Bipolar Transister

The Common Base Configuration :

If the base is common to the input and output circuits, it is know as common base configuration as shown in fig. 1.

Fig. 1

For a pnp transistor the largest current components are due to holes. Holes flow from emitter to collector and few holes flow down towards ground out of the base terminal. The current directions are shown in fig. 1.

(I_E = I_C + I_B ).

For a forward biased junction, V_EB is positive and for a reverse biased junction V_CB is negative. The complete transistor can be described by the following two relations, which give the input voltage V_EB and output current I_C in terms of the output voltage (V_CB) and input current I_E.

V_EB = f₁(V_CB, I_E)
I_C= f₂(V_CB, I_E) 

The output characteristic:

The collector current I_C is completely determined by the input current I_E and the V_CB voltage. The relationship is given in fig. 2. It is a plot of I_C versus V_CB, with emitter current I_E as parameter. The curves are known as the output or collector or static characteristics. The transistor consists of two diodes placed in series back to back (with two cathodes connected together). The complete characteristic can be divided in three regions.

Figure 7.2

(1). Active region:

In this region the collector diode is reverse biased and the emitter diode is forward biased. Consider first that the emitter current is zero. Then the collector current is small and equals the reverse saturation current I_CO of the collector junction considered as a diode.

If the forward current I_B is increased, then a fraction of I_E ie. a_dcI_E will reach the collector. In the active region, the collector current is essentially independent of collector voltage and depends only upon the emitter current. Because a_dc is, less than one but almost equal to unity, the magnitude of the collector current is slightly less that of emitter current. The collector current is almost constant and work as a current source.

The collector current slightly increases with voltage. This is due to early effect. At higher voltage collector gathers in a few more electrons. This reduces the base current. The difference is so small, that it is usually neglected. If the collector voltage is increased, then space charge width increases; this decreased the effective base width. Then there is less chance for recombination within the base region.

(2). Saturation region:

The region to the left of the ordinate V_CB = 0, and above the I_E = 0, characteristic in which both emitter and collector junction are forward biased, is called saturation region.

When collector diode is forward biased, there is large change in collector current with small changes in collector voltage. A forward bias means, that p is made positive with respect to n, there is a flow of holes from p to n. This changes the collector current direction. If diode is sufficiently forward biased the current changes rapidly. It does not depend upon emitter current.

(3). Cut off region:

The region below I_E = 0 and to the right of V_CB for which emitter and collector junctions are both reversed biased is referred to cutoff region. The characteristics I_E = 0, is similar to other characteristics but not coincident with horizontal axis. The collector current is same as I_CO. I_CBOCO. It means collector to base current with emitter open. This is also temperature dependent. is frequently used for I

The Input Characteristic:

In the active region the input diode is forward biased, therefore, input characteristic is simply the forward biased characteristic of the emitter to base diode for various collector voltages. fig. 3. Below cut in voltage (0.7 or 0.3) the emitter current is very small. The curve with the collector open represents the forward biased emitter diode. Because of the early effect the emitter current increases for same VEB. (The diode becomes better diode). When the collector is shorted to the base, the emitter current increases for a given VEB since the collector now removes minority carriers from the base, and hence base can attract more holes from the emitter. This mean that the curve VCB= 0, is shifted from the character when VCB = open.

Fig. 3

Equivalent circuit of a transistor: (Common Base)

