How a square wave is built from sine waves, what RMS and PEP measure, and how analog-to-digital conversion works.
Syllabus: Fourier analysis; RMS measurements; average RF power and peak envelope power (PEP); analog/digital conversion
Compendium articles on the ideas in this lesson, beyond what the exam asks.
Practise the 11 pool questions for this group. Answers are shuffled, and every one comes with a one-line "why".
Fourier analysis shows that a signal is a sum of sine waves. A square wave is a sine wave plus its odd harmonics (3f, 5f, 7f...), each weaker than the last. Add more and the corners sharpen.
The time domain is amplitude at different times (an oscilloscope). The frequency domain is amplitude at each frequency (a spectrum analyzer).
RememberSquare wave = sine + odd harmonics. Time domain = amplitude versus time.
RMS is the steady DC voltage that heats a resistor as much as the wave does. For a sine it is 0.707 × peak, but other shapes differ. A true-RMS meter calculates it properly for sinusoidal and non-sinusoidal signals.
RememberUse a true-RMS meter when the waveform is not a clean sine.
PEP (peak envelope power) is the power at the highest peaks. Average power is what you get over time. An unprocessed SSB voice signal has a PEP-to-average ratio of about 2.5 to 1, set by speech characteristics: brief loud peaks, long quiet gaps.
RememberThe PEP-to-average ratio comes from the voice, not the amplifier or the carrier suppression.
An analog-to-digital converter (ADC) rounds each sample to one of 2^N levels, so 8 bits = 2^8 = 256 levels. Gain ahead of it does not change that count. A digital-to-analog converter (DAC) outputs stair-steps; a low-pass filter removes the sampling artifacts.
Remember8 bits = 256 levels. DAC output filter = remove sampling artifacts.
| Converter | How it works | Why you care |
|---|---|---|
| Successive approximation | Settles on the value one bit at a time | A type of ADC |
| Flash (direct) | Compares every level at once | Very high speed lets a software defined radio digitize high frequencies |
Quality is judged by total harmonic distortion (THD). Dither is a little noise added to the input to reduce quantization noise: it lets a signal smaller than one step still show up.
RememberTHD measures converter quality. Dither = deliberate small noise.