THEORY 27 :- FILTERS

Filter Circuits

The filter is a device that allows passing the dc component of the load and blocks the ac component of the rectifier output. Thus the output of the filter circuit will be a steady dc voltage.

The filter circuit can be constructed by the combination of components like capacitors, resistors, and inductors. Inductor is used for its property that it allows only dc components to pass and blocks ac signals. Capacitor is used so as to block the dc and allows ac to pass. All the combinations and their working are explained in detail below.

Series Inductor Filter

The circuit diagram of a full wave rectifier with a series inductor filter is given below.

As the name of the filter circuit suggests, the Inductor L is connected in series between the rectifier circuit and the load. The inductor carries the property of opposing the change in current that flows through it.

In other words, the inductor offers high impedance to the ripples and no impedance to the desired dc components. Thus the ripple components will be eliminated. When the rectifier output current increases above a certain value, energy is stored in it in the form of a magnetic field and this energy is given up when the output current falls below the average value. Thus all the sudden changes in current that occurs in the circuit will be smoothened by placing the inductor in series between the rectifier and the load.

The waveform below shows the use of inductor in the circuit.

From the circuit, for zero frequency dc voltage, the choke resistance Ri in series with the load resistance RL forms a voltage divider circuit, and thus the dc voltage across the load is

Vdc = RL/(Ri + RL)

Vdc is the output from a full wave rectifier. In this case, the value of Ri is negligibly small when compared to RL.

The effect of higher harmonic voltages can be easily neglected as better filtering for the higher harmonic components take place. This is because of the fact that with the increase in frequency, the reactance of the inductor also increases. It should be noted that a decrease in the value of load resistance or an increase in the value of load current will decrease the amount of ripples in the circuit. So, the series inductor filter is mostly used in cases of high load current or small load resistance. A simple series inductor filter may not be properly used. It is always better to use a shunt capacitor (C) with series inductor (L) to form an LC Filter.

Shunt Capacitor Filter

As the name suggests, a capacitor is used as the filter and this high value capacitor is shunted or placed across the load impedance. This capacitor, when placed across a rectifier gets charged and stores the charged energy during the conduction period. When the rectifier is not conducting, this energy charged by the capacitor is delivered back to the load. Through this energy storage and delivery process, the time duration during which the current flows through the load resistor gets increased and the ripples are decreased by a great amount. Thus for the ripple component with a frequency of ‘f’ megahertz, the capacitor ‘C’ will offer a very low impedance. The value of this impedance can be written as:

Shunt Capacitor Impedance = 1/2 fC

Thus the dc components of the input signal along with the few residual ripple components, is only allowed to go through the load resistance RLoad. The high amount of ripple components of current gets bypassed through the capacitor C.

Now let us look at the working of Half-wave rectifier and Full-wave rectifier with Capacitor filters, their output filtered waveform, ripple factor, merits and demerits in detail.

2.1 Half-wave Rectifier with Capacitor Filter

The circuit diagram above shows a half-wave rectifier with a capacitor filter. The filter is applied across the load RLoad. The output of the RLoad is VLoad, the current through it is ILoad. The current through the capacitor is Ic.

During the positive half cycle of the input ac voltage, the diode D will be forward biased and thus starts conducting. During this period, the capacitor ‘C’ starts charging to the maximum value of the supply voltage Vsm. When the capacitor is fully charged, it holds the charge until the input ac supply to the rectifier reaches the negative half cycle. As soon as the negative half supply is reached, the diode gets reverse biased and thus stops conducting. During the non-conducting period, the capacitor ‘C’ discharges all the stored charges through the output load resistance RLoad. As the voltage across RLoad and the voltage across the capacitor ‘C’ are the same (VLoad = Vc), they decrease exponentially with a time constant (C*RLoad) along the curve of the non-conducting period. This is shown in the graph below.

The value of the discharge time constant (C*RLoad) being very large, the capacitor ‘C’ will not have enough time to discharge properly. As soon as the capacitor starts discharging, the time becomes over. Thus the value of RLoad at the discharge time will also be high and have just a little less value that the output of RLoad. This is when the positive half cycle repeats again and the diode starts conducting. The condition to be considered at this stage is that the rectified voltage takes value more than the capacitor voltage . When the condition occurs the capacitor starts charging to a value of Vsm. The condition again changes when the negative half cycle comes into pace, and the whole cycle is again repeated to form the output waveform as shown above. The output shows a nearly constant dc voltage at the load and that the output voltage is increased considerably.

