A singel phase transformer with secondary voltage 230V 50Hz delivers p...
Calculation of Various Parameters of Half Wave Controlled Rectifier Circuit
Given Data:
- Secondary Voltage (Vs) = 230V
- Frequency (f) = 50Hz
- Load Resistance (R) = 10ohm
- Firing Angle (α) = 60 degree
Rectification Efficiency
Rectification efficiency is the ratio of DC output power to the AC input power.
DC output power, Pdc = (Vdc^2)/R
AC input power, Pac = (Vs^2)/R
Rectification efficiency, η = Pdc/Pac
Substituting the values, we get:
- DC output power, Pdc = (Vdc^2)/R = (230/sqrt(2))^2/10 = 2640.67W
- AC input power, Pac = (Vs^2)/R = (230)^2/10 = 5290W
- Rectification efficiency, η = Pdc/Pac = 2640.67/5290 = 0.499 or 49.9%
Form Factor
Form factor is the ratio of RMS value to the average value of the output voltage.
RMS value of output voltage, Vrms = Vdc/sqrt(2)
Average value of output voltage, Vavg = Vdc/π
Form factor, FF = Vrms/Vavg
Substituting the values, we get:
- RMS value of output voltage, Vrms = Vdc/sqrt(2) = (230/sqrt(2))/2 = 81.92V
- Average value of output voltage, Vavg = Vdc/π = (230/π)*cos(60) = 65.83V
- Form factor, FF = Vrms/Vavg = 81.92/65.83 = 1.24
Voltage Ripple Factor
Voltage ripple factor is the ratio of the RMS value of the ripple voltage to the DC output voltage.
RMS value of ripple voltage, Vr = Vdc*(1/π)*sqrt((1-cosα)/2)
Voltage ripple factor, Vrf = Vr/Vdc
Substituting the values, we get:
- RMS value of ripple voltage, Vr = Vdc*(1/π)*sqrt((1-cosα)/2) = (230/sqrt(2))*(1/π)*sqrt((1-cos60)/2) = 26.79V
- Voltage ripple factor, Vrf = Vr/Vdc = 26.79/115.03 = 0.232 or 23.2%
Transformer Utilization Factor
Transformer utilization factor is the ratio of DC output power