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**THERMAL RUNAWAY:**

The collector current for the CE circuit is given by I_{C} = βI_{B}+(1+β)I_{CO} . The three variables in the equation, β, I_{B}, and I_{CO} increase with rise in temperature. In particular, the reverse saturation current or leakage current I_{CO }changes greatly with temperature. Specifically, it doubles for every 10^{o}C rise in temperature. The collector current I_{C }causes the collector base junction temperature to rise which in turn, increase I_{CO}, as a result I_{C} will increase still further, which will further increase the temperature at the collector base junction. This process will become cumulative at the collector base junction leading to *“thermal runaway”*. Consequently, the ratings of the transistor are exceeded which may destroy the transistor itself.

The collector is made larger in size than the emitter in order to facilitate the heat dissipation at the collector junction. However if the circuit is designed such that the base current I_{B }is made to decrease automatically with rise in temperature, then the decrease in βI_{B} will compensate for increase in the (1+β)I_{CO}, keeping I_{C} almost constant.

**THERMAL RESISTANCE**

Consider transistor used in a circuit where the ambient temperature of the air around the transistor is T_{A}^{o}C and the temperature of the collector-base junction of the transistor is T_{J}^{o}C.

Due to heating within the transistor, T_{J} is higher than T_{A}. As the temperature difference T_{J}- T_{A} is greater, the power dissipated in the transistor, P_{D} will be greater, i.e,

(T_{J}- T_{A}) ∝ P_{D}

The equation can be written as T_{J}- T_{A }=P_{D}, where is the constant of proportionality and is called the Thermal resistance. Rearranging the above equation= (T_{J}- T_{A}) /P_{D}. Hence is measured in ^{o}C/W which may be as small as 0.2^{ o}C/W for a high power transistor that has an efficient heat sink of up to 1000^{o}C/W for small signal, low power transistor which have no cooling provision.

As Θ represents total thermal resistance from a transistor junction to the ambient temperature, it is referred to as Θ_{J-A}. However, for power transistors, thermal resistance is given as Θ_{J-C}.

The amount of resistance from junction to ambience is considered to consist of 2 parts.

Θ_{J-A} = Θ_{J-C} - Θ_{C-A}.

which indicates that the heat dissipated in the junction must make its way to the surrounding air through two series paths from junction to case and from case to air. Hence the power dissipated is given as-

P_{D} = (T_{J}- T_{A}) / Θ _{J-A}

=(T_{J}- T_{A} )/ Θ _{J-C} + Θ _{C-A})

Θ_{J-C} is determined by the type of manufacturer of the transistor and how it is located in the case, but Θ_{C-A} is determined by the surface area of the case or flange and its contact with air. If the effective surface area of the transistor case could be increased, the resistance to heat flows could be increased Θ_{C-A}, could be decreased. This can be achieved by the use of a heat sink.

The heat sink is a relatively large, finned, usually black metallic heat conducting device in close contact with transistor case or flange. Many versions of heat sink exist depending upon the shape and size of the transistor. Larger the heat sink smaller is the thermal resistance Θ_{HS-A}.

This thermal resistance is not added to Θ_{C-A} in series, but is instead in parallel with it and if Θ_{HS-A} is much less than Θ_{C-A}, then Θ_{C-A} will be reduced significantly, thereby improving the dissipation capability of the transistor. Thus

Θ _{J-A}=Θ _{J-C} + Θ _{C-A}|| Θ_{HS-A}.

**4.8 CONDITION FOR THERMAL STABILITY:**

For preventing thermal runaway, the required condition is the rate at which the** **heat is released at the collector junction should not exceed the rate at which the heat can be dissipated under steady state conditions. Hence the condition to be satisfied to avoid thermal runaway is given by-

If the circuit is properly designed, then the transistor cannot runaway below a specified ambient temperature or even under any condition.

In the self biased circuit the transistor is biased in the active region. The power generated at the junction without any signal is

Let us assume that the quiescent collector and the emitter currents are equal. Then

The condition to prevent thermal runaway can be written as

As Θ and are positive, should be negative in order to satisfy the above condition.

Differentiating equation (1) w.r.t I_{C }we get

Hence to avoid thermal runaway it is necessary that

SinceV_{CE}=V_{CC}-I_{C}(R_{E}+R_{C}) then eq (4) implies that V_{CE}<V_{CC}/2. If the inequality of eq (4) is not satisfied and V_{CE}<V_{CC}/2, then from eq(3), is positive., and the corresponding eq(2) should be satisfied. Other wise thermal runaway will occur.

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