:45.279 harmonic is the fundamental itself, would be one megahertz. The 121 00:07:45.360 --> 00:07:48.560 speed of light is three million meters per second three 122 00:07:48.600 --> 00:07:51.959 times ten to the eight, somewhat slower in wires and 123 00:07:52.680 --> 00:07:57.240 cables when it flows to a medium. The wavelength of 124 00:07:57.399 --> 00:08:00.920 radio is a distance it travels very one complete cycle, 125 00:08:02.199 --> 00:08:04.680 So wavelength is equal to the speed of light over 126 00:08:04.720 --> 00:08:10.240 the frequency. Frequency is the speed of light over the wavelength. 127 00:08:12.480 --> 00:08:16.839 Radio wave can be referred to by frequency or wavelength 128 00:08:16.879 --> 00:08:20.000 because of the speed of light constant, so sometimes you'll 129 00:08:20.000 --> 00:08:24.560 hear it talk about one megahertz or so many meters. 130 00:08:24.720 --> 00:08:28.040 We're going to talk about parallel and series and parallel circuits. 131 00:08:28.079 --> 00:08:30.959 A circuit is any complete path through which current can flow. 132 00:08:31.000 --> 00:08:34.480 It's called the circuit. A series circuit where you have 133 00:08:34.519 --> 00:08:37.879 two or more components are connected so that the same 134 00:08:37.879 --> 00:08:40.960 current flows through all the components. That's a series circuit. 135 00:08:41.159 --> 00:08:45.559 The same current flows a parallel circuit. The same voltage 136 00:08:45.600 --> 00:08:50.120 is across all the applied components, So series circuit current 137 00:08:50.159 --> 00:08:54.120 flows through all of the pieces. Parallel circuit voltage is 138 00:08:54.159 --> 00:08:56.879 the same. The current is split between the different components, 139 00:08:56.919 --> 00:09:01.039 but the voltage is the same. So remember our dB formulas. 140 00:09:02.519 --> 00:09:05.480 DB's equal the ten log of the power ratio or 141 00:09:05.559 --> 00:09:09.440 twenty log the voltage ratio. Comparing a measured power or 142 00:09:09.480 --> 00:09:15.720 voltage to a reference value. DB's equal to ten log 143 00:09:15.960 --> 00:09:20.480 of the power over the power reference or twenty log 144 00:09:20.559 --> 00:09:26.240 the voltage measured over the voltage reference. Positive DV values 145 00:09:26.279 --> 00:09:28.440 mean that the ratio is greater than one, or it's 146 00:09:28.480 --> 00:09:32.840 called gain. Negative dB values ratio of less than one 147 00:09:33.759 --> 00:09:38.480 is called loss or attenuation. So you'll hear we talked 148 00:09:38.519 --> 00:09:40.960 that we use dbs a lot in amateur radio, and 149 00:09:41.000 --> 00:09:44.000 you'll say plus's and verminus dB. That talks about either 150 00:09:44.080 --> 00:09:49.639 gain or loss. Okay, what dB change represents a factor 151 00:09:49.639 --> 00:09:54.159 of two increase or or or decrease in power. So 152 00:09:54.240 --> 00:09:56.240 remember we talked about a factor of two. When you 153 00:09:56.279 --> 00:10:02.840 double something, it's three dB, right, because remember that's a power. 154 00:10:02.960 --> 00:10:05.879 Ratio of two divided by one is two, and the 155 00:10:05.919 --> 00:10:08.600 log of two is actually three point is point three 156 00:10:08.919 --> 00:10:11.120 times ten. That's where you get the three dB, So 157 00:10:11.960 --> 00:10:13.799 factor of two. So we use factor of two a 158 00:10:13.840 --> 00:10:17.039 lot in amateurad and we talk about we've doubled the power. 