# 26.2.2 Smoothing

### Smoothing

• In rectification, to produce a steady direct current  or voltage from an alternating current  or voltage, a smoothing capacitor is necessary
• Smoothing is defined as:

The reduction in the variation of the output voltage or current

• This works in the following ways:
• A single capacitor with capacitance C is connected in parallel with a load resistor of resistance R
• The capacitor charges up from the input voltage and maintains the voltage at a high level
• As it discharges gradually through the resistor when the rectified voltage drops but the voltage then rises again and the capacitor charges up again
• The resulting graph of a smoothed output voltage Vout and output current against time is a ‘ripple’ shape
• The amount of smoothing is controlled by the capacitance C of the capacitor and the resistance R of the load resistor
• The less the rippling effect, the smoother the rectified current and voltage output
• The slower the capacitor discharges, the more the smoothing that occurs ie. smaller ripples
• This can be achieved by using:
• A capacitor with greater capacitance C
• A resistance with larger resistor R
• Recall that the product RC is the time constant τ of a resistor
• This means that the time constant of the capacitor must be greater than the time interval between the adjacent peaks of the output signal

#### Worked example

Step 1:

Calculate the time constant with the 60 pF capacitor

τ = RC = (2.6 × 103) × (60 × 10-12) = 1.56 × 10-7 s  = 156 ns

Step 2:

Compare time constant of 60 pF capacitor with interval between adjacent peaks of the output signal

• The time interval between adjacent peaks is 80 ms
• The time constant of 156 ns is too small and the 60 pF capacitor will discharge far too quickly
• There would be no smoothing of the output voltages
• Therefore, the 60 pF capacitor is not suitable

Step 3:

Calculate the time constant with the 800 µF capacitor

τ = RC = (2.6 × 103) × (800 × 10-6) = 2.08 s

Step 4:

Compare time constant of 60 pF capacitor with interval between adjacent peaks of the output signal

• The time constant of 2.08 s is much larger than 80 ms
• The capacitor will not discharge completely between the positive cycles of the half-wave rectified signal
• Therefore, the 800 µF capacitor would be suitable for the smoothing task

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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