2026-08-20
Radar receivers, RSSI meters, and spectrum analyzers face a nasty measurement problem: the signal you're trying to quantify might be 1 microvolt or 10 millivolts, and you need to know which — now, not after a slow ADC and a log-lookup. An 80 dB dynamic range spans 10,000:1 in voltage. A linear amplifier saturates instantly at the top end and disappears into noise at the bottom. The successive detection log amplifier (or "log amp") solves this by turning power measurement into geometry: it cascades identical limiting amplifiers, taps the output of each stage, and sums the detected currents to produce a voltage proportional to log(input power).
Here's the trick. Stack N identical limiting amplifier stages, each with gain G (say 10 dB) and a hard saturation limit Vlim. Attach a rectifier ("detector") to the output of every stage, and sum all detector currents onto one node. For a tiny input, only the last stage's output has risen above the detector threshold — one detector contributes. Bump the input up by 10 dB: now the second-to-last stage also saturates, and two detectors contribute. Each additional 10 dB of input lights up one more detector. The sum grows linearly with the number of saturated stages, which grows logarithmically with the input voltage.
The output voltage looks like a piecewise-linear approximation to a true logarithm, with a kink at each stage's saturation point. Slope is typically 20–25 mV/dB. With 8 stages of 10 dB each, you get 80 dB of range on a single-cycle DC output.
Concrete example — Analog Devices AD8307: 500 MHz, 92 dB dynamic range, 25 mV/dB output slope, response time under 500 ns. A GSM base station uses one on every receive channel to feed the automatic gain control loop — the log amp says "the incoming signal is −73 dBm," the AGC adjusts the LNA bias accordingly, and the ADC sees a signal at a sane amplitude regardless of whether the phone is next door or three kilometers away.
Rule of thumb: N cascaded stages of gain G (dB) give you roughly N × G dB of dynamic range. Want 90 dB? Seven stages of ~13 dB each, or nine stages of 10 dB. Fewer stages with more gain each means more ripple in the log conformance; more stages with less gain each means smoother output but more silicon and more current.
The elegance: no ADC, no lookup table, no DSP — the log function is the topology.