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# Negative Resistance and Transistor Stability

Author: Leonard Krugman

Consider the general expression for input resistance

 Eq. (3-13)

It is evident that the input resistance can have a negative value. The input resistance r1 is positive as long as r11 is greater than. This condition is most difficult to attain when the output is shorted, namely when RL = 0. For the transistor to be stable under this condition, r11r22 must be greater than r12r21. The stability factor is the ratio of r12r21 to r11r22. The stability factor must be less than unity for short-circuit stability. Substituting the equivalent transistor parameters for the grounded base connection into the stability equation, the following relationship is obtained:

 r11r22 > r12r21 becomes (rc + rb) (re + rb) > rb (rm + rb) Eq. (3-42)

Expanding equation 3-42,

rcre + rcrb + rbre + rb2 > rhrm + rb2

Dividing through by rb

 Eq. (343)

This equation emphasizes the importance of the backward transfer resistance rb, since when rb = 0, the transistor must have a positive input resistance.

On the other hand, if the value of rb is increased by adding external resistance, it is possible to reach a condition where a normally positive input resistance becomes negative. Notice, however, that increasing the total base resistance eventually causes the input resistance to become negative only if re + rc is less than rm. In the case of the junction transistor, rc is always greater than rm, and increasing the base resistance cannot produce a negative input resistance.

The conditions for negative output resistance are obtained similarly. In the general output resistance equation,

 Eq. (3-21)

the output resistance ro is positive provided that r22 is greater than

This condition for stability is most difficult to meet when the generator resistance is equal to zero. For the transistor to be stable under this condition, rnr22 again must be greater than r12r21. The same stability factor and equations then exist for both the input and output resistances. It is evident, then, that one method of fabricating a transistor oscillator is by adding sufficient resistance to the base arm. Typical circuits incorporating this principle will be considered in Chapter 6.

Last Update: 2010-11-17