Thus, in short:

·       If the value of load resistance is large, the discharge time constant will be of a high value, and thus the capacitors’ time to discharge will get over soon. This lowers the amount of ripples in the output and increases the output voltage. If the load resistance is small, the discharge time constant will be less, and the ripples will be more with decrease in output voltage.

·      The value of the capacitor used plays an important role in determining the output ripples and the average dc level. If the capacitor value is high, the amount of charge it can store will be high and the amount it discharges will be less. Thus the ripples will be less and the average dc level will be high. But, there is a limit on how much capacitance can b increased. If the capacitor value is increased to a very high value, the amount of current required to charge the capacitor to a given voltage will be high. This value of current depends on the manufacturer of the diode and will be surely limited to a certain value. Thus, there is a limit in increasing the capacitor value in a half-wave rectifier shunt capacitor filter circuit.

·         Poor voltage regulation.

Ripple Factor

The rms value depends on the peak value of charging and discharging magnitude, Vpeak.

Vac rms = Vpeak/2

Vpeak = Idc/fC

Ripple Factor = Vac rms/Vdc = (Vpeak/2 ) * (1/Idc.RLoad)

                           = Idc/(2 .Idc.RLoad.f.C) = 1/(2 fCRLoad)

2.2 Full-wave Rectifier with Shunt Capacitor Filter

The circuit diagram of a full-wave rectifier wit capacitor filter is shown below.

The filter capacitor C is placed across the resistance load RLoad. The whole working is pretty much similar to that of a half-wave rectifier with shunt capacitor explained above. The only difference is that two pulses of current will charge the capacitor during alternate positive (D1) and negative (D2) half cycles. Similarly capacitor C discharges twice through RLoad during one full cycle. This is shown in the waveform below.

The load current reduces by a smaller amount before the next pulse is received as there are 2 current pulses per cycle. This causes a good reduction in ripples and a further increase in the average dc load current.

L-C Filters

In the simple shunt capacitor filter circuit explained above, we have concluded that the capacitor will reduce the ripple voltage, but causes the diode current to increase .This large current may damage the diode and will further cause heating problem and decrease the efficiency of the filter. On the other hand, a simple series inductor reduces both the peak and effective values of the output current and output voltage. Then if we combine both the filter (L and C), a new filter called the L-C filter can be designed which will have a good efficiency, with restricted diode current and enough ripple removal factor .The voltage stabilizing action of shunt capacitor and the current smoothing action of series inductor filter can be combined to form a perfect practical filter circuit.

L-C filters can be of two types: Choke Input L-section Filter and L-C Capacitor input filter

Choke Input L-Section Filter

An inductor filter increases the ripple factor with the increase in load current Rload. A capacitor filter has an inversely proportional ripple factor with respect to load resistance. Economically, both inductor filter and capacitor filter are not suitable for high end purpose

L-C inductor input or L-section filter consists of an inductor ‘ L’ connected in series with a half or full wave rectifier and a capacitor ’C’ across the load. This arrangement is also called a choke input filter or L-section filter because it’s shape resembles and inverted L-shape. To increase the smoothing action using the filter circuit, just one L-C circuit will not be enough. Several L-section filters will be arranged to obtain a smooth filtered output. The circuit diagram and smoothened waveform of a Full wave rectifier output is shown below.

Choke Input L-Section Filter

An inductor filter increases the ripple factor with the increase in load current Rload. A capacitor filter has an inversely proportional ripple factor with respect to load resistance. Economically, both inductor filter and capacitor filter are not suitable for high end purpose

L-C inductor input or L-section filter consists of an inductor ‘ L’ connected in series with a half or full wave rectifier and a capacitor ’C’ across the load. This arrangement is also called a choke input filter or L-section filter because it’s shape resembles and inverted L-shape. To increase the smoothing action using the filter circuit, just one L-C circuit will not be enough. Several L-section filters will be arranged to obtain a smooth filtered output. The circuit diagram and smoothened waveform of a Full wave rectifier output is shown below. 