In an ideal transistor, adc= 1. This means all emitter electrons entering the base region go on to the collector. Therefore, collector current equals emitter current. For transistor action, emitter diode acts like a forward bias diode and collector diode acts like a current source. The equivalent circuits of npn and pnp transistors are shown in fig. 4. The current source arrow points for conventional current. The current source is controlled by emitter current. Common Base Amplifier: The common base amplifier circuit is shown in Fig. 1. The VEE source forward biases the emitter diode and VCC source reverse biased collector diode. The ac source vin is connected to emitter through a coupling capacitor so that it blocks dc. This ac voltage produces small fluctuation in currents and voltages. The load resistance RL is also connected to collector through coupling capacitor so the fluctuation in collector base voltage will be observed across RL. The dc equivalent circuit is obtained by reducing all ac sources to zero and opening all capacitors. The dc collector current is same as IE and VCB is given by VCBCCCC. = V - I R Fig. 1 These current and voltage fix the Q point. The ac equivalent circuit is obtained by reducing all dc sources to zero and shorting all coupling capacitors. r'e represents the ac resistance of the diode as shown in Fig. 2. Fig. 2 Fig. 3, shows the diode curve relating IE and VBE. In the absence of ac signal, the transistor operates at Q point (point of intersection of load line and input characteristic). When the ac signal is applied, the emitter current and voltage also change. If the signal is small, the operating point swings sinusoidally about Q point (A to B). Fig .3 If the ac signal is small, the points A and B are close to Q, and arc A B can be approximated by a straight line and diode appears to be a resistance given by If the input signal is small, input voltage and current will be sinusoidal but if the input voltage is large then current will no longer be sinusoidal because of the non linearity of diode curve. The emitter current is elongated on the positive half cycle and compressed on negative half cycle. Therefore the output will also be distorted. r'e is the ratio of ΔVBE and Δ IE and its value depends upon the location of Q. Higher up the Q point small will be the value of r' e because the same change in VBE produces large change in IE. The slope of the curve at Q determines the value of r'e. From calculation it can be proved that. In general, the current through a diode is given by Where q is he charge on electron, V is the drop across diode, T is the temperature and K is a constant. On differentiating w.r.t V, we get, The value of (q / KT) at 25°C is approximately 40. Therefore, or,       To a close approximation the small changes in collector current equal the small changes in emitter current. In the ac equivalent circuit, the current �iC' is shown upward because if �ie' increases, then �iC' also increases in the same direction. Voltage gain: Since the ac input voltage source is connected across r'e. Therefore, the ac emitter current is given by ie = Vin / r'e or,        Vin = ie r'e The output voltage is given by Vout = ic (RC || RL) Under open circuit condition vout = ic Rc

Fig. 4

Example-1

Find the voltage gain and output of the amplifier shown in fig. 4, if input voltage is 1.5mV.

Fig. 4

Solution:

The emitter dc current I E is given by

Therefore, emitter ac resistance =

or,           A_V= 56.6

and, V_out = 1.5 x 56.6 = 84.9 mV

Example-2

Repeat example-1 if ac source has resistance R s = 100 W .

Solution:

The ac equivalent circuit with ac source resistance is shown in fig. 5.

Fig. 5

The emitter ac current is given by

or,              

Therefore, voltage gain of the amplifier =

    

and,                       V_out = 1.5 x 8.71 =13.1 mV


Common Emitter Curves:

The common emitter configuration of BJT is shown in fig. 1.

Fig. 1

In C.E. configuration the emitter is made common to the input and output. It is also referred to as grounded emitter configuration. It is most commonly used configuration. In this, base current and output voltages are taken as impendent parameters and input voltage and output current as dependent parameters

V_BE = f₁ ( I_B, V_CE )
I_C = f₂( I_B, V_CE )

Input Characteristic:

The curve between I_B and V_BE for different values of V_CE are shown in fig. 2. Since the base emitter junction of a transistor is a diode, therefore the characteristic is similar to diode one. With higher values of V_CEBE is zero and I_B is also zero. collector gathers slightly more electrons and therefore base current reduces. Normally this effect is neglected. (Early effect). When collector is shorted with emitter then the input characteristic is the characteristic of a forward biased diode when V

Fig. 2

Lecture - 6: Bipolar Transistor

When the emitter diode is forward biased and collector diode is reverse biased as shown in fig. 4 then one expect large emitter current and small collector current but collector current is almost as large as emitter current.

