What Is a Half-Wave Rectifier? Circuit and Waveform

To convert electrical energy to a usable form by passing one polarity of an AC voltage and blocking the other, a half-wave rectifier uses a single diode as a rectification device. The resultant output (when not filtered) will be pulsating DC, with a pulse repetition rate equal to the input AC frequency, so it produces current that only flows in one direction through the load. The amount of current going through the load will increase and decrease to zero once during every input cycle. For this reason, unfiltered half-wave DC voltage cannot be considered smooth or regulated.

To change between positive-output and negative-output DC from an AC voltage using a half-wave rectifier, it is necessary to reverse the polarity of the diode. The other components of the circuit remain unchanged.

What Is a Half-Wave Rectifier?

The minimum configuration of a half-wave rectification circuit consists of an AC source, one series-connected diode, and one resistive load connected to the AC source. An isolation transformer may be included for electrical isolation or conversion of voltage levels, but it is not part of the half-wave rectifier definition. While the diode is forward-biased, current flows from the AC source to the load. While the diode is reverse-biased, the series connection to the load is open and therefore an ideal resistive load is not receiving any current.

The positive half-cycle of the input AC voltage will be retained when the anode of the diode is oriented toward the AC source and the cathode of the diode is oriented toward the load, with the output measured from the load to the return conductor. Conversely, when there is a reversal of polarity of the diode (the cathode is connected to the source and the anode is connected to the load), the negative half-cycle of the AC input voltage is retained.

How a Half-Wave Rectifier Works

Positive Half-Cycle

In the positive half-cycle of an AC waveform the source voltage is positive, the diode is in forward bias mode and, in the ideal model, behaves like a closed switch, allowing current to flow from the source through the diode to the load and back to the source. The output voltage of the load is positive and follows the same positive half-sine shape as the load current. A real diode does not produce an output voltage that is perfectly equal to that of the source due to voltage drops across the diode during conduction and its dynamic resistance, as well as the limitations of the source impedance on the current flowing through the diode. Conduction will begin only after the instantaneous source voltage has reached a level sufficient to supply the voltage necessary for the diode to conduct current at the given temperature and operating point.

Negative Half-Cycle

During the negative half-cycle of the AC waveform, the polarity of the voltage from the source is reversed; therefore, the diode transitions from the forward-biased mode to the reverse-biased mode, and thus blocks the current path. In a purely resistive circuit that has not been filtered, the current and output voltage will be zero until the start of the next accepted half-cycle. However, a physical diode does have reverse leakage current, which is a function of the diode’s specifications, reverse voltage, and junction temperature. In addition, this reverse leakage current is not included in the idealized half-cycle waveform model for a diode.

Output Waveform and Ripple Frequency

A half-wave rectifier produces one same-polarity output pulse for every complete input cycle, so the output pulse frequency is the same as the AC input frequency; a 50 Hz input will produce 50 output pulses per second, and a 60 Hz input will produce 60 output pulses. Reversing the diode will change the polarity of the output pulse but not its frequency.

Figure 2. Normalized waveforms. The real forward-drop trace and capacitor discharge are illustrative; actual values depend on the source, diode, load, frequency, and capacitance.

The name pulsating DC comes from the fact that the polarity of pulsating DC does not change across the load, while the amplitude of pulsating DC changes continuously. Thus, rectification controls the direction in which current flows; filtering reduces the variation; and regulation maintains a controlled output as variations occur in either the input or the load. These three processes are separate functions.

Half-Wave Rectifier Formulas and Assumptions

The formulas that follow are valid for: a sinusoidal waveform as an input, an ideal diode, a purely resistive load, a defined positive output reference, and no reservoir capacitor. With that said, Vm is the input peak voltage at the rectifier, Im is the peak load current, RL is the resistance in the load circuit, and all values should be calculated over an entire input period.

In hand-calculation models for certain types of silicon diodes, the fixed voltage loss of approximately 0.7 V can be used as a rough approximation, but this is not a universal threshold across all silicon diode technologies. The amount of forward voltage that a silicon diode drops in its forward conducting region will vary based on the type of silicon diode, the amount of current it carries, the temperature of the silicon diode during its forward conduction time, and the conduction time. An example of this is the Vishay 1N4001-1N4007 data sheet, which specifies a maximum instantaneous forward voltage of 1.1 V at 1 A. When the forward voltage loss is significant relative to Vm, it is best to use the actual data sheet.

