The four detectors, in the order they were developed — each one adding hardware to fix a shortcoming of the last.

(b) Slope detector — simplest. A single tuned circuit operated on the slope of its resonance curve converts frequency changes into amplitude changes, followed by an ordinary envelope detector. One tuned circuit and one diode — but the slope is only approximately linear, so distortion is heavy.

(a) Balanced slope detector — next. Two slope detectors, tuned above and below the carrier, with their outputs subtracted. The curvature of one circuit cancels that of the other, giving the familiar S-shaped response and much better linearity. It doubles the tuned circuits and diodes, hence more complex than (b).

(d) Phase (Foster–Seeley) discriminator — more complex again. It uses a centre-tapped transformer with primary and secondary tuned to the same frequency, plus a coupling capacitor and RF choke, and converts frequency deviation into a phase difference between primary and secondary voltages. The linearity is excellent and only one alignment frequency is needed, but the transformer arrangement is elaborate.

(c) Ratio detector — the most complex. It takes the phase discriminator's circuit and reverses one diode, adds a large stabilising electrolytic capacitor and takes the output from a different point, so that the output depends on the ratio of the two diode voltages rather than their difference. That ratio is insensitive to amplitude, so the detector rejects AM noise on its own and the receiver needs no separate limiter stage — the extra components buy that immunity.

So the increasing order is (b), (a), (d), (c).

The pattern: complexity rises exactly as linearity and noise immunity improve — one tuned circuit, then two, then a phase-sensitive transformer, then the amplitude-insensitive ratio arrangement that removes the need for a limiter.

Hence, the increasing order of circuit complexity is (b), (a), (d), (c).