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
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