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Following a half-wave rectifier

Key idea: A diode passes one half of an A.C. cycle and blocks the other in half-wave rectification. The output flows one way but pulses once per input cycle.

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  • GCE A-Level H2 Physics 2027
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Many devices need a current that flows in one direction only, but the mains supply is alternating. Converting A.C. into a current in one direction is called rectification, and the simplest way to do it is with a single diode.

The diode

In the ideal model, a diode lets conventional current pass from its anode to its cathode. The bar in the circuit symbol marks the cathode; forward current runs towards that bar. A diode is not a current source. When the diode is forward biased it conducts, and an ideal diode then has no p.d. across it. When it is reverse biased it blocks, and there is no current.

Check your understanding 1 One direction, steady current?

An ideal diode passes positive half-cycles of a sinusoidal supply and blocks negative half-cycles. Before reading the output trace, predict the current during the negative half-cycle and the number of output pulses per full input cycle.

Unit: A
Show answer

The blocked current is zero, with one pulse per input cycle. One direction does not mean constant magnitude.

Half-wave rectification

Place one diode in series with the supply and the load resistor.

Ideal single-diode half-wave rectifierA sinusoidal alternating-voltage source is connected in series with an ideal diode and load resistor. The diode anode is on the source side and its cathode is on the load side. An output voltmeter is connected across the load with positive polarity at the top. Arrows show clockwise conventional current during the conducting half-cycle; notes state that the opposite half-cycle is blocked.Single diode selects one half-cyclesinusoidal inputvᵢₙ changes polarityideal diodeanodecathodeconventional IloadRV+−Vₒᵤₜ across R+−conducting half-cycle:top terminal positiveForward biased: diode conductsI flows clockwise; Vₒᵤₜ is a positive pulse.Reverse biased: diode blocksIdeal model: I = 0 and Vₒᵤₜ = 0.
Ideal single-diode half-wave rectifierA sinusoidal alternating-voltage source is connected in series with an ideal diode and load resistor. The diode anode is on the source side and its cathode is on the load side. An output voltmeter is connected across the load with positive polarity at the top. Arrows show clockwise conventional current during the conducting half-cycle; notes state that the opposite half-cycle is blocked.Single diode selects one half-cyclesinusoidal inputvᵢₙ changes polarityideal diodeanodecathodeconventional IloadRV+−Vₒᵤₜ across R+−conducting half-cycle:top terminal positiveForward biased: diode conductsI flows clockwise; Vₒᵤₜ is a positive pulse.Reverse biased: diode blocksIdeal model: I = 0 and Vₒᵤₜ = 0.
When the source makes the diode's anode positive relative to its cathode, conventional current passes through the load and Vout is positive. On the opposite half-cycle the ideal diode blocks, so I = 0 and Vout = 0.

Take the load voltage as the p.d. of the top terminal of the load relative to the bottom one.

  • When the top terminal of the supply is positive, the diode is forward biased. It conducts, and the load voltage follows the supply voltage.
  • When the top terminal of the supply is negative, the diode is reverse biased and blocks the current.

Input and ideal half-wave output

Two cycles of a 50 Hz input. Voltage is divided by the input peak V₀; the load reference remains top minus bottom. The diode passes one half-cycle and blocks the other. Reversing it passes the opposite half-cycles.

Scroll across the figure to read all labels.

