Bipolar Junction Transistors-Characteristics and Biasing

Bipolar Junction Transistors

Three-terminal devices are far more useful than two-terminal ones, such as diodes studied earlier in chatper-1, because they can be used in a multitude of applications, ranging from signal amplification to designing of digital logic and memory circuits. The basic principle involved is the use of the voltage between two terminals to control the current flowing in the third terminal. In this way, a three terminal device can be used to realize controlled source, which is the basic for amplifier design. Also, in extreme, the control signal can be used to cause current in third terminal to change from zero to a large value, thus allowing the device to act as a switch.

The transistor consists of two pn-junctions, the emitter emitter-base junction (EBJ) and the collector the collector-base junction (CBJ). Depending on the bias condition (forward or reverse) of each of these junctions, different modes of operation of BJT are obtained, as shown in Table.

S. No.	Mode	EBJ	CBJ	Properties	Applications
1.	Cut-off	Reverse bias	Reverse bias	Very high internal resistance	OFF switch
2.	Active	Forward bias	Reverse Bias	Excellent transistor action	Amplifier
3.	Saturation	Forward bias	Forward bias	Very low internal resistance	ON switch
4.	Reverse active	Reverse bias	Forward bias	Very poor transistor action	Attenuator (Practically not used)

Table : BJT Modes of Operation

• Mode refers to the way how two junctions of BJT are biased.
• As we will see shortly, charge carriers of both polarities—that is, electrons and holes—participate in the current conduction process in a bipolar transistor, which is the reason for naming it bipolar bipolar.

Device Structure

The bipolar transistor has three separately doped regions and two p-n junctions. Figure shows the basic structure of an npn bipolar transistor and pnp bipolar transistor, along with the circuit symbols. The three terminal connections are called the emitter emitter, base and collector collector. The width of the base region is small compared to the minority carrier diffusion length. Generally the sequence of length of the three regions are W_B < W_E < W_C.

Note:

An important point to note from the devices shown in figure is that bipolar transistor is not a symmetrical device. Although the transistor may contain two n-regions or two p-regions, the impurity doping concentrations in the emitter and collector are different and the geometry of these regions can be vastly different.

There are few specific features that differentiate one region from the other region. That are

Emitter Region

• A region which supplies or emits majority carriers, for example in pnp transistor emitter will supply holes and in npn transistor it supplies electrons.
• Emitter is heavily doped, so that it can emit large number of carriers.
• Impurities are added in the ratio 1 : 10³.

Collector Region

• A region which receives or collects majority carriers coming from emitter.
• It is moderately doped and largest in size.
• Large collector will help in rapid transfer of heat to the surroundings.
• In a transistor collector junction develops large amount of heat because it operates at higher current and higher voltage.
• If collector is lightly doped it’s conductivity will decrease, which is undesired.
• If collector is heavily doped breakdown voltage of collector junction will decrease which is also undesired. Therefore collector is moderately doped so that it has better conductivity and collector junction has higher breakdown voltage.

Base Region

• A region through which majority carriers travel from emitter to collector.
• Base is lightly doped and small in size, i.e. it has narrow width (10–6 m).
• The number of electron-hole recombination inside base will be reduced by keeping it narrow in width and by doping it lightly.
• Impurities are added in ratio 1 : 10⁸.

Early Effect

When BJT is biased in active region the emitter junction (J_E) is forward-biased but the collector junction is reverse-biased, then in figure the barrier width at J_E is negligible as compared to space charge width W at J_C.
The transition region at junction is a region of uncovered charges on both sides of junction at positions occupied by impurity atoms. As the voltage applied across the junction increases, transition region penetrates deeper into collector and base. As neutrality of charges must be maintained, so the number of uncovered charges on each side remains equal. Since the doping in base is substantially smaller than that of collector, the penetration of the transition region into the base is much larger than that in collector. Hence the collector depletion region is neglected in figure, and all immobile charges are indicated in base region.

If metallurgical base width is WB, then the effective electrical base width is . W’_B = W_B – W. This modulation of effective base width by reverse bias V_CB is known as the Early effect Early effect or Base width modulation.

Consequences of Early Effect

The decrease in W’_B with increase in reverse collector voltage has three consequences.

1. When |V_CB| is increased the effective base width of transistor decreases so there are less chances of recombination of charge carriers within the base region. As a result α increases with increasing |V_CB|.

2. With decrease in base width the concentration gradient of minority carriers is increased within the base. As we have,
where W’_B is effective basewidth.

consequently I_E also increases. Hence we see that I_E increases due to increase in gradient of concentration of holes.
Also in BJT, voltage applied across one junction has effect on current passing through other junction therefore junctions J_E and J_C are called interactive junctions.

3. At large value of |V_CB| depletion region can fully occupy the base region or in other words for extremely large voltages, W’_B may be reduced to zero. This phenomenon is known as punch through or reach through.

When punch-through occurs effective base width becomes zero and collector region gets electrically shorted to emitter. Due to this shorting, the negative voltage applied at collector reaches emitter also. This results in heavy current flow which can damage the transistor.

