Bias Selection

Author: Leonard Krugman

It can be shown mathematically that the condition for locating the operating point in the center of the negative-resistance region is: E_e (2αR_c + R_E) = E_cR_E. This relationship indicates that the extent of the negative-resistance range depends upon the bias batteries and the values of R_E and R_c. The emitter-to-collector current gain α is, of course, fixed for a given transistor. For the characteristic in Fig. 6-10 (B), then, all the parameters are specified with the exception of E_e and R_E. Notice, however, that these quantities are related to the value of d-c emitter current bias I_e that is required to establish a d-c operating point in the center of the negative resistance region. This condition is:

E_e = R_EI_e.

The two conditional equations can be combined to evaluate R_E in terms of known quantities:

Eq. (6-2)

Since R_E also equals , equation 6-2 limits the value of the emitter bias battery to less than that of E_c. The limiting value of E_e = E_c is reached when R_c = 0.

As a numerical example, if the values associated with Fig. 6-10 (B) are used so that the bias current at the center of the negative resistance region is I_e = 0.75 ma, then

and

E_e = I_eR_E = .75 × 10^-3 × 31.5 × 10³ = 23.6 volts.

The negative resistance of the oscillator is equal to the slope of the

characteristics in that region. Then

This value defines the maximum limit of the impedance of the L-C series emitter circuit at resonance.