Two cycles of a 50 Hz input. Voltage is divided by the input peak V₀; the load reference remains top minus bottom. The diode passes one half-cycle and blocks the other. Reversing it passes the opposite half-cycles.Two cycles of a 50 Hz input. Voltage is divided by the input peak V₀; the load reference remains top minus bottom. The diode passes one half-cycle and blocks the other. Reversing it passes the opposite half-cycles.
Two cycles of a 50 Hz input. Voltage is divided by the input peak V₀; the load reference remains top minus bottom. The diode passes one half-cycle and blocks the other. Reversing it passes the opposite half-cycles.
Open full-size graph
What to noticeCalculated ideal-model values; not experimental measurements.
View figure data
Figure data: Input and ideal half-wave output
Time, t (ms)Sinusoidal inputPositive half-wave outputReversed diode output
0.00.000000.000000.00000
0.10.031410.031410.00000
0.20.062790.062790.00000
0.30.094110.094110.00000
0.40.125330.125330.00000
0.50.156430.156430.00000
0.60.187380.187380.00000
0.70.218140.218140.00000
0.80.248690.248690.00000
0.90.278990.278990.00000
1.00.309020.309020.00000
1.10.338740.338740.00000
1.20.368120.368120.00000
1.30.397150.397150.00000
1.40.425780.425780.00000
1.50.453990.453990.00000
1.60.481750.481750.00000
1.70.509040.509040.00000
1.80.535830.535830.00000
1.90.562080.562080.00000
2.00.587790.587790.00000
2.10.612910.612910.00000
2.20.637420.637420.00000
2.30.661310.661310.00000
2.40.684550.684550.00000
2.50.707110.707110.00000
2.60.728970.728970.00000
2.70.750110.750110.00000
2.80.770510.770510.00000
2.90.790160.790160.00000
3.00.809020.809020.00000
3.10.827080.827080.00000
3.20.844330.844330.00000
3.30.860740.860740.00000
3.40.876310.876310.00000
3.50.891010.891010.00000
3.60.904830.904830.00000
3.70.917750.917750.00000
3.80.929780.929780.00000
3.90.940880.940880.00000
4.00.951060.951060.00000
4.10.960290.960290.00000
4.20.968580.968580.00000
4.30.975920.975920.00000
4.40.982290.982290.00000
4.50.987690.987690.00000
4.60.992110.992110.00000
4.70.995560.995560.00000
4.80.998030.998030.00000
4.90.999510.999510.00000
5.01.000001.000000.00000
5.10.999510.999510.00000
5.20.998030.998030.00000
5.30.995560.995560.00000
5.40.992110.992110.00000
5.50.987690.987690.00000
5.60.982290.982290.00000
5.70.975920.975920.00000
5.80.968580.968580.00000
5.90.960290.960290.00000
6.00.951060.951060.00000
6.10.940880.940880.00000
6.20.929780.929780.00000
6.30.917750.917750.00000
6.40.904830.904830.00000
6.50.891010.891010.00000
6.60.876310.876310.00000
6.70.860740.860740.00000
6.80.844330.844330.00000
6.90.827080.827080.00000
7.00.809020.809020.00000
7.10.790160.790160.00000
7.20.770510.770510.00000
7.30.750110.750110.00000
7.40.728970.728970.00000
7.50.707110.707110.00000
7.60.684550.684550.00000
7.70.661310.661310.00000
7.80.637420.637420.00000
7.90.612910.612910.00000
8.00.587790.587790.00000
