BASIC ELECTRONICS Subject Code: ELN-15/5 IA marks: 5 Hours per week : 04 Exam Hours 03 Total Hrs: 5 Exam Marks: 100 CHAPTER 1 CONDUCTION IN SEMICONDUCTORS Electrons and holes in an intrinsic semiconductors, conductivity of a semiconductor, carrier concentrations in an intrinsic semiconductor, donor and acceptor impurities, charge densities in a semiconductor, Fermi level in a semiconductor having impurities, diffusion, carrier life time, Hall effect. 05 Hrs. The branch of engineering which deals with the flow of Electrons through vacuum, gas or semiconductor is called Electronics. Electronics essentially deals with electronic devices and their utilization. Atomic Structure Atom is the basic building block of all the elements. It consists of the central nucleus of positive charge around which small negatively charged particles called electrons revolve in different paths or orbits. An Electrostatic force of attraction between electrons and the nucleus holds up electrons in different orbits. Electrostatic force. + Centrifugal force. Figure1.1. Atomic structure
Nucleus is the central part of an atom and contains protons and neutrons. A proton is positively charged particle, while the neutron has the same mass as the proton, but has no charge. Therefore,nucleus of an atom is positively charged. atomic weight = no. of protons + no. of neutrons An electron is a negatively charged particle having negligible mass. The charge on an electron is equal but opposite to that on a proton. Also the number of electrons is equal to the number of protons in an atom under ordinary conditions. Therefore an atom is neutral as a whole. atomic number = no. of protons or electrons in an atom The number of electrons in any orbit is given by n where n is the number of the orbit. For example, I orbit contains x1 = electrons II orbit contains x = 8 electrons III orbit contains x3 = 18 electrons and so on The last orbit cannot have more than 8 electrons. The last but one orbit cannot have more than 18 electrons. Positive and negative ions Protons and electrons are equal in number hence if an atom loses an electron it has lost negative charge therefore it becomes positively charged and is referred as positive ion. If an atom gains an electron it becomes negatively charged and is referred to as negative ion. Valence electrons The electrons in the outermost orbit of an atom are known as valence electrons. The outermost orbit can have a maximum of 8 electrons. The valence electrons determine the physical and chemical properties of a material.
When the number of valence electrons of an atom is less than 4, the material is usually a metal and a conductor. Examples are sodium, magnesium and aluminium, which have 1, and 3 valence electrons respectively. When the number of valence electrons of an atom is more than 4, the material is usually a non-metal and an insulator. Examples are nitrogen, sulphur and neon, which have 5,6 and 8 valence electrons respectively. When the number of valence electrons of an atom is 4 the material has both metal and non-metal properties and is usually a semi-conductor. Examples are carbon, silicon and germanium. Free electrons The valence electrons of different material possess different energies. The greater the energy of a valence electron, the lesser it is bound to the nucleus. In certain substances, particularly metals, the valence electrons possess so much energy that they are very loosely attached to the nucleus. The loosely attached valence electrons move at random within the material and are called free electrons. The valence electrons, which are loosely attached to the nucleus, are known as free electrons. Energy bands In case of a single isolated atom an electron in any orbit has definite energy. When atoms are brought together as in solids, an atom is influenced by the forces from other atoms. Hence an electron in any orbit can have a range of energies rather than single energy. These range of energy levels are known as Energy bands. Within any material there are two distinct energy bands in which electrons may exist viz Valence band and conduction band.
