A rectified voltage (or current) is a voltage with a DC value not equal to zero and without any change in polarity. A pure sine wave has a DC (or average) value of zero because the signal positive voltage during the first half cycle (if the signal is positive) is exactly equal to the signal in the negative half cycle.
A rectifier is a circuit that normally takes as input a signal with a DC value equal to zero, and returns as output a signal with a DC value not equal to zero and, more important, the output signal is either completely positive or completely negative. This rectified signal does not have any change in sign (polarity).
A typical rectifier can be built with diodes and resistors. Several arrangements are available depending on what kind of rectifier you want to have. In general we find two broad types of rectifiers: halfwave rectifiers (HWR) and fullwave rectifiers (FWR).
HWR
A halfwave rectifier is a device that rectifies only a half cycle of the signal at the input. For instance, Figure 7.1 shows a halfwave rectifier build with a resistor (normally called the load) and a PN diode. In the figure the input voltage is a sine wave. At the output the signal is half rectified because only (in this case) the positive half cycle is rectified whereas the negative half cycle of the input is replaced with zero voltage.
The DC or average value of the rectified voltage can be determined by dividing the total area between the voltage and the horizontal axis of one period by the period. For the particular case of sinusoidal voltages or currents the DC value can be calculated by means of the following formula
 (7.1)

where V_{P} is the peak value of the rectified voltage and is determined with the following equation
 (7.2)

If the diode is a silicon diode, or
 (7.3)

for a germanium diode.
In both cases Vm is the peak value of the input voltage.
FWR
A fullwave rectifier is the device that rectifies both the positive half cycle and the negative half cycle of the input voltage. Figure 7.2 shows an arrangement called a Bridge Rectifier that fully rectifies an input signal.
In the figure we show the input as a sinusoidal signal. As you can see the Bridge Rectifier is made up of four PN diodes and the load resistor where the output is measured. Another arrangement to build a fullwave rectifier makes use of a transformer with a defined center tap, two diodes and the load^{1}.
The DC or average value of the rectified voltage in this case can be determined by mean of the following equation.
 (7.4)

where V_{p} is defined by Eq. 7.2 or by Eq. 7.3.
The Ripple
A rectified voltage is not a pure DC voltage because, as you can see, even if the polarity does not change (a requirement for a DC signal), its magnitude changes from a minimum value to a maximum value. This sweep of the signal constitutes what is called the ripple, and is normally measured as a peaktopeak value.
There are several methods to convert a rectified voltage into a pure DC voltage, similar to the voltages (or currents) produced by a typical power supply or a battery. The next section presents the basic steps needed to accomplish this.
A Power Supply
A rectified voltage can be transformed into a DC voltage by adding at least two more elements to the basic rectifier. Each one of these components will perform a particular task as we can gather with the following discussion.
The filter stage – In order to be able to generate a constant DC voltage from the rectified signal we must, first of all, smooth the ripple. We decrease the peaktopeak value of the ripple if we apply a filter circuit at the output of the rectifier. The simplest of all filters is a capacitor in parallel with the resistor of the rectifier, as is shown in Fig. 7.3. In this experiment we present a fullwave rectifier. The same idea can be applied to a halfwave rectifier.
With this filter in place – as you will see when the experiment is finished – the output voltage across the load will be an oscillating voltage but with a peaktopeak value much smaller than the output voltage without the filter. However, this voltage is not yet a constant voltage even if the oscillations are very small. In order to, finally, generate a constant voltage we have to add the second element.
The regulator stage  To generate a constant DC voltage from a slowly changing voltage we need a voltage regulator. As you may remember from the last experiment, voltage regulation can be achieved with a Zener diode connected in reverse bias across the voltage that we want to regulate. Thus, in this case, if we connect a Zener diode across the load, the output voltage will be constant and equal to the zener voltage at breakdown (V_{z}). The Zener diode should be chosen such that its breakdown voltage is close to the DC voltage of the rectifier as expressed by Eq. 7.1 or Eq. 7.4 above. Figure 7.4 shows a complete VoltageRegulated Power Supply. As you can see the power supply if formed by the rectifier, the filter and the voltage regulator.
Figure 7.4: Voltage – Regulated Power Supply
A rectified voltage (or current) is a voltage with a DC value not equal to zero and without any change in polarity. A pure sine wave has a DC (or average) value of zero because the signal positive voltage during the first half cycle (if the signal is positive) is exactly equal to the signal in the negative half cycle.
A rectifier is a circuit that normally takes as input a signal with a DC value equal to zero, and returns as output a signal with a DC value not equal to zero and, more important, the output signal is either completely positive or completely negative. This rectified signal does not have any change in sign (polarity).
A typical rectifier can be built with diodes and resistors. Several arrangements are available depending on what kind of rectifier you want to have. In general we find two broad types of rectifiers: halfwave rectifiers (HWR) and fullwave rectifiers (FWR).
HWR
A halfwave rectifier is a device that rectifies only a half cycle of the signal at the input. For instance, Figure 7.1 shows a halfwave rectifier build with a resistor (normally called the load) and a PN diode. In the figure the...
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