Stability Factor

Stability Factor

• We know that, the IC is a Unction of ICO, VBE and P Thus, it is convenient to introduce the three partial derivatives of IC with respect to these variables. These derivates are called stability factors S, S' and S" and are defined as follows :

Important Concept

1. Ideally, stability factor should be perfectly zero to keep operating point stable.

2. Practically stability factor should have the value as minimum as possible. Thermal stability of a circuit is assessed by deriving a stability factor, S.

3. Stability factor indicates the degree of change in operating point due to variation in temperature.

1. Standard Equation for Derivation

• For a common emitter configuration collector current is given as,

When I_CBO changes by ΔI_Cand I_CBO, I_B changes by ∂ I_B and I_C .So this equation becomes,

• The above equation can be considered as a standard equation for derivation of stability factors of other biasing circuits.

Important Concept

The general procedure to obtain stability factors for various biasing circuits is as follows :

Step 1 : Obtain the expression for Ig.

Step 2 : Obtain 3 IB I 3 lc and use it in equation 5 to get S.

Step 3 : In standard equation of Ic, replace lg in terms of VBE to get S'.

Step 4 : Differentiate the equation obtained in step 3 with respect to P to get S''.

2. Stability Factors for Fixed Bias

Stability factor S

Ex. 2.7.1 Derive the expression for the stability factor S of the fixed bias circuit.

Sol. : Step 1 : Obtain the value of ∂ I_B/∂ I_C

For fixed bias circuit,

I_B = V_CC - V_BE / R_B

Differentiating w.r.t. Ic and considering V_BE to be independent of I_C we get,

∂ I_B / ∂ I_C = 0

Step 2 : Substituting the value of ∂ I_B / ∂ I_C in expression of S.

S = 1 + β / 1 – β(∂ I_B / ∂ I_C ) + 1 + β / 1 – 0 = 1 + β

Ex. 2.7.2 A germanium transistor is to be operated at zero signal Ic = 1 mA. If the collector supply voltage V_CC  = 12 V, what is the vale of R_B in the base resistor method ? Assume β = 00. If another transistor of same batch with β = 50 is used, what will be new value of zero signal I_C for same R_B ? Comment on the results.

AU : Dec.-18, Marks 13

Sol. :

Comment : It is clear from the above example that with the change in transistor parameter β the zero signal collector current has changed from 1 mA to 0.5 mA. Therefore, the base resistor method cannot provide stabilization.

Review Questions

1. Define the stability factors and explain their significance.

2. Derive stability factors for fixed bias circuit.