Two views of the same signal
Which of the following describes a signal in the time domain?
Amplitude at different times.
The oscilloscope view. The frequency domain — the spectrum analyser view — shows amplitude at different frequencies.
What technique shows that a square wave is made up of a sine wave and its odd harmonics?
Fourier analysis.
Fourier’s result is that any periodic waveform is a sum of sine waves at harmonics of its fundamental. A square wave is the fundamental plus its odd harmonics in declining amplitude — which is not a mathematical curiosity but the explanation for two practical facts:
- A switching amplifier radiates harmonics, because its output really is a sum of them, which is why the circuits lesson insisted on an output filter.
- Sharp CW keying produces clicks, because a fast rise time is a sharp-edged waveform, and sharp edges are made of high harmonics.
The FFT from the SDR lesson is the computational version of this transform.
True RMS
What is the benefit of making voltage measurements with a true-RMS calculating meter?
RMS is measured for both sinusoidal and non-sinusoidal signals
An ordinary AC meter rectifies, averages, and multiplies by 1.11 — a constant that is correct only for a sine wave. On anything else it reads wrong, and it does not warn you.
A true-RMS meter squares, averages, and takes the root, which is the definition. It reads correctly on a distorted waveform, a switching supply’s output, or a modulated signal — exactly the cases where you most want a reliable number. This is the meter worth paying for.
PEP-to-average ratio
What is the approximate ratio of PEP-to-average power in an unprocessed single-sideband phone signal?
2.5 to 1
What determines the PEP-to-average power ratio of an unprocessed single-sideband phone signal?
Speech characteristics.
Speech is peaky: brief loud syllables between quiet gaps. So an SSB signal at 100 W PEP averages about 40 W, and the ratio depends on the speaker — voice, accent, microphone technique.
Two consequences already met elsewhere: a speech processor raises the average by compressing this ratio, and the duty cycle that matters for RF exposure and for transmitter heating is far lower on SSB than on a constant-carrier mode.
ADC architectures
Three ways to turn a voltage into a number, each with a purpose.
| Type | How | Suits |
|---|---|---|
| Successive approximation | binary search, one bit per step | general purpose, good resolution |
| Flash (direct) | comparators for every level at once | very high speed — digitizing high frequencies |
| Sigma-delta | oversample and filter | audio, very high resolution, slow |
Why are direct or flash conversion analog-to-digital converters used for a software defined radio?
Very high speed allows digitizing high frequencies
A flash converter decides in one step, because it compares against every level simultaneously. The cost is 2ⁿ−1 comparators, so an 8-bit flash needs 255 of them and a 16-bit one is impractical. Speed bought with silicon.
How many different input levels can be encoded by an analog-to-digital converter with 8-bit resolution?
256.
2⁸ = 256. Same powers-of-two arithmetic as the flip-flop divider chain.
Dither, filtering, and quality
What is “dither” with respect to analog-to-digital converters?
A small amount of noise added to the input signal to reduce quantization noise
Counterintuitive and real. A signal sitting between two quantisation levels always rounds the same way, producing a fixed error that appears as distortion. Adding a little noise makes the rounding vary, so averaging over time recovers information finer than one step. Noise deliberately added to improve resolution.
What is the purpose of a low-pass filter used at the output of a digital-to-analog converter?
Remove spurious sampling artifacts from the output signal.
A DAC’s output is a staircase, full of energy at the sample rate and its harmonics. The reconstruction filter smooths it — the counterpart of the anti-alias filter on the way in.
Which of the following is a measure of the quality of an analog-to-digital converter?
Total harmonic distortion.
THD captures how faithfully the converter reproduces a signal, which bit depth alone does not: a converter can have 16 bits of resolution and 12 bits’ worth of honest performance.
Check yourself
- Why does a square wave contain odd harmonics, and what does that predict about a Class D amplifier?
- Your averaging AC meter reads 10 V on a switching supply’s output. Trustworthy?
- How many levels does a 12-bit ADC resolve?
Answers
- Fourier analysis shows a square wave is its fundamental plus odd harmonics. A Class D amplifier’s output is a switching waveform, so it radiates those harmonics — hence the mandatory output filter.
- No. An averaging meter’s 1.11 factor is correct only for a sine wave. Use a true-RMS meter.
- 2¹² = 4096.