rectification

Rectification

Rectifier

The purpose of a rectifier is to convert an AC waveform into a DC waveform. There are two different rectification circuits, known as 'half-wave' and 'full-wave' rectifiers. Both use components called diodes to convert AC into DC.

A diode is a device which only allows current to flow through it in one direction. In this direction, the diode is said to be 'forward-biased' and the only effect on the signal is that there will be a voltage loss of around 0.7V. In the opposite direction, the diode is said to be 'reverse-biased' and no current will flow though it.

The Half-wave Rectifier

The half-wave rectifier is the simplest type of rectifier since it only uses one diode, as shown in figure 1.

Figure 1: A half-wave rectifier

Figure 2 shows the AC input waveform to this circuit and the resulting output. As you can see, when the AC input is positive, the diode is forward-biased and lets the current through. When the AC input is negative, the diode is reverse-biased and the diode does not let any current through, meaning the output is 0V. Because there is a 0.7V voltage loss across the diode, the peak output voltage will be 0.7V less than Vs.

Figure 2: Half-wave rectification

While the output of the half-wave rectifier is DC (it is all positive), it would not be suitable as a power supply for a circuit. Firstly, the output voltage continually varies between 0V and Vs-0.7V, and secondly, for half the time there is no output at all.

The Full-wave Rectifier

The circuit in figure 3 addresses the second of these problems since at no time is the output voltage 0V. This time four diodes are arranged so that both the positive and negative parts of the AC waveform are converted to DC. The resulting waveform is shown in figure 4.

Figure 3: A full-wave rectifier

Figure 4: Full-wave rectification

When the AC input is positive, diodes A and B are forward-biased, while diodes C and D are reverse-biased. When the AC input is negative, the opposite is true - diodes C and D are forward-biased, while diodes A and B are reverse-biased.

One disadvantage of the full-wave rectifier is that there is a voltage loss of 1.4V across the diodes. Why not 2.8V as there are four diodes? Remember that only two of the diodes are passing current at any one time!

While the full-wave rectifier is an improvement on the half-wave rectifier, its output still isn't suitable as a power supply for most circuits since the output voltage still varies between 0V and Vs-1.4V. So, if you put 12V AC in, you will 10.6V DC out.

From: http://www.eleinmec.com/article.asp?18

Ripple

Most circuits will require 'smoothing' of the DC output of a rectifier, and this is a simple matter since it involves only one capacitor, as shown in figure 1. Figure 1: A smoothing capacitor

The output waveform in figure 2 shows how smoothing works. During the first half of the voltage peaks from the rectifier, when the voltage increases, the capacitor charges up. Then, while the voltage decreases to zero in the second half of the peaks, the capacitor releases its stored energy to keep the output voltage as constant as possible. Such a capacitor is called a 'smoothing' or 'reservoir' capacitor when it is used in this application. Figure 2: Smoothing

Ripple

If the voltage peaks from the rectifier were not continually charging up the capacitor, it would eventually discharge and the output voltage would decrease all the way down to 0V. The discharging that does occur between peaks gives rise to a small 'ripple' voltage. The amount of ripple is affected by a combination of three factors:

The value of the capacitor. The larger the capacitor value, the more charge it can store, and the slower it will discharge. Therefore, smoothing capacitors are normally electrolytic capacitors with values over 470F.
The amount of current used by the circuit. If the circuit connected to the power supply takes a lot of current, the capacitor will discharge more quickly and there will be a higher ripple voltage.
The frequency of the peaks. The more frequent the voltage peaks from the rectifier, the more often the capacitor will be charged, and the lower the ripple voltage will be.

If you want to calculate the ripple voltage, you can use this formula...

...where V_r is the ripple voltage in Volts, I is the current taken by the circuit in Amps, C is the value of the smoothing capacitor in Farads, and F is the frequency of the peaks from the rectifier, in Hertz. This will be 50Hz in the case of the UK mains supply.

The ripple voltage should not be more than 10% of Vs - if it is, increase the value of the smoothing capacitor.

Useful Link :Ref: By Tim Surtell http://www.eleinmec.com

The text below is copied from the above link.

DC TESLA COIL DESIGN

This page discusses the application of a DC supply to Tesla Coiling. This page covers the simple resistive charging arrangement and contains a link to the more complex DC resonant charging topology. The latter was used by Greg Leyh in his Electrum coil design.

Although the title says "DC Tesla Coil Design", the Tesla Coil itself is still inherently an AC device. The tank capacitor still sees a polarity reversal during ringdown, regardless of the type of supply used to charge it. However, there are several benefits to using a DC supply to charge the tank capacitor.