As shown in the circuit diagram above, the inductor L allows the dc to pass but restricts the flow of ac components as its dc resistance is very small and ac impedance is large.  After a signal passes through the choke, if there is any fluctuation remaining the current, it will be fully bypassed before it reaches the load by the shunt capacitor because the value of Xc is much smaller than Rload. The number of ripples can be reduced to a great amount by making the value of XL greater than Xc at ripple frequency.

Ripple Factor

Ripple Factor = Vac rms/Vdc =   (√2/3)(Xc/XL) = (√2/3)(1/[2wc])(1/[2wL]) = 1/(6√2w²LC)

Though the L-C filter has all these advantages, it has now become quite obsolete due the huge size of inductors and its cost of manufacturing. Nowadays, IC voltage regulators are more commonly used along with active filters, that reduce the ripples and keeps the output dc voltage constant.

The diagram of L-C Capacitor input filter and waveform is shown below.

As shown in the circuit diagram above, the inductor L allows the dc to pass but restricts the flow of ac components as its dc resistance is very small and ac impedance is large.  After a signal passes through the choke, if there is any fluctuation remaining the current, it will be fully bypassed before it reaches the load by the shunt capacitor because the value of Xc is much smaller than Rload. The number of ripples can be reduced to a great amount by making the value of XL greater than Xc at ripple frequency.

Ripple Factor

Ripple Factor = Vac rms/Vdc =   (√2/3)(Xc/XL) = (√2/3)(1/[2wc])(1/[2wL]) = 1/(6√2w²LC)

Though the L-C filter has all these advantages, it has now become quite obsolete due the huge size of inductors and its cost of manufacturing. Nowadays, IC voltage regulators are more commonly used along with active filters, that reduce the ripples and keeps the output dc voltage constant.

The diagram of L-C Capacitor input filter and waveform is shown below.

Π – Filter or Capacitance Input Filter

The name pi – Filter implies to the resemblance of the circuit to a Π shape with two shunt capacitances (C1 and C2) and an inductance filter ‘L’. As the rectifier output is provided directly into the capacitor it also called a capacitor input filter.

he output from the rectifier is first given to the shunt capacitor C. The rectifier used can be half or full wave and the capacitors are usually electrolytic even though they large in size. In practical applications, the two capacitances are enclosed in a metal container which acts as a common ground for the two capacitors. Circuit diagram and the waveform are given below.

When compared to other type of filters, the Π – Filter has some advantages like higher dc voltage and smaller ripple factor.  But it also has some disadvantages like poor voltage regulation, high peak diode current, and high peak inverse voltage.

This filter is divided into two – a capacitor filter and a L-section filter. The capacitor C1 does most of the filtering in the circuit and the remaining ripple os removed by the L-section filter (L-C2). C1 is selected to provide very low reactance to the ripple frequency. The voltage regulation is poor for this circuit as the output voltage falls off rapidly with the increase in load current.

Ripple Factor

Ripple Factor = √2/(8w³C1C2LRload)

R-C Filter

We have already discussed about the drawbacks of using a pi-filter. The main reason for all these drawbacks is the use of inductor in the filter circuit. If we use a resistance in series, instead of the inductor as the filter, these drawbacks can be overcome. Thus the circuit is named as R-C filter. In this circuit, the ripples have to be made to drop across the resistance R instead of the load resistance RL. For this, the value of RL is kept much larger than the value of reactance of capacitor C2 (XC2). This means that each section reduces the ripple by a factor of at least 10.

Though the circuit nullifies certain drawbacks of the pi-filter, the circuit on its own has some problems as well. The filter has very poor voltage regulation. There is a large voltage drop in the resistance R. The circuit also develops a lot of heat and this has to be dissipated through enough and adequate ventilation. Thus, the filter is only suitable for small load current or large load resistance circuits.

COMPARISION OF RECTIFIERS CIRCUITS

 

Bridge Rectifier

 

Bridge Rectifier

Bridge rectifiers as a type of full-wave rectifier that uses four or more diodes in a bridge circuit configuration to efficiently convert alternating (AC) current to a direct (DC) current. In the next few sections, let us learn more about its construction, working, and more.

