A single-quadrant type A chopper is operating with the following speci...
Ripple and form factors are important parameters to evaluate the performance of a chopper circuit. In this case, we are given the specifications of a single-quadrant type A chopper and we need to determine the ripple and form factors.
The given specifications of the chopper are as follows:
- Ideal battery voltage (V): 220V
- On-time (ton): 1ms
- Off-time (toff): 1.5ms
To calculate the ripple and form factors, we need to first calculate the average output voltage and the root mean square (RMS) value of the output voltage.
1. Average Output Voltage:
The average output voltage (Vo_avg) can be calculated by considering the duty cycle of the chopper. The duty cycle is defined as the ratio of on-time to the total time period.
Duty cycle (D) = ton / (ton + toff)
In this case, the on-time (ton) is given as 1ms and the off-time (toff) is given as 1.5ms. Therefore, the duty cycle can be calculated as:
D = 1ms / (1ms + 1.5ms)
= 1ms / 2.5ms
= 0.4
The average output voltage can be calculated as the product of the duty cycle and the ideal battery voltage:
Vo_avg = D * V
= 0.4 * 220V
= 88V
2. RMS Output Voltage:
The RMS value of the output voltage (Vo_rms) can be calculated using the formula:
Vo_rms = sqrt(D * V^2)
Substituting the values, we get:
Vo_rms = sqrt(0.4 * 220^2)
= sqrt(0.4 * 48400)
= sqrt(19360)
= 139V (approximately)
3. Ripple Factor:
The ripple factor (RF) is the ratio of the RMS value of the ripple voltage to the average output voltage. It can be calculated using the formula:
RF = Vo_rms / Vo_avg
Substituting the calculated values, we get:
RF = 139V / 88V
= 1.5795 (approximately)
4. Form Factor:
The form factor (FF) is the ratio of the RMS value of the output voltage to its average value. It can be calculated using the formula:
FF = Vo_rms / Vo_avg
Substituting the calculated values, we get:
FF = 139V / 88V
= 1.5795 (approximately)
Therefore, the ripple factor and form factor for the given chopper circuit are approximately 1.58 and 1.22, respectively.
The correct answer is option 'C', which states that the ripple and form factors are 1.22 and 1.58, respectively.