As with AC charging, a high voltage power supply is used to charge the tank capacitor of the Tesla Coil. However the main difference is that the source of power is a smooth DC supply, rather than an AC supply operating at the mains frequency. This results in some significant differences in behaviour, most of which are advantageous. (See advantages and disadvantages section later.) In particular the removal of the line frequency from the charging circuit can allow the firing rate of the rotary spark gap to be varied over a wide range without encountering any beating or surging problems.

The DC charging arrangement can be broken down into two separate stages:

The High Voltage DC supply. (HVDC)
The charging circuit.

Both of these stages will be described in detail in the sections that follow…

HVDC SUPPLY

The job of the HVDC supply is to provide a constant high voltage output of fixed polarity to the charging circuit that follows. A perfect supply would provide its rated voltage with no ripple, and its output voltage would not drop when current is drawn from it. In practice this ideal supply can rarely be realised, and a compromise must be made. It is in the areas of ripple and regulation where this compromise is made.

There are many different ways to build a HVDC supply. Possible designs stretch from simple single phase supplies to elaborate 3-phase arrangements. There is a trade-off between simplicity of the design and the performance. Some of the more common alternatives are shown below.

Single phase supply

One of the simplest arrangements for a HVDC supply is shown below:

This design uses a step-up transformer followed by a bridge rectifier and a smoothing capacitor. The rectifier converts the high voltage AC from the transformer into pulsed DC, and the smoothing capacitor acts like a reservoir and holds the peak voltage for the time between peaks.

The DC output voltage from this arrangement is equal to 1.41 times the RMS voltage rating of the transformer. (i.e. It is equal to the peak output voltage from the secondary winding of the transformer.)

Although this circuit is cheap and simple, it exhibits a few shortfalls. The output from the rectifier pulses at twice the supply frequency, (100Hz in the UK), and falls to zero between peaks. This means that the supply would exhibit 100% voltage ripple without the inclusion of the smoothing capacitor. In addition to this the relatively long duration between peaks means that the smoothing capacitor needs to be large to "hold up" the supply and achieve an acceptably low amount of ripple.

We can estimate the size of smoothing capacitor required to obtain a particular percentage of ripple. This is done by assuming that a constant current is drawn from the capacitor over the 10ms time between charging pulses.

For example:

A 10kW 10kV supply must supply 1A average current. If we are prepared to accept 10% ripple, then the voltage across the smoothing capacitor is permitted to fall by 1kV over the 10ms duration between charging peaks. We can use the equation:

C = I x t / V

to find the required smoothing capacitance.

C = 1 x 0.01 / 1000 = 10 uF

This is a big capacitor which implies high cost. The 500 Joules of energy that it stores are also highly dangerous. Clearly a trade-off exists between voltage ripple, and the size and cost of the smoothing capacitor. Fortunately the demands made of the smoothing capacitor and the resulting voltage ripple can both be reduced by choosing a more elaborate supply arrangement.

3-pulse rectifier supply

The circuit below shows a simple 3-phase HVDC supply:

This design uses 3 independent step-up transformers followed by a 3-pulse rectifier and a smoothing capacitor.

This 3-pulse rectifier essentially consists of 3 identical half-wave supplies feeding into one smoothing capacitor.

Since the phases are spaced at 120 degrees relative to each other, then the capacitor sees 3 charging pulses during each cycle of the mains supply.

The DC output voltage from this arrangement is also equal to 1.41 times the RMS voltage rating of the transformer.

There are two advantages of this arrangement compared to the single phase supply described previously. Firstly, the duration between charging pulses is now only 6.67ms instead of 10ms when used on a 50Hz supply. This means that the smoothing capacitor does not need to be as big because it does not need to hold up the voltage for so long. Secondly, the output voltage from this 3-pulse rectifier does not fall right down to zero between pulses. This is because the 3-phases overlap slightly, and the voltage ripple is actually 50% if no smoothing capacitor is used.

Clearly we are heading in the right direction by reducing the time between charging pulses, and by reducing the "un-smoothed" ripple. Both of these things reduce the demands on the smoothing capacitor. This reduces the system cost, and ultimately will give superior performance.

Although the 3-pulse rectifier circuit is superior to a single phase supply, I would not recommend actually building this supply for a number of reasons. The 3-pulse rectifier only uses 3 HV diodes, so it is simple and cheap, but it is not very efficient because it only makes use of the positive half-cycles from each transformer. Secondly, the fact that it only uses the positive cycles from each transformer implies an asymmetric loading on the secondaries of each transformer. This DC current component is undesirable as it can result in saturation of the transformer cores.

