A power supply like that of Fig. 28.23 is supposed to deliver 22-V DC at a maximum current of 18

step 1 So here for our solution for a cycle 50 Hz AC, the time period we have t is equals to 1 over 50

A power supply like that of Fig. 28.23 is supposed to...

A power supply like that of Fig. $28.23$ is supposed to deliver $22-\mathrm{V}$ DC at a maximum current of $180 \mathrm{~mA}$. The transformer's peak output voltage can charge the capacitor to a full $22 \mathrm{~V}$, and the primary is supplied with $50-\mathrm{Hz} \mathrm{AC}$. What capacitance will ensure that the output voltage stays within $4 \%$ of the rated $22 \mathrm{~V}$ ?

Key Concepts

Ripple Voltage

Ripple voltage refers to the periodic variation (or “ripple”) in the DC output voltage of a power supply that occurs due to incomplete suppression of the alternating waveform after rectification. It is an important parameter in power supply design because excessive ripple can affect the performance of electronic circuits. Designers typically specify a maximum allowable ripple voltage to ensure that the DC output remains within a certain tolerance of the desired value.

Capacitor Filtering

Capacitor filtering is a common technique used to smooth out the pulsating DC voltage produced by rectifiers. In a power supply, the capacitor charges up to the peak voltage during the conduction phase of the rectifier and then discharges when the input voltage falls, providing a more constant DC level. The size of the capacitor directly affects the amount of smoothing achieved, with larger capacitance values generally resulting in a lower ripple voltage.

RC Discharge in Power Supplies

This concept involves understanding how a capacitor discharges through a load during the intervals when the supply voltage is not being replenished. It is quantified by the relation ?V = I·?t / C, where ?V is the allowable voltage drop (ripple), I is the load current, ?t is the time interval between charging cycles, and C is the capacitance. This relationship is vital in selecting the proper capacitor value to ensure the voltage remains within design limits.

Rectifier and Frequency Considerations

When converting AC to DC, the rectification process introduces considerations regarding the frequency of the AC source. For a half?wave rectifier, the capacitor discharges over one full cycle of the input AC, while a full?wave rectifier effectively doubles the charging frequency, reducing the discharge period (?t). This discharge time directly influences the required capacitance to maintain a given ripple voltage level. Understanding the role of the input AC frequency is essential for accurately calculating the capacitor value necessary for proper filtering.

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