WEBVTT NOTE Reading a Waveform: Peak, Peak-to-Peak, and RMS 1 00:00:00.000 --> 00:00:10.682 The problem. "What is the voltage of this AC signal?" has three defensible answers, and they differ by a factor of nearly three. 2 00:00:10.682 --> 00:00:23.033 Which one is meant depends on what you are measuring with and what you are trying to find out. There is a diagram here. A sine wave over two cycles. 3 00:00:23.033 --> 00:00:34.383 Vertical markers show peak amplitude from the zero line to the crest, peak-to-peak from trough to crest, and RMS at about 0.707 of peak. 4 00:00:34.383 --> 00:00:41.560 A horizontal marker shows one period between successive positive-going zero crossings. 5 00:00:41.560 --> 00:00:57.336 The three measurements. Peak is the maximum instantaneous voltage, measured from the zero line to the crest. It is what determines whether a component's voltage rating is exceeded, and what actually breaks things. 6 00:00:57.336 --> 00:01:05.113 Peak-to-peak is the full swing, trough to crest. For a symmetrical waveform it is exactly twice the peak. 7 00:01:05.113 --> 00:01:13.927 This is what an oscilloscope shows you most directly, because a scope draws the whole waveform and you read the height. 8 00:01:13.927 --> 00:01:28.000 RMS, root mean square, is the equivalent DC value: the DC voltage that would produce the same heating in a resistor. This is what an AC voltmeter reports and what power calculations require. 9 00:01:28.000 --> 00:01:47.151 The conversions (sine waves only). V RMS equals 0.707 times V peak V peak equals 1.414 times V RMS V peak minus to minus peak equals 2 times V peak The 0.707 is 1/√2 and the 1.414 is √2. 10 00:01:47.151 --> 00:02:05.685 They are reciprocals, which is a useful check: if you multiply by the wrong one you get an answer that is out by a factor of two, in the direction that should look obviously wrong. 11 00:02:05.685 --> 00:02:23.189 These constants hold only for a sine wave. A square wave has an RMS equal to its peak. A sawtooth is different again. An SSB voice envelope is different moment to moment. 12 00:02:23.189 --> 00:02:36.368 This is not a footnote, it is why average-responding meters mislead on modulated signals, and why a "true RMS" meter costs more. 13 00:02:36.368 --> 00:02:54.137 The example that matters. North American household mains is 120 volts. That is an RMS figure. Its peak is 120 times 1.414 = 170 volts, and its peak-to-peak swing is 340 volts. 14 00:02:54.137 --> 00:03:12.008 That is the number to have in mind around a power supply. Insulation, capacitor ratings, and the shock you receive all respond to peak, not to the number printed on the outlet. 15 00:03:12.008 --> 00:03:31.045 Why the meter and the scope disagree. Put the same signal on both and you will read, say, 10 V on the multimeter and 28.3 V on the oscilloscope. Neither is wrong: The meter reports 10 V RMS. 16 00:03:31.045 --> 00:03:52.688 The scope shows 28.3 V peak-to-peak, which is 2 times 1.414 times 10. The conversion between them is a factor of 2√2, about 2.83. When a bench reading disagrees with a calculation by roughly that factor, this is why. 17 00:03:52.688 --> 00:04:07.230 Where this shows up in radio. Transmitter power is specified in PEP, peak envelope power, which is the average power during one RF cycle at the crest of the modulation envelope. 18 00:04:07.230 --> 00:04:22.100 The FCC's amateur power limits are written in PEP for exactly this reason. Receiver specifications are usually in microvolts RMS. Component ratings are usually peak or peak-inverse. 19 00:04:22.100 --> 00:04:39.106 Reading a specification without checking which measurement it uses is how people conclude their radio is broken when it is working exactly as designed. Check yourself. A sine wave measures 50 V peak-to-peak. 20 00:04:39.106 --> 00:04:53.648 What is its RMS voltage? Why does a square wave not follow the 0.707 rule? Your scope shows 340 V peak-to-peak on a mains transformer secondary. What would an AC voltmeter read? 21 00:04:59.648 --> 00:05:26.731 Peak is 25 V; RMS is 25 times 0.707 = 17.7 V. Because 0.707 comes from averaging the square of a sinusoid. A square wave sits at its peak the whole time, so its RMS equals its peak. 22 00:05:26.731 --> 00:05:34.063 Peak is 170 V, so RMS is 170 times 0.707 = 120 V.