A rectifier known as a “half wave rectifier” only lets one half-cycle of an AC voltage waveform pass through it while blocking the other half-cycle. A single diode is all that is needed to construct half-wave rectifiers, which are used to convert AC voltage to DC voltage.
A device that transforms alternating current (AC) into direct current (DC) is known as a rectifier. A diode or a group of diodes are used to accomplish this. Half wave rectifiers utilize one diode, while a full wave rectifier utilizes numerous diodes.
Utilizing the fact that diodes only permit current to flow in one direction, a half wave rectifier functions
Half Wave Rectifier Theory
The simplest rectifier available is a half wave rectifier. We will take a gander at a total half wave rectifier circuit later – yet we should initially see precisely exact thing this sort of rectifier is doing.
The fundamental idea of a half-wave rectifier is depicted in the following diagram. When a half-wave rectifier processes a standard AC waveform, only half of the waveform is retained. As can be seen below, half-wave rectifiers will block the other half-cycle on the DC side and only permit one half-cycle (positive or negative) of the AC voltage.
Theory of a Half Wave Rectifier
A half-wave rectifier can be constructed with just one diode. The half-wave rectifier is really only doing this.
Putting an AC waveform with positive and negative cycles through a DC device can have destructive (and potentially hazardous) effects due to the fact that DC systems are intended to have current flowing in a single direction and a constant voltage, as we will discuss further. Therefore, to convert AC input power into DC output power, we make use of half-wave rectifiers.
However, the diode is only one component of a half-wave rectifier circuit’s three main components:
The following is a schematic of a half wave rectifier, resistive load, transformer, and diode:
The process by which a half-wave rectifier transforms an AC voltage into a DC output will now be discussed.
First, a high AC voltage is applied to the step-down transformer’s primary side, and then a low voltage is applied to the diode’s secondary winding.
The diode will be forward biased during the positive half cycle of the AC voltage, and the current will flow through it. During the negative half pattern of the air conditioner voltage, the diode will be converse one-sided and the progression of current will be impeded. Figure 3 shows the secondary side’s final output voltage waveform (DC).
Let’s get a little deeper into the theory behind this because it might appear to be a bit confusing at first.
The secondary side of the circuit will be our primary focus. The half-wave rectifier’s circuit diagram can be simplified as follows by using a source voltage to replace the secondary transformer coils:
The transformer component of the circuit is no longer a distraction.
The equivalent circuit effectively becomes for the positive half cycle of the AC source voltage as follows:
This is because the diode is biased in the opposite direction, allowing current to flow through it. As a result, our circuit is closed.
However, the equivalent circuit for the negative half cycle of the AC source voltage is as follows:
No current can flow through the diode now that it is in reverse bias mode. We now have an open circuit as a result. The output voltage is zero because no current can flow to the load during this time.
Since an AC waveform will oscillate between positive and negative multiple times per second (depending on frequency), all of this happens quickly.
After rectification (i.e., conversion from AC to DC), the half wave rectifier waveform looks like the following on the input side (Vin) and on the output side (Vout):
Actually, a positive half wave rectifier is depicted in the graph above. This rectifier only allows positive half-cycles through the diode and blocks negative half-cycles. It is a half-wave rectifier.
Figure 4 depicts the voltage waveform before and after a positive half wave rectifier
On the other hand, a rectifier with a negative half-wave only allows negative half-cycles to pass through the diode and blocks the positive half-cycle. The diode’s direction is the only difference between a posive and negative half wave rectifier.
The diode is now pointing in the opposite direction, as depicted in figure 5 below. As a result, only when the AC waveform is in its negative half cycle will the diode be forward biased.
Capacitor Filter with Half-Wave Rectifier The pulsating DC waveform that we have derived from the previous theory is the output waveform. Using a half wave rectifier without a filter produces this result.
Components called filters are used to smooth out pulsating DC waveforms into steady DC waveforms. They accomplish this by reducing the waveform’s DC ripples.
Although it is theoretically possible to use half-wave rectifiers without filters, they cannot be used in any real-world situations. We must “smooth out” this pulsating waveform in order for it to be useful in the real world because DC equipment needs a constant waveform.
Because of this, we actually use filters and half wave rectifiers. A filter can be a capacitor or an inductor, but the most common type is a half wave rectifier with a capacitor filter.
The circuit chart underneath shows how a capacitive channel is can be utilized to smoothen out a throbbing DC waveform into a consistent DC waveform.
Formula for a Half Wave Rectifier We will now use the previous theory and graphs to calculate the various half wave rectifier formulas.
The unwanted AC component that remains after converting the AC voltage waveform into a DC waveform is referred to as the “Ripple Factor” of the Half Wave Rectifier. Even though we make every effort to eliminate all AC components, a small amount remains on the output side, which causes the DC waveform to pulsate. “Ripple” refers to this undesirable component of the AC.
