DocID024230 Rev 1

3/15

AN4250

Power factor

15

1

Power factor

In the power electrical circuit, the power factor represents an index measuring the available

main power used.

The general power factor definition is given by the ratio between the active power and the

apparent power:

Equation 1

Its value varies from 0 to 1. In the efficient system, the value of the power factor should be

equal to 1.

In the classic Graetz rectifier with capacitive filter, the voltage and current waveforms are not

sinusoidal.

Figure 1. Schematics of a single phase diode bridge rectifier

The sinusoidal voltage main is expressed by the following equation:

Equation 2

The current expression, not being sinusoidal, can be represented in fourier series:

Equation 3

The active power is given by the following formula:

Equation 4

Apparent

P

Active

P

S

P

F

P

.

.

.

.

=

=

D1

1N4148

D2

1N4148

D3

1N4148

D4

1N4148

100µ

C1

R1

1K

V1

SINE(0 12 50 0 0 0)

;tran 2

.tran 50ms

12 m s 15 m s 18 m s 21 m s 24 m s 27 m s 30 m s 33 m s 36 m s 39 m s 42 m s 45 m s 48 m s

-1 V

0V

1V

2V

3V

4V

5V

6V

7V

8V

9V

10 V

11 V

12 V

13 V

-4 0 0 m A

-3 5 0 m A

-3 0 0 m A

-2 5 0 m A

-2 0 0 m A

-1 5 0 m A

-1 0 0 m A

-5 0 m A

0m A

50 m A

10 0m A

15 0m A

V( n 0 0 2 )

V( n 0 0 1 )

I( V 1 )

AM17349v1

)

(

2

ϕ

=

t

sen

V

V

eff

mains

.....

)

5

5

sin(

2

)

3

3

sin(

2

)

1

sin(

2

5

3

1

+

+

+

+

+

+

=

ϕ

ω

ϕ

ω

ϕ

ω

t

t

t

I

I

I

ϕ

cos

1

I

P

=