Fixed bias circuit is the simplest biasing circuit for BJT. If an equation can be obtained for it's stability factor, we can easily comment about it's stability. Let's begin..
The simplest biasing circuit but has least stability.
In an amplifier circuit, Ic and VCE together define operating point for BJT. Equations for Ic and VCE are as follows.
-------(3)
------(4)
Stability in fixed bias:
. ------(6)
This equation gives a very high value to stability factor(because β is very high), an undesirable condition. So it has least stability.
Circuit diagram for fixed bias
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| fig 1 |
The simplest biasing circuit but has least stability.
It consists of a dc voltage Vcc for biasing and base resistor RB. Together they provide a 'fixed' base current(IB). (For a given circuit, values of Vcc and RB are constant, so they provide a fixed current).
In order to justify the above statement, let us write an equation for IB.
For that, consider equation for Vcc, 
------(1)
Therefore, 
a constant ----(2)
In an amplifier circuit, Ic and VCE together define operating point for BJT. Equations for Ic and VCE are as follows.
Stability in fixed bias:
Take general equation for stability factor. It is given in the post 'Stability factors & Biasing circuits'. It is here for your our convenience, 
-----(5)
This equation contains two terms -β and dIB /dIc. Among them β is constant and check dIB /dIc . From equation(2), we know that, IB is constant and is independent of variations in Ic. So dIB /dIc is almost zero. Now the equation become
This equation contains two terms -β and dIB /dIc. Among them β is constant and check dIB /dIc . From equation(2), we know that, IB is constant and is independent of variations in Ic. So dIB /dIc is almost zero. Now the equation become
This equation gives a very high value to stability factor(because β is very high), an undesirable condition. So it has least stability.