What are the methods of transistor biasing? – What is transistor biasing

2.  Proper minimum base-emitter voltage (V_BE)

The value of potential barrier is 0.7 volt for silicon and once the potential barrier overcome the base current and hence collector current increases sharply.

If base emitter voltage V_BE falls below these values during any part of the signal, that part will be amplified two lesser extent due to small collector current. This will result in unfaithful amplification.

3.  Proper minimum collector emitter voltage (V_CE)

For faithful amplification V_CE should not fall below 0.5 volt germanium transistor and 1 volt for silicon transistor. When V_CE is too low the collector base junction is not properly reverse biased. So this decreases the collector current (I_C) while base current (I_B) increases. Hence the value of β falls.

And result on faithful amplification the transistor biasing can achieve with a bias battery or associating a circuit with a transistor.

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What is meant by transistor biasing? 

The proper flow of zero signal collector current and maintenance of proper collector emitter voltage (V_CE) during the passage of signal is known as transistor biasing.

It has already been discussed that for faithful amplification, a transistor amplifier must satisfy three basic conditions, namely : (1) Proper zero signal collector current, (2) proper base-emitter voltage at any instant and (3) proper collector emitter voltage at any instant. It is the fulfilment of these conditions that is known as transistor biasing.

The basic purpose of transistor biasing is to keep the base emitter junction properly forward biased and the collector base junction reverse biased during signal application.

This can be achieved by connecting a circuit with a bias battery or a transistor. The latter method is more efficient and is frequently employed.

The circuit which provides transistor biasing is known as biasing circuit. It may be noted that transistor biasing is very essential for proper operation of transistors in any circuit.

Need for transistor biasing

The biasing network connected to the transistor must meet the following requirements : 

1. It should ensure proper zero signal collector current I_C. 
2. It must be ensured that V_CE is not less than 1 volt for silicon and 0.5 volt for germanium transistor at any time.
3. It should ensure stabilisation of the operating point.

What is stabilisation?

The process of making the operating point independent of temperature changes or variations in transistor parameters is known as stabilisation.

The collector current in a transistor changes rapidly when

1.  Temperature changes
2.  Transistor is replaced by another of the same type. This is due to inherent variations of transistor parameters.

When the temperature changes or the transistor is replace, the operating point ( zero signal I_C and V_CE ) also changes. 

Once stabilisation is achieved, the zero signal I_C and V_CE become independent of temperature variation or replacement of transistor that is the operating point is fixed. A good biasing circuit always ensures stabilisation of operating point.

Need for stabilization

Stabilisation of an operating point which is necessary due to the

1.  Temperature dependence of I_C
2.  Individual variation
3.  Thermal runaway

1.  Temperature dependence of I_C

The expression for collector current I_C is

I_C = βI_B + (β + 1) I_CBO

The collector leakage current I_CBO is greatly affected by temperature variations. Hence to come out of this, the biasing condition is set so that the zero signal collector current I_C = 1 mA. Therefore, there is a need to stabilize the operating point i.e. to keep the I_C stable.

2.  Individual variation

Since the value of β and value of V_BE are not the same for each transistor, so there is a tendency to change the operating point whenever one transistor is change. Therefore it is necessary to stabilize the operating point.

3.  Thermal runaway

The flow of collector current generates heat inside the transistor. This increases the temperature of transistor and if no stabilisation is done, the collector leakage current I_CBO also increases as it is highly temperature dependent.

The increased I_CBO increases I_C by (β + 1) I_CBO. This increased I_C will further increase the temperature of transistor which in turn will increase I_CBO.

This effect is cumulative and within a few seconds, I_C may increase to a large value causing to burn out transistor. This self destruction of an unstable transistor due to overheating is called thermal runway.

What is stability factor

The rate of change of the collector current I_C at constant β and I_B with respect to the collector leakage current I_CO  is called stability factor. The stability factor is denoted by S.

It is necessary to keep I_C constant in the face of variations of I_CBO (sometimes represented as I_CO). The extent to which a biasing circuit is successful in achieving this goal is measured by stability factor S. 