Energy level Conduction band Forbidden gap Valence band Figure1. Energy level diagram The range of energies possessed by valence electrons is called valence band. The range of energies possessed by free electrons is called conduction band. Valence band and conduction band are separated by an energy gap in which no electrons normally exist this gap is called forbidden gap. Electrons in conduction band are either escaped from their atoms (free electrons) or only weakly held to the nucleus. Thereby by the electrons in conduction band may be easily moved around within the material by applying relatively small amount of energy. (either by increasing the temperature or by focusing light on the material etc. ) This is the reason why the conductivity of the material increases with increase in temperature. But much larger amount of energy must be applied in order to extract an electron from the valence band because electrons in valence band are usually in the normal orbit around a nucleus. For any given material, the forbidden gap may be large, small or non-existent. Classification of materials based on Energy band theory Based on the width of the forbidden gap, materials are broadly classified as conductors, Insulators and semiconductors. Conduction band overlap Conduction band Forbidden Gap E G =6eV Conduction band Forbidden Gap E G =1eV Valence band Valence band Valence band (a) Conductor (b) Insulator (c) Semiconductor
Conductors Conductors are those substances, which allow electric current to pass through them. Example: Copper, Al, salt solutions, etc. In terms of energy bands, conductors are those substances in which there is no forbidden gap. Valence and conduction band overlap as shown in fig (a). For this reason, very large number of electrons are available for conduction even at extremely low temperatures. Thus, conduction is possible even by a very weak electric field. Insulators Insulators are those substances, which do not allow electric current to pass through them. Example: Rubber, glass, wood etc. In terms of energy bands, insulators are those substances in which the forbidden gap is very large. Thus valence and conduction band are widely separated as shown in fig (b). Therefore insulators do not conduct electricity even with the application of a large electric field or by heating or at very high temperatures. Semiconductors Semiconductors are those substances whose conductivity lies in between that of a conductor and Insulator. Example: Silicon, germanium, Cealenium, Gallium, arsenide etc. In terms of energy bands, semiconductors are those substances in which the forbidden gap is narrow. Thus valence and conduction bands are moderately separated as shown in fig(c). In semiconductors, the valence band is partially filled, the conduction band is also partially filled, and the energy gap between conduction band and valence band is narrow. Therefore, comparatively smaller electric field is required to push the electrons from valence band to conduction band. At low temperatures the valence band is completely filled and conduction band is completely empty. Therefore, at very low temperature a semi-conductor actually behaves as an insulator.
Conduction in solids Conduction in any given material occurs when a voltage of suitable magnitude is applied to it, which causes the charge carriers within the material to move in a desired direction. This may be due to electron motion or hole transfer or both. Electron motion Free electrons in the conduction band are moved under the influence of the applied electric field. Since electrons have negative charge they are repelled by the negative terminal of the applied voltage and attracted towards the positive terminal. Hole transfer Hole transfer involves the movement of holes. Holes may be thought of positive charged particles and as such they move through an electric field in a direction opposite to that of electrons. I I + + V (a) Conductor Flow of electrons V (b) Semiconductor Flow of electrons Flow of current Flow of holes Flow of current In a good conductor (metal) as shown in fig (a) the current flow is due to free electrons only. In a semiconductor as shown in fig (b). The current flow is due to both holes and electrons moving in opposite directions. The unit of electric current is Ampere (A) and since the flow of electric current is constituted by the movement of electrons in conduction band and holes in valence band, electrons and holes are referred as charge carriers.
Classification of semiconductors Semiconductors are classified into two types. a) Intrinsic semiconductors. b) Extrinsic semiconductors. a) Intrinsic semiconductors A semiconductor in an extremely pure form is known as Intrinsic semiconductor. Example: Silicon, germanium. Both silicon and Germanium are tetravalent (having 4 valence electrons). Each atom forms a covalent bond or electron pair bond with the electrons of neighboring atom. The structure is shown below. Silicon or Germanium Valence electron Covalent bond Figure1.3. Crystalline structure of Silicon (or Germanium) At low temperature At low temperature, all the valence electrons are tightly bounded the nucleus hence no free electrons are available for conduction. The semiconductor therefore behaves as an Insulator at absolute zero temperature.
At room temperature Free electron Valence electron Holes Figure 1.4. Crystalline structure of Silicon (or Germanium) at room temperature At room temperature, some of the valence electrons gain enough thermal energy to break up the covalent bonds. This breaking up of covalent bonds sets the electrons free and are available for conduction. When an electron escapes from a covalent bond and becomes free electrons a vacancy is created in a covalent bond as shown in figure above. Such a vacancy is called Hole. It carries positive charge and moves under the influence of an electric field in the direction of the electric field applied. Numbers of holes are equal to the number of electrons since, a hole is nothing but an absence of electrons. Extrinsic Semiconductor When an impurity is added to an Intrinsic semiconductor its conductivity changes. This process of adding impurity to a semiconductor is called Doping and the impure semiconductor is called extrinsic semiconductor. Depending on the type of impurity added, extrinsic semiconductors are further classified as n-type and p-type semiconductor.
n-type semiconductor Si Si Si Si As free e - Si Si Si Si Figure 1.5 n-type semiconductor Conduction band Forbidden gap Fermi level Valence band Figure1.6 Energy band diagram for n-type semiconductor When a small current of Pentavalent impurity is added to a pure semiconductor it is called as n-type semiconductor. Addition of Pentavalent impurity provides a large number of free electrons in a semiconductor crystal. Typical example for pentavalent impurities are Arsenic, Antimony and Phosphorus etc. Such impurities which produce n-type semiconductors are known as Donor impurities because they donate or provide free electrons to the semiconductor crystal. To understand the formation of n-type semiconductor, consider a pure silicon crystal with an impurity say arsenic added to it as shown in figure 1.5.
