# Single Phase Correction

Straightening converts the oscillating sinusoidal AC voltage source into a constant current DC voltage source via diodes, thyristors, transistors or transducers. This straightening process can take many forms with half-wave, full wave, uncontrolled and fully controlled rectifiers that convert a single-phase or three-phase weld into a fixed DC level. In this lesson, we will look at single-phase correction and all its forms.

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Rectifiers are one of the basic building blocks of AC power conversion with half-wave or full wave straightening, usually performed by semiconductor diodes. Diodes allow alternating currents to flow forward through them, blocking the flow of current in the opposite direction, creating a constant DC voltage level, making them ideal for correction.

However, the direct current directed with diodes is not as pure as, for example, obtained from a battery source, but there are voltage changes in the form of fluctuations superimposed on it as a result of alternative feeding.

However, for single-phase straightening to occur, we need a constant voltage and an AC sinusoidal waveform at frequency.

## AC Sinusoidal WaveForm

AC waveforms usually have two numbers associated with them. The first number refers to the degree of rotation of the waveform along the x-axis, where the alternator rotates from 0 to 360o. This value is known as the period (T), defined as the range taken to complete a full cycle of the waveform. Periods are measured in degrees, times or radiant units. The relationship between the periods of sinus waves and the frequency is defined as follows: T = 1/ε.

The second number indicates the amplitude of the current or voltage value along the y-axis. This number gives instantaneous value to some peak or maximum values (AMAX, VMAX, or IMAX) from zero, indicating the maximum amplitude of sine waves before returning to zero. For a sinusoidal waveform, there are two maximum or peak values, one for positive and one for negative half-cycles.

But in addition to these two values, there are two other values that interest us for the purpose of correction. One is the Average Value of sinusoidal waveforms and the other is the RMS Value. The average value of a waveform is obtained by adding instant voltage (or current) values over a half-cycle and is found as follows: 0.6365*VP. Note that the average value on a full cycle of a symmetrical sine wave will be zero, as the average positive half wave is canceled by the opposite average negative half wave. This is +1 + (-1) = 0.

The RMS, root mean square, or effective value of a sinusoid (sinusoid is another name for sinus wave) transmits the same amount of energy to a resistance, as a DC source of the same value does. The average square root (rms) value of a sinusoidal voltage (or current) is defined as: 0.7071*VP.

## Single Phase Rectifier

All single-phase rectifiers use solid state devices as a primary AC-to-DC conversion device. Single-phase uncontrolled half-wave rectifiers are the simplest and possibly most widely used straightening circuit for small power levels, as their output is greatly affected by the reassurance of the connected load.

For uncontrolled rectifier circuits, semiconductor diodes are the most widely used device and are arranged to form a half-wave or full wave rectifier circuit. The advantage of using diode as an straightening device is that by design, they are one-way devices with a built-in one-way pn-connection.

This pn-connection eliminates half the supply, transforming the duplex alternative feed into a one-way one-way current. Depending on the connection of the diode, for example, it can exceed the positive half of the AC waveform when it is forward-sided, eliminating negative semi-cycle when the diode is inverted.

The opposite is true by eliminating the positive half or waveform and passing the negative half. In both cases, the output of a single diode rectifier consists of only one half of the 360o waveform, as shown.

## Half-wave Straightening

The above single phase half wave rectifier configuration exceeds the positive half of the AC feed waveform by eliminateing the negative half. By reversing the direction of the diode, we can pass the negative halves and eliminate the positive half of the AC waveform. Therefore, the output will be a series of positive or negative blows.

Thus, there is no voltage or current applied to the connected load, RL for half of each cycle. In other words, since the voltage on the load resistance, RL, runs only half the input cycle, it consists of only half waveforms, positive or negative, hence the name of the half-wave rectifier.

Hopefully we can see that the diode allows the current to flow in one direction, producing an output consisting only of half cycles. This vibrating output waveform not only changes to ON and OFF in each cycle, it is only available at 50% of the time, and with a fully resistant load, this high voltage and current fluctuation content is at its maximum.