159 00:10:17.679 --> 00:10:20.120 The power is divided by half. Well, that's a three 160 00:10:20.240 --> 00:10:25.879 dB change. So how many watts of electrical power is 161 00:10:26.639 --> 00:10:29.559 used for four hundred volts DC is applied to a 162 00:10:29.600 --> 00:10:33.399 four hundred zero load. We'll remember our own's law formula 163 00:10:35.159 --> 00:10:39.240 of If you're looking at power. It's power squared, which 164 00:10:39.279 --> 00:10:42.000 is four hundred square divided by eight hundred. So sixteen 165 00:10:42.039 --> 00:10:46.360 hundred divided by sixteen thousand divided by eight hundred homes 166 00:10:46.440 --> 00:10:52.480 would be two hundred watts. How many watts of electrical 167 00:10:52.480 --> 00:10:55.120 power used by a twelve volt light bulb that draws 168 00:10:55.159 --> 00:10:57.879 point two amps? Okay? So which formul we're going to 169 00:10:57.960 --> 00:11:00.759 use here? So we're trying to find power, and we 170 00:11:00.840 --> 00:11:04.960 know power is equal to voltage times current, so twelve 171 00:11:05.080 --> 00:11:09.080 times point two is going to give us two point 172 00:11:09.159 --> 00:11:12.240 four watts. All right, So you've got to remember your 173 00:11:12.240 --> 00:11:18.799 own law equation the relationships between power, voltage and current. Okay, 174 00:11:18.840 --> 00:11:21.519 So how many watts are asking for power are consumed 175 00:11:21.559 --> 00:11:25.759 when a current of seven milliampers flows through a twelve 176 00:11:26.840 --> 00:11:30.159 twelve hundred and fifty oh resistor? All right, So we're 177 00:11:30.200 --> 00:11:32.720 given a current in million amps, so we probably need 178 00:11:32.759 --> 00:11:35.679 to convert that to amps, So seven million amps is 179 00:11:35.840 --> 00:11:39.840 point zero zero seven amps. Remember power is equal to 180 00:11:41.039 --> 00:11:46.240 the current square times resistance, So if I square point 181 00:11:46.879 --> 00:11:51.480 seven and I multiply that times twelve hundred and fifty ohms, 182 00:11:51.480 --> 00:11:54.799 you're going to get about sixty one milliwatts, all right, 183 00:11:54.879 --> 00:11:58.120 So when you see this question on the test, it 184 00:11:58.159 --> 00:12:01.200 seems like it's a lot of complicated math. But it's 185 00:12:01.279 --> 00:12:04.159 zero point oh seven square times twelve fifty and it's 186 00:12:04.200 --> 00:12:06.600 gonna be in milli watts. I've got million ams and ohms, 187 00:12:06.639 --> 00:12:09.159 I'm gonna have a milli watt answer. So remember they 188 00:12:09.159 --> 00:12:12.480 give you sixty one million watts and sixty one watts. Well, 189 00:12:12.519 --> 00:12:14.360 it's not gonna be sixty one watts, so the answer 190 00:12:14.480 --> 00:12:18.320 is sixty one milli watts. Okay, what percentage of power 191 00:12:18.360 --> 00:12:22.039 loss is equivalent to a loss of one dB? Okay, 192 00:12:22.080 --> 00:12:28.240 so if you if you remember, it's twenty log of 193 00:12:28.360 --> 00:12:33.480 one dB, so this is gonna be about twenty uh 194 00:12:34.519 --> 00:12:39.440 twenty percent. So one dB loss is uh, about eighty 195 00:12:39.480 --> 00:12:41.840 percent of your of your power is gonna make it through, 196 00:12:41.879 --> 00:12:44.720 and twenty is gonna be lost. Remember three dB is half, 197 00:12:45.039 --> 00:12:48.559 so one DB's about a third of that, so twenty 198 00:12:48.559 --> 00:12:51.480 point six percent. Remember the power equation is equal to 199 00:12:51.480 --> 00:12:56.080 the voltage square divided by resistance for DC. However, what 200 00:12:56.240 --> 00:12:58.840 is the value of E for AC power? So for 201 00:12:58.919 --> 00:13:02.919 AC power, it's