We know that a silicon atom has 4 valence electrons and Arsenic has 5 valence electrons. When Arsenic is added as impurity to silicon, the 4 valence electrons of silicon make co-valent bond with 4 valence electrons of Arsenic. The 5 th Valence electrons finds no place in the covalent bond thus, it becomes free and travels to the conduction band as shown in figure. Therefore, for each arsenic atom added, one free electron will be available in the silicon crystal. Though each arsenic atom provides one free electrons yet an extremely small amount of arsenic impurity provides enough atoms to supply millions of free electrons. Due to thermal energy, still hole election pairs are generated but the number of free electrons are very large in number when compared to holes. So in an n-type semiconductor electrons are majority charge carriers and holes are minority charge carriers. Since the current conduction is pre-dominantly by free electrons( -vely charges) it is called as n-type semiconductor( n- means ve). p-type semiconductor Si Si Si hole Si Ga Si Si Si Si Figure 1.7 p-type semiconductor
Conduction band Forbidden gap Fermi level Valence band Figure 1.8 Energy band diagram for p-type semiconductor When a small amount of trivalent impurity is added to a pure semiconductor it is called p-type semiconductor. The addition of trivalent impurity provides large number of holes in the semiconductor crystals. Example: Gallium, Indium or Boron etc. Such impurities which produce p-type semiconductors are known as acceptor impurities because the holes created can accept the electrons in the semi conductor crystal. To understand the formation of p-type semiconductor, consider a pure silicon crystal with an impurity say gallium added to it as shown in figure 1.7. We know that silicon atom has 4 valence electrons and Gallium has 3 electrons. When Gallium is added as impurity to silicon, the 3 valence electrons of gallium make 3 covalent bonds with 3 valence electrons of silicon. The 4 th valence electrons of silicon cannot make a covalent bond with that of Gallium because of short of one electron as shown above. This absence of electron is called a hole. Therefore for each gallium atom added one hole is created, a small amount of Gallium provides millions of holes. Due to thermal energy, still hole-electron pairs are generated but the number of holes are very large compared to the number of electrons. Therefore, in a p-type semiconductor holes are majority carriers and electrons are minority carriers. Since the current conduction is predominantly by hole( + charges) it is called as p-type semiconductor( p means +ve)
Drift and Diffusion current The flow of current through a semiconductor material is normally referred to as one of the two types. Drift current If an electron is subjected to an electric field in free space it will accelerate in a straight line form the ve terminal to the + ve terminal of the applied voltage. However in the case of conductor or semiconductor at room temperature, a free electrons under the influence of electric field will move towards the +ve terminal of the applied voltage but will continuously collide with atoms all the ways as shown in figure 1.9. Electron drift due to field conduction when electric field is present semiconductor + Applied voltage Figure 1.9 Conduction when no electric field is applied Each time, when the electron strikes an atom, it rebounds in a random direction but the presence of electric field doesnot stop the collisions and random motion. As a result the electrons drift in a direction of the applied electric field. The current produced in this way is called as Drift current and it is the usual kind of current flow that occurs in a conductor. Diffusion current The directional movement of charge carriers due to their concentration gradient produces a component of current known as Diffusion current. The mechanism of transport of charges in a semiconductor when no electric field is applied called diffusion. It is encountered only in semiconductors and is normally absent in conductors.
heavy concentration of electrons less concentration electrons Diffusion current Even distribution Net diffusion current is zero With no applied voltage if the number of charge carriers (either holes or electrons) in one region of a semiconductor is less compared to the rest of the region then there exist a concentration gradient. Since the charge carriers are either all electrons or all holes they sine polarity of charge and thus there is a force of repulsion between them. As a result, the carriers tend to move gradually or diffuse from the region of higher concentration to the region of lower concentration. This process is called diffusion and electric current produced due to this process is called diffusion current. This process continues until all the carriers are evenly distributed through the material. Hence when there is no applied voltage, the net diffusion current will be zero.
Fermi-level Fermi level indicates the level of energy in the forbidden gap. 1. Fermi-level for an Intrinsic semiconductor Energy level E C Conduction band E f Fermilevel E V Valence band Forbidden gap E C E V E f Conduction band energy level Valence band energy level fermi level We know that the Intrinsic semiconductor acts as an insulator at absolute zero temperature because there are free electrons and holes available but as the temperature increases electron hole pairs are generated and hence number of electrons will be equal to number of holes. Therefore, the possibility of obtaining an electron in the conduction band will be equal to the probability of obtaining a hole in the valence band. If Ec is the lowest energy level of Conduction band and Ev is the highest energy level of the valence band then the fermi level E f is exactly at the center of these two levels as shown above.
