Common-Emitter Biasing Circuits – part – I

Common-emitter configuration is the most popular of the three transistor amplifier configurations because it offers considerable current gain as well as voltage gain.

Some of the commonly used common-emitter biasing circuits include the following

• Fixed bias circuit
• Emitter bias circuit
• Voltage-divider bias with emitter bias circuit
• Collector-to-base bias circuits

Figure below shows the fixed-bias circuit. It is one of the simplest possible transistor-biasing circuits. The biasing components for this circuit include two resistors, base resistor (R_B) and collector resistor (R_C), and a supply voltage (V_CC). Typical values of resistors R_B and R_C is of the order of few hundreds of kilo-ohms and few kilo-ohms respectively. Capacitors C_i and C_o are referred to as the input and the output coupling capacitors, respectively. The base–emitter junction gets forward-biased through supply voltage (V_CC) and R_B. The collector–base junction is reverse-biased through supply voltage (VC_C) and resistor R_C.

Fixed-bias circuit

Figure below shows the DC equivalent of a fixed-bias circuit.

DC equivalent of fixed-bias circuit

Applying Kirchhoff’s voltage law to the base–emitter section, we get

The value of base current (I_B) therefore is

As V_BE << V_CC, base current (I_B) can be approximated as

The collector current (I_C) of the transistor is given as

Where,
β is the transistor current gain.

Therefore,

Applying Kirchhoff”s voltage law to the collector–emitter section we get

Or

Hence, the quiescent point for a fixed-bias circuit is given by

If we superimpose the straight line defined by V_cc-l_B R_B-V_BE= 0 on the transistor output characteristics, we can determine the operating point of the circuit and also how the operating point changes with change in the value of circuit parameters. This is referred to as load-line analysis.

To draw the load line, substitute I_C = 0 in equation

We get

This point appears on the horizontal axis (0, V_CC) of the output characteristics

IC can be evaluated by substituting VCE = 0 in equation

We get

This point appears on the vertical axis (V_CC/R_C, 0) of the output characteristics.

The load line is obtained by joining these two points as shown in Figure below. The operating point is established on the load line by determining the level of base current (I_B). The point of intersection of the load line with the curve corresponding to the calculated value of IB gives the operating point as shown in the figure. The operating point shifts with the change in the value of circuit parameters.

Load-line analysis of the fixed-bias circuit

The operating point moves up the load line if the value of I_B increases and moves down the load line when the value of I_B decreases as shown in Figure below.

Variation of operating point with base current

With all other parameters held constant and the value of the collector resistor (R_Cis changed, then the load line shifts as shown in Figure below.

Variation of operating point with collector resistor

The variation of the load line and the operating point due to change in the supply voltage (V_CC) is illustrated in Figure below.

Variation of operating point with supply voltage

The advantage of a fixed-bias circuit is that it is the simplest possible biasing circuit requiring a very few components. However, it offers worst stability against variations in temperature or transistor gain (β) as compared to the other configurations. It is prone to thermal runaway and is very rarely used.

Emitter-bias configuration (also referred to as self-bias circuit) is the same as that of fixed-bias circuit except that it has an emitter resistor (R_E) between the transistor–emitter terminal and ground. Figure below shows the circuit diagram of an emitter-bias circuit.

Emitter-bias configuration

The addition of the resistor R_E introduces current-series negative feedback as a voltage proportional to the output current is fed-back into the input. This provides improved stabilization to the circuit.

. Figure below shows the DC equivalent of the emitter-bias configuration.

DC equivalent of the emitter–bias configuration

Applying Kirchhoff’s voltage law to the base–emitter loop we get

As I_E = (β + 1)I_B, the above equation can be simplified to give base current as given below

As Voltage V_BE is small as compared to V_CC, it can therefore be neglected. Therefore,

The value of the input resistance for the emitter-bias circuit is given by

Applying Kirchhoff’s voltage law to the collector–emitter loop, we get

Collector–emitter voltage (V_CE) is therefore expressed as

As the emitter current (I_E) is approximately equal to the collector current (I_C), therefore

The voltage of the emitter terminal of the transistor (V_E) is given by

The Q-point for the emitter-bias circuit is given by

The emitter-bias circuit offers stability against variations in collector current (due to change in temperature or change in the transistor gain (β)). When the collector current increases, the emitter voltage increases which in turn results in a decrease in the base–emitter potential. This further leads to a decrease in the value of base current and therefore, the collector current also decreases. This compensates for the initial increase in the value of collector current.

The load line for emitter-bias configuration is given by

Substituting I_C = 0 in above equation, we get

This point appears on the horizontal axis (0, V_CC) of the output characteristics.

Substituting V_CE = 0 in above equation, we obtain I_C as

This point appears on the vertical axis (V_CC/(R_C + R_E), 0) of the output characteristics.

The load line is obtained by joining these two points as shown in Figure below. The operating point is established on the load line by determining the level of I_B.

Load-line analysis of the emitter-bias circuit

The emitter-bias circuit offers better stability as compared to the fixed-bias circuit. However, maximum stability is offered by the circuit when the ratio R_B/R_E is as small as possible. Thus, R_E should have a large value or R_B should have a small value.

If the value of resistor R_E is large, larger collector supply voltage (V_CC) is required. In addition, increase in R_E increases the negative feedback and hence the gain of the circuit is reduced. For small values of resistor R_B, a separate base supply voltage is needed. This which adds to the circuit complexity.