Worked Example: 10 V Peak and a 1 kohm Load

With a peak sine input of 10 V and loading of 1 kohm, the maximum possible peak current is 10 mA. Average output voltage is calculated as (10/π) = 3.18 V, and RMS output voltage is calculated as (10/2) = 5.00 V. The average output current and RMS output current of a 10 V sine wave peak and 1 kohm load will equate to 3.18 mA and 5.00 mA respectively. So DC output power is VDC^2/RL = 10.1 mW. The input AC power in the basic resistive model is (VRMS^2/RL) = 25.0 mW and therefore, the rectification efficiency (DC output to AC input) is equal to 10.1 mW/25.0 mW = 40.5% efficiency. The theoretical unfiltered PIV is 10 V, but a real diode requires extra margin for input-voltage tolerance and transient overvoltage. The average output voltage should not be calculated by simply subtracting a fixed diode drop from VDC. The angle of conduction and the I/V curve of the diode must also be considered.

Half-Wave Rectifier with a Capacitor Filter

A reservoir capacitor is added across the load to form a capacitor-filter half-wave rectifier. During the period in which the rising source voltage exceeds the stored capacitor voltage plus the forward drop of the diode, the capacitor will be charged. Once the crest of the source voltage has passed, the voltage of the capacitor will be higher than the instantaneous voltage from the source; therefore, the diode is turned off and the capacitor then supplies the load until such a time as the source has reached a voltage level that is above the capacitor voltage plus the diode forward requirement for recharging the capacitor.

For a capacitor with small ripple and approximately constant load current, one can reasonably estimate that Vpp is equal to Iload/(fin × C). For example: A 10 mA load on a 50 Hz half-wave rectifier using a 1000 μF capacitor would create an estimated voltage ripple of approximately 0.20 V peak-to-peak; with the frequency increased to 60 Hz the estimate drops to approximately 0.17 V peak-to-peak. This approximation becomes inaccurate if the ripple is large, if the load has large nonlinearities, or when changes in the source impedance considerably change the charge pulse.

By increasing the capacitance to the reservoir, the discharge droop of the capacitor is reduced but regulation is not created; however, the increase in capacitance also has a tendency to narrow the conduction interval of the diode and therefore can increase peak and surge current in the diode, transformer, wiring, and capacitor. The effective results will vary based on the source resistance, capacitor ESR, load current, frequency and behaviour of the diode. The reverse stress on the diode with a charged reservoir capacitor can approach approximately (2Vm) – (forward drop of diode), rather than the unfiltered value Vm, and the exact value is based on the topology and charge of the reservoir capacitor.

Half-Wave and Full-Wave Rectifiers

In the following numerical examples, all comparisons of the various rectifier configurations utilize the same sinusoidal peak Vm, ideal diodes, resistive load, and no filter capacitors. The voltage drops and PIV requirements specific to the different bridge and center-tapped circuits will need to be evaluated separately from this example.

The full-wave rectifier utilises both input halves; i.e. for each input cycle, the capacitor has an opportunity to be recharged twice with respect to that input cycle. This shortens the interval for a capacitor to be discharged, allowing for less capacitance to be necessary for a given load to achieve a set ripple spec. However, the full-wave rectifier still generates a pulsating DC voltage and cannot be used in lieu of filtering or voltage regulation.

Applications, Advantages, and Limitations

The main benefit of the half-wave rectifier is that it requires only one diode to produce a DC voltage signal and can therefore reduce component count. However, its disadvantages include poor utilisation of the waveform, a long interval of no conduction during the voltage cycle, a high amount of unfiltered ripple voltage, a greater burden on the filter, and also possibly high capacitor recharge currents. Thus, the applicability of a half-wave circuit depends more on what the load requires than on simplicity.