not peak, it's not average. It's called 202 00:13:03.519 --> 00:13:07.399 root means square r or RMS. So we're talking about AC. Now. 203 00:13:07.480 --> 00:13:10.159 We were talking about direct current a minute ago, batteries 204 00:13:10.159 --> 00:13:12.759 and resistors. Now we're talking about a C alternating current 205 00:13:13.240 --> 00:13:16.320 alternating power. If our if RMS voltage is used in 206 00:13:16.360 --> 00:13:19.399 the equations shown for calculating power, the result of the 207 00:13:19.440 --> 00:13:23.840 AC signal is the same as for an unvarying DC voltage. Okay, 208 00:13:23.919 --> 00:13:26.399 So the RMS for a sine wave is point seven 209 00:13:26.519 --> 00:13:31.440 zero seven times the sine waves peak voltage. And this 210 00:13:31.799 --> 00:13:35.720 picture here shows on a sine wave there's r MS, 211 00:13:36.200 --> 00:13:40.320 there's peak to peak, and there's peak and uh, those 212 00:13:40.600 --> 00:13:43.639 are related. They're they're they're related, and they're shown here 213 00:13:43.679 --> 00:13:46.519 on this chart. Uh what they're talking about, and it's 214 00:13:46.559 --> 00:13:48.879 it has to do with the with the with the 215 00:13:48.919 --> 00:13:53.159 percent of the power inside the at the wave form. 216 00:13:53.399 --> 00:13:56.519 Point seven h seven is the RMS or the average 217 00:13:56.639 --> 00:13:59.840 power of that signal. And all right, some of the 218 00:14:00.080 --> 00:14:03.080 eight form formulas that we use for voltage is voltage 219 00:14:03.240 --> 00:14:06.799 RMS is a point seven oh seven times the voltage 220 00:14:06.840 --> 00:14:11.120 peak peak to peak divided by two. The voltage peak 221 00:14:11.240 --> 00:14:14.440 is one point four times voltage RMS. Volts peak to 222 00:14:14.440 --> 00:14:18.000 peak is two point eight two eight volts times RMS. 223 00:14:18.399 --> 00:14:22.200 So these relationships, these formulas here are important to understand. 224 00:14:22.279 --> 00:14:24.559 Just something you're gonna have to sort of memorize and 225 00:14:24.600 --> 00:14:27.000 take a look at. Assign wave with the peak voltage 226 00:14:27.000 --> 00:14:29.960 of seventeen volts, for example, has an RMS voltage of 227 00:14:30.600 --> 00:14:33.399 twelve point five twelve twelve volts. You're gonna take the 228 00:14:33.399 --> 00:14:37.679 peak voltage seventeen multiply times point seven oh seven, it's 229 00:14:37.720 --> 00:14:41.720 twelve volts. RMS as sign wave with the peak voltage 230 00:14:41.720 --> 00:14:45.039 of one hundred volts would be a Remember it's a 231 00:14:45.080 --> 00:14:47.039 peak to peak voltage, so you go peak the peak 232 00:14:47.039 --> 00:14:49.840 divided by two, it's fifty volts peak times point seven 233 00:14:49.919 --> 00:14:53.639 oh seven, it's thirty thirty five point four volts RMS. 234 00:14:53.840 --> 00:14:57.559 Assign wave an RMS voltage of twelve or twenty volts 235 00:14:57.720 --> 00:15:00.399 has what peak the peak voltage value, So this one 236 00:15:00.440 --> 00:15:04.919 hundred and twenty volts is what's in your household ac here. 237 00:15:05.919 --> 00:15:08.240 So if you put it in the silloscope in the outlet, 238 00:15:08.399 --> 00:15:10.480 checked it out, it would be three hundred and thirty 239 00:15:10.519 --> 00:15:12.799 nine volts peak to peak. It's a pretty good sized signal, 240 00:15:13.399 --> 00:15:18.679 but it's one hundred and twenty volts RMS. All right, 241 00:15:18.879 --> 00:15:22.840 here's some definitions of measurement of peak envelope power. PEP 242 00:15:23.519 --> 00:15:26.519 stands