Fig. 4

When emitter diodes forward biased and the applied voltage is more than 0.7 V (barrier potential) then larger number of majority carriers (electrons in n-type) diffuse across the junction.

Once the electrons are injected by the emitter enter into the base, they become minority carriers. These electrons do not have separate identities from those, which are thermally generated, in the base region itself. The base is made very thin and is very lightly doped. Because of this only few electrons traveling from the emitter to base region recombine with holes. This gives rise to recombination current. The rest of the electrons exist for more time. Since the collector diode is reverse biased, (n is connected to positive supply) therefore most of the electrons are pushed into collector layer. These collector elections can then flow into the external collector lead.

Thus, there is a steady stream of electrons leaving the negative source terminal and entering the emitter region. The V_EB forward bias forces these emitter electrons to enter the base region. The thin and lightly doped base gives almost all those electrons enough lifetime to diffuse into the depletion layer. The depletion layer field pushes a steady stream of electron into the collector region. These electrons leave the collector and flow into the positive terminal of the voltage source. In most transistor, more than 95% of the emitter injected electrons flow to the collector, less than 5% fall into base holes and flow out the external base lead. But the collector current is less than emitter current.

Relation between different currents in a transistor:

The total current flowing into the transistor must be equal to the total current flowing out of it. Hence, the emitter current I_E is equal to the sum of the collector (I_C ) and base current (I_B). That is,

I_E = I_C + I_B

The currents directions are positive directions. The total collector current I_C is made up of two components.

1. The fraction of emitter (electron) current which reaches the collector ( a_dc I_E )

2. The normal reverse leakage current I_CO

a_dc is known as large signal current gain or dc alpha. It is always positive. Since collector current is almost equal to the I_E therefore αdc I_E varies from 0.9 to 0.98. Usually, the reverse leakage current is very small compared to the total collector current.

NOTE: The forward bias on the emitter diode controls the number of free electrons infected into the base. The larger (V_BE) forward voltage, the greater the number of injected electrons. The reverse bias on the collector diode has little influence on the number of electrons that enter the collector. Increasing V_CB does not change the number of free electrons arriving at the collector junction layer.

The symbol of npn and pnp transistors are shown in fig. 5.

Fig. 5

Breakdown Voltages:

Since the two halves of a transistor are diodes, two much reverse voltage on either diode can cause breakdown. The breakdown voltage depends on the width of the depletion layer and the doping levels. Because of the heavy doping level, the emitter diode has a low breakdown voltage approximately 5 to 30 V. The collector diode is less heavily doped so its breakdown voltage is higher around 20 to 300 V. 0http://ecmagic.blogspot.com

Biploar transistor:www.ecmagic.blogspot.com

A transistor is basically a Si on Ge crystal containing three separate regions. It can be either NPN or PNP type fig. 1. The middle region is called the base and the outer two regions are called emitter and the collector. The outer layers although they are of same type but their functions cannot be changed. They have different physical and electrical properties. In most transistors, emitter is heavily doped. Its job is to emit or inject electrons into the base. These bases are lightly doped and very thin, it passes most of the emitter-injected electrons on to the collector. The doping level of collector is intermediate between the heavy doping of emitter and the light doping of the base. The collector is so named because it collects electrons from base. The collector is the largest of the three regions; it must dissipate more heat than the emitter or base. The transistor has two junctions. One between emitter and the base and other between the base and the collector. Because of this the transistor is similar to two diodes, one emitter diode and other collector base diode.

Fig .1

When transistor is made, the diffusion of free electrons across the junction produces two depletion layers. For each of these depletion layers, the barrier potential is 0.7 V for Si transistor and 0.3 V for Ge transistor.

The depletion layers do not have the same width, because different regions have different doping levels. The more heavily doped a region is, the greater the concentration of ions near the junction. This means the depletion layer penetrates more deeply into the base and slightly into emitter. Similarly, it penetration more into collector. The thickness of collector depletion layer is large while the base depletion layer is small as shown in fig. 2.