The ripple factor, denoted by or r, is what we use to measure the half-wave rectifier’s ability to convert AC voltage into DC voltage. The ratio of the rectifier’s RMS values for the AC voltage on the input side and the DC voltage on the output side is known as the ripple factor.
The ripple factor’s formula is:
which can be rearranged to match as well:
The half wave rectifier has a ripple factor of 1.21, or = 1.21.
Keep in mind that we want to keep the ripple factor as low as possible in order to build a good rectifier. For this reason we use capacitors and inductors as channels to diminish the waves in the circuit.
Efficiency of a Half Wave Rectifier The ratio of the output DC power to the input AC power is called the efficiency of the rectifier (). The efficiency can be calculated as follows:
RMS value of Half Wave Rectifier To determine the RMS value of a half wave rectifier, we need to calculate the current across the load. Half wave rectifiers have an efficiency of 40.6% (max = 40.6%). The average load current (IDC) is equal to: If the instantaneous load current is equal to iL = Imsint.
Where Imax is the peak instantaneous current across the load, and Im is equal to that. As a result, the IDC (output DC current) across the load is:
The RMS load current (Irms) of a half-wave rectifier is equal to the average current (IDC) multiplied by /2. As a result, the half wave rectifier’s load current’s RMS value (Irms) is:
I_rms = fracI_m2 at the beginning of the equation, where Im is equal to Imax, which is the peak instantaneous current across the load.
The Half Wave Rectifier’s Peak Inverse Voltage (PIV) is the highest voltage the diode can withstand when biased in the opposite direction. The diode will fail if more voltage is applied than the PIV.
Structure Component of Half Wave Rectifier
Structure factor (F.F) is the proportion between RMS worth and normal worth, as displayed in the equation underneath:
A half wave rectifier has a form factor of 1.57, or F.F=1.57.
DC Voltage at the Output The voltage at the output (VDC) across the load resistor is represented by:
Half-wave rectifiers are less common than full-wave rectifiers in their applications. Despite this, there are still some uses for them:
The main advantage of half-wave rectifiers is their simplicity, which makes them ideal for signal peak applications, signal demodulation applications, and rectification applications. They are less expensive to set up and build because they don’t need as many parts.
Thusly, the primary benefits of half-wave rectifiers are:
Simpler (fewer components), with lower initial costs due to the absence of equipment. Despite the fact that increased power losses result in higher initial costs, half-wave rectifiers have the following drawbacks:
Each sinewave only receives one half-cycle, and the remaining half-cycle is wasted. Power goes out as a result.
They have a low voltage at their output.
Three-Phase Half Wave Rectifier All of the aforementioned theory has dealt with a single-phase half wave rectifier. However, the output current we get is not entirely DC and still contains a lot of ripple (i.e. it has a high ripple factor). A three-phase half wave rectifier has distinct characteristics despite sharing the same operating principle. The efficiency, RMS output values, waveform, and ripple factor are not the same.
When converting three-phase AC power into DC power, the three-phase half wave rectifier is utilized. Since the switches in this case are diodes, they cannot be controlled. That is to say, there is no way to control when these switches turn on and off.
A three-phase supply and a three-phase transformer are typically used to construct a three-phase half wave diode rectifier, with the secondary winding of the transformer always being connected via star connection. This is because a return path for power flow requires the neutral point to connect the load back to the secondary windings of the transformer.
The following is a typical three-phase half wave rectifier configuration for supplying a purely resistive load. Here, the transformer’s phases are viewed as distinct alternating sources. The circuit below demonstrates the simulation and measurement of voltages. In this case, we have connected a voltmeter to each source and load separately.
The three-stage voltages are displayed underneath.
The voltage that runs through the resistive load is depicted below. Black is used to show the voltage.
As can be seen from the preceding illustration, the diode D1 conducts when the R phase’s voltage is greater than that of the other two phases. This condition begins when the R phase is at a 30o angle and continues after each complete cycle. That is to say, at 390o, the diode DI will conduct again. Diode D2 takes over conductivity from diode D1, which stops conducting at an angle of 150 degrees because the voltage in the B phase rises above that in the other two phases at this point. Therefore, the conductivity of each diode is 120 degrees at 150 degrees minus 30 degrees.
The resulting DC voltage signal has a ripple instead of a flat waveform, so it is not strictly DC. Additionally, the ripple has a frequency of 150 Hz, or 3 x 50.
The equation above demonstrates that the voltage ripple is significant. The RMS value of the output voltage is given by, the ripple voltage is equal to, and the voltage ripple factor is equal to. The average output voltage across the resistive load is given by. This is undesirable because it causes an excessive loss of power.
DC output power, AC input power, and efficiency. Even though a three-phase half-wave rectifier appears to be more efficient than a three-phase full-wave diode rectifier, its efficiency is still lower. Even though three-phase half-wave rectifiers are less expensive, the money saved from their higher power losses is negligible. As a result, the use of three-phase half-wave rectifiers in industry is uncommon.
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