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Half-Wave Rectifier

Fig.1 Fig.1a

If voltage drop within the tube is neglected, the current will consist of unidirectional pulses having the form of half sine waves. The average (dc) value of the half-wave rectified output is determined by finding the area under the curve over a full cycle, as shown in Fig.1

** Vavg = area/period = Vp/Pi** where

Another formula used is:

The average value is indicated by an dc volmeter.

Fig.2 Fig.2a

The transformer secondary winding is provided with a center tap. In this circuit arrangement, a pulse of load current flows during each alternation of one input cycle. For each input cycle both tubes conduct alternately and current flows across the load resistor R*l* in the same direction. Fig.2a
The output pulse frequency is called __ RIPPLE FREQUENCY__ and is the same as the frequency of the input sine wave (line frequency). The maximum voltage across the tube occurs in the nonconducting (reverse) cycle, and its value is equal to the peak voltage of the transformer. This peak inverse voltage must not exceed the voltage breakdown rating of the tube.

The ripple frequency at the output of the full-wave rectifier is therefore __twice the line frequency__. Because of the higher pulse frequency, filtering is much easier and the average output voltage (current) is twice that of an half-way rectifier.

*Vavg = area/period = 2Vp/Pi*

- Capacitor Filter
- LC choke-input filter
- LC capacitor-input
*PI*filter - RC capacitor-input
*PI*filter

Fig.3

Capacitors are used as shunt elements to bypass the ac signal to ground.
A Capacitor opposes rapid change in voltage by it's capacitive reactance **Xc**. The capacitive reactance is determined by the frequency **f** and capacitance **C**, measured in Ohms.

From the formula we see that by increasing the frequency or the capacitance, the Xc will decrease. A low Xc will provide better filtering. Another way to look at this is:
A capacitor C1 is connected across the output parallel with the load Rl.
Evidently, the ability to reduce the ripple component depends upon the time constant of *RlC1*. The greater the load current, the more rapid the discharge of the capacitor and the lower the average value of output voltage. Making this capacitor large (increase time constance) will reduce the ripple voltage.

For example: we have a circuit connected to the 32uF capacitor filter of an half-way rectifier, which draws 25 mA at 250 average D-C voltage.

Calculating the load resistance: Rl = 250 / 0.025 = 10000 = 10k Ohm

Calculating reactance Xc at 60 Hz ripple frequency: Xc = 0.159 / 60 * 0.000032 = 82.8 Ohm

As we can see in Fig.3a, Xc represents very low resistance to the ripple current compared to 10000 Ohms of load resistance.

Fig.3a

Most of the ripple voltage is shorted to ground.
This type of filter has very limited application. It is used in circuits with low current draw and/or the ripple voltage is not critical.

To measure the smoothness of the d-c output of the filter, the terms * ripple factor* or *percent ripple* are used.

Ripple factor formula:** Ripple Factor = ripple voltage / average d-c output voltage**

Percent Ripple = ripple factor x 100

The lower the ripple factor, the better the filter. To measure the rms ripple voltage, the ripple component of the waveform is passed trough an rms meter. The average value of the d-c component is indicated by a d-c volt meter.

**You can further reduce the output-voltage ripple by minimizing the current ripple that the output capacitor is forced to absorb, so the use of multiple small caps instead of a single large component can be beneficial.**

**LC Choke-Input Filter** is shown in Fig.4

Fig.4

This filter consists of an input filter-choke L1 and an output filter capacitor C1. Reactance of the choke Xl reduces the amplitude of the ripple voltage as it opposes any change in current flow (ripple current), but developes little resistance to the d-c component.

The ripple voltage of the filter capacitor C1 is small due to the constant charging current flowing through L1. As a result, the output voltage never reaches the peak value of the applied voltage, it is approximately __equal to the average rectified voltage of the supply.__

**The choke input filter has voltage regulation ability.**

If we take a 5 Henry, 150 Ohm choke and connect it to a full-wave rectifier, we will have the following a-c reactances:

Calculating Xl= 6.28 x 120 x 5 = 3760 = 3.76kOhm

Calculating Xc= 0.159 / 120 x 0.000032= 41.84= 42 Ohm

As we can see in Fig.4a , the choke developes high resistance for ripple currents ("chokes-off") but has little resistance (150 Ohm) for d-c currents. The low reactance Xc of the capacitor C1 (42 Ohm), shunts any remining ripple current around the load to ground. The larger the value of the filter capacitor, the better the filtering action.

Fig.4a

Choke-input filter however, must maintain minimum load current to preserve filtering and regulation ability.

Lcrit. = E / I [Henrys, Volts, mA] ;where E=rectifier output voltage, I= current through the filter.

If the load current falls below a critical minimum, the filter effect deteriotates rapidly. In that state, it will act as a capacitive-input filter. A special choke, called __swinging choke__ is used where the load current is fluctuating. Swinging chokes are build with a small air gap. The air gap causes the inductance of the choke to vary with the load current.

**LC Capacitor-Input or PI Filter **is shown in Fig.5

Fig.5

It can be seen as a capacitor filter followed by an LC filter. In operation, the capacitor C1 is charged to peak voltage available from the rectifier and is gradually discharged by the load current. Ripple current and voltage are smoothed out by L1 and C2. No further current is supplied by the rectifier until C1 voltage drops below rectifier output voltage. This operation is shown in Fig.5a.

Fig.5a

At small load currents the reactance of the choke has little effect and the filtering is done by reactace X1 of capacitor C1 and reactance X2 of capacitor C2. With increasing load current, reactance of the choke L1 increases and X1, X2 decreases. The complementary nature of these components ensure __good filtering over a wide range of load current.__

**RC Capacitor-Input filter** is shown in Fig.6

Fig.6

C1 performs exactly the same functions as in single *Capacitor Filter* described above.
Resistance R1, load resistance Rl and reactance X2 of the capacitor C2 represent a voltage devider. Since the resistance of R1 is higher than X2, most of the ripple voltage drops across R1. Any remining ripple voltage is shunted by X2 to ground. The RC filter has some disadvatages, however. First, the voltage drop across R1 lowers the output voltage of the power supply. Second, power is wasted in R1 and is dissipated in the form of heat. __The RC capacitor-input filter is limited to applications with small and constant current draw.__

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