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Phase comparison technique is the most widely used technique for all practical directional, distance, differential and carrier relays.

In a phase comparator, the operation of the relay takes place when the phase relation between two inputs S_{1} and S_{2} varies within certain specified limits. Both inputs must exist for an output to occur; ideally, operation is independent of their amplitudes, and depends only on their phase relationship. The function, as defined by the boundary of marginal operation, is represented by two straight lines from the origin of the complex plane.

Mathematically, the condition of operation is given as –

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– α_{1} ≤ θ ≤ α_{2}

Where, θ is the angle by which S_{1} lags behind S_{2}. If α_{1} = α_{2} = 90° the comparator is called the cosine comparator and if α_{1} = 0 and α_{2} = 180°, it is called the sine comparator.

**Static phase comparators are of two types viz.: **

1. Coincidence type phase comparator and

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2. Vector product phase comparator.

**1. Coincidence Type Phase Comparators****: **

The basic concept of phase comparison is simpler in that it is possible to deal with signals of equal strength whose coincidence or non-coincidence is readily measurable. Let us consider two sinusoidal signals S_{1} and S_{2}. Their period of coincidence depends upon their phase difference. Fig 3.17 illustrates the coincidence of signals S_{1} and S_{2} for different phase angles.

It can be seen that the period of coincidence of two sinusoidal signals S_{1} and S_{2} is = (180° – θ) where 0 is the phase angle between S_{1} and S_{2}. It means if the operation is desired for a phase angle θ less than 90°, then coincidence period should be greater than 90°. Thus, the criterions for operation becomes – 90° ≤ θ ≤ 90°.

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By measuring the period of coincidence, it is possible to design the circuit to give an output a YES or a NO depending upon the phase relation of the input signals.

**Different techniques can be used to measure the period of coincidence, some of them are given below: **

**i. Spikes and Block Coincidence Techniques in Phase Comparator: **

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In such a comparator, one of the inputs is converted to square wave and the other into a pulse of short duration at the instant of its zero crossing, peak value or at any angle (preferably at the instant of its peak value). The squared and spike signals are fed through an AND gate. Figure 3.18 shows the schematic block diagram and waveforms. If these two signals coincide at any time, the output then only would be available from the AND gate.

**The output obtainable depends on the instant of spiking and is as follows for different phase difference ranges: **

(i) With spike derived at peak value, output is available for – 90° ≤ θ ≤ 90°

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(ii) With spike derived at zero value, output is available for 0 ≤ θ ≤ 180°.

(iii)* *With spike derived at any other instant a, output is available for 0 ≤ θ ≤ 180° – α

Squaring of one input signal is obtained by first limiting it and then amplifying it so that the rectangular block is in phase with the original sine wave. The spike is produced by a peaking transformer or by squaring the wave through the diodes and feeding it through a transformer. The spike is obtained at zero value of the sine wave in each case. This is shifted as per requirement through the delay circuit. A comparison is made after every half cycle. The main drawback of such a comparator is that in case of spurious spikes due to any switching or external interference, the relay may operate which is not desirable. Shielding of the circuit against electric and magnetic fields is, therefore, essential.

**ii. Phase Comparator with Phase Splitting Technique****: **

Figure 3.19 illustrates this method in which both the input signals S_{1} and S_{2} are split into two components S_{1 }∠-45°, S_{1} ∠45°, S_{2} ∠-45°, and S_{2 }∠45° with respect to the original signal. The four components are then fed into an AND gate which gives an output when all the four inputs are simultaneously positive at any time in the cycle. The coincidence of all the four signals is possible when the phase angle θ satisfies the condition -90° ≤ θ ≤ 90°.

**iii. Integrating Phase Comparator: **

In this comparator the two input voltage signals are fed into an AND gate the output of which is integrated to measure the period of coincidence of the two signals. If the period of coincidence exceeds 90°, the output is obtained so that the condition is -90° ≤ θ ≤ 90° for operation. In earlier integrator phase comparators, transistor- type AND gate used to be employed. But in recent types the periods of coincidence are integrated and then fed into a level detector. The critical operating threshold occurs when the periods of coincidence and non-coincidence are equal i.e. θ = ± 90°.

The input signals S_{1} and S_{2} are compared in a coincidence circuit producing standard output pulses, which are positive when both the signals are of the same polarity (either both positive or both negative) and negative when they are of opposite polarity. The output pulses are fed into an integrating circuit whose output increases linearly during the period when the pulse is positive and falls at the same rate when the polarity reverses. The level detector switches when the output from the integrator exceeds some preset value, and resets when the output falls below some second value.

**iv. Integrating Type Phase Comparator with Rectifier Bridge and Gate: **

Such a phase comparator has the advantage of simplicity and economy. The circuit is illustrated in Fig. 3.21 (a). It consists of a rectifier phase comparator followed by a polarity detection circuit, R-C charging circuit and a level detector. It is a circulating current bridge whose output current is supplied to a centre tapped resistance R-R. The output current is equal to the smaller of the two input currents.

The path of the current through the bridge is established by the larger of two input currents and depends upon their relative instantaneous polarity. If i_{1} exceeds i_{2}, the currents will flow in top and bottom rectifiers; 1 and 2 if i_{1} is positive and in diagonal rectifiers 3 and 4 if i_{1} is negative. When i_{2} exceeds i_{1} the current flows in rectifiers 1 and 4 if i_{2} is positive and in rectifiers 2 and 3 if i_{2} is negative. If i_{1} and i_{2} are of the same polarity, the output voltage (voltage across R-R) is positive, and if of opposite polarity the output voltage will be negative.

It means the output voltage is positive during positive or negative coincidence periods and negative during non-coincidence period. This is illustrated in Fig. 3.21 (b). The operating time with single bridge is less than half a cycle. The bridge gives more circular characteristics than the amplitude comparator bridge and hence it is preferred for mho and directional relays.

**2. Vector Product Phase Comparators****: **

The output of such devices is proportional to the vector product of the two input quantities. These devices include Hall Effect phase comparator and the magneto-resistivity phase comparator.