Signals & communication
Decibels, spectra & bandwidth
Use ratios to describe a signal chain without enormous numbers.
Decibels express a ratio, not an absolute amount by themselves. Power ratios use 10log₁₀; amplitude ratios use 20log₁₀ only when the relevant impedance relationship is accounted for. dBm references 1 mW. A spectrum describes a signal by frequency components: a sine has one ideal frequency, while sharp edges need many harmonics. Bandwidth determines which components a system can carry.
Modulation & carrying information
Change a carrier in a controlled way to carry a message.
Modulation maps information onto a carrier. AM varies amplitude; FM varies instantaneous frequency; phase modulation varies phase. Digital schemes choose among symbol states, which can represent one or more bits. Receivers need filtering, gain and a way to recover timing or carrier information. Noise, available bandwidth and transmitted power all affect reliable communication.
Transmission lines, reflections & matching
A wire stops behaving like an instant connection when timing gets fast.
A transmission line has distributed inductance and capacitance, a characteristic impedance and a propagation delay. Fast digital edges can need transmission-line treatment even at a modest repetition rate. A load mismatched to the line reflects part of the incident wave. Termination controls reflections; antennas intentionally couple energy into space and also require impedance and layout attention.