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
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 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.
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.
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
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.
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
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.
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 Vr 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
The text below is copied from the above link.
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
- The High Voltage DC supply. (HVDC)
- The charging circuit.
Both of these stages will be described in detail in the sections
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
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
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
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
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
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.)