*What is Crest Factor or Peak Factor? Its formula & Derivation*

*What is Crest Factor or Peak Factor? Its formula & Derivation*

The ratio of Peak value to root mean square(RMS) value of AC quantity is called **Crest Factor** or **Peak Factor.** Any periodic waveform has its varying magnitude with time. The waveform attains maximum or peak value at a point of time. The direct current has its maximum amplitude at all the times i,e. it has constant magnitude and the magnitude does not change with time. In case of the alternating current, the instantaneous value varies with time and attains maximum or peak value and again the magnitude gets decreased.

**What is Crest Factor?**

The **crest factor** of an AC current or voltage waveform is the ratio of its peak value to root mean square(RMS) value.The crest factor of an AC voltage or current can be found by measuring its peak value and root mean square value.The root mean square value of an AC current is equal to the heating effect produced by the AC current that is equal to the heating effect produced by the DC current. The root mean square value of an perfect sinusoidal AC voltage or current has certain relationship with its peak or maximum value.

### **RMS Value of AC Waveform**

**Crest Factor Formula Derivation**

The crest factor of an AC current or voltage waveform can be mathematically expressed as;

### Importance of Crest Factor

**flat top voltage waveform.**

### **Crest Factor of sinusoidal and non sinusoidal waveform**

**From above figure;**

**Crest Factor of sinusoidal waveform**

**I peak/ Irms**= 8.20/5.8=1.414

**Crest Factor of non sinusoidal waveform**

### **Significance of Crest Factor**

**Power Supply Capacity Selection **

**Current Transformer(CT) Selection **

If the peak current is too high, the metering CT inputs can clip, causing inaccurate readings.This means that when measuring loads with high current crest factors, CT current rating needs to be selected considering crest factor of the load. For example, if your load draws 15 amps RMS, but has a crest factor of 4.0, then the peak current is 60 amps. If you use a 20 amp CT, the meter will not be able to accurately measure the 30 amp peak current.

The following graph shows the maximum RMS current for accurate measurements as a function of the current waveform crest factor. The current is shown as a percentage of CT rated current. For example, if you have a 10 amp load with a crest factor of 3.0, the maximum CT current is approximately 58%. Fifty-eight percent of 20 amps is 11.60, which is higher than 10 amps, so your measurements should be accurate.

On the other hand, if you have a 100 amp load with a crest factor of 4.0, the maximum CT current is 42%. Forty-two percent of a 250 amp CT is 105 amps, so you would need a 250 amp CT to accurately measure this 100 amp load.

If crest factor of the load is not known, the crest factor can be assumed to be in the range in 1.4 to 1.5 and CT current rating 150% of the expected RMS current can be selected for measurement.So if the measuring currents up to 50 amps, select a 75 amp CT.