. Fermi-level in a semiconductors having impurities (Extrinsic) a) Fermi-level for n-type Semiconductor Let a donar impurity be added to an Intrinsic semiconductor then the donar energy level (E D ) shown by the dotted lines is very close to conduction band energy level (E c ). Therefore the unbonded valence electrons of the impurity atoms can very easily jump into the conduction band and become free electros thus, at room temperature almost all the extra electrons of pentavalent impurity will jump to the conduction band. The donar energy level (E D ) is just below conduction band level (Ec) as shown in figure1.10(a). Due to a large number of free electrons, the probability of electrons occupying the energy level towards the conduction band will be more hence, fermi level shifts towards the conduction band. Conduction band E C moves upward Fermi level E D E f E V Valence band E D Energy level of donar impurity Figure 1.10 (a) Energy level diagram for n-type semiconductor
b) Fermi-level for P-type semiconductor Let an acceptor impurity be added to an Intrinsic semiconductor then the acceptor energy level (Ea) shown by dotted lines is very close to the valence band shown by dotted lines is very close to the valence band energy level (Ev). Therefore the valence band electrons of the impurity atom can very easily jump into the valence band thereby creating holes in the valence band. E C Conduction band Fermi level E f E A E V Valence band E A Energy level of acceptor impurity Figure 1.11 (b) Energy level diagram for P-type semiconductor The acceptor energy level (E A ) is just above the valence band level as shown in figure 1.11 (b). Due to large number of holes the probability of holes occupying the energy level towards the valence band will be more and hence, the fermi level gets shifted towards the valence band.
HALL EFFECT If a piece of metal or semiconductor carrying a current I is placed in a transverse magnetic field B then an electric field E is induced in the direction perpendicular to both I and B. This phenomenon is known as Hall effect. Y(+ve) Surface- Z (+ve) I B + + + + + + + + Surface -1 d w X (+ve) V H Hall effect is normally used to determine whether a semi-conductor is n-type or p-type. To find whether the semiconductor is n-type or p-type i) In the figure. above, If I is in the +ve X direction and B is in the +ve Z direction, then a force will be exerted on the charge carriers (holes and electrons) in the ve Y direction. ii) This force is independent of whether the charge carriers are electrons or holes. Due to this force the charge carriers ( holes and electrons) will be forced downward towards surface 1 as shown. iii) If the semiconductor is N-type, then electrons will be the charge carriers and these electrons will accumulate on surface 1 making that surface vely charged with respect to surface. Hence a potential called Hall voltage appears between the surfaces 1 and. iv) Similarly when surface 1 is positively charged with respect to surface, then the semiconductor is of P-type. In this way, by seeing the polarity of Hall voltage we can determine whether the semiconductor is of P-type or N-type.
Applications of Hall effect Hall effect is used to determine, carrier concentration, conductivity and mobility. The sign of the current carrying charge. Charge density. It is used as magnetic field meter. Carrier lifetime (τ) In a pure semiconductor, we know that number of holes are equal to the number of electrons. Thermal agitation however, continues to produce new hole electron pairs while other hole-electron pair disappear as a result of recombination. On an average, a hole will exist for τ p second and an electron will exist for τ n second before recombination. This time is called the carrier lifetime or Mean lifetime. The average time an electron or hole can exist in the free state is called carrier lifetime.
CHAPTER SEMICONDUCTOR DIODE When a p-type semiconductor material is suitably joined to n-type semiconductor the contact surface is called a p-n junction. The p-n junction is also called as semiconductor diode. p n + + (b) (a) Fig..0 (a) p-n junction Depletion region Fig.0 (b) symbolic representation The left side material is a p-type semiconductor having ve acceptor ions and +vely charged holes. The right side material is n-type semiconductor having +ve donor ions and free electrons. Suppose the two pieces are suitably treated to form pn junction, then there is a tendency for the free electrons from n-type to diffuse over to the p-side and holes from p-type to the n-side. This process is called diffusion. As the free electrons move across the junction from n-type to p-type, +ve donor ions are uncovered. Hence a +ve charge is built on the n-side of the junction. At the same time, the free electrons cross the junction and uncover the ve acceptor ions by filling in the holes. Therefore a net ve charge is established on p-side of the junction. When a sufficient number of donor and acceptor ions is uncovered further diffusion is prevented. Thus a barrier is set up against further movement of charge carriers. This is called potential barrier or junction barrier Vo. The potential barrier is of the order of 0.1 to 0.3V. Note: outside this barrier on each side of the junction, the material is still neutral. Only inside the barrier, there is a +ve charge on n-side and ve charge on p-side. This region is called depletion layer.