Fig. 2

If both the junctions are forward biased using two d.c sources, as shown in fig. 3a. free electrons (majority carriers) enter the emitter and collector of the transistor, joins at the base and come out of the base. Because both the diodes are forward biased, the emitter and collector currents are large.

Fig. 3a

Fig. 3b

If both the junction are reverse biased as shown in fig. 3b, then small currents flows through both junctions only due to thermally produced minority carriers and surface leakage. Thermally produced carriers are temperature dependent it approximately doubles for every 10 degree celsius rise in ambient temperature. The surface leakage current increases with voltage.

semiconducter diodes

Space charge capacitance C_T of diode:

Reverse bias causes majority carriers to move away from the junction, thereby creating more ions. Hence the thickness of depletion region increases. This region behaves as the dielectric material used for making capacitors. The p-type and n-type conducting on each side of dielectric act as the plate. The incremental capacitance C_T is defined by

Since

Therefore, (E-1)

where, dQ is the increase in charge caused by a change dV in voltage. C_T is not constant, it depends upon applied voltage, there fore it is defined as dQ / dV.

When p-n junction is forward biased, then also a capacitance is defined called diffusion capacitance C_D (rate of change of injected charge with voltage) to take into account the time delay in moving the charges across the junction by the diffusion process. It is considered as a fictitious element that allow us to predict time delay.

If the amount of charge to be moved across the junction is increased, the time delay is greater, it follows that diffusion capacitance varies directly with the magnitude of forward current.

(E-2)

Relationship between Diode Current and Diode Voltage

An exponential relationship exists between the carrier density and applied potential of diode junction as given in equation E-3. This exponential relationship of the current i_D and the voltage v_D holds over a range of at least seven orders of magnitudes of current - that is a factor of 10⁷.

(E-3)

Where,

i_D= Current through the diode (dependent variable in this expression)
v_D= Potential difference across the diode terminals (independent variable in this expression)
I_O= Reverse saturation current (of the order of 10^-15 A for small signal diodes, but I_O is a strong function of temperature)
q = Electron charge: 1.60 x 10^-19 joules/volt
k = Boltzmann's constant: 1.38 x l0^-23 joules /° K
T = Absolute temperature in degrees Kelvin (°K = 273 + temperature in °C)
n = Empirical scaling constant between 0.5 and 2, sometimes referred to as the Exponential Ideality Factor

The empirical constant, n, is a number that can vary according to the voltage and current levels. It depends on electron drift, diffusion, and carrier recombination in the depletion region. Among the quantities affecting the value of n are the diode manufacture, levels of doping and purity of materials. If n=1, the value of k T/ q is 26 mV at 25°C. When n=2, k T/ q becomes 52 mV.

For germanium diodes, n is usually considered to be close to 1. For silicon diodes, n is in the range of 1.3 to 1.6. n is assumed 1 for all junctions all throughout unless otherwise noted.

Equation (E-3) can be simplified by defining V_T =k T/q, yielding

(E-4)

At room temperature (25°C) with forward-bias voltage only the first term in the parentheses is dominant and the current is approximately given by

(E-5)

The current-voltage (l-V) characteristic of the diode, as defined by (E-3) is illustrated in fig. 1. The curve in the figure consists of two exponential curves. However, the exponent values are such that for voltages and currents experienced in practical circuits, the curve sections are close to being straight lines. For voltages less than V_ON, the curve is approximated by a straight line of slope close to zero. Since the slope is the conductance (i.e., i / v), the conductance is very small in this region, and the equivalent resistance is very high. For voltages above V_ON, the curve is approximated by a straight line with a very large slope. The conductance is therefore very large, and the diode has a very small equivalent resistance.

