0195136047.pdf

16.1 POWER SEMICONDUCTOR-CONTROLLED DRIVES 759

The rms value of a periodic waveform is given by

Vrms=

[

1

T

∫T

0

v^2 L(t) dt

] 1 / 2

(16.1.5)

For a sinusoidal voltagevL(t)=Vmsinωtfor 0≤t≤T/2, the rms value of the output voltage is

Vrms=

[

1

T

∫T/ 2

0

(Vmsinωt)^2 dt

] 1 / 2

=

Vm

2

= 0. 5 Vm (16.1.6)

Irms=

Vrms

R

=

0. 5 Vm

R

(16.1.7)

The output dc powerPdcis given by

Pdc=VdcIdc=

( 0. 318 Vm)^2

R

(16.1.8)

The output average ac powerPacis given by

Pac=VrmsIrms=

( 0. 5 Vm)^2

R

(16.1.9)

Theefficiencyor therectification ratioof the rectifier, which is a figure of merit used for
comparison, is then

Efficiency=η=

Pdc

Pac

=

( 0. 318 Vm)^2

( 0. 5 Vm)^2

= 0. 404 ,or 40.4% (16.1.10)

Theform factoris FF=Vrms/Vdc, which gives a measure of the shape of the output voltage.
In our case,

FF=

Vrms

Vdc

=

0. 5 Vm

0. 318 Vm

= 1. 57 ,or 157% (16.1.11)

Theripple factoris RF=Vac/Vdc, which gives a measure of the ripple content. In our case,

RF=

Vac

Vdc

=

√(

Vrms

Vdc

) 2

− 1 =

√

FF^2 − 1 =

√

1. 572 − 1 = 1. 21 ,or 121% (16.1.12)

Thetransformer utilization factor(TUF) is given by

TUF=

Pdc

VsIs

(16.1.13)

whereVsandIsare the rms voltage and rms current, respectively, of the transformer secondary.
In our case, the rms voltage of the transformer secondary is

Vs=

[

1

T

∫T

0

(Vmsinωt)^2 dt

] 1 / 2

=

Vm

√

2

= 0. 707 Vm (16.1.14)

The rms value of the transformer secondary current is the same as that of the load,

Is=

0. 5 Vm

R

(16.1.15)

Hence,

TUF=

0. 3182

0. 707 × 0. 5

= 0. 286 (16.1.16)

Thepeak inverse voltage(PIV), which is the peak reverse blocking voltage, is given by