Construction

The construction of a bridge rectifier is shown in the figure below. The bridge rectifier circuit is made of four diodes D1, D2, D3, D4, and a load resistor RL. The four diodes are connected in a closed-loop configuration to efficiently convert the alternating current (AC) into Direct Current (DC). The main advantage of this configuration is the absence of the expensive center-tapped transformer. Therefore, the size and cost are reduced.

The input signal is applied across terminals A and B and the output DC signal is obtained across the load resistor RL connected between terminals C and D. The four diodes are arranged in such a way that only two diodes conduct electricity during each half cycle. D1 and D3 are pairs that conduct electric current during the positive half cycle/. Likewise, diodes D2 and D4 conduct electric current during a negative half cycle.

Working

When an AC signal is applied across the bridge rectifier, during the positive half cycle, terminal A becomes positive while terminal B becomes negative. This results in diodes D1 and D3 to become forward biased while D2 and D4 become reverse biased.

The current flow during the positive half-cycle is shown in the figure below:

During the negative half-cycle, terminal B becomes positive while the terminal A becomes negative. This causes diodes D2 and D4 to become forward biased and diode D1 and D3 to be reverse biased.

The current flow during the negative half cycle is shown in the figure below:

From the figures given above, we notice that the current flow across load resistor RL is the same during the positive half cycle and the negative half cycles. The output DC signal polarity may be either completely positive or negative. In our case, it is completely positive. If the direction of diodes is reversed then we get a complete negative DC voltage.

Thus, a bridge rectifier allows electric current during both positive and negative half cycles of the input AC signal.

The output waveforms of the bridge rectifier are shown in the below figure.

Characteristics of Bridge Rectifier

Ripple Factor

The smoothness of the output DC signal is measured by a factor known as the ripple factor. The output DC signal with fewer ripples is considered a smooth DC signal while the output with high ripples is considered a high pulsating DC signal.

Mathematically, the ripple factor is defined as the ratio of ripple voltage to the pure DC voltage.

The ripple factor for a bridge rectifier is given by

For bridge rectifiers, the ripple factor is 0.48.

Peak Inverse Voltage

The maximum voltage that a diode can withstand in the reverse bias condition is known as a peak inverse voltage. During the positive half cycle, the diodes D1 and D3 are in the conducting state while D2 and D4 are in the non-conducting state. Similarly, during the negative half cycle, diodes D2 and D4 are in the conducting state, and diodes D1 and D3 are in the non-conducting state.

 

Efficiency

The rectifier efficiency determines how efficiently the rectifier converts Alternating Current (AC) into Direct Current (DC). Rectifier efficiency is defined as the ratio of the DC output power to the AC input power. The maximum efficiency of a bridge rectifier is 81.2%.

Advantages

• The efficiency of the bridge rectifier is higher than the efficiency of a half-wave rectifier. However, the rectifier efficiency of the bridge rectifier and the center-tapped full-wave rectifier is the same.
• The DC output signal of the bridge rectifier is smoother than the output DC signal of a half-wave rectifier.
• In a half-wave rectifier, only half of the input AC signal is used and the other half is blocked. Half of the input signal is wasted in a half-wave rectifier. However, in a bridge rectifier, the electric current is allowed during both positive and negative half cycles of the input AC signal. Hence, the output DC signal is almost equal to the input AC signal.

Disadvantages

• The circuit of a bridge rectifier is complex when compared to a half-wave rectifier and center-tapped full-wave rectifier. Bridge rectifiers use 4 diodes while half-wave rectifiers and center tapped full wave rectifiers use only two diodes.
• When more diodes are used more power loss occurs. In a center-tapped full-wave rectifier, only one diode conducts during each half cycle. But in a bridge rectifier, two diodes connected in series conduct during each half cycle. Hence, the voltage drop is higher in a bridge rectifier.

Key Difference between Half Wave Rectifier and Full Wave Rectifier

Difference between Half Wave Rectifier and Full Wave Rectifier

Parameter	Half Wave Rectifier	Full Wave Rectifier
Definition	The half-wave rectifier is a rectifier which is used for converting the one-half cycle of AC input to DC output	A full-wave rectifier is a rectifier which is used for converting both the half cycles of AC input into DC output
No. of diodes used	1	2 or 4 depending on the type of circuit
Form factor	1.57	1.11
Rectifier efficiency	40.6%	81.2%
Ripple factor	Ripple factor of a half-wave rectifier is more	Ripple factor of a full-wave rectifier is less

 

Theory 26.2 :- Full Wave Rectifier

What is Full Wave Rectifier?