This vibrating DC means that the equivalent DC value that falls during load resistance is only half of the RL's therefore sinusoidal waveform value. Since waveforms are the maximum value of the sinus function 1 ( sin(90o), the Average or Average DC value taken from half of a sinusoid is defined as follows: 0.637 x maximum amplitude value.

This means that during a positive half-cycle, AAVE equals 0.637*AMAX. However, since negative half-cycles are removed due to straightening by the reverse-sided diode, the average value of the waveform during this negative half-cycle will be zero, as shown.

## Average Value of Sinusoids

So for a half-wave rectifier, there is an average value of 0.637*AMAX at 50% of the time, and 50% of the time has zero. If the maximum amplitude is 1, the average or DC value equivalent seen throughout the load resistance, RL will be as follows:

Therefore, for a half-wave rectifier with vibrating DC, the corresponding expressions for the average voltage or current value are given as follows:

Note that the maximum value is that of the amax input waveform, but we can also use its RMS or "root average square" value to find the equivalent DC output value of the single-phase half-wave rectifier. To determine the average voltage for the half-wave rectifier, we multiply the RMS by 0.9 (form factor) and divide the product by 2, that is, multiply by 0.45:

Next, we can see that a half-wave rectifier circuit, depending on the direction of the diodes, converts the positive or negative half of an AC waveform into a pulsed DC output with an equivalent DC value of*0.318 AMAX or 0.45*ARMS, as shown.

## Half Wave Rectifier Average Voltage

## Full wave Straightening

Unlike the previous half-wave rectifier, the full wave rectifier uses both halves of the input sinusoidal waveform to provide a one-way output. This is because the full wave rectifier consists mainly of two half-wave rectifiers connected to each other to feed the load.

The single-phase full wave rectifier does this using four diodes arranged in a bridge arrangement that, as before, exceeds the positive half of the waveform but reverses the negative half of the sine wave to create a vibrating DC output. Even if the voltage and current output from the rectifier is vibrating, the input does not reverse direction using 100% of the waveform, thus providing full wave straightening.

## Single Phase Full Wave Bridge Rectifier

This bridge configuration of diodes provides full wave straightening, since at any time two of the four diodes are forward and the other two are inverted. Therefore, for the half-wave rectifier, there are two diodes instead of a single diode in the transmission path. Therefore, there will be a voltage amplitude difference between VIN and VOUT due to two forward voltage decreases of serial connected diodes. Here, as before, we will accept ideal diodes for the simplicity of mathematics.

So how does a single-phase full wave rectifier work? During the positive semi-cycle of the VIN, the D1 and D4 diodes are polarized forward, while the D2 and D3 diodes are inverted. Then the current flows along the following path for the positive half cycle of the input waveform: D1 – A – RL – B – D4 and back to the source.

During the negative semi-cycle of the VIN, the D3 and D2 diodes are polarized forward, while the D4 and D1 diodes are inverted. Then the current flows along the following path for the negative half loop of the input waveform: D3 – A – RL – B – D2 and back to the source.

In both cases, the positive and negative half-cycles of the input waveform produce positive output peaks regardless of the polarity of the input waveform, and therefore the load current always flows in the SAME direction along the RL load between points A and B or nodes. Thus, the negative half-cycle of the resource becomes a positive half-cycle in load.

Therefore, no matter which diode set is conductive, node A is always more positive than node B. Therefore, the load current and voltage are one-way or dc, which gives us the output waveform below.

## Full Wave Rectifier Output WaveForm

Although this vibrating output waveform uses 100% of the input waveform, the average DC voltage (or current) is not the same value. We remember from above that the average or average DC value taken from half of a sinusoid is defined as follows: 0.637 x maximum amplitude value. However, unlike the above half wave rectifier, full wave rectifiers have two positive half cycles per input waveform and give a different average value, as shown to us.

