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Comparators; time delay circuits and level detector

Short answer

An amplitude comparator trips when |S1| > |S2| (magnitude comparison); a phase comparator trips when −90° ≤ φ ≤ +90° (phase angle comparison). Time delay circuits provide intentional delay: RC charging (definite or inverse time), digital counters, or integrating op-amps. A level detector (op-amp comparator or Schmitt trigger with hysteresis) gives a logic output when input exceeds a set threshold, serving as the pick-up element in static relays.

What do you understand by amplitude comparator and phase comparator? Write short notes on (i) Time Delay Circuits and (ii) Level Detector.

Amplitude comparator and phase comparator

A comparator in a static relay compares two signals S1 (operating) and S2 (restraining) derived from the relay current and voltage.

  • Amplitude comparator: compares magnitudes only. It trips when |S1| > |S2|, irrespective of the phase angle. Example: impedance relay with S1 = I·Z_r, S2 = V → trips when Z < Z_r. Built with rectifier bridges (circulating-current or opposed-voltage type) or op-amps.
  • Phase comparator: compares the phase angle φ between S1 and S2 only. It trips when −90° ≤ φ ≤ +90° (or another set range), irrespective of magnitudes. Example: mho relay with S1 = I·Z_r − V, S2 = V. Built with coincidence circuits (AND gate measuring overlap > 5 ms at 50 Hz) or Hall-effect devices.
  • They are dual: an amplitude comparator with (S1, S2) acts like a phase comparator with (S1 + S2, S1 − S2).

(i) Time delay circuits

Time delay circuits give an intentional delay between fault detection and trip, for grading and to avoid tripping on transients.

 V_in ─►[R]─┬─────►[Level detector]─► output
            │       (V_c > V_ref ?)
           [C]
            │
           ─┴─ (transistor resets C
                 when input removed)
  • RC charging type: a capacitor charges through a resistor; when its voltage reaches a reference, the level detector switches. Delay t = RC·ln[V/(V − V_ref)]. Making the charging current proportional to the fault current gives an inverse characteristic; constant current gives definite time.
  • Digital (counter) type: an oscillator and counter count pulses; delay = N × clock period. Very accurate and long delays possible.
  • Integrating op-amp type: integrator output rises linearly with time.

(ii) Level detector

A level detector gives an output (logic 1) when its input signal exceeds a set threshold, and no output below it. It acts as the "pick-up" element of a static relay.

  • Usually an op-amp comparator or a Schmitt trigger with hysteresis so that noise does not cause chattering.
  • Threshold set by a reference voltage (potentiometer or Zener).
  • Used in overcurrent/over-voltage relays (pick-up), after comparators, and in time-delay circuits.

✓ Answer checked by Claude Opus 5.5 (high effort)

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