8.10.562080.562080.00000
8.20.535830.535830.00000
8.30.509040.509040.00000
8.40.481750.481750.00000
8.50.453990.453990.00000
8.60.425780.425780.00000
8.70.397150.397150.00000
8.80.368120.368120.00000
8.90.338740.338740.00000
9.00.309020.309020.00000
9.10.278990.278990.00000
9.20.248690.248690.00000
9.30.218140.218140.00000
9.40.187380.187380.00000
9.50.156430.156430.00000
9.60.125330.125330.00000
9.70.094110.094110.00000
9.80.062790.062790.00000
9.90.031410.031410.00000
10.00.000000.000000.00000
10.1-0.031410.00000-0.03141
10.2-0.062790.00000-0.06279
10.3-0.094110.00000-0.09411
10.4-0.125330.00000-0.12533
10.5-0.156430.00000-0.15643
10.6-0.187380.00000-0.18738
10.7-0.218140.00000-0.21814
10.8-0.248690.00000-0.24869
10.9-0.278990.00000-0.27899
11.0-0.309020.00000-0.30902
11.1-0.338740.00000-0.33874
11.2-0.368120.00000-0.36812
11.3-0.397150.00000-0.39715
11.4-0.425780.00000-0.42578
11.5-0.453990.00000-0.45399
11.6-0.481750.00000-0.48175
11.7-0.509040.00000-0.50904
11.8-0.535830.00000-0.53583
11.9-0.562080.00000-0.56208
12.0-0.587790.00000-0.58779
12.1-0.612910.00000-0.61291
12.2-0.637420.00000-0.63742
12.3-0.661310.00000-0.66131
12.4-0.684550.00000-0.68455
12.5-0.707110.00000-0.70711
12.6-0.728970.00000-0.72897
12.7-0.750110.00000-0.75011
12.8-0.770510.00000-0.77051
12.9-0.790160.00000-0.79016
13.0-0.809020.00000-0.80902
13.1-0.827080.00000-0.82708
13.2-0.844330.00000-0.84433
13.3-0.860740.00000-0.86074
13.4-0.876310.00000-0.87631
13.5-0.891010.00000-0.89101
13.6-0.904830.00000-0.90483
13.7-0.917750.00000-0.91775
13.8-0.929780.00000-0.92978
13.9-0.940880.00000-0.94088
14.0-0.951060.00000-0.95106
14.1-0.960290.00000-0.96029
14.2-0.968580.00000-0.96858
14.3-0.975920.00000-0.97592
14.4-0.982290.00000-0.98229
14.5-0.987690.00000-0.98769
14.6-0.992110.00000-0.99211
14.7-0.995560.00000-0.99556
14.8-0.998030.00000-0.99803
14.9-0.999510.00000-0.99951
15.0-1.000000.00000-1.00000
15.1-0.999510.00000-0.99951
15.2-0.998030.00000-0.99803
15.3-0.995560.00000-0.99556
15.4-0.992110.00000-0.99211
15.5-0.987690.00000-0.98769
15.6-0.982290.00000-0.98229
15.7-0.975920.00000-0.97592
15.8-0.968580.00000-0.96858
15.9-0.960290.00000-0.96029
16.0-0.951060.00000-0.95106
16.1-0.940880.00000-0.94088
16.2-0.929780.00000-0.92978
16.3-0.917750.00000-0.91775
16.4-0.904830.00000-0.90483
16.5-0.891010.00000-0.89101
16.6-0.876310.00000-0.87631
16.7-0.860740.00000-0.86074
16.8-0.844330.00000-0.84433
16.9-0.827080.00000-0.82708
17.0-0.809020.00000-0.80902
17.1-0.790160.00000-0.79016
17.2-0.770510.00000-0.77051
17.3-0.750110.00000-0.75011
17.4-0.728970.00000-0.72897
17.5-0.707110.00000-0.70711
17.6-0.684550.00000-0.68455
17.7-0.661310.00000-0.66131
17.8-0.637420.00000-0.63742
17.9-0.612910.00000-0.61291
18.0-0.587790.00000-0.58779
18.1-0.562080.00000-0.56208
18.2-0.535830.00000-0.53583
18.3-0.509040.00000-0.50904
18.4-0.481750.00000-0.48175
18.5-0.453990.00000-0.45399
18.6-0.425780.00000-0.42578