.1 Biasing: Connecting a p-n junction to an external d.c. voltage source is called biasing. 1. Forward biasing. Reverse biasing 1. Forward biasing When external voltage applied to the junction is in such a direction that it cancels the potential barrier, thus permitting current flow is called forward biasing. To apply forward bias, connect +ve terminal of the battery to p-type and ve terminal to n-type as shown in fig..1 below. The applied forward potential establishes the electric field which acts against the field due to potential barrier. Therefore the resultant field is weakened and the barier height is reduced at the junction as shown in fig..1. Since the potential barrier voltage is very small, a small forward voltage is sufficient to completely eliminate the barrier. Once the potential barrier is eliminated by the forward voltage, junction resistance becomes almost zero and a low resistance path is established for the entire circuit. Therefore current flows in the circuit. This is called forward current. p n no external field External field Fig..1 forward biasing of p-n junction
. Reverse biasing When the external voltage applied to the junction is in such a direction the potential barrier is increased it is called reverse biasing. To apply reverse bias, connect ve terminal of the battery to p-type and +ve terminal to n-type as shown in figure below. The applied reverse voltage establishes an electric field which acts in the same direction as the field due to potential barrier. Therefore the resultant field at the junction is strengthened and the barrier height is increased as shown in fig... The increased potential barrier prevents the flow of charge carriers across the junction. Thus a high resistance path is established for the entire circuit and hence current does not flow. p n external field no external field Fig.. Reverse biasing of p-n junction
. Volt- Ampere characteristics(v-i) R V A V diode (i) I F (ma) Break over Voltage V R Knee voltage V F I R (µa) (ii) Fig..3 V-I characteristics of p-n junction diode. (i) Circuit diagram (ii) Characteristics The V-I characteristics of a semiconductor diode can be obtained with the help of the circuit shown in fig..3 (i) The supply voltage V is a regulated power supply, the diode is forward biased in the circuit shown. The resistor R is a current limiting resistor. The voltage across the diode is measured with the help of voltmeter and the current is recorded using an ammeter. By varying the supply voltage different sets of voltage and currents are obtained. By plotting these values on a graph, the forward characteristics can be obtained. It can be noted from the graph the current remains zero till the diode voltage attains the barrier potential. For silicon diode, the barrier potential is 0.7 V and for Germanium diode, it is 0.3 V. The barrier potential is also called as knee voltage or cur-in voltage.
The reverse characteristics can be obtained by reverse biasing the diode. It can be noted that at a particular reverse voltage, the reverse current increases rapidly. This voltage is called breakdown voltage..3 Diode current equation The current in a diode is given by the diode current equation I = I 0 ( e V/ηV T 1) Where, I------ diode current I 0 ------ reverse saturation current V------ diode voltage η------- semiconductor constant =1 for Ge, for Si. V T ------ Voltage equivalent of temperature= T/11,600 (Temperature T is in Kelvin) Note----- If the temperature is given in 0 C then it can be converted to Kelvin by the help of following relation, 0 C+73 = K.4 Diode equivalent circuit It is generally profitable to replace a device or system by its equivalent circuit. Once the device is replaced by its equivalent circuit, the resulting network can be solved by traditional circuit analysis technique. switch I f r f V F V F Vo (i) (ii ) Fig..4 Diode equivalent circuit. (i) symbol (ii) equivalent circuit The forward current I f flowing through the diode causes a voltage drop in its internal resistance r f. Therefore the forward voltage V F applied across the actual diode has to overcome 1. potential barrier Vo. internal drop I f r f V f = Vo + I f r f For silicon diode Vo=0.7V whereas for Germanium diode Vo = 0.3 V. For ideal diode r f =0.
4.1 Basic Definitions 1.Knee voltage or Cut-in Voltage. It is the forward voltage at which the diode starts conducting.. Breakdown voltage It is the reverse voltage at which the diode (p-n junction) breaks down with sudden rise in reverse current. 3. Peak-inverse voltage (PIV) It is the max. reverse voltage that can be applied to a p-n junction without causing damage to the junction. If the reverse voltage across the junction exceeds its peak-inverse voltage, then the junction exceeds its Peak-inverse voltage, then the junction gets destroyed because of excessive heat. In rectification, one thing to be kept in mind is that care should be taken that reverse voltage across the diode during ve half cycle of a.c. doesnot exceed the peak-inverse voltage of the diode. 4. Maximum Forward current It is the Max. instantaneous forward current that a p-n junction can conduct without damaging the junction. If the forward current is more than the specified rating then the junction gets destroyed due to over heating. 5.Maximum Power rating It is the maximum power that can be dissipated at the junction without damaging it. The power dissipated across the junction is equal to the product of junction current and the voltage across the junction.