The stability factor indicates the change in I_C due to the change in I_CO. To achieve grater thermal stability, it is desirable to have a stability factor as low as possible. Ideal value of S is 1. But in practice it is never possible to achieve it.

So now we will see the general expression of stability factor for CE configuration can be obtain as follows :

I_C = β I_B + (β+1) I_CO

Differentiating the above expression with respect to I_C ,  so we get

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What are the methods of transistor biasing?

Biasing in the transistor amplifier circuits drawn so far was done with the help of a battery V_BB which is separate from the battery V_CC used in the output circuit.

However, in the interest of simplicity and economy, it is desirable that transistor circuit should have a single source of supply-the one in the output circuit (that is  V_CC).

The most commonly used methods for achieving transistor biasing from a single source of supply (that is V_CC) are the following :

1.  Base resistor method
2.  Emitter bias method
3.  Biasing with collector-feedback resistor
4.  Voltage – divider method

1.  Base resistor method 

In this method, a high resistance R_B is connected between the base and the positive end of supply. Here, the required zero signal base current is provided by V_CC and it flows through R_B.

It is required to find the value of R_B so that required collector current ( I_C ) flows in the zero signal conditions. Let I_C be the required zero signal collector current. Then, base current I_B = I_C / β.

Considering the path ABENA, and applying KVL (Kirchhoff’s voltage low), we get,

V_CC = I_B R_B + V_BE 

I_B R_B = V_CC − V_BE

R_B = ( V_CC − V_BE ) / I_B

Since V_BE is generally quit small as compared to V_CC ,

R_B = V_CC/ I_B 

Stability factor 

In this biasing I_B is independent of I_C so that  dI_B / dI_C =0. Putting the value of dI_B / dI_C =0 in the above expression , we get ,

Stability factor, S = β + 1

This means I_C changes (β + 1) times as much as any change in I_CO. Due to a large value of S the base resistor method it has pour thermal stability.

Advantages base resistor method

• This bias circuit is very simple as only one resistance are be is require.
• Biasing condition can easily be set and the calculation are simple.

Disadvantages of base resistor method

• This method provides poor stabilization.
• Because of thus stability factor is very high their are strong chances of thermal runaway.

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2.  Emitter bias method 

This circuit differs from the base-bias circuit in two important respects.

First of all, it uses two separate DC voltage sources, one positive (+ V_CC) and the other is negative (− V_EE). Normally, the two supply voltages will be equal. For example, if V_CC = + 20 V (D. C.), then V_EE = − 20V (D. C.).

Secondly, there is a resistor R_E in the emitter circuit.

We will first redraw the circuit in Figure-1 as it usually appears in schematic diagrams. This means removing the battery symbols as shown in Figure-2. All the information on the diagram is still there ( see figure-2 ) except that it is in condensed form.

This is a negative supply voltage − V_EE apply to the bottom of R_E and a positive voltage of + V_CC apply to the top of R_C.

Circuit analysis of Emitter Bias

You can see the emitter bias circuit in Figure-2. We will find the Q-point values (that is DC I_C and DC V_CE ) for this circuit.

1.  Collector current (I_C) 

Applying KVL (Kirchhoff’s voltage low) to the base-emitter circuit in Figure-2, we have,

− I_B R_B − V_BE − I_E R_E + V_EE = 0

Therefore,  V_EE = I_B R_B + V_BE + I_E R_E

Now,  I_C ≃ I_E and I_C = βI_B

Therefore,  I_B ≃ I_E / β

Putting I_B = I_E / β in the above equation, we have,

V_EE = ( I_E / β ) R_B + I_E R_E + V_BE

V_EE − V_BE = I_E ( R_B / β + R_E )

Since,  I_C ≃ I_E  we have, 

2.  Collector emitter voltage (V_CE) 

By applying KVL (Kirchhoff’s voltage low) to the collector side of the emitter bias circuit in Figure-2 we have,

V_CC − I_C R_C − V_CE − I_C R_E + V_EE = 0

V_CE  = V_CC  + V_EE − I_C ( R_C + R_E )

Stability factor for emitter bias

The collector current for an emitter bias circuit is given by the expression for I_C

It is clear that I_C is dependent on V_BE and β, both of which change with temperature.