18.7-0.397150.00000-0.39715
18.8-0.368120.00000-0.36812
18.9-0.338740.00000-0.33874
19.0-0.309020.00000-0.30902
19.1-0.278990.00000-0.27899
19.2-0.248690.00000-0.24869
19.3-0.218140.00000-0.21814
19.4-0.187380.00000-0.18738
19.5-0.156430.00000-0.15643
19.6-0.125330.00000-0.12533
19.7-0.094110.00000-0.09411
19.8-0.062790.00000-0.06279
19.9-0.031410.00000-0.03141
20.00.000000.000000.00000
20.10.031410.031410.00000
20.20.062790.062790.00000
20.30.094110.094110.00000
20.40.125330.125330.00000
20.50.156430.156430.00000
20.60.187380.187380.00000
20.70.218140.218140.00000
20.80.248690.248690.00000
20.90.278990.278990.00000
21.00.309020.309020.00000
21.10.338740.338740.00000
21.20.368120.368120.00000
21.30.397150.397150.00000
21.40.425780.425780.00000
21.50.453990.453990.00000
21.60.481750.481750.00000
21.70.509040.509040.00000
21.80.535830.535830.00000
21.90.562080.562080.00000
22.00.587790.587790.00000
22.10.612910.612910.00000
22.20.637420.637420.00000
22.30.661310.661310.00000
22.40.684550.684550.00000
22.50.707110.707110.00000
22.60.728970.728970.00000
22.70.750110.750110.00000
22.80.770510.770510.00000
22.90.790160.790160.00000
23.00.809020.809020.00000
23.10.827080.827080.00000
23.20.844330.844330.00000
23.30.860740.860740.00000
23.40.876310.876310.00000
23.50.891010.891010.00000
23.60.904830.904830.00000
23.70.917750.917750.00000
23.80.929780.929780.00000
23.90.940880.940880.00000
24.00.951060.951060.00000
24.10.960290.960290.00000
24.20.968580.968580.00000
24.30.975920.975920.00000
24.40.982290.982290.00000
24.50.987690.987690.00000
24.60.992110.992110.00000
24.70.995560.995560.00000
24.80.998030.998030.00000
24.90.999510.999510.00000
25.01.000001.000000.00000
25.10.999510.999510.00000
25.20.998030.998030.00000
25.30.995560.995560.00000
25.40.992110.992110.00000
25.50.987690.987690.00000
25.60.982290.982290.00000
25.70.975920.975920.00000
25.80.968580.968580.00000
25.90.960290.960290.00000
26.00.951060.951060.00000
26.10.940880.940880.00000
26.20.929780.929780.00000
26.30.917750.917750.00000
26.40.904830.904830.00000
26.50.891010.891010.00000
26.60.876310.876310.00000
26.70.860740.860740.00000
26.80.844330.844330.00000
26.90.827080.827080.00000
27.00.809020.809020.00000
27.10.790160.790160.00000
27.20.770510.770510.00000
27.30.750110.750110.00000
27.40.728970.728970.00000
27.50.707110.707110.00000
27.60.684550.684550.00000
27.70.661310.661310.00000
27.80.637420.637420.00000
27.90.612910.612910.00000
28.00.587790.587790.00000
28.10.562080.562080.00000
28.20.535830.535830.00000
28.30.509040.509040.00000
28.40.481750.481750.00000
28.50.453990.453990.00000
28.60.425780.425780.00000
28.70.397150.397150.00000
28.80.368120.368120.00000
28.90.338740.338740.00000
29.00.309020.309020.00000
29.10.278990.278990.00000
29.20.248690.248690.00000
29.30.218140.218140.00000
29.40.187380.187380.00000
29.50.156430.156430.00000
29.60.125330.125330.00000
