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 Qpoint. When, for instance, a resistor is added to a circuit to make it more stable, the student should know the reason for the change.
Fixedbias Circuit
The circuit (also known as Basebias circuit) – see Figure 9.1 – is the most simple of all CommonEmitter circuits. It provides a straightforward introduction to the DC bias analysis of transistors. The Qpoint, however, is extremely betadependent. 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 9.1^{3}
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 I_{C} = βI_{B}, we get an equation for the emitter current as a function of the base current only.
  (9.4)

Finally, the collectortoemitter voltage is calculated from
  (9.5)

Because V_{E} = 0 V, we have,
and,
^{3}Notice that we are neglecting the leakage current, I_{CEO}. If this current is not neglected, the equation for I_{C}would 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: Fixedbias with emitter resistor circuit
The base and collector currents are found to be:
  (9.8)

and,
respectively,
The emitter current, I_{E}, can be found, as usual, with the help of the equation
The terminal voltages can be found as follows: The collector to ground voltage is given by,
the emitter voltage (from emitter to ground) is
and the base voltage can be determined from
or
Finally, the collectortoemitter voltage is given by
or
assuming that I_{E} ≈ I_{C}.
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,
If we use the approximation β ≈ β + 1, Equation 9.17 becomes
The collector current can be found from
or,
By dividing numerator and denominator of Eq. 9.20 by β, we get the following equation for I_{C}
The emitter current is given by
or, we could use the equivalent Equation 9.4,
The terminal voltages can be found using the transistor currents:
The collector voltage is given by
and the base voltage is determined from
  (9.26)

The transistor voltage V_{CE} is determined using Equations 9.25 and 9.24^{4}
(Notice that in the above equation we made use of the approximation I_{C} ≈ I_{E})
It should be clear that if we can make R_{E} » R_{B}/β_{DC}, then Equation 9.21 becomes
and
This condition makes the Qpoint current, I_{C}, independent of β.
^{4} Remember that V_{CE} = V_{C} – V_{E}
CommonEmitter Voltage Divider
An improvement visàvis stability with respect to changes in the value of β is provided by the addition of a second resistor in the input of the commonemitter 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, V_{TH}, and the equivalent input resistance, R_{TH}^{5} These two parameters are given by the following equations:
and
or, in equation form,
With these two values defined, the important currents and voltages can be found.
The base current is given by
The collector and emitter currents are both a function of I_{B},
and
or,
The terminal voltages are calculated as follows:
and
The Qpoint transistor voltage, V_{CE} is found by the following equation:
Finally, the two input currents – I_{1} and I_{2} – are calculated from:
and
or,
^{5} These are called the Thevènin voltage, V_{TH}, as seen from the base of the circuit, and the Thevènin resistance, R_{TH}.CollectorFeedback 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:
and
or,
Figure 9.5: Collectorfeedback Circuit
The collector voltage, V_{C}, the emitter voltage V_{E}, and the base voltage, V_{B}, are calculated using the standard equations given by:
and,
The Qpoint transistor voltage is calculated from
In some applications of the feedback circuit the emitter resistor, R_{E}, is not needed. In this case the equations presented in this section are still valid, if you replace R_{E} = 0
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