for peak envelope power. It's the average power of 243 00:15:26.600 --> 00:15:30.519 one complete RF cycle at the peak of the signal's envelope, 244 00:15:30.919 --> 00:15:33.519 a convenient way of measuring the max power of amplitude 245 00:15:33.519 --> 00:15:39.000 modulated signals. However, this definition is confusing, and let's talk 246 00:15:39.039 --> 00:15:42.519 about it a little bit. PEP or peak envelope power, 247 00:15:42.639 --> 00:15:45.480 is the average power of one complete RF cycle at 248 00:15:45.519 --> 00:15:48.840 the peak of the signals envelope. PEP is used because 249 00:15:48.879 --> 00:15:52.440 it's a convenient way to measure or specify the maximum 250 00:15:52.480 --> 00:15:57.240 power of amplitude modulated signals. And here's an example of 251 00:15:58.519 --> 00:16:02.720 peak of what the peak envelope power is. To calculate 252 00:16:02.879 --> 00:16:05.799 average AC power, you need to know the load impedance 253 00:16:06.120 --> 00:16:10.600 and the RMS voltage measure. The r measure measure the 254 00:16:10.720 --> 00:16:13.799 RF voltage at the very peak of the modulated signals envelope. 255 00:16:13.919 --> 00:16:17.240 This is the peak envelope voltage has shown in the figure. 256 00:16:18.679 --> 00:16:22.039 Once the RF cycle is is identified, we calculate the 257 00:16:22.120 --> 00:16:26.159 average power over its complete duration. That's the red area 258 00:16:26.279 --> 00:16:31.440 in this figure. Note that we calculate the power in 259 00:16:31.480 --> 00:16:35.120 both the positive and negative half cycles, and the negative 260 00:16:35.519 --> 00:16:38.559 they don't cancel out because they're shown in this In 261 00:16:38.639 --> 00:16:42.960 this example, Uh, the peak envelope voltage is squared, making 262 00:16:43.039 --> 00:16:47.159 both of them positive. So uh, start by measuring the 263 00:16:47.200 --> 00:16:50.919 amplitude of the peak, usually in volts, that is the 264 00:16:50.960 --> 00:16:54.000 peak envelope the pev in the figure on the previous slide. 265 00:16:54.159 --> 00:16:58.360 Then applied the following formula. So you notice here you're 266 00:16:58.399 --> 00:17:03.240 looking for where's the peaks on this little slide right here, right? So, uh, 267 00:17:03.720 --> 00:17:07.359 this one is higher than these, So that's there. There's 268 00:17:07.400 --> 00:17:10.359 the peak on the pop positive, there's a peak on 269 00:17:10.400 --> 00:17:13.240 the negative. So those are the pulses you wanna you 270 00:17:13.279 --> 00:17:16.640 wanna figure out. So so when when when you're trying 271 00:17:16.640 --> 00:17:20.119 to say, what's my transmitted output power, it's gonna be 272 00:17:20.200 --> 00:17:24.359 when you're at the peaks. These smaller peaks take less 273 00:17:24.400 --> 00:17:27.480 power than the taller ones, right, So you're looking for 274 00:17:27.559 --> 00:17:32.000 the tallest peak envelope power, right, the peak voltage is there. 275 00:17:32.279 --> 00:17:35.960 Peak envelope power is equal to volt armis square divided 276 00:17:36.000 --> 00:17:39.119 by r. For an example, if we have fifty volts 277 00:17:39.119 --> 00:17:42.960 across a fifty ome load, the peak envelope power is 278 00:17:44.039 --> 00:17:48.039 fifty times zero point seven oh seven. To get the 279 00:17:48.200 --> 00:17:52.920 RMS value divided by the load gets twenty five watts. 