Instability in Collector Current

In the preceding section we have seen that for faithful reproduction of the input signal we need a stable Q-point. In other words we can say that dc collector current should be fixed in a particular circuit. But as we know that collector current can be given by the following equation:

I_C = βI_V + (1 + β)I_CO

I_C can be unstable due to following reasons.

1. Variations in I_CO :
I_CO is reverse saturation current of collector junction. It increases with increase in temperature due to increase in the concentration of minority carriers

If temperature increases by 1°C then I_CO increases by 7%
For each 10°C rise in temperature I_CO doubles.

Hence we see that variation in temperature causes change in I_CO and as a result I_C also varies.

2. Variations in V_BE:
V_BE is forward voltage of emitter junction. When temperature increases by 1°C, V_BE decreases by 2.5 mV.

Hence changes in temperature create change in V_BE due to which base current (I_B) changes. Hence, from above equation we conclude that collector current I_C also varies.

3. Variations in β:
β varies either due to transistor replacement or due to variations in temperature.
(a) When a transistor is replaced with another transistor, β value will vary because it is practically difficult to find two transistors having exactly equal β.
(b) For a given transistor β also increases with increase in temperature.

• Hence from above discussion we conclude that I_c is unstable due to variations in I_co, β, and V_BE i.e.

I_c = f(I_co, V_BE, β)

“The above equation is read as I_c is a function of I_co, β and V_BE.”

By using partial differentiation, we have

where S, S′ and S″ are the stability factors.

From above equation we conclude that for greater stability in I_c, ∆I_c should be smaller which is possible when stability factors are smaller.

Instability in I_c has two undesired effects:

(a) Operating point will drift or vary along the load line which may result in distorted output and in worst case operating point may move into saturation or cut-off region.

(b) Thermal runaway may occur which damages a BJT.

Hence collector current (I_c) should be made stable with either stabilization or compensation methods.

Calculation of Stability Factor (S)

Stability factor (S) is rate of change of I_c with respect to reverse saturation current I_co,

Differentiating above equation with respect to I_c assuming β and V_BE are constant

BJT Biasing

Biasing refers to providing appropriate DC voltages and DC currents to an electronic device to operate it in a desired way. Biasing of BJT is done for following purposes:

(i)To operate the BJT in active region so that it can be used as an amplifier.
(ii) To maintain I_c stable so that operating point does not drift and thermal runaway cannot take place.
Commonly used biasing circuits are:
(i) Fixed bias circuit.
(ii) Collector to base bias circuit.
(iii) Self bias circuit.

Fixed Bias Circuit

In figure below, the base current is derived from supply voltage V_cc by resistor R_B. This type of biasing is called fixed bias as V_cc and R_B are fixed quantities.

Collector to Base Bias Circuit

An improvement in bias stability is obtained if tapping for bias is taken from the collector terminal instead of from the collector supply point as shown in figure.

Stability Factor

To calculate stability factor, differentiating equation (3.11) with respect to I_C ; we have

∂I_B/∂I_C= -R_C/R_B + R_C

Putting above value in equation (3.7), we have

Advantage

Here stability factor is smaller than (β + 1), hence an improvement in stability is obtained over fixed bias circuit.

Disadvantage

• Stability factor depends upon R_C. If R_C becomes smaller or zero then stability factor becomes very large and I_C does not remain stable.
• Resistance R_B connected from collector to base causes negative feedback due to which voltage gain of the amplifier circuit decreases.

Self-Bias, Emitter Bias, or Voltage-Divider Bias

If the collector resistance R_C is very small, for example, in a transformer-coupled circuit, then from equation (3.14)
we see that there is no improvement in stabilization in collector-to-base bias circuit over the fixed-bias circuit. A circuit which can be used even if there is zero D_C resistance in series with the collector terminal is self-biasing configuration of Figure (a). The current in resistance R_e in emitter lead causes a voltage drop which is in direction of reverse-biasing the emitter junction. Since this junction must be forward-biased, the base voltage is obtained from supply through R₁, R₂ network. Note that if R_b= R₁ || R₂ → 0, then base to ground voltage V_BN is independent of I_CO. Under these circumstances we may verify that S = ∂I_C/∂I_CO   → 1
For best stability R₁ and R₂ must be kept as small as possible.         

By using equations (3.18) and (3.19) we can easily calculate operating point for self-bias circuit.

Stability Factor

To calculate stability factor, differentiate equation (3.17) with respect to I_C

• Note that S varies between 1 for small R_b/R_e and 1 + β for R_b/R_e → ∞.
• Smaller the value of R_b, better is stabilization. Note that even if R_b approaches zero, the value of S can not be reduced below unity. Hence I_c always increases more than I_co.
• As R_b is reduced while Q-point is held fixed, the current drawn in R₁, R₂ network from supply VCC increases.
• Also, if R_e is increased while R_b is held constant, then to operate at the same quiescent current, the magnitude of V_CC must be increased.
• In either case a loss of power (decreased efficiency) is disadvantage which accompanies the improvement in stability.
• In order to avoid the loses of AC (signal) gain because of feedback caused by R_e, this resistance is often bypassed by a large capacitance (> 10 µF), so that its reactance at frequencies under consideration is very small.