Full-wave rectifier circuits are used for producing an output voltage or output current which is purely DC. The main advantage of a full-wave rectifier over half-wave rectifier is that such as the average output voltage is higher in full-wave rectifier, there is less ripple produced in full-wave rectifier when compared to the half-wave rectifier.

Working of Full Wave Rectifier

The full-wave rectifier utilizes both halves of each a.c input. When the p-n junction is forward biased, the diode offers low resistance and when it is reversing biased it gives high resistance. The circuit is designed in such a manner that in the first half cycle if the diode is forward biased then in the second half cycle it is reverse biased and so on.

Characteristics of Full Wave Rectifier

Following are the characteristics of full-wave rectifier:

Ripple Factor

Ripple factor for a full-wave rectifier is given as:

DC Current

Currents from both the diodes D1 and D2 are in the same direction when they flow towards load resistor RL. The current produced by both the diodes is the ratio of Imax to π, therefore the DC current is given as:

Where,

 Imax is the maximum DC load current

DC Output Voltage

DC output voltage is obtained at the load resistor RL and is given as:

Where,

Vmax is the maximum secondary voltage

Form Factor

The form factor is the ratio of RMS value of current to the output DC voltage. The form factor of a full-wave rectifier is given as 1.11

Rectifier Efficiency

Rectifier efficiency is used as a parameter to determine the efficiency of the rectifier to convert AC into DC. It is the ratio of DC output power to the AC input power. The rectifier efficiency of a full-wave rectifier is 81.2%.

Advantages of Full Wave Rectifier

• The rectifier efficiency of a full-wave rectifier is high
• The power loss is very low
• Number of ripples generated are less

Disadvantages of Full Wave Rectifier

• Very expensive

Types of Full Wave Rectifier

There are two main types of full-wave rectifiers, and they are:

• Two diodes full-wave rectifier circuit (requires a center-tapped transformer and is used in vacuum tubes)
• Bridge rectifier circuit (doesn’t require a centre-tapped transformer and is used along with transformers for efficient usage)

Applications of Full Wave Rectifier

Following are the uses of full-wave rectifier:

• Full-wave rectifiers are used for supplying polarized voltage in welding and for this bridge rectifiers are used.
• Full-wave rectifiers are used for detecting the amplitude of modulated radio signals.

Theory 26.1 :- Half Wave Rectifier

What is Half Wave Rectifier?

In a half-wave rectifier, one half of each a.c input cycle is rectified. When the p-n junction diode is forward biased, it gives little resistance and when it is reversing biased it provides high resistance. During one-half cycles, the diode is forward biased when the input voltage is applied and in the opposite half cycle, it is reverse biased. During alternate half-cycles, the optimum result can be obtained.

Working of Half Wave Rectifier

The half-wave rectifier has both positive and negative cycles. During the positive half of the input, the current will flow from positive to negative which will generate only a positive half cycle of the a.c supply. When a.c supply is applied to the transformer, the voltage will be decreasing at the secondary winding of the diode. All the variations in the a.c supply will reduce, and we will get the pulsating d.c voltage to the load resistor.

n the second half cycle, the current will flow from negative to positive and the diode will be reverse biased. Thus, at the output side, there will be no current generated, and we cannot get power at the load resistance. A small amount of reverse current will flow during reverse bias due to minority carriers.

 

Characteristics of Half Wave Rectifier

Following are the characteristics of half-wave rectifier:

Ripple Factor

Ripples are the oscillations that are obtained in DC which is corrected by using filters such as inductors and capacitors. These ripples are measured with the help of the ripple factor and are denoted by γ. Ripple factor tells us the number of ripples presents in the output DC. Higher the ripple factor, more is the oscillation at the output DC and lower is the ripple factor, less is the oscillation at the output DC.

Ripple factor is the ratio of RMS value of the AC component of the output voltage to the DC component of the output voltage. 

