377
Bipolar Junction Transistor Compact Models
V CE = V BE − V BC . Therefore, at V CE = 0, and V BE ≥ f BE , V BE = V BC , where f BE is
the built-in-potential of EB-junction (Equation 2.109). Under this condition,
both the EB- and CB-junctions are forward biased, resulting in a decrease in
the barrier height for electrons at both EB- and CB-junctions (Equation 2.100).
Consequently, both emitter and collector junctions inject electrons into the
base. Under this biasing condition, the electric field does not favor transport
of electrons to the collector (or emitter) terminal and I C = 0 and the device
is in saturation. Thus, for 0 ≤ V CE < V BE , the npn-BJT operates in the saturation regime since both the EB- and CB-junctions are forward biased. As V CE
increases from V CE = 0 due to the increasing collector supply voltage V CC , V BC
gradually becomes less forward biased and the CB-junction barrier height
gradually increases. Therefore, electron injection from the emitter to base
dominates over that from the collector to base and I C increases with the
increase in V CE as shown in Figure 11.6. At V CE = V BE (or, V BC = 0), the npnBJT is at the onset of transition from the saturation region to the normal active
mode of operation, and for V CE > V BE , the npn-BJT operates in the normal
active linear regime. Therefore, the loci of the point V CE = V BE on I C –V CE plot
separates the saturation and linear regions of BJTs as shown in Figure 11.6.
Again, when V CE < 0, both the EB- and CB-junctions are reverse biased. This
increases the potential barrier height of electrons for both the pn- junctions
and there is no electron injection from the emitter or collector to the base
region of the transistor resulting in I C ≈ 0. Under this condition, the device
operates in the cutoff region as shown in Figure 11.6. Similarly, we can explain
the pnp-BJT characteristics. Note the difference between the MOSFET and
BJT linear and saturation region of operations (Section 4.4.4.1).
11.5 Compact BJT Model
In order to develop a complete BJT model for circuit CAD, we first develop
the basic DC model using the Ebers–Moll formulation and then include the
different parasitic elements of the BJT structure and physical effects.
11.5.1 Basic DC Model: EM1
In order to derive a basic BJT current model, let us consider an npn-BJT device
shown in Figure 11.7. As seen from Figure 11.7, a BJT structure can be considered as two back-to-back pn-junctions. For the simplicity of basic model formulation, we assume that all the parasitic elements such as series resistances
and junction capacitances are negligibly small.
Now, let us assume that the npn-BJT is biased in the normal active mode of
operation (V BE ≥ f BE and V BC < 0). Then when the EB pn-junction is forward
biased, a forward current I F flows through the EB pn-junction and a current
α F I F flows across the CB pn-junction, where α F is the forward current gain
Bipolar Junction Transistor Compact Models
V CE = V BE − V BC . Therefore, at V CE = 0, and V BE ≥ f BE , V BE = V BC , where f BE is
the built-in-potential of EB-junction (Equation 2.109). Under this condition,
both the EB- and CB-junctions are forward biased, resulting in a decrease in
the barrier height for electrons at both EB- and CB-junctions (Equation 2.100).
Consequently, both emitter and collector junctions inject electrons into the
base. Under this biasing condition, the electric field does not favor transport
of electrons to the collector (or emitter) terminal and I C = 0 and the device
is in saturation. Thus, for 0 ≤ V CE < V BE , the npn-BJT operates in the saturation regime since both the EB- and CB-junctions are forward biased. As V CE
increases from V CE = 0 due to the increasing collector supply voltage V CC , V BC
gradually becomes less forward biased and the CB-junction barrier height
gradually increases. Therefore, electron injection from the emitter to base
dominates over that from the collector to base and I C increases with the
increase in V CE as shown in Figure 11.6. At V CE = V BE (or, V BC = 0), the npnBJT is at the onset of transition from the saturation region to the normal active
mode of operation, and for V CE > V BE , the npn-BJT operates in the normal
active linear regime. Therefore, the loci of the point V CE = V BE on I C –V CE plot
separates the saturation and linear regions of BJTs as shown in Figure 11.6.
Again, when V CE < 0, both the EB- and CB-junctions are reverse biased. This
increases the potential barrier height of electrons for both the pn- junctions
and there is no electron injection from the emitter or collector to the base
region of the transistor resulting in I C ≈ 0. Under this condition, the device
operates in the cutoff region as shown in Figure 11.6. Similarly, we can explain
the pnp-BJT characteristics. Note the difference between the MOSFET and
BJT linear and saturation region of operations (Section 4.4.4.1).
11.5 Compact BJT Model
In order to develop a complete BJT model for circuit CAD, we first develop
the basic DC model using the Ebers–Moll formulation and then include the
different parasitic elements of the BJT structure and physical effects.
11.5.1 Basic DC Model: EM1
In order to derive a basic BJT current model, let us consider an npn-BJT device
shown in Figure 11.7. As seen from Figure 11.7, a BJT structure can be considered as two back-to-back pn-junctions. For the simplicity of basic model formulation, we assume that all the parasitic elements such as series resistances
and junction capacitances are negligibly small.
Now, let us assume that the npn-BJT is biased in the normal active mode of
operation (V BE ≥ f BE and V BC < 0). Then when the EB pn-junction is forward
biased, a forward current I F flows through the EB pn-junction and a current
α F I F flows across the CB pn-junction, where α F is the forward current gain