Fig.1 - Diode Voltage relationship

The slope of the curves of fig.1 changes as the current and voltage change since the l-V characteristic follows the exponential relationship of relationship of equation (E-4). Differentiate the equation (E-4) to find the slope at any arbitrary value of v_Dor i_D,

(E-6)

This slope is the equivalent conductance of the diode at the specified values of v_D or i_D.

We can approximate the slope as a linear function of the diode current. To eliminate the exponential function, we substitute equation (E-4) into the exponential of equation (E-7) to obtain

(E-7)

A realistic assumption is that I_O<< i_D equation (E-7) then yields,

(E-8)

The approximation applies if the diode is forward biased. The dynamic resistance is the reciprocal of this expression.

(E-9)

Although r_d is a function of i_d, we can approximate it as a constant if the variation of i_D is small. This corresponds to approximating the exponential function as a straight line within a specific operating range.

Normally, the term R_f to denote diode forward resistance. R_f is composed of r_d and the contact resistance. The contact resistance is a relatively small resistance composed of the resistance of the actual connection to the diode and the resistance of the semiconductor prior to the junction. The reverse-bias resistance is extremely large and is often approximated as infinity.

Temperature Effects:

Temperature plays an important role in determining the characteristic of diodes. As temperature increases, the turn-on voltage, v_ON, decreases. Alternatively, a decrease in temperature results in an increase in v_ON. This is illustrated in fig. 2, where V_ON varies linearly with temperature which is evidenced by the evenly spaced curves for increasing temperature in 25 °C increments.

The temperature relationship is described by equation

V_ON(T_New ) � V_ON(T_room) = k_T(T_New � T _room) (E-10)

Fig. 2 - Dependence of iD on temperature versus vD for real diode (kT = -2.0 mV /°C)

where,

T_room= room temperature, or 25°C.
T_New= new temperature of diode in °C.
V_ON(T_room ) = diode voltage at room temperature.
V_ON (T_New) = diode voltage at new temperature.
k_T = temperature coefficient in V/°C.

Although k_T varies with changing operating parameters, standard engineering practice permits approximation as a constant. Values of k_T for the various types of diodes at room temperature are given as follows:

k_T= -2.5 mV/°C for germanium diodes
k_T = -2.0 mV/°C for silicon diodes

The reverse saturation current, I_O also depends on temperature. At room temperature, it increases approximately 16% per °C for silicon and 10% per °C for germanium diodes. In other words, I_O approximately doubles for every 5 °C increase in temperature for silicon, and for every 7 °C for germanium. The expression for the reverse saturation current as a function of temperature can be approximated as

(E-11)

where K_i= 0.15/°C ( for silicon) and T1 and T2 are two arbitrary temperatures.

semi conductors

The symbol of diode is shown in fig. 4. The terminal connected to p-layer is called anode (A) and the terminal connected to n-layer is called cathode (K)

Fig.4

Reverse Bias:

If positive terminal of dc source is connected to cathode and negative terminal is connected to anode, the diode is called reverse biased as shown in fig. 5.

Fig.5

When the diode is reverse biased then the depletion region width increases, majority carriers move away from the junction and there is no flow of current due to majority carriers but there are thermally produced electron hole pair also. If these electrons and holes are generated in the vicinity of junction then there is a flow of current. The negative voltage applied to the diode will tend to attract the holes thus generated and repel the electrons. At the same time, the positive voltage will attract the electrons towards the battery and repel the holes. This will cause current to flow in the circuit. This current is usually very small (interms of micro amp to nano amp). Since this current is due to minority carriers and these number of minority carriers are fixed at a given temperature therefore, the current is almost constant known as reverse saturation current I_CO.

In actual diode, the current is not almost constant but increases slightly with voltage. This is due to surface leakage current. The surface of diode follows ohmic law (V=IR). The resistance under reverse bias condition is very high 100k to mega ohms. When the reverse voltage is increased, then at certain voltage, then breakdown to diode takes place and it conducts heavily. This is due to avalanche or zener breakdown. The characteristic of the diode is shown in fig. 6.

