This model is used to demonstrate the regenerative or latching action due to positive feedback in the thyristor. A thyristor can be considered as two complementary transistors. One being pnp and the other npn. The twotransistor model is shown in figure 4.3 below.
Figure 4.3 TwoTransistor Model of Thyristor
The collector current I_{C} of a transistor is related to the emitter current I_{E} and the leakage current of the collector base junction I_{CBO} as
.............(1)
The emitter current of transistor Q_{1} is the anode current I_{A} of the thyristor and collector current I_{C1} is given by
.............(2)
where a_{1} and I_{CBO1} are the current gain and leakage current respectively for transistor Q_{1}.
Similarly, the collector current for transistor Q_{2} is I_{C2} where
.............(3)
where a_{2} and I_{CBO2} are the current gain and leakage current respectively for transistor Q_{2}.
Combining the two collector currents I_{C1} and I_{C2} yields
.............(4)
When a gate current I_{G} is applied to the thyristor
.............(5)
Solving for anode current I_{A} in equation 5 yields
The current gain a_{1} varies with emitter current I_{E1} which is equal to I_{A}; and a_{2} varies with emitter current I_{E2} which is equal to I_{k}.
A typical variation of current gain a with emitter current I_{E} is shown in figure 4.4.
Figure 4.4 Typical Variation of Current Gain With Emitter Current
If the gate current I_{G} is increased from zero to some positive value, this will increase the anode current I_{A} as shown by equation 6. An increase of I_{A} which is an increase of I_{E1} would increase a_{1} as shown in figure 4.4 and also a_{2} since . The increase in values of both a_{1} and a_{2} would further increase the value of anode current I_{A} which is a regenerative or positive feedback effect.
If a_{1} and a_{2} approach unity, the denominator of equation 6 approaches zero and a large value of anode current is produced causing the thyristor to turn on as a result of the application of a small gate current.
The capacitance of the pn junctions are shown in figure 4.5 below.
Figure 4.5 Twotransistor Transient Model of Thyristor
Under transient conditions, the capacitances of the pn junctions influence the characteristics of the thyristor.
If a thyristor is in the blocking state and a rapidly rising voltage is applied to the device, high currents would flow through the junction capacitors. The current through capacitor C_{j2} can be expressed as
where
C_{j2} = capacitance of junction j2
V_{j2} = voltage of junction j2
q_{j2} = charge in junction j2
If the rate of rise of voltage dv/dt is large, then i_{j2} would be large, which would result in increased leakage currents I_{CBO1} and I_{CBO2}. High enough values of I_{CBO1} and I_{CBO2} may cause a_{1} and a_{2} to approach unity, resulting in undesirable turn on of the thyristor.
It must be noted that a large current through the junction capacitors may cause damage to the device.
