Answer :
The average output voltage can be controlled, allowing for voltage regulation in various applications.
To calculate the firing angle of the switching devices in a three-phase fully controlled rectifier, we need to consider the relationship between the average output voltage and the firing angle.
The average output voltage of a three-phase fully controlled rectifier can be calculated using the formula:
V_avg = (3√2 / π) * Vm * cos(α)
where:
V_avg is the average output voltage,
Vm is the maximum possible output voltage,
α is the firing angle of the switching devices.
Source voltage (Vm) = 220V
Frequency (f) = 50Hz
Load resistance = R
We know that the maximum possible output voltage is given by:
Vm = √2 * V_source
Vm = √2 * 220V
Next, we are given that the required average output voltage is 70% of the maximum possible output voltage:
V_avg = 0.7 * Vm
Now, we can rearrange the formula to solve for the firing angle (α):
α = cos^(-1)((V_avg * π) / (3√2 * Vm))
Substitute the given values and calculate the firing angle (α).
Regarding the second part of your question:
b) The function of a Buck and Boost Chopper is to control the output voltage by adjusting the duty cycle of the chopper. A Buck Chopper is used to step down the output voltage, while a Boost Chopper is used to step up the output voltage. By varying the duty cycle (on-off time ratio) of the chopper, the average output voltage can be controlled, allowing for voltage regulation in various applications.
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(a) The firing angle of the switching devices is 65.56°
(b) The Buck chopper (step-down chopper) is used for decreasing the output voltage of a DC source.
The boost chopper (step-up chopper) is used for increasing the output voltage of a DC source.
(a) Calculation of firing angle of the switching devices:
Given, V_s = 220 V, f = 50 Hz, R_L = load resistance, V_o = 0.7 (maximum possible output voltage)
Let's first find the maximum possible output voltage;
The peak voltage of a 220 Vrms sinusoidal waveform is given as follows:
[tex]V_p = \sqrt{2 \times V_rms}\\= \sqrt{2 \times 220} \\= 311.13[/tex]
Vmaximum possible output voltage, [tex]V_o = V_p/\pi\\= 311.13/\pi\\ = 99.04 V[/tex]
For a fully controlled rectifier, the output voltage is given as: [tex]V_o = (2\sqrt2/\pi) \times V_s \cos(a)[/tex]
Therefore, [tex]\cos(a) = V_o / [(2\sqrt2/\pi) \times V_s]\\= (0.7 \times 99.04) / [(2\sqrt2/\pi) \times 220]\\= 0.429[/tex]
Therefore, [tex]a = \cos^{-1}(0.429)= 65.56\textdegree[/tex]
Thus, the firing angle of the switching devices is 65.56°
(b) Function of Buck and Boost Chopper:
The Buck chopper (step-down chopper) is used for decreasing the output voltage of a DC source. This is done by turning on and off the switching device in a controlled manner so that the average value of the voltage across the load decreases.
The boost chopper (step-up chopper) is used for increasing the output voltage of a DC source. This is done by turning on and off the switching device in a controlled manner so that the average value of the voltage across the load increases.
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