A far more efficient supply can be built by using only 3 more diodes…

6-pulse rectifier supply

The circuit below shows a 3-phase supply using a 6-pulse rectifier:

This design uses 3 independent step-up transformers followed by a 6-pulse bridge rectifier and a smoothing capacitor.

This 6-pulse rectifier is like a "full-wave" version of the 3-pulse design shown above.

Since both positive and negative half-cycles are used from all 3 phases, the capacitor now sees 6 charging pulses during each cycle of the mains supply.

The DC output voltage from this arrangement is 73% higher than that obtained from the 3-pulse and single phase designs, because the 6-pulse rectifier extracts the maximum phase-to-phase voltage. A 73% increase in voltage implies a tripling of the energy in the Tesla Coil's primary capacitor, just for the cost of 3 additional HV diodes ! The output voltage for this arrangement is equal to 2.45 times the RMS voltage rating of the transformer.

There are a number of other advantages of this 6-pulse arrangement compared to the two supplies discussed previously. Firstly, the duration between charging pulses is now only 3.33ms with a 50Hz supply. This means that the size of the smoothing capacitor can be reduced again, because it does not need to hold up the voltage for so long. Secondly, the output voltage from this 6-pulse rectifier only falls to 86% between peaks. This is because the 6 pulses overlap considerably, and the ripple is only 14% without any smoothing capacitor. The reduced ripple means that the 6-pulse supply could be used for Tesla Coil purposes without requiring any smoothing capacitor.

Eliminating the smoothing capacitor represents a significant cost reduction in the HVDC supply, and also removes a potentially dangerous source of stored energy from the system. For this reason the author recommends the 6-pulse HVDC supply for DC Tesla Coil use.

12-pulse rectifier supply

The process of using more charging pulses per supply cycle can be taken further in order to reduce the "un-smoothed" ripple at the output of the supply. The circuit below shows a more elaborate supply using a 3-phase supply and a 12-pulse rectifier:

This design uses 6 separate step-up transformers followed by a 12-pulse rectifier and a smoothing capacitor.

The top half of the circuit is the same as the 6-pulse rectifier described above. (The secondary windings of the three transformers are connected in Star Y configuration.)

The bottom half of the circuit is basically another 6-pulse rectifier, however the secondary windings of these transformers are connected in Delta configuration.

This has the effect of shifting the phase of the bottom rectifier pulses by 30 degrees so that they interleave perfectly between the pulses from the top rectifier.

When the outputs from the two 6-pulse rectifiers are combined, the smoothing capacitor sees a total of 12 charging pulses during each cycle of the mains supply !

The DC output voltage from this arrangement is also equal to 2.45 times the RMS voltage rating of the transformer, so there is no voltage gain in moving from the 6-pulse arrangement to the more complex 12-pulse arrangement. However the duration between charging pulses is now only 1.67 ms with a 50Hz supply, making life very easy for any smoothing capacitor, if one is required at all.

The output from the 12-pulse rectifier only falls to 97% of its maximum voltage between peaks. This equates to a ripple of only 3.5% compared to 14% for the 6-pulse design above. Such a low ripple percentage makes this arrangement more than adequate for our application without employing any smoothing capacitor at all.

It should be realised that the lower 3 transformers in the circuit above, need to have their secondary windings rated at 1.73 times the voltage of the upper 3 transformers. This is because the secondary windings of the lower transformers are connected in Delta configuration, and the upper ones are connected in Star (Y) configuration. If the output voltages of the lower transformers are not scaled up accordingly, the 12-pulse rectifier circuit will not function correctly.

Although the 12-pulse rectifier represents a technically elegant HVDC supply, with minimal ripple, and no smoothing capacitor, the Tesla Coil designer must consider whether the added cost, complexity (and weight) can be justified by the low ripple at the DC output. For most applications the moderate ripple from the 6-pulse arrangement is likely acceptable, but if you happen to come across a surplus 12-pulse HVDC supply for the right price...

(Note that dedicated 3-phase transformers could be used instead of three discrete transformers in most of the circuits above. However careful attention must be paid to the way in which the 3 HV secondary windings are connected together. Most of the circuits show here require that they are connected in star configuration as access is required to the neutral for them to work correctly. Whether using separate transformers or a single 3-phase unit, always pay attention to the dots next to the windings in these circuits to ensure correct phasing.)