Fig.6

Forward bias:

When the diode is forward bias, then majority carriers are pushed towards junction, when they collide and recombination takes place. Number of majority carriers are fixed in semiconductor. Therefore as each electron is eliminated at the junction, a new electron must be introduced, this comes from battery. At the same time, one hole must be created in p-layer. This is formed by extracting one electron from p-layer. Therefore, there is a flow of carriers and thus flow of current.

A pure silicon crystal or germanium crystal is known as an intrinsic semiconductor. There are not enough free electrons and holes in an intrinsic semi-conductor to produce a usable current. The electrical action of these can be modified by doping means adding impurity atoms to a crystal to increase either the number of free holes or no of free electrons.

When a crystal has been doped, it is called a extrinsic semi-conductor. They are of two types

• n-type semiconductor having free electrons as majority carriers

• p-type semiconductor having free holes as majority carriers

By themselves, these doped materials are of little use. However, if a junction is made by joining p-type semiconductor to n-type semiconductor a useful device is produced known as diode. It will allow current to flow through it only in one direction. The unidirectional properties of a diode allow current flow when forward biased and disallow current flow when reversed biased. This is called rectification process and therefore it is also called rectifier.

How is it possible that by properly joining two semiconductors each of which, by itself, will freely conduct the current in any direct refuses to allow conduction in one direction. Consider first the condition of p-type and n-type germanium just prior to joining fig. 1. The majority and minority carriers are in constant motion. The minority carriers are thermally produced and they exist only for short time after which they recombine and neutralize each other. In the mean time, other minority carriers have been produced and this process goes on and on. The number of these electron hole pair that exist at any one time depends upon the temperature. The number of majority carriers is however, fixed depending on the number of impurity atoms available. While the electrons and holes are in motion but the atoms are fixed in place and do not move.

Fig.1

As soon as, the junction is formed, the following processes are initiated fig. 2.

Fig.2

Holes from the p-side diffuse into n-side where they recombine with free electrons. Free electrons from n-side diffuse into p-side where they recombine with free holes. The diffusion of electrons and holes is due to the fact that large no of electrons are concentrated in one area and large no of holes are concentrated in another area. When these electrons and holes begin to diffuse across the junction then they collide each other and negative charge in the electrons cancels the positive charge of the hole and both will lose their charges. The diffusion of holes and electrons is an electric current referred to as a recombination current. The recombination process decay exponentially with both time and distance from the junction. Thus most of the recombination occurs just after the junction is made and very near to junction. A measure of the rate of recombination is the lifetime defined as the time required for the density of carriers to decrease to 37% to the original concentration

The impurity atoms are fixed in their individual places. The atoms itself is a part of the crystal and so cannot move. When the electrons and hole meet, their individual charge is cancelled and this leaves the originating impurity atoms with a net charge, the atom that produced the electron now lack an electronic and so becomes charged positively, whereas the atoms that produced the hole now lacks a positive charge and becomes negative.

The electrically charged atoms are called ions since they are no longer neutral. These ions produce an electric field as shown in fig. 3. After several collisions occur, the electric field is great enough to repel rest of the majority carriers away of the junction. For example, an electron trying to diffuse from n to p side is repelled by the negative charge of the p-side. Thus diffusion process does not continue indefinitely but continues as long as the field is developed.

Fig.3

This region is produced immediately surrounding the junction that has no majority carriers. The majority carriers have been repelled away from the junction and junction is depleted from carriers. The junction is known as the barrier region or depletion region. The electric field represents a potential difference across the junction also called space charge potential or barrier potential . This potential is 0.7v for Si at 25^o celcious and 0.3v for Ge.

The physical width of the depletion region depends on the doping level. If very heavy doping is used, the depletion region is physically thin because diffusion charge need not travel far across the junction before recombination takes place (short life time). If doping is light, then depletion is more wide (long life time).