If R_E >> R_B / β, then the expression for I_C becomes ,

I_C = (V_EE − V_BE ) / R_E

This condition makes I_C (≃ I_E ) independent of β.

If V_EE >> V_BE, then I_C becomes ,

I_C (≃ I_E ) = V_EE / R_E

This condition makes I_C ( ≃ I_E  ) independent of V_BE.

IF I_C (≃ I_E ) is independent of β and V_{BE ,} then the Q-point is not significantly affected by variation in these parameters. Thus emitter bias can provide a stable Q-point if properly designed. 

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3.  Biasing with collector feedback resistor

In this method one end of R_B is connected to the base and the other end is connected to the collector. Here V_CB  forward bias the base emitter junction and hence base current I_B flows through R_B. The required value of I_B required to give zero signal collector current I_C can be determined as follows. 

V_CC = I_C R_C + I_B R_B + V_BE

I_B R_B = V_CC − V_BE − I_C R_C

R_B = ( V_CC − V_BE − I_C R_C ) / I_B

Because , I_C = β I_B

Alternatively,  V_CE = V_BE + V_CB

V_CB = V_CE − V_BE

R_B = V_CB / I_B = ( V_CE − V_BE ) / I_B

Where, I_B = I_C / β

Here the stability factor S is less than β + 1. Therefore this method provides better thermal stability than fixed bias.

Advantages 

• It is a simple method as it requires less resistors. 
• The circuit provides some stabilization of the operating point.

Disadvantages

• The circuit does not provide good stabilization, therefore the operating point may change.
• The circuit provide negative feedback which reduces the gain of the amplifier.

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4.  Voltage divider bias method

This is the most widely use method of providing biasing and stabilisation to transistors. In this method, two resistance R₁ and R₂ are connected to the supply voltage V_CC and provide biasing.

The emitter resistance R_E provides stabilisation. The name “voltage divider” comes from the voltage divider formed by R₁ and R₂. The voltage drop across R₂ forward biases the base-emitter junction. This causes base current and hence collector current to flow in zero signal conditions.

Circuit analysis of voltage divider bias

Suppose the current flowing through resistance R₁ is I₁. Since the base current I_B is very small, so it can be assumed that current flowing through R₂ is also I₁.

1.  Collector current I_C

I₁ = V_CC / ( R₁ + R₂ )

Voltage across resistance R₂ is 

Applying KVL (Kirchhoff’s voltage low) to base circuit

V₂ = V_BE + V_E

= V_BE + I_E R_E

I_E = ( V₂ − V_BE ) / R_E

Since, I_E ≃ I_C

I_C = (V₂ − V_BE ) / R_E

From the above expression it is clear that I_C does not depend upon β. Although I_C depends on V_BE but practically V₂ is very much grater than V_BE  so I_C is practically independent of V_BE.

Hence in this circuit I_C is almost independent of transistor parameters and hence good stabilisation is ensure.

2.  Collector-emitter voltage ( V_CE )

Applying KVL (Kirchhoff’s voltage low) to the collector side , 

V_CC = I_C R_C + V_CE + I_E R_E

= I_C R_C + V_CE + I_C R_E            (Because I_E≃ I_C )

= I_C ( R_C + R_E ) + V_CE

Therefore,  V_CE = V_CC − I_C ( R_C + R_E )

Stabilisation 

In this circuit, excellent stabilisation is provided by R_E. 

V₂ = V_BE + I_C R_E

Suppose collector current I_C increase due to rise in temperature. This will increase the voltage drop across emitter resistance R_E. Since voltage drop across R₂ is independent of I_C , therefore, V_BE decreases.

And this in turn cause I_B to decrease. So the decreased value of I_B restores I_C to the original value.

Stability factor

It can be shown mathematically the stability factor of the circuit is

Where,  R₀ = ( R₁ R₂ ) / ( R₁ + R₂ )

If ratio R₀ / R_E is very small, then R₀ / R_E can be neglected as compared to 1 and the stability factor becomes   

The stability factor in this circuit nearly equal to 1 in actual practice the circuit may have stability factor around 10. Thus smallest possible value of S and leads to the maximum possible thermal stability.

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