---
title: "Comparators used in static relays"
subject: "Switchgear and Protection"
chapter: 8
key: "semester_6/switchgear_and_protection:comparators-static-relay"
source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/comparators-static-relay
site: BCT Engineering
---

# Comparators used in static relays

Switchgear and Protection · Chapter 8: Static and Digital Relays

- Asked in: 2076 Bhadra, 8 marks; 2077 Chaitra, 8 marks (asked 2 times)
- Video: [Phase and Amplitude Comparators | Static Relays | Switchgear and Protection | 5 Min Concept](https://www.youtube.com/watch?v=F5FgwlMdZk0) — TechInsight
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/comparators-static-relay
- Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-8

## Question

Define comparator (phase comparator) and explain the types of comparators used in static relays.

## Short answer

A comparator is the measuring element of a static relay comparing two signals S1 and S2. An amplitude comparator trips when |S1| > |S2| regardless of phase; types include circulating-current, opposed-voltage, averaging, and sampling. A phase comparator trips when the phase angle φ between S1 and S2 lies within ±90°; types include vector product, coincidence (AND gate measuring overlap >5 ms), rectifier bridge, and integrating. They are dual: amplitude comparator with (S1,S2) equals phase comparator with (S1+S2, S1−S2).

## Answer

A **comparator** is the measuring element of a static relay. It compares two input quantities (signals S1 and S2, formed from the relay voltage and current) either in **amplitude** or in **phase**, and gives a trip output when a set condition is met. A **phase comparator** compares only the phase angle between S1 and S2 and operates when the angle lies within a set range (normally −90° ≤ φ ≤ +90°), whatever their magnitudes.

#### 1. Amplitude comparator

Compares only the magnitudes: trip when |S1| > |S2| (operating > restraining), whatever the phase.

```text
S1 ─►[Rectifier B1]─┐
                    ├─►[ |S1| − |S2| ]─►[Level det.]─► trip
S2 ─►[Rectifier B2]─┘    (> 0 ?)
```

Types:
- **Circulating-current type:** two rectifier bridges; their currents are compared in a polarised relay/moving-coil element.
- **Opposed-voltage type:** rectified voltages are opposed across a resistor; there is an output when the operating voltage is larger.
- **Averaging type** and **sampling (instantaneous) type** comparators using transistors/op-amps.

Example: impedance relay, |I·Z_r| > |V|.

#### 2. Phase comparator

Compares phase angle only: trip when −90° ≤ arg(S1/S2) ≤ +90°.

Types:
- **Vector product type:** a Hall-effect or magneto-resistive device gives an output ∝ |S1||S2|cos φ; a positive output means trip.
- **Coincidence type:** S1 and S2 are converted to square waves, and an AND gate measures the time for which both are positive. Coincidence > 5 ms (a quarter cycle at 50 Hz) means |φ| < 90° → trip.
- **Rectifier bridge phase comparator** and **integrating type**.

```text
S1 ─►[Squarer]─┐
               ├─►[AND]─►[Integrator]─►[Level det]─► trip
S2 ─►[Squarer]─┘          (> 5 ms ?)
```

Example: mho relay, S1 = I·Z_r − V and S2 = V.

#### Duality

An amplitude comparator with inputs S1, S2 is equivalent to a phase comparator with inputs (S1 + S2) and (S1 − S2), and vice versa. Hence any characteristic can be obtained with either comparator by mixing the inputs suitably.

| Point | Amplitude comparator | Phase comparator |
|---|---|---|
| Compares | Magnitudes | Phase angle |
| Trip condition | \|S1\| > \|S2\| | −90° ≤ φ ≤ 90° |
| Typical use | Impedance, overcurrent | Mho, directional |
| Common circuit | Rectifier bridges | Coincidence (AND) |

## Check yourself

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

1. An amplitude comparator trips when:
   A. |S1| > |S2| regardless of phase
   B. The angle is within +/-90 degrees
   C. S1 and S2 are equal in phase
   D. |S1| < 0
   Answer: A. It compares only magnitudes of operating and restraining signals. (Key point: Amplitude comparator)

2. A phase comparator operates when the angle between S1 and S2 lies in:
   A. 0 to 180 degrees
   B. -90 to +90 degrees, whatever the magnitudes
   C. 90 to 270 degrees
   D. Exactly 0 degrees
   Answer: B. It compares only phase angle, with trip for -90 <= phi <= +90. (Key point: Phase comparator condition)

3. In the coincidence type phase comparator, what indicates tripping at 50 Hz?
   A. AND gate output lasting more than 5 ms
   B. Output lasting less than 5 ms
   C. Both waves negative
   D. Equal magnitudes
   Answer: A. 5 ms is a quarter cycle, corresponding to |phi| < 90 degrees. (Key point: Coincidence type)

4. What does the duality of comparators state?
   A. Amplitude comparator with S1, S2 equals phase comparator with S1+S2 and S1-S2
   B. Phase comparators cannot give any characteristic
   C. Amplitude comparators work only for mho
   D. They are unrelated
   Answer: A. Any characteristic can be obtained with either comparator by mixing inputs. (Key point: Duality)

## Related in Switchgear and Protection

- [Static vs electromagnetic relays; components](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-vs-electromagnetic-relays) — Switchgear and Protection, chapter 8, asked 4×
- [Types of static relays; merits and demerits](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-relay-types-merits) — Switchgear and Protection, chapter 8, asked 2×
- [Static overvoltage and undervoltage relays](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-over-under-voltage-relay) — Switchgear and Protection, chapter 8
- [Comparators; time delay circuits and level detector](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aamplitude-phase-comparator-notes) — Switchgear and Protection, chapter 8

## Related in other subjects

- [Classification and merits of comparators](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Aclassification-of-comparators) — Metrology, chapter 7
- [Transistor as static switch and base drive](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Atransistor-static-switch-base-drive) — Power Electronics, chapter 1, asked 4×
- [Power transistor V-I and static switch](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Apower-transistor-vi-static-switch) — Power Electronics, chapter 1, asked 2×
- [Syntax of static](https://www.bctengineer.com/question.md?key=semester_1%2Fcomputer_programming%3Asyntax-static) — Computer Programming, chapter 6