.5 RECTIFIERS Rectifiers are the circuit which converts ac to dc Rectifiers are grouped into tow categories depending on the period of conductions. 1. Half-wave rectifier. Full- wave rectifier..5.1 Half-wave rectifier The circuit diagram of a half-wave rectifier is shown in fig..5 below along with the I/P and O/P waveforms. V i (i) t V o π π t Fig..5 Half wave rectifier (i) Circuit diagram (ii) waveforms (ii) The transformer is employed in order to step-down the supply voltage and also to prevent from shocks. The diode is used to rectify the a.c. signal while, the pulsating d.c. is taken across the load resistor R L.
During the +ve half cycle, the end X of the secondary is +ve and end Y is -ve. Thus, forward biasing the diode. As the diode is forward biased, the current flows through the load R L and a voltage is developed across it. During the ve half-cycle the end Y is +ve and end X is ve thus, reverse biasing the diode. As the diode is reverse biased there is no flow of current through R L thereby the output voltage is zero..5. Efficiency of a rectifier The ratio of d.c. power to the applied imp ac power is known as rectifier efficiency. Rectifier efficiency η = d. c. power. output input. a. c. power.5.3derivation of rectifier efficiency of Half wave rectifier Let V = V m sinθ be the voltage across the secondary winding r f = diode resistance R L = load resistance d.c. power I av = I dc = π 1 1 VmSinθ i. dθ = dθ π 0 π rl + RL Vm = Sinθdθ π ( rf R + L) π 0 π 0 Vm = π ( + rf RL ) Im = π d.c. power P dc = I dc * R L Im R π = L ------------------------------ (1)
a.c. power input The a.c. power input is given by P ac = I rms ( r f + R L ) π 1 I rms = π i 0 dθ Squaring both sides we get π 1 I rms = π i 0 dθ But i = Im Sinθ I rms = π 1 θ θ π (Im Sin ) d 0 ( current flows through diode only for duration 0 to Π ) I m I rms = 4 I = rms I m I m P ac = f + η P ( r R ) I dc = = * Pac I m m π L --------------------------------------------() L ( r + R ) f R L η = 0.406 rf 1+ R L -------------------------------------------------(3) The efficiency is maximum if r f is negligible as compared to R L Therefore maximum rectifier efficiency = 40.6 %
.5.4 Full-wave rectifier Full-wave rectifier are of two types 1. Centre tapped full-wave rectifier. Bridge rectifier.5.4.1centre tapped full wave rectifier Vin (i) Vout π π (ii) Fig..6 Centre tapped Full wave rectifier (i) Circuit diagram (ii) waveforms The circuit diagram of a center tapped full wave rectifier is shown in fig..6 above. It employs two diodes and a center tap transformer. The a.c. signal to be rectified is applied to the primary of the transformer and the d.c. output is taken across the load R L. During the +ve half-cycle end X is +ve and end Y is ve this makes diode D 1 forward biased and thus a current i 1 flows through it and load resistor R L. Diode D is reverse biased and the current i is zero.
During the ve half-cycle end Y is +Ve and end X is Ve. Now diode D is forward biased and thus a current i flows through it and load resistor R L. Diode D 1 is reversed and the current i 1 = 0. Disadvantages Since, each diode uses only one-half of the transformer secondary voltage the d.c. output is comparatively small. It is difficult to locate the center-tap on secondary winding of the transformer. The diodes used must have high Peak-inverse voltage..5.4. Bridge rectifier Vout (i) D1D3 DD4 D1D4 (ii) Fig..7 Full wave bridge wave rectifier (i) Circuit diagram (ii) waveforms. The circuit diagram of a bridge rectifer is shown above. It uses four diodes and a transformer. t During the +ve half-cycle, end A is +ve and end B is ve thus diodes D 1 and D 3 are forward bias while diodes D and D 4 are reverse biased thus a current flows through diode D 1, load R L ( C to D) and diode D 3.
