The Ebers-Moll representation of the BJT

Butterfly’s Page 1

The Ebers-Moll representation of the BJT

Ebers-Moll model for pnp transistor is shown in the figure. It consists of two back-to-

back connected diodes whose cathodes are connected. The base region is common to both

emitter and collector junctions. Since base region is very narrow considerable interaction

exists between the junctions. This coupling is represented by the controlled current sources.

The current IED and ICD are relative to VEB by the diode volt-ampere relation and is given by

)1(1//

TCBTEB VV

CSR

VV

ESCDREDE IIIII --------(1)

1)1(//

TCBTEB VV

CS

VV

ESFCDEDFC IIIII ----(2)

The relationships expressed in Eq(1) and Eq(2) are known as the Ebers-Moll equations. The

quantities IES and ICS in above equations are the reverse saturation currents of the emitter-

base and collector-base junctions, respectively.

The parameters αF and αR are each less than unity. The four quantities IES, ICS, αF, αR are

function of doping densities and transistor geometry and they related by

αFIES = αRICS ------------(3)

The Ebers-Moll representation of the BJT

Butterfly’s Page 2

and 0.98 ≤ αF ≤ 0.998 and 0.40 ≤ αF ≤ 0.8

and IES and ICS are in the order of 10-15 A, both depends on the junction areas.

Eber-Moll equations for npn transistor:

The directions of all current components and junction voltages for an npn transistor

are reversed from those for a pnp device as shown Fig. The Ebers-Moll equations for an npn

device are given below.

)1(1//

TCBTEB VV

CSR

VV

ESE III --------(4)

1)1(//

TCBTEB VV

CS

VV

ESFC III -------(5)

Large-Signal Current Gains:

Let us consider npn for the situation that emitter-base is forward biased(VEB<0) and that the

collector and base terminals are short-circuited(VCB=0). Under these conditions Eq(4) and (5)

becomes

1/

TEB VV

ESE II

and

)1(/

TEB VV

ESFC II

EFC II and F is defined as

0

CBV

E

C

FI

I -------(6)

The quantity αF is called common-base forward short-circuit current gain.

The Ebers-Moll representation of the BJT

Butterfly’s Page 3

Similarly, when VCB<0, the common-base reverse short-circuit current gain αR is determined

as

0

EBV

C

ER

I

I ------(7)