DC Current

DC current is given as:

Where,  Imax is the maximum DC load current

DC Output Voltage

The output DC voltage appears at the load resistor RL which is obtained by multiplying output DC voltage with the load resistor RL. The output DC voltage is given as: 

Where,VSmax is the maximum secondary voltage

Form Factor

The form factor is the ratio of RMS value to the DC value. For a half-wave rectifier, the form factor is 1.57.

 Rectifier Efficiency

Rectifier efficiency is the ratio of output DC power to the input AC power. For a half-wave rectifier, rectifier efficiency is 40.6%.

Applications of Half Wave Rectifier

Following are the uses of half-wave rectification:

 Power rectification: Half wave rectifier is used along with a transformer for power rectification as powering equipment.

Signal demodulation: Half wave rectifiers are used for demodulating the AM signals.

Signal peak detector: Half wave rectifier is used for detecting the peak of the incoming waveform.

Advantages of Half Wave Rectifier

Affordable

Simple connections

Easy to use as the connections are simple

Number of components used are less

Disadvantages of Half Wave Rectifier

Ripple production is more

Harmonics are generated

Utilization of the transformer is very low

The efficiency of rectification is low

Key Differences Between Diode and Transistor

1. The diode is a semiconductor device which allows the current to flow only in one direction, whereas the transistor transfers the resistance from the low resistance region to high resistance region.
2. The diode is used for converting the AC to DC or for rectifications whereas the transistor is mainly used for amplification and as a regulator.
3. The diode has two terminals namely anode and cathode.The anode is the positive terminal, and the cathode is the negative terminal of the diode. The transistor has three terminals; they are the emitter, collector and base.
4. The diode is a type of uncontrolled switch whereas the transistor is a controlled switch.
5. The transistor is mainly classified into two types, i.e., the Bipolar junction transistor and Field Effecting Transistor. The BJT uses both the electrons and hole as a charge carrier, and the FET is a unipolar transistor. The diode has many types, for example, photodiodes, Zener Diode, Tunnel Diode, Varactor Diode, etc.
6. The P-type and N-type is the two region of the diode. The hole is the majority charge carrier of the P-region and electrons is the majority charge carrier of the N – region of the diode. The transistor has three regions, namely emitter, base and collector. Among the three regions, the base is the smallest region, and the collector is the largest region of the transistor.
7. The diode has only one depletion layer between P – type and N – type whereas the transistor has two depletion layer, one is between emitter and base region, and the other is between the base and collector region.

Basis For  Comparison

	Diode	Transistor
Definition	A semiconductor device in which current flows only in one direction.	A semiconductor device which transfers the weak signal from low resistance circuit to high resistance circuit.
Symbol
Uses	Rectification	Regulator, Amplification and Rectification
Terminal	Two (Anode and Cathode)	Three (Emitter, Base and Collector)
Switch	Uncontrolled	Controlled
Types	Junction diode, Light emitting diode, Photodiodes, Schottky diodes, Tunnel, Veractor and Zener diode.	Bipolar transistor and Field Effect Transistor.
Region	P-region and N-region	Emitter, Collector and Base
Depletion Region	One	Two

 

Key Differences Between PN-Junction and Zener Diode

 

The following are the key differences between the PN junction and Zener diode.

1. The semiconductor which conducts only in one direction is known as the PN-junction diode. And the Zener diode is the silicon diode which is optimized to operate in the breakdown region.
2. The reverse current flow through the diode damage the PN-junction diodes. The reverse current flows through the diode when it is connected in reverse biased. The reverse biasing means the p-type material is connected to the negative terminal of the supply and the n-type material is connected to the positive terminal of the supply. But the Zener diode allows the current to pass through both the direction.
3. The doping level of the PN-junction diode is low as compared to Zener diode. The width of the depletion region depends on their doping level. If the doping level of the diode is high,  their depletion region is low and vice versa.
4. The breakdown in PN-junction diode occurs at high voltage level, whereas in PN-junction diode it occurs at low voltage levels. The breakdown is the phenomenon of making the depletion region conductive. The heavily doped diode has a low depletion region.
5. The PN-junction obey the ohm’s law whereas Zener diode does not obey the ohms law. The ohms law said that the voltage applies across the diode is equal to the product of the current and resistance applied across the diodes.
6. The PN-junction diode is mainly used for rectification purpose, whereas the Zener diode is used for providing the constant voltage to the load whose voltage vary.