280 00:17:54.119 --> 00:17:57.359 If a fifty load is dissipating twelve hundred watts pep, 281 00:17:58.160 --> 00:18:02.960 the RMS voltage is square root of the peak envelope power, 282 00:18:03.000 --> 00:18:06.519 which is twelve hundred times of resistance fifty homes two 283 00:18:06.599 --> 00:18:12.240 hundred and forty five volts. So these are these little formulas, 284 00:18:12.319 --> 00:18:15.519 these relationships. Is probably the most math you're gonna have 285 00:18:15.599 --> 00:18:18.920 to know for this general class license. It's not too bad. 286 00:18:18.960 --> 00:18:21.680 You just got to understand a few of them. If 287 00:18:21.680 --> 00:18:24.799 in a silloscope measures two hundredvolts peak to peak across 288 00:18:24.799 --> 00:18:28.680 a fifty home load, what would be the peak envelope power? 289 00:18:29.559 --> 00:18:32.960 All right, So we've got to take we've got peak 290 00:18:33.000 --> 00:18:36.319 to peak, right, So peak to peak RMS is point 291 00:18:36.400 --> 00:18:39.559 seven oh seven times the peak to peak divided by two, 292 00:18:40.240 --> 00:18:42.279 all right, that's where you get the RMS value. And 293 00:18:42.279 --> 00:18:44.359 then you're gonna divide that by the fifty on loads. 294 00:18:44.359 --> 00:18:49.079 So point seven seven times two hundred squared one hundred 295 00:18:49.079 --> 00:18:52.720 watts for the same device that five hundred volts peak 296 00:18:52.759 --> 00:18:58.759 to peak, the peak envelope power would be six hundred 297 00:18:58.720 --> 00:19:02.799 and twenty five watts. Okay, So one hundred wats six 298 00:19:02.839 --> 00:19:07.440 hundred and twenty five watts, So PP equals the average 299 00:19:07.480 --> 00:19:12.920 power if an amplitude modulated signal is not modulated. Okay. 300 00:19:13.079 --> 00:19:16.599 An example this one is when modulation is removed from 301 00:19:16.599 --> 00:19:19.599 the AM signal, leaving only the carrier, or when or 302 00:19:19.640 --> 00:19:24.359 when a CW transmitter is key. An FM signal is 303 00:19:24.480 --> 00:19:27.480 constant power signal, so PEP is always equal to the 304 00:19:27.519 --> 00:19:30.319 average power of an FM signal. In other words, if 305 00:19:30.359 --> 00:19:33.440 an average reading WAT meter connected to your transmitter reads 306 00:19:33.759 --> 00:19:36.519 one thousand and sixty watts, when you close the key 307 00:19:36.559 --> 00:19:40.720 on CW your PW, your PEP output power will be 308 00:19:41.119 --> 00:19:44.720 one thousand and sixty watts. Okay. So what is the 309 00:19:44.759 --> 00:19:48.079 PEP produced by two hundred volts the peak across a 310 00:19:49.039 --> 00:19:53.799 fifty O dummy load? Okay? So how would you do 311 00:19:53.880 --> 00:19:55.880 this one? Well, I guess I need to put that. 312 00:19:55.920 --> 00:20:00.279 Should have told you. So it's going to be peak 313 00:20:00.319 --> 00:20:02.680 envelope power two hundred watts peak to peak. So you 314 00:20:02.759 --> 00:20:04.920 got to convert that to peak. So two hundred divided 315 00:20:04.960 --> 00:20:10.480 by two divided by fifty is one hundred zermes. What 316 00:20:10.599 --> 00:20:13.279 value of an AC signal produces the same power dissipation 317 00:20:13.359 --> 00:20:17.799 and a resistor as a DC voltage of the same value. Okay, 318 00:20:18.079 --> 00:20:22.240 it's gonna be the RMS value because an AC signal, 319 00:20:22.279 --> 00:20:26.599 remember is peak to peak. But the RMS value is 320 00:20:26.599 --> 00:20:28.720 the point seven to seven. That's the equivalent of the 321 00:20:28.759 --> 00:20:34.359 DC power of the of the DC voltage. RMS is 322 00:20:34.400 --> 00:20:36.119 what you want to use. What is the peak to 323 00:20:36.160 --> 00:20:39.200 peak voltage of a sine wave when an RMS voltage 324 