## Relationship between frequency and speed

Table of Contents

Relationship between frequency and speed

When there are two poles, one full rotation will result in one full pulse for each cycle, both positive and negative. The speed or number of revolutions per second (rpm/60) of the rotating field will directly affect the frequency in cycles per second (Hz).

If the ac synchronous generator has multiple poles (having, say, two, four, six, or eight poles…), then for a speed of one revolution per second (1 rpm/60), the frequency per revolution will be one, two, three, or four …, cycles per revolution, respectively. Therefore, the number of pairs of poles equals the frequency per revolution. Since the frequency directly depends on both the speed (rpm/60) and the number of pole pairs (P/2), these two factors can be combined into a single equation.

### Relationship between frequency and speed

### Where

P is the number of poles

N is the speed in rpm (rev/min)

f is. the frequency in hertz

**Ï‰ _{m }**is the speed in radians per second (rad/s)

**Ï‰e**Â is the speed electrical radians per second.

### Synchronous Speed

The synchronous speed is defined as the speed at which the rotating magnetic field of an electric machine rotates. It is denoted by N_{s}

Synchronous Speed, NS=120f/P

The number of field poles on the rotor of a given Alternator is fixed,. So in order to Generate an output with the desired Frequency, the rotor must be run at Synchronous speed. So, for an Alternator, the Frequency of the Generated voltage in the Armature winding and the rotor speed (N) have a constant relationship. The speed Ns is known asÂ **synchronous speed**. An electrical machine that runs at synchronous speed is known asÂ **synchronous machine**.