Thermal Runaway

The maximum average power P_D(max) which a transistor can dissipate depends upon the transistor consideration and may lie in the range from a few milliwatts to 200 W. The maximum power is limited by the temperature that collector-to-base junction can withstand. The junction temperature may rise either due to rise in ambient temperature or due to self-heating. The maximum power dissipation is usually specified for transistor enclosure (case) of ambient temperature of 25°C. The problem of self-heating results from the power dissipated at collector junction. As a consequence of junction power dissipation, the junction temperature rises, and this in turn increases the collector current, with a subsequent increase in power dissipation. If this phenomenon, referred to thermal runaway, continues, it may result in permanent damage to the transistor.

Thermal Resistance

It is found experimentally that the steady-state temperature rise at collector junction is proportional to the power dissipated at the junction, or

∆T = T_J – T_A = θP_D

where T_J and T_A are the junction and ambient temperature, respectively, in degrees centigrade, and P_D is the power in watts dissipated at collector junction. The constant of proportionality θ is called the thermal resistance.

• The value of thermal resistance depends on the size of transistor, on convection or radiation to the surroundings, on forced-air cooling (if used), and on the thermal connection of the device to metal chassis or to heat sink.
• Typical values for various transistor designs vary from 0.2°C/W for a high-power transistor with an efficient heat sink to 1000°C/W for a low-power transistor in free air.

Power Derating Curve for BJT

The maximum collector power P_C allowed for safe operation is specified at 25°C. For ambient temperature above
this value, P_C must be decreased and at the extreme temperature at which the transistor may operate, P_C is reduced to zero. A typical power-temperature derating curve, supplied in manufacturer’s specification sheet, is indicated in figure below.

The Condition for Thermal Stability

We now obtain the restrictions to be met if thermal runaway is to be avoided. The required condition is that the rate at which heat is released at collector junction must not exceed the rate at which heat can be dissipated ; that is,

Equation (3.30) gives the condition to avoid thermal runaway.

BJT Biasing in Integrated Circuits (ICs)

Self-bias circuit is preferred to bias BJT in amplifiers which are formed on PCB.
Self bias circuits can not be used to bias BJT in IC amplifiers because R₁ are R₂ are large resistances and they require greater area of silicon chip.
The chip area required to fabricate a resistor is proportional to the value of resistance.
To fabricate higher resistance large chip area is required ; therefore BJT is biased in IC amplifiers using special circuits known as current mirror.

Constant Current Source (Basic Current Mirror)

A constant current source makes use of the fact that for a transistor in active mode of operation, the collector current is relatively independent of collector voltage. In basic circuit shown in figure below transistors Q₁ and Q₂ are matched as the circuit is fabricated using IC technology. It may be noted that bases and emitters of Q₁ and Q₂ are tied together and thus have the same V_BE. In addition, transistor Q1 is connected as a diode by shorting its collector to base.

The input current I_ref flows through diode connected transistor Q₁ and thus establishes a voltage across Q₁. This voltage in turn appears between the base and emitter of Q₂. Since Q₂ is identical to Q₁, the emitter current of Q₂ will be equal to emitter current of Q₁ which is approximately equal to I_ref.
Thus, we can say that as long as Q₂ is maintained in active region, its collector current I_C2 = I_O will be approximately equal to I_ref. Since the output current Io is reflection or mirror of the reference current I_ref, the circuit is often referred to as current mirror.
This mirror effect is however, valid only for large values of β. To study the effect of β on the operation of the current mirror circuit, we analyze it further.

Analysis

The collector currents I_C1 and I_C2 for transistors Q₁ and Q₂ can be approximately expressed as

From equation (3.36), for β >> 1, β/(β + 2) is almost unity and the output current I_O is equal to the reference current, I_ref which for a given R₁ is constant. Typical I_O varies by about 3% for 50 ≤ β ≤ 200.

Widlar Current Source

The basic current mirror has a limitation. Whenever, we need low value current source, the value of the resistance R1 required is sufficiently high and can not be fabricated economically in I_C circuits. The figure below shows Widlar current source which is particularly suitable for low value of currents. The circuit differs from basic current mirror only in the resistance R_E that is included in the emitter lead of Q₂. It can be seen that due to R_E, the base-emitter voltage V_BE2 is less than V_BE1 and consequently current Io is smaller than I_C1

The ratio of collector currents IC1  and IC2 using equation (3.31) and (3.32) is given by

Current Repeaters

The basic current mirror of can be used to source current to more than one load. Such a circuit is called current repeater and is shown in figure below. If all the transistors are identical, then the current I_C = I_C1⋅⋅⋅ ⋅⋅⋅ = I_CN ≅ Iref.

Note:

It is possible to achieve different values of I_C1, I_C2,….I_CN by scaling the emitter area of transistor Q₁, Q₂, … … Q_N. The same can also be achieved by using emitter resistance as in the Widlar current source.

Wilson Current Source

The Wilson current source shown in figure below provides an output current I_O, which is nearly equal to I_ref and also exhibits a very high output resistance.

Analysis

substantially greater than simple current mirror or Widlar current mirror.

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