During the ve half-cycle, end B is +ve and end A is ve thus diodes D and D 4 are forward biased while the diodes D 1 and D 3 are reverse biased. Now the flow of current is through diode D 4 load R L ( D to C) and diode D. Thus, the waveform is same as in the case of center-tapped full wave rectifier. Advantages The need for center-taped transformer is eliminated. The output is twice when compared to center-tapped full wave rectifier. for the same secondary voltage. The peak inverse voltage is one-half(1/) compared to center-tapped full wave rectifier. Can be used where large amount of power is required. Disadvantages It requires four diodes. The use of two extra diodes cause an additional voltage drop thereby reducing the output voltage..5.6 Efficiency of Full-wave rectifier Let V = V m sinθ be the voltage across the secondary winding I = Imsinθ be the current flowing in secondary circuit r f = diode resistance R L = load resistance dc power output Pdc I = R dc L -----------------------------(1) I dc = I av π 1 = i. dθ π 0 I av I av π 1 = Im Sinθ. dθ π 0 I m = -------------------------------------------------------- () π P dc I m = π R L ------------------------------------------ (3)
input ac power ac rms ( r R ) P = I + ---------------------------------------- (4) f 1 I rms = dθ π i 0 Squaring both sides we get π 1 I rms = π i 0 π dθ L I rms π 1 = θ π (Im Sin ) 0 dθ I I = m rms I m I rms = ------------------------------------------------ ----- (5) I m P ac = f + P ( r R ) I dc η = = * Pac I m η = 0.81 rf 1+ R L m π L --------------------------------------------(6) L ( r + R ) f R L -------------------------------------------------(7) The efficiency will be maximum if r f is negligible as compared to R L. Maximum efficiency = 81. % This is the double the efficiency due to half wave rectifier. Therefore a Full-wave rectifier is twice as effective as a half-wave rectifier.
.6 Comparision of Rectifiers Particulars Half wave rectifier Centre-tapped Full wave rectifier 1. No. of diodes 1 Bridge rectifier 4. I dc I m / Π I m /Π I m /Π 3. V dc V m / Π V m / Π V m / Π 4.I rms I m / I m / I m / 5.Efficiency 40.6 % 81. % 81. % 6.PIV V m V m V m 7.Ripple factor 1.1 0.48 0.48 Note: The relation between turns ratio and voltages of primary and secondary of the transformer is given by o N 1 / N = V p / V s RMS value of voltage and Max. value of voltage is related by the equation. V rms = V m / ( for full-cycle of ac) If the type of diode is not specified then assume the diode to be of silicon type. For an ideal diode, forward resistance r f = 0 and cut-in voltage, V γ = 0.
.7 Ripple factor The pulsating output of a rectifier consists of d.c. component and a.c. component ( also known as ripple). The a.c. component is undesirable and account for the pulsations in the rectifier output. The effectiveness of a rectifier depends upon the magnitude of a.c. component in the output : the smaller this component, the more effective is the rectifier. The ratio of rms value of a.c. component to the d.c. component in the rectifier output is known as ripple factor Iac r = Idc.7.1 Ripple factor for Half-wave rectification By definition the effective (ie rms) value of total load current is given by I = I + I rms ac dc OR I ac = I rms I dc Where I dc = value of dc component I ac = rms value of ac component Divide both R.H.S and L.H.S. by I dc we get I I ac dc = 1 I dc I rms I dc I rms r = 1 --------------------------------------------------(1) I dc I m for half-wave rectification, we have I I rms = I m I dc = π Substituting above values in equation (1) we get, ripple factor r = 1.1 It is clear that a.c. component exceeds dc component in the output of a half-wave rectifier.
.7. Ripple factor for full-wave rectification For full wave rectification we have I rms = I m I dc = I m π Substituting above values in equation (1) we get, ripple factor r = 0.48 This shows that in the output of Full-wave rectifier, the d.c. component is more than the a.c. component.8 FILTERS We know that the output of the rectifier is pulsating d.c. ie the output obtained by the rectifier is not pure d.c. but it contains some ac components along with the dc o/p. These ac components are called as Ripples, which are undesirable or unwanted. To minimize the ripples in the rectifier output filter circuits are used. These circuits are normally connected between the rectifier and load as shown below. Vi Rectifier Vo Filter pure dc o/p Pulsating d.c. output Filter is a circuit which converts pulsating dc output from a rectifier to a steady dc output. In otherwords, filters are used to reduce the amplitudes of the unwanted ac components in the rectifier. Note: A capacitor passes ac signal readily but blocks dc.