## Full Wave Rectifier Average Value

Because there is an average value of 0.637*AMAX for each positive peak, and since there are two peaks per input waveform, this means that the two lots collected together are the average value. Therefore, the DC output voltage of the full wave rectifier is twice that of the DC output voltage of the previous half-wave rectifier. If the maximum amplitude is 1, the average or DC value equivalent seen throughout the load resistance, RL will be as follows:

Therefore, the corresponding expressions for the average Voltage or current value for the full wave rectifier are given as follows:

As before, the maximum value is that of the AMAX input waveform, but we can also use its RMS or root average squared value to find the equivalent DC output value of the single-phase full wave rectifier. To determine the average voltage for the full wave rectifier, we multiply the RMS by 0.9:

Then we can see that the full wave rectifier circuit converts both the positive or negative half of the AC waveform into a pulsed DC output with a value of*0.637 AMAX or 0.9*ARMS, as shown.

## Full wave Rectifier Average Voltage

## Full wave Half controlled Bridge Rectifier

Full wave straightening has many advantages over the simpler half-wave rectifier, such as that the output voltage is more consistent, has a higher average output voltage, doubles the input frequency with the straightening process and requires a smaller capacitance value softening capacitor. If anyone's necessary. However, we can improve the design of the bridge rectifier by using a tristor instead of a diode in its design.

By replacing the diodes in the single-phase bridge rectifier with thyristors, we can create a phase-controlled AC-DC rectifier to convert the constant AC supply voltage into a controlled DC output voltage. Semi-controlled or fully controlled phase-controlled rectifiers have many applications in variable voltage power supplies and engine control.

A single-phase bridge rectifier is what is called an "uncontrolled rectifier", in which the applied input voltage is transmitted directly to the output terminals, which provide a constant average DC equivalent value. To convert an uncontrolled bridge rectifier into a single-phase semi-controlled rectifier circuit, we only need to replace two diodes with thyristors (SCRs), as shown.

## Half Controlled Bridge Rectifier

In a semi-controlled rectifier configuration, the average DC load voltage is controlled using two thyristors and two diodes. As we learned in our tutorial on thyristors, a thyristor will only transmit when an Anod (A) is more positive than the Cathode (K) and an ignition pulse is applied to its Door (G) (ON) status). Terminal. Otherwise, it remains passive.

We also learned that once it is "ON", a tristor is made "OFF" again only when the door signal is removed and the anode current falls under the thyristors holding the IH, as the AC supply voltage reverses it. Therefore, after the AC supply voltage has passed the zero voltage transition of the voltage from the anod to the cathode, when can we control it, delaying the ignition pulse applied to the thyristor door terminal for a controlled period or angle (α)? the thyristor begins to transmit the current and therefore controls the average output voltage.

## Half Controlled Bridge Rectifier

During the positive half-cycle of the input waveform, the current flows along the following path: SCR1 and D2 and return to the source. During the negative semi-cycle of the VIN, transmission passes through SCR2 and D1 and returns to the source.

So it is clear that for any load current to flow, a thyristor (SCR1 or SCR2) from the upper group and the corresponding diode from the subgroup (D2 or D1) must act together.

## Fully controlled Bridge Rectifier

Single-phase fully controlled bridge rectifiers are more commonly known as AC-DC converters. Fully controlled bridge converters are widely used in speed control of DC machines and are easily achieved by replacing all four diodes of a bridge rectifier with tristors as shown.

### Fully controlled Bridge Rectifier

In a fully controlled rectifier configuration, the average DC load voltage is controlled using two thyristors per half loop. ScR1 and SCR4 thyristors are fired together as a pair during positive half-cycle, while SCR3 and SCR4 thyristors are fired together as a pair during negative half-cycle. This is 180o after SCR1 and SCR4.

Then, during continuous transmission mode, four thyristors are switched continuously as alternative pairs to maintain the average or equivalent DC output voltage. As with the semi-controlled rectifier, the output voltage can be completely controlled by changing the thyristor ignition latency (α).