---
title: "Comparators; time delay circuits and level detector"
subject: "Switchgear and Protection"
chapter: 8
key: "semester_6/switchgear_and_protection:amplitude-phase-comparator-notes"
source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/amplitude-phase-comparator-notes
site: BCT Engineering
---

# Comparators; time delay circuits and level detector

Switchgear and Protection · Chapter 8: Static and Digital Relays

- Asked in: 2072 Asoj, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/amplitude-phase-comparator-notes
- Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-8

## Question

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

## Answer

#### 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.

```text
 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. An amplitude comparator in a static relay operates when:
   A. The phase angle between S1 and S2 lies within +-90 degrees
   B. |S1| > |S2|, irrespective of phase angle
   C. |S1| = 0
   D. S1 and S2 are in phase for more than 5 ms
   Answer: B. An amplitude comparator compares magnitudes only and trips when the operating signal exceeds the restraining signal. (Key point: Amplitude comparator)

2. Which statement about a phase comparator is correct?
   A. It compares the magnitudes of S1 and S2 only
   B. It trips when -90 deg <= phi <= +90 deg, irrespective of magnitudes
   C. It needs rectifier bridges only, never coincidence circuits
   D. It is used only for overcurrent relays
   Answer: B. A phase comparator considers only the angle between S1 and S2, e.g. coincidence circuits measuring overlap over 5 ms at 50 Hz. (Key point: Phase comparator)

3. In an RC time delay circuit, how is an inverse characteristic obtained rather than definite time?
   A. Using a counter and oscillator
   B. Making the capacitor charging current proportional to the fault current
   C. Using constant charging current
   D. Increasing the reference voltage with time
   Answer: B. A charging current proportional to the fault current makes delay shorter for larger faults (inverse); constant current gives definite time. (Key point: Time delay circuit types)

4. Why is a Schmitt trigger (with hysteresis) commonly used as the level detector?
   A. To amplify the signal 1000 times
   B. So noise near the threshold does not cause chattering
   C. To produce a time delay
   D. To measure the phase angle
   Answer: B. Hysteresis gives different pick-up and drop-off levels, preventing chatter when the input is close to the threshold. (Key point: Level detector features)

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