.8.1 Types of Filters 1. Capacitor Filter (C-Filter). Inductor Filter 3. Choke Input Filter (LC-filter) 4. Capacitor Input Filter (Π-filter).8. Capacitor Filter( C-filter) Vin a e f (i) t b d c o/p without filter V 1 t Vo o/p with filter a e t Fig..8 Capacitor filter ( C-filter) (i) Circuit diagram (ii) waveforms
When the Input signal rises from o to a the diode is forward biased therefore it starts conducting since the capacitor acts as a short circuit for ac signal it gets charged up to the peak of the input signal and the dc component flows through the load R L. When the input signal fall from a to b the diode gets reverse biased. This is mainly because of the voltage across the capacitor obtained during the period o to a is more when comapared to V i. Therefore there is no conduction of current through the diode. Now the charged capacitor acts as a battery and it starts discharging through the load R L. Mean while the input signal passes through b,c,d section. When the signal reaches the point d the diode is still reverse biased since the capacitor voltage is more than the input voltage. When the signal reaches point e, the input voltage can be expected to be more than the capacitor voltage. When the input signal moves from e to f the capacitor gets charged to its peak value again. The diode gets reverse biased and the capacitor starts discharging. The final output across R L is shown in Fig..8 The ripple factor for a Half-wave rectifier with C-filer is given by r= 1/ 3f C R L f-----the line frequency ( Hz) C-----capacitance ( F) R L------- Load resistance (Ω) Ripple factor for full-wave rectifier with C-filter is given by r = 1/ 4 3 f C R L.8.3 Advantages of C-Filter low cost, small size and good characteristics. It is preferred for small load currents ( upto 50 ma) It is commonly used in transistor radio, batteries eliminator etc.
.9 Zener Diode The reverse voltage characteristics of a semiconductor diode including the breakdown region is shown below. V V z 0 I Fig..9 Zener diode characteristics Zener diodes are the diodes which are designed to operate in the breakdown region. They are also called as Breakdown diode or Avalanche diodes. The symbol of Zener diode is shown below P N Fig..10 Symbol of Zener diode The breakdown in the Zener diode at the voltage V z may be due to any of the following mechanisms. 1. Avalanche breakdown Depletion region charge carriers striking the atoms ( ) ( ) P N -ve terminal +ve terminal minority charge carriers Fig..11 Avalanche breakdown in Zener diode We know that when the diode is reverse biased a small reverse saturation current I 0 flows across the junction because of the minority cariers in the depletion region.
The velocity of the minority charge carriers is directly proportional to the applied voltage. Hence when the reverse bias voltage is increased, the velocity of minority charge carriers will also increase and consequently their energy content will also increase. When these high energy charge carriers strikes the atom within the depletion region they cause other charge carriers to break away from their atoms and join the flow of current across the junction as shown above. The additional charge carriers generated in this way strikes other atoms and generate new carriers by making them to break away from their atoms. This cumulative process is referred to as avalanche multiplication which results in the flow of large reverse current and this breakdown of the diode is called avalanche breakdown..zener breakdown We have electric field strength = Reverse voltage/ Depletion region Depletion region ( ) ( ) P N -ve terminal +ve terminal electrons pulled out of their covalent bonds because of high intensity electric field Fig..1 Zener breakdown in Zener diode From the above relation we see that the reverse voltage is directly proportional to the electric field hence, a small increase in reverse voltage produces a very high intensity electric field with ina narrow Depletion region. Therefore when the reverse voltage to a diode is increased, under the influence of high intensity electric filed large numbr of electrons within the depletion region break the covalent bonds with their atoms as shown above and thus a large reverse current flows through the diode. This breakdown is referred to as Zener breakdown.
.9.1 Zener voltage regulator The circuit diagram of Zener voltage regulator is shown below R s I I Z I L Vin V Z R L V o Fig..13 Zener voltage regulator. A zener diode of breakdown voltage V Z is connected in reverse biased condition across the load R L such that it operates in breakdown region. Any fluctuations in the current are absorbed by the series resistance R s. The Zener will maintain a constant voltage V Z ( equal to V o ) across the load unless the input voltage does not fall below the zener breakdown voltage V Z. Case(i) When input voltage V in varies and R L is constant R s I I Z I L Vin V Z R L V o If the input voltage increases, the Zener diode which is in the breakdown region is equivalent to a battery V Z as shown in figure. The output voltage remains constant at V Z (equal to Vo) and the excess voltage is dropped across the series resistance R S. We know that for a zener diode under breakdown region large change in current produces very small change in voltage, thereby the output voltage remains constant. Case (ii) When V in is constant and R L varies. R s I I Z I L Vin V Z R L V o
If there is a decrease in the load resistance R L and the input voltage remains constant then there is a increase in load current. Since V in is constant the current cannot come from the source. This addition load current is driven from the battery V Z and we know that even for a large decrease in current the Zener output voltage V z remains same. Hence the output voltage across the load is also constant..