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Differential coefficient of transmission of a current
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6.3. Differential coefficient of transmission of a current
In the equation (6.7) for an integrated (static) transmission factor of an emitter current 
. Coefficient of injection 
the efficiency of emitter junction characterizes, and coefficient of diffusive transport 
characterizes processes in basis, diffusive transport and recombination of carriers, with which attends this process; coefficient M is inlet for the account of processes in collector junction and almost always M=1. The equation of a collector current 
, where 
is static parameter of fissile condition of insert (fissile condition), displays link between direct currents. Coefficient 
is defined by the formula 
and this formula displays link between stationary values of a control current 
and value of an output current 
.
For variable signals, which amplitude order much less grades of supply voltages, link between collector currents and emitter is defined by derivation of a relation (6.7) as functions two arguments in the conjecture 
=const, i.e.
, or
. (6.16)
- differential transmission factor of an emitter current in circuit with CB, which always is more than integrated coefficient 
. Calculations display, that at major levels of injection, when 
(see of the formula (6.1), (6.4)), derivative 
aspires to zero and 
. Therefore for the analysis of a major signal integrated (static) coefficient 
is always used.
In consequent viewing is not done variances between 
and 
. Using a label 
, but in each case the applications of these magnitudes should be remembered a level of injection.
6.4. Ebers-Moll’s model
Links between currents and voltages in the transistor for four conditions of insert are well compounded with convenient and clear mathematical Ebers-Moll’s model, grounded on a dual circuit consisting of two diodes (emitter and collector), switched on meeting, and two current sources mapping interaction of these diodes (fig. 6.5).
(6.17)
. (6.18)
where 
and 
- thermal currents emitter and collector junctions accordingly, metered at short-circuit on exit and input accordingly (
=0 and 
=0).
. (6.19)
where 
and 
- back currents of emitter and collector junctions measured accordingly at abruption of a collector and the emitter. With the account (6.18), (6.19) relations (6.17) are conversed to an aspect
; (6.20)
; (6.21)
. (6.22)
Fig. 6.5. Equivalent nonlinear Ebers-Moll’s model for BT
In computing methods of the analysis of transistor circuits with the help of a computer the wide circulation was received by nonlinear model of the Gummel-Pun’s transistor, which grounded on the solution of integrated relations for charges and links exterior electrical performances a charge in basis of transistor structure. It is very precise model explaining many physical effects, but its exposition needs major number of parameters, so for the analysis in a wide frequency range 25 parameters are necessary. The sequential simplification of Gummel-Pun’s model eventually reduces in the elementary Ebers-Moll’s model. Therefore at the analysis of the concrete circuits it is necessary to search for the reasonable compromise between an exactitude of the solution and complexity of model.
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