29.70.094110.094110.00000
29.80.062790.062790.00000
29.90.031410.031410.00000
30.00.000000.000000.00000
30.1-0.031410.00000-0.03141
30.2-0.062790.00000-0.06279
30.3-0.094110.00000-0.09411
30.4-0.125330.00000-0.12533
30.5-0.156430.00000-0.15643
30.6-0.187380.00000-0.18738
30.7-0.218140.00000-0.21814
30.8-0.248690.00000-0.24869
30.9-0.278990.00000-0.27899
31.0-0.309020.00000-0.30902
31.1-0.338740.00000-0.33874
31.2-0.368120.00000-0.36812
31.3-0.397150.00000-0.39715
31.4-0.425780.00000-0.42578
31.5-0.453990.00000-0.45399
31.6-0.481750.00000-0.48175
31.7-0.509040.00000-0.50904
31.8-0.535830.00000-0.53583
31.9-0.562080.00000-0.56208
32.0-0.587790.00000-0.58779
32.1-0.612910.00000-0.61291
32.2-0.637420.00000-0.63742
32.3-0.661310.00000-0.66131
32.4-0.684550.00000-0.68455
32.5-0.707110.00000-0.70711
32.6-0.728970.00000-0.72897
32.7-0.750110.00000-0.75011
32.8-0.770510.00000-0.77051
32.9-0.790160.00000-0.79016
33.0-0.809020.00000-0.80902
33.1-0.827080.00000-0.82708
33.2-0.844330.00000-0.84433
33.3-0.860740.00000-0.86074
33.4-0.876310.00000-0.87631
33.5-0.891010.00000-0.89101
33.6-0.904830.00000-0.90483
33.7-0.917750.00000-0.91775
33.8-0.929780.00000-0.92978
33.9-0.940880.00000-0.94088
34.0-0.951060.00000-0.95106
34.1-0.960290.00000-0.96029
34.2-0.968580.00000-0.96858
34.3-0.975920.00000-0.97592
34.4-0.982290.00000-0.98229
34.5-0.987690.00000-0.98769
34.6-0.992110.00000-0.99211
34.7-0.995560.00000-0.99556
34.8-0.998030.00000-0.99803
34.9-0.999510.00000-0.99951
35.0-1.000000.00000-1.00000
35.1-0.999510.00000-0.99951
35.2-0.998030.00000-0.99803
35.3-0.995560.00000-0.99556
35.4-0.992110.00000-0.99211
35.5-0.987690.00000-0.98769
35.6-0.982290.00000-0.98229
35.7-0.975920.00000-0.97592
35.8-0.968580.00000-0.96858
35.9-0.960290.00000-0.96029
36.0-0.951060.00000-0.95106
36.1-0.940880.00000-0.94088
36.2-0.929780.00000-0.92978
36.3-0.917750.00000-0.91775
36.4-0.904830.00000-0.90483
36.5-0.891010.00000-0.89101
36.6-0.876310.00000-0.87631
36.7-0.860740.00000-0.86074
36.8-0.844330.00000-0.84433
36.9-0.827080.00000-0.82708
37.0-0.809020.00000-0.80902
37.1-0.790160.00000-0.79016
37.2-0.770510.00000-0.77051
37.3-0.750110.00000-0.75011
37.4-0.728970.00000-0.72897
37.5-0.707110.00000-0.70711
37.6-0.684550.00000-0.68455
37.7-0.661310.00000-0.66131
37.8-0.637420.00000-0.63742
37.9-0.612910.00000-0.61291
38.0-0.587790.00000-0.58779
38.1-0.562080.00000-0.56208
38.2-0.535830.00000-0.53583
38.3-0.509040.00000-0.50904
38.4-0.481750.00000-0.48175
38.5-0.453990.00000-0.45399
38.6-0.425780.00000-0.42578
38.7-0.397150.00000-0.39715
38.8-0.368120.00000-0.36812
38.9-0.338740.00000-0.33874
39.0-0.309020.00000-0.30902
39.1-0.278990.00000-0.27899
39.2-0.248690.00000-0.24869
39.3-0.218140.00000-0.21814
39.4-0.187380.00000-0.18738
39.5-0.156430.00000-0.15643
39.6-0.125330.00000-0.12533
39.7-0.094110.00000-0.09411
39.8-0.062790.00000-0.06279
39.9-0.031410.00000-0.03141
40.00.000000.000000.00000