00:20:39.200 --> 00:20:42.279 of one hundred and twenty volts, so it's gonna be 325 00:20:42.279 --> 00:20:45.839 one hundred and twenty volts times one point four, which 326 00:20:45.880 --> 00:20:48.200 is gonna be around three hundred and thirty nine volts, 327 00:20:48.240 --> 00:20:52.200 I believe, yep. So this is what Again, if you 328 00:20:52.240 --> 00:20:55.480 measured the AC outlet at your house within ASILL scope, 329 00:20:55.720 --> 00:20:58.240 you'd see three hundred and thirty nine volts peak to peak. 330 00:20:59.799 --> 00:21:01.720 But what we're told it's one hundred and twenty volts. 331 00:21:01.720 --> 00:21:04.440 That's the r MESS value. Okay. The ARMISS value is 332 00:21:04.440 --> 00:21:08.319 what we normally characterize for the AC voltage at your house. 333 00:21:10.440 --> 00:21:12.400 What's the ARMIST voltage of a signed way with the 334 00:21:12.480 --> 00:21:18.000 value of seventeen volts peak? Okay, so it'll be seventeen 335 00:21:18.079 --> 00:21:21.400 times zero point seven, which will be around twelve volts. 336 00:21:23.559 --> 00:21:25.839 What's the ratio of a peak to peak average power 337 00:21:25.920 --> 00:21:31.680 of an unmodulated carrier. Okay, peak to peak to average, 338 00:21:32.279 --> 00:21:37.880 it's about points. Well, it'd be one peak to peak. 339 00:21:38.839 --> 00:21:42.440 Oh for the ratio of a peak to peak to 340 00:21:42.640 --> 00:21:46.480 average power of an unmodulated carrier is it's unmodulates. What's 341 00:21:46.519 --> 00:21:49.599 exactly the same. All right. Once you modulate it, then 342 00:21:49.640 --> 00:21:51.880 the power is going to get less point seven oh seven. 343 00:21:51.880 --> 00:21:55.759 But if it's unmodulated, all the powers is at the 344 00:21:55.799 --> 00:21:58.079 carrier itself, so it's one. The ratio is the same. 345 00:21:59.039 --> 00:22:01.000 What's the arm miss volt? Did you across a fifty 346 00:22:01.079 --> 00:22:06.480 zero load dissipating twelve hundred watts? Okay, so we're gonna 347 00:22:06.480 --> 00:22:10.720 say equals I R fifty divided by that's gonna be 348 00:22:10.799 --> 00:22:16.559 about twelve hundred uh divided by fifty that square met 349 00:22:16.559 --> 00:22:20.599 to that, it's gonna be about two hundred and fifty 350 00:22:20.960 --> 00:22:23.319 volts two hundred and forty five volts. What is the 351 00:22:23.319 --> 00:22:25.920 peak envelope power of an unmodulated care If the average 352 00:22:25.960 --> 00:22:30.839 power is one thousand and sixty watts, it's it's unmodulated, 353 00:22:30.920 --> 00:22:35.400 so it's gonna be one thousand and sixty watts. What's 354 00:22:35.440 --> 00:22:37.880 the peak envelope power of five hundred volts peak to 355 00:22:37.920 --> 00:22:48.839 peak across a fifty load about sixty peak to peak 356 00:22:48.880 --> 00:22:51.640 cross about six hundred, yeah, six hundred watts. Now we're 357 00:22:51.640 --> 00:22:55.319 gonna talk about some basic components. We're done with the 358 00:22:55.319 --> 00:23:02.119 math for a while. Three most basic components resistors. They're 359 00:23:02.160 --> 00:23:06.279 designated to have an R. They're used to resist the 360 00:23:06.319 --> 00:23:09.799 flow of electricity, and they're measured in omes. So resistance 361 00:23:10.079 --> 00:23:15.680 are omes. Capacitors usually shown designated with the letter C. 362 00:23:16.160 --> 00:23:19.920 They store electrical energy and they're measured in fare ads. 363 00:23:20.759 --> 00:23:26.079 Then inductors designated with L store magnetic energy measured in Henri's. 364 00:23:26.240 --> 