What is a Form Factor : Peak Factor & Its Derivations

At the time when the supply of heaters and motors took place, the power stations provided a good sinusoidal signal voltage, and the load receives a sinusoidal wave current. The entire system is manufactured in the way to manage this signal where this seems to be ideal for efficient distribution. But there happened one issue which was that the transmission system brought in magnetizing current along with the load current. This led to the situation that reactive current falls behind the supplied voltage level by 900 which seems to be not useful and also it is generally not metered for minimal users. But the transformers, generators, and cables required to be rated for this additional current also, and then this situation led to the concept of Form factor and Power factor. And today, this article explains the form factor meaning, its definition, and related scenarios.

What is a Form Factor?

Form factor signifies in describing the design, size, and physical features of either hardware or software device. Form factor in computers defines any physical specification related to the system which is the crucial aspect for connection compatibility. The most observable example of form factor is the variation between laptop and desktop. Even though the functionality and few components are similar, their shape and connection differ.

The hardware device form factor is based on the design of the component which fits into the hardware unit. The shape and design of the component are altered depending on the connections and power ratings.

Form factor ratio is defined as the RMS (Root Mean Square) of the wave and the rectified voltage of the wave. This is the simple way of referring to the distortion and heating effect of the signal. In a mathematical expression, it is represented as

K_f = RMS value/Average value

This is the form factor definition.

Corresponding to A.C current, the Kf is

K_f = RMS current/Average current = 0.707 Im/0.637 Im = 1.11

Corresponding to A.C voltage

K_f = RMS voltage/Average voltage = 0.707 Vm/0.637 Vm = 1.11

There exists a relation between the RMS value, peak, and average values of a varying quantity. So, form factors and power factors are used in defining the relationship between these three values.

Derivation

The RMS value of a continuous signal w.r.t time is given by

RMS = sqrt[1/Tʃ_t0 ^t0+T [x(t)]²]dt

In a similar way, the rectified average value of a continuous signal is

Avg = [1/Tʃ_t0 ^t0+T |x(t)|]dt

Form factor is given by the quotient of the above two values which is

kf = RMS/Avg = { sqrt[1/Tʃ_t0 ^t0+T [x(t)]²]dt }/{ [1/Tʃ_t0 ^t0+T |x(t)|]dt }

RMS signifies the deviation in the above function distance w.r.t average and it is more affected by huge variations in the non-rectified average value. This is greater than the absolute distance from the defined average value. So, the form factor will not minimal than one and it has no imaginary upper boundary limits for the functions with a necessary variation.

The total RMS value is given by

Total RMS = sqrt [RMS₁² + RMS₂² + ……..RMS_n²]

This can be implemented for integrating signals which have various frequency levels. As the average value on the similar domain can be combined as Avg₁ + Avg₂ ………+ Avg_n, the form factor of a complex signal consisting of various waves with similar frequency level is measured as

Total Form factor (k_ftotal) = {RMS₁ + RMS₂ ………+ RMS_n}/ { Avg₁ + Avg₂ ………+ Avg_n }

The form factor values for different types of sine waveforms is given by:

Peak Factor

The peak factor is also called as crest factor. In the case of AC signal, peak factor is defined as the ratio of its maximum value to the RMS value. This RMS value of the signal is equal to the heating effect delivered by the AC wave and that is the same as the heating effect of DC current. For an ideal AC sine wave, the RMS value has a specific relation with the crest value.

The RMS value of the AC signal is derived as follows:

Vrms = √{1/πʃ₀^π V² dϴ}

Vrms² = {1/πʃ₀^π Vm² Sin²ϴ dϴ}

Vrms² = { Vm² /πʃ₀^π Sin²ϴ dϴ}

Vrms² = { Vm² /πʃ₀^π (1-cos²ϴ)/2  dϴ}

Vrms² = { Vm² /2π [(1-cos²ϴ]₀^π  dϴ}

On evaluating the above expression, we get

Vrms² = Vm²/2

So, Vrms = Vm/√2

With this RMS value, the peak factor is expressed as below:

Peak factor = Vmaximum/Vrms

We have Vrms = Vm/√2

With this, we have

Peak factor = Vm/Vm/√2 = √2

Peak (or) Crest factor = √2 = 1.414

Form Factor of Half Wave Rectifier

As it was already discussed the form factor is the ratio of RMS value to the average value. It is given by

Form factor = RMS value/average value

In the case of HWR, the form factor of a half-wave rectifier is given by

Form factor of HWR = (Vm/2)/(Vm/π)

Kf in HWR = πVm/2Vm = 1.57

So, this is all about the Form Factor. This article has thoroughly explained the concepts of Form Factor and Peak factor, its derivation, definition, ratio, and motherboard form factors. Apart from this, know how the power factor is related to the form factor?