Smoothed Full-wave Rectification (Figure C25.3)
The rectified a.c. has become a d.c. signal already, but it is not steady enough for many operations, therefore further shaping of the signal is required. In order to smooth the voltage, a storage capacitor is used. It stores charge while the input is increasing and discharges slowly while the input is decreasing.
During the first half-cycle, a current flows through diode P, capacitor, resistor and diode Q. The capacitor is charged up and stores charge. The voltage across the capacitor is qual to the voltage across the resistor. This occurs until the voltage across the capacitor equals the peak voltage of the supply. After the point of peak voltage, the applied voltage decrease. The potential of the plate of the capacitor is greater than the potential of the supply. So, the capacitor discharges through the resistor. The voltage across the capacitor decreases exponentially, so the signal keeps in a more steady level, except for a small ripple.
This is the smoothed full-wave rectification.
Filtered and Smoothed Full-wave Rectification (Figure C25.4)
After using the storage capacitor, the output voltage still contains small ripples. In order to have a steady voltage, a smoothing inductor and a smoothing capacitor are used.
The smoothing inductor has a high reactance to block the alternating voltage. Therefore, most of the ripple voltage is developed across the inductor. The smoothing capacitor has a high reactance to block the steady voltage. So, most of the steady voltage is developed across the smoothing capacitor and the resistor.
In a short summary, the smoothing capacitor has a lower reactance when compared with the smoothing inductor, so most of the ripple disappears across the smoothing capacitor. This is the filtered and smoothed full-wave rectification.
Procedure:
Half-wave rectifying circuit
- Set up the apparatus according to Figure C25.5 for testing the operation of the half-wave rectifying circuit.
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Use the CRO to confirm that the selected output of the low voltage power supply is an a.c. If so, measure its peak voltage v1 and frequency f1.
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Use the CRO to display the signal across the resistor. Sketch the waveform and comment on its shape. Measure its peak voltage v2 and frequency f2. Compare v2 with v1 and f2 with f1, and account for any difference between them.
Full-wave rectifying circuit
- Set up the apparatus according to Figure C25.6 for testing the operation of the full-wave rectifying circuit.
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Use the CRO to display the signal across the resistor. Sketch the waveform and comment on its shape. Measure its peak voltage v3 and frequency f3. Compare v3 with v2 and f3 with f2, and account for any difference between them.
Smoothing circuit
- Take turn to use the capacitor of 10 μF, 100 μF, 500 and 1000 μF as the storage capacitor and connect it across the resistor. While changing the storage capacitance from the lowest to the highest value, monitor the signal across the resistor by using the CRO.
- Sketch several waveforms to show the effect of changing the storage capacitance, and explain why it is better to use larger capacitance for the reservoir capacitor.
Filter circuit
- While keeping the storage capacitor at 100 μF, disconnect the resistor and replace it with the series combination of the 1100-turn inductor (with C-cores) and the 100-μF capacitor (as smoothing capacitor). Then connect the resistor across the smoothing capacitor.
- While removing the C-cores from the inductor, monitor the signal across the resistor by using the CRO.
- Sketch two waveforms to show the effect of putting on and off the C-cores of the inductor, and explain why it is better to use the C-cores in the inductor.
Experiment Results and Data Evaluation:
Time base= 2 ms cm-1 = 2×10-3 s cm-1
Power supply = 6 V
Half-wave rectifying circuit
v1 = 4 V
f1 = = = 83.3 Hz
Waveform of the low voltage power supply displayed on the CRO (waveform A):
v2 = 3.4V
f2 = = = 83.3 Hz
Waveform of the signal across the resistor displayed on the CRO (waveform B):
Full-wave rectifying circuit
V3 = 3.4 V
f3 = = = 83.3 Hz
Waveform of the signal across the resistor displayed on the CRO (waveform C):
Smoothing circuit
Capacitor of 10 μF is used.
Waveform of the signal across the resistor displayed on the CRO (waveform D1):
Capacitor of 100 μF is used.
Waveform of the signal across the resistor displayed on the CRO (waveform D2):
Capacitor of 500 μF is used.
Waveform of the signal across the resistor displayed on the CRO (waveform D3):
Capacitor of 1000 μF is used.
Waveform of the signal across the resistor displayed on the CRO (waveform D4):
Filter circuit
1100-turn inductor with C-core.
Waveform of the signal across the resistor displayed on the CRO (waveform E1):
1100-turn inductor without C-core.
Waveform of the signal across the resistor displayed on the CRO (waveform E2):
Discussion:
Error analysis
- The power supply has some problems. The waveform of the signal across the resistor displayed on the CRO in “half-wave rectifying circuit” part is out of our expectation. According to the teacher, the waveform is like this because of the power supply, the component inside the power supply may be damaged. So, error occurs.
- The plug leads are not enough, so alligator clip leads are used. The alligator clip leads cannot clip to other wires firmly; they are loose. The display becomes unstable; the display changes to different waveforms rapidly. When measuring, accurate data cannot be measured.
Half-wave rectifying circuit
When comparing waveform A and waveform B, the latter one only shows a half cycle of the a.c., only shows the positive voltage of the a.c and does not show the negative voltage part like what waveform A does. The peak voltage v1 is larger than the peak voltage v2; it is because the wire and diode are not ideal and have resistances, so some voltage is developed there. The frequencies f1 and f2 are the same.
Full-wave rectifying circuit
When comparing waveform B and waveform C, the latter one shows the positive voltage of the a.c. like what the former one does, and it also shows the negative voltage part, but it is reflected along the x-axis to the upper part of the graph. Both have the same peak voltage and frequency.
Smoothing circuit
When a capacitor of higher capacitance is used rather than a low capacitance capacitor, the rectified voltage produced is smoother than that by the latter one. This is because the time constant of the circuit is larger and the capacitor discharges more slowly. Also the voltage across the resistor decreases when a capacitor of higher capacitance is used.
The capacitance of a storage capacitor should not be too large. If it is too large, the diodes may be damaged because of the large flow of charge generated by the capacitor.
Filter circuit
When waveforms E1 and E2 are compared, the former one is just like a straight line, but the latter one has large ripples, even larger than those in waveform D4. The C-cores are used to concentrate the magnetic field in order to produce induced emf with high efficiency. If C-cores are absent, the efficiency will be too high, and that explains waveform E2. Therefore, it is better to use the C-cores in the inductor.
Virtually, all electronic devices need d.c. signal, so rectification of a.c. signal is always necessary. For example, when using florescent lamp tube, if rectification is not used, the light will keep flashing and make people feel sick. But if rectification is used, the flashing problem will be better than better, at least the flashing cannot be notice through naked eyes. Rectification is very important because it can make the power supply as stable as d.c., as all electronic devices require d.c. signal.
Conclusion:
This experiment is done successfully, an a.c. signal is rectified using a half-wave rectifying circuit, an a.c. signal is rectified using a full-wave rectifying circuit, a full-wave rectified a.c. signal is smoothed using a smoothing circuit, and a smoothed full-wave rectified a.c. signal is filtered using a filter circuit.