00:23:33.559 So capacitors store electrical energy, inductor store magnetic energy, so 365 00:23:33.960 --> 00:23:40.079 omes fare ads and Henri's R, C and L. Typical 366 00:23:40.119 --> 00:23:43.599 values associated with components include the nominal value, the tolerance, 367 00:23:44.039 --> 00:23:47.319 temperature coefficient, and power rating. So if you go by 368 00:23:47.400 --> 00:23:50.839 a capacitor with a certain value like say one hundred 369 00:23:50.880 --> 00:23:53.720 microfarads or a hundred peokle fareds, it'll come with the 370 00:23:53.799 --> 00:23:56.519 tolerance nominal values one hundred peokle ferreeds, but has a 371 00:23:56.559 --> 00:24:01.400 tolerance plus or minus a certain amount temperature co efficient, How, 372 00:24:01.680 --> 00:24:05.160 what's the tolerance versus what's the capacity's over temperature and 373 00:24:05.200 --> 00:24:10.000 a power rating. Capacitors are volts, so those are typically 374 00:24:10.000 --> 00:24:15.960 the characteristics that describe the component that you're buying. Some 375 00:24:16.039 --> 00:24:18.680 schematic symbols. As you recall from the technician class, a 376 00:24:18.720 --> 00:24:24.519 schematic is as a paper drawing of electrical components connected together. 377 00:24:25.839 --> 00:24:30.240 And resistors have looked like the little squiggly line here, 378 00:24:30.240 --> 00:24:33.799 and there's different symbols for different types of resistors. These 379 00:24:33.799 --> 00:24:37.559 are the common ones. There's a fixed resistor, variable photo resistor, 380 00:24:37.759 --> 00:24:44.720 adjustable tact resistor, a theoristor. Capacitors show up on schematics 381 00:24:44.759 --> 00:24:48.960 look like this, and there's different kinds of capacitors, fixed 382 00:24:49.000 --> 00:24:53.279 and non polarized and polarized which we call electrolytic variable 383 00:24:53.319 --> 00:24:57.079 capacitors feed through. So this is how they be represented 384 00:24:57.119 --> 00:25:01.200 on electrical schematic. Remember, electrical schematic is how you hook 385 00:25:01.279 --> 00:25:05.039 interconnect these components together to form a circuit. An inductor 386 00:25:05.079 --> 00:25:11.440 symbol usually looks like this. Uh, there's air core, iron core. Uh, 387 00:25:11.480 --> 00:25:16.640 there's actually transformers. A variant of these fair eyed beads 388 00:25:16.799 --> 00:25:19.599 is an example of an inductor. So these are what 389 00:25:19.640 --> 00:25:22.039 the symbols look like. There's different kinds of tubes with 390 00:25:22.119 --> 00:25:31.039 different kinds of uh uh interface, different kinds of oh connections. 391 00:25:31.119 --> 00:25:36.519 There's they're they're they're like diodes. There's a triode, a pentode, 392 00:25:36.519 --> 00:25:41.480 and a cathod. It's how many uh uh this anodes 393 00:25:41.480 --> 00:25:45.200 and cathods do they have? And they come in different varieties, 394 00:25:45.279 --> 00:25:49.440 different sizes, different types for different functions and uh These 395 00:25:49.440 --> 00:25:55.799 are the symbols for tubes wiring. Again, when you have 396 00:25:55.839 --> 00:25:58.279 your electrical schematic and you've got wire shown on there, 397 00:25:58.480 --> 00:26:01.079 you can these are symbols for our wires connected? Are 398 00:26:01.079 --> 00:26:04.359 they not connected? Are there several wires that form like 399 00:26:04.400 --> 00:26:08.039 a data bus? Is it a ribbon cable? Multi cables? 400 00:26:08.480 --> 00:26:10.799 Is it a coaxial cable? These are ways to show 401 00:26:11.200 --> 00:26:15.680