AM Envelope and Peak Detection

Half-wave diodes can be used to recover one polarity of the modulated carrier signal, or in detecting peaks of a signal. When using the half-wave diode as an AM envelope detector, the RC network must be able to discharge slowly enough to reject carrier ripple and yet quickly enough to track changes in the modulation envelope. For small signals, the forward voltage of the diode and the source impedance become important. In cases where the signal is near the forward-voltage region of a diode, Schottky or biased detectors may be a preferable option.

Polarity Sensing, Triggering, and Measurement

One-polarity signals can be used for simple polarity detection, zero-crossing support circuits, pulse triggering, and some analog AC measurement inputs. The receiving stage must handle the amplitude of the incoming pulse and the interval in which the pulse is at a zero value; the diode must also withstand the opposite half-cycle. Therefore, a half-wave circuit designed as is does not inherently provide logic-level protection or isolation and would not provide accurate RMS measurements unless appropriate scaling and methods of clamping, isolating or conditioning the incoming signal have been employed.

Reduced-Power Resistive Loads

Utilising a series diode on a resistive heater or incandescent lamp would allow for an intentional reduction in average power (or RMS voltage) when the load and switch configuration is properly rated for the asymmetrical current it will produce. This is a limited method for power control and not a general-purpose DC power source, however. For transformer-fed loads, motors, magnetic components, and equipment which normally operate on symmetrical mains current, the presence of a DC component may create problems. Safety, conducted emissions, harmonics, and applicable product standards govern any mains-connected implementation.

When a Half-Wave Rectifier Is the Wrong Choice

Generally, for regulated power supplies, precision analogue rails, higher load currents, low-ripple load requirements, or efficient transformer use, a full-wave circuit would be preferable. When a very large reservoir capacitor would be required to bridge the entire input cycle, the narrow recharging pulses will add additional stress to the system both electrically and thermally. The one-diode topology should be chosen only when the load accepts the resulting waveform or when producing one polarity of the signal is a function of the design.

Selecting the Diode and Checking the PCB Implementation

Reverse-voltage rating. VRRM must be higher than the calculated worst-case PIV obtained from the application, with a design margin that accounts for the input tolerance, capacitor charge level and switching transients. A common practice is to use VRRM of 1.5 – 2 times the maximum calculated PIV. This accounts for the mains tolerance of approximately +/-10% and switching transients that could otherwise consume the entire margin. For applications with more extreme transients, VRRM near the top of the range or the use of a transient suppressor may be warranted.

Forward and surge current. Average Forward Current, Repetitive Peak Forward Current, and Non-repetitive Surge Current should be verified for each application. Depending on the capacitance of the reservoir capacitor, the charging pulse may exceed the average load current significantly.

Forward loss and temperature. For every diode, use the curve from the data sheet for “Forward Voltage Drop vs. Forward Current” at the expected forward current and junction temperature, and verify power dissipation and thermal resistance against the intended ambient temperature and copper area.

Switching behavior. At line frequency, reverse recovery is typically secondary to the other ratings (i.e. voltage, current and thermal) of a standard diode. However, as the switching frequency is increased, reverse-recovery time, junction capacitance and switching loss will be more important in determining the best diode for the application. Depending on the switching frequency, it may be appropriate to choose a Schottky diode, fast-recovery diode, or standard rectifier diode.

Leakage. Reverse leakage current increases with temperature. In high-impedance detectors, long-hold peak circuits, or low-current supplies, leakage current can be an important design consideration. For most applications, general-purpose silicon rectifier diodes can provide reverse leakage currents on the order of single-digit microamps at room temperature, increasing to the tens of microamps level with increased junction temperature. Rather than assuming a constant value, always refer to the specific data sheet for a curve of “Leakage Current vs. Temperature”.

Verify with the PCB that the following considerations are taken into account: the surge-current path; capacitor ripple-current and ESR ratings; the path for diode thermal dissipation; current-loop area; creepage and clearance; accessible test points for the source, diode and load waveforms; and the use of proper probe and isolation techniques for measuring oscilloscope waveforms where circuit voltage and reference are concerned. A grounded bench probe must never be connected indiscriminately to a non-isolated mains node.

Typical Rectifier Diode Families

The specific ratings will vary significantly between manufacturers and parts; therefore, this information should be treated as a starting range and not a substitute for the data sheet.