The output is a series of positive half-cycles separated by gaps. The current in the load is always in the same direction, but it is not steady: it rises and falls in every pulse, and is zero half the time. There is one pulse per input cycle, so the pulses have the same frequency as the supply. With an ideal diode the peak of the output equals the peak of the input. Reversing the diode passes the negative half-cycles instead.

Because the output is not a complete sinusoid, V₀/square root of 2 does not give its r.m.s. value. That relation still applies to the input.

Check your understanding 2 Sketch the output

For the circuit above, sketch the load voltage over two complete supply cycles on paper. Include the zero level and period. Explain why the output is unidirectional but not steady, and what happens to the trace if the diode is reversed.

Show answer

Compare your sketch with the displayed trace: positive half-sine pulses, a zero interval for every blocked negative half-cycle, unchanged peak voltage and one pulse per period. Reversing the diode passes negative half-cycles and blocks positive ones when the voltage reference stays top relative to bottom. Check the shape and labels on paper; the written response is self-review.

Worked example 1

Following both half-cycles

Problem

A 50.0 Hz sinusoidal supply with a peak voltage of 12.0 V is connected to a 200 Ω resistor through an ideal diode, as in the circuit above. Describe the current in the resistor during one cycle, and find its peak value and the frequency of the pulses.

Show full solution

  1. Conducting half-cycle

    Method

    Find the current when the diode is forward biased.

    Reason

    An ideal conducting diode has no p.d. across it, so the whole supply voltage is across the resistor.

    Working

    Answer

    The current follows the supply voltage, with a peak of I₀ = 12.0/200 = 0.0600 A

  2. Blocking half-cycle

    Reason

    A reverse-biased diode lets no current through.

    Working

    Answer

    The current is zero for the whole of the other half-cycle.

  3. Pulse frequency

    Working

    Answer

    One pulse in each 20.0 ms cycle, so the pulses have a frequency of 50.0 Hz.

Guided practice 2

When the diode blocks

About 2 min

Problem

In the circuit above, the top terminal of the supply is negative and its voltage is -9.0 V. Find the load p.d. (top relative to bottom) and the magnitude of the p.d. across the diode.

Find both p.d.s

Unit: V
Unit: V

Hints

Hint 1

current first

Decide whether there is a current. Then use V = IR for the load, and remember that the p.d.s in the loop add up to the supply voltage.

Show full solution

  1. Both p.d.s

    Working

    Answer

    The diode is reverse biased, so I = 0 and the load p.d. is IR = 0. The whole 9.0 V is across the diode.

Try it yourself 3

Reversing the diode

Minimal support

Problem

The diode in the circuit is turned round. The load voltage is still measured as top terminal relative to bottom. The supply has a peak of 10.0 V and a frequency of 60.0 Hz, and its top terminal voltage is zero and increasing at t = 0. Find the load voltage at t = 4.17 ms and at t = 12.5 ms.

Find the load voltages

Unit: V
Unit: V

Hints

Hint 1

supply first

Express each time as a fraction of the period T = 1/60.0 s to find the supply voltage. The reversed diode conducts only when the top terminal of the supply is negative.

Show solution step by step

  1. Supply voltages

    Reason

    T = 16.7 ms, so 4.17 ms is (1/4)T and 12.5 ms is (3/4)T.

    Working

    Answer

    The supply is at + 10.0 V at 4.17 ms and at -10.0 V at 12.5 ms.

  2. Load voltages

    Working

    Answer

    At 4.17 ms the reversed diode is reverse biased, so the load voltage is 0. At 12.5 ms it conducts, so the load voltage follows the supply: -10.0 V.

Exam-style question 1

A rectified output

5 marks

Examination question

A sinusoidal supply of r.m.s. voltage 6.00 V and frequency 50.0 Hz is connected to a resistor through a single ideal diode.

(a) Calculate the peak voltage across the resistor. [2 marks]

(b) Describe how the voltage across the resistor varies during one cycle of the supply. [2 marks]

(c) State the frequency of the voltage pulses across the resistor. [1 mark]

Write your answer before viewing the mark scheme

Show solution step by step

  1. (a) Peak voltage

    2 marks

    Method

    Find the peak of the sinusoidal supply.

    Reason

    The supply is a full sinusoid, and an ideal conducting diode passes its peak to the resistor unchanged.

    Working

    Answer

    V₀ = square root of 2 × 6.00 = 8.49 V

  2. (b) Variation

    2 marks

    Reason

    The diode conducts for one half-cycle and blocks for the other.

    Working

    Answer

    For one half-cycle the voltage follows the supply, rising to 8.49 V and falling back to zero. For the other half-cycle it is zero.

  3. (c) Frequency

    1 mark

    Working

    Answer

    50.0 Hz: one pulse per cycle of the supply

Common mistakes

  • Calling the output steady D.C.; it is in one direction, but it varies and is zero half the time.
  • Halving the peak; an ideal diode passes the peak unchanged and only removes half of each cycle.
  • Doubling the frequency; a single diode gives one pulse per cycle.
  • Using V₀/square root of 2 for the r.m.s. value of the rectified output.

Spotted an error? Report a correction

Syllabus and review details

Last reviewed:

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