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Electronics I Laboratory Manual

# BJT Bias I

The following sections will present some important BJT bias circuits.  The student should pay special attention to the changes that are made to the circuits as we go along in order to stabilize the Q-point.  When, for instance, a resistor is added to a circuit to make it more stable, the student should know the reason for the change.

Fixed-bias Circuit

The circuit (also known as Base-bias circuit) – see Figure 9.1 – is the most simple of all Common-Emitter circuits.  It provides a straightforward introduction to the DC bias analysis of transistors.  The Q-point, however, is extremely beta-dependent.  Because of this, this circuit has limited applicability.  The DC bias equations are as follows:

The base current is given by,

 (9.1)

The collector current can be calculated with the transistor equation by using Equation 9.13

 (9.2)

Also, the emitter current can be found by using the standard transistor equation

 (9.3)

By substituting the collector current in the last equation by IC  = βIB, we get an equation for the emitter current as a function of the base current only.

 (9.4)

Finally, the collector-to-emitter voltage is calculated from

 (9.5)

Because VE = 0 V, we have,

 VC = VCE (9.6)

and,

 VB = VBE (9.7)

3Notice that we are neglecting the leakage current, ICEO.  If this current is not neglected, the equation for ICwould be:

Base Bias with Emitter Resistor

To improve stability of the Base Bias circuit shown in Figure 9.1 a resistor is added to the emitter of the transistor as is shown in Figure 9.2

Figure 9.2:  Fixed-bias with emitter resistor circuit

The base and collector currents are found to be:

 (9.8)

and,

 (9.9)

respectively,

The emitter current, IE, can be found, as usual, with the help of the equation

 (9.10)

The terminal voltages can be found as follows:  The collector to ground voltage is given by,

 (9.11)

the emitter voltage (from emitter to ground) is

 (9.12)

and the base voltage can be determined from

 (9.13)

or

 (9.14)

Finally, the collector-to-emitter voltage is given by

 (9.15)

or

 (9.16)

assuming that IE ≈ IC.

Emitter Bias

This circuit, shown in Figure 9.3, requires two separate power supplies, one connected.

This arrangement provides more stability than the other two circuits presented.
The equations for the currents and voltages are given by,

 (9.17)

If we use the approximation ββ + 1, Equation 9.17 becomes

 (9.18)

The collector current can be found from

 (9.19)

or,

 (9.20)

By dividing numerator and denominator of Eq. 9.20 by β, we get the following equation for IC

 (9.21)

The emitter current is given by

 (9.22)

or, we could use the equivalent Equation 9.4,

 (9.23)

The terminal voltages can be found using the transistor currents:

 (9.24)

The collector voltage is given by

 (9.25)

and the base voltage is determined from

 (9.26)

The transistor voltage VCE is determined using Equations 9.25 and 9.244

 (9.27)

(Notice that in the above equation we made use of the approximation IC ≈ IE)

It should be clear that if we can make RE » RBDC, then Equation 9.21 becomes

 (9.28)

and

 (9.29)

This condition makes the Q-point current, IC, independent of β.

4 Remember that VCE = VC VE

Common-Emitter Voltage Divider

An improvement vis-à-vis stability with respect to changes in the value of β is provided by the addition of a second resistor in the input of the common-emitter circuit of Section 9.4.2 on page 85.

This circuit is shown in Figure 9.4.  The equations for the calculation of the currents and the voltages are presented here.

Two important parameters needed for the calculations are the base voltage, VTH, and the equivalent input resistance, RTH5 These two parameters are given by the following equations:

 (9.30)

and

 (9.31)

or, in equation form,

 (9.32)

With these two values defined, the important currents and voltages can be found.

The base current is given by

 (9.33)

The collector and emitter currents are both a function of IB,

 (9.34)

and

 (9.35)

or,

 (9.36)

The terminal voltages are calculated as follows:

 (9.37)

 (9.38)

and

 (9.39)

The Q-point transistor voltage, VCE is found by the following equation:

 (9.40)

Finally, the two input currents – I1 and I2 – are calculated from:

 (9.41)

and

 (9.42)

or,

 (9.43)

5 These are called the Thevènin voltage, VTH, as seen from the base of the circuit, and the Thevènin resistance, RTH.

Collector-Feedback Bias

Another way to improve stability is by introducing a feedback path from collector to base as shown in the feedbackcircuit of Figure 9.5.

The current and voltage equations are as follows:

 (9.44)

 (9.45)

and

 (9.46)

or,

Figure 9.5:  Collector-feedback Circuit

 (9.47)

The collector voltage, VC, the emitter voltage VE, and the base voltage, VB, are calculated using the standard equations given by:

 (9.48)

 (9.49)

and,

 (9.50)

The Q-point transistor voltage is calculated from

 (9.51)

 Note:

In some applications of the feedback circuit the emitter resistor, RE, is not needed.  In this case the equations presented in this section are still valid, if you replace RE = 0