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Chapter 12: Problem 24

A \(160-\mathrm{W}\) silicon power transistor operated with a heat sink \(\left(\theta_{S A}=1.5^{\circ} \mathrm{C} / \mathrm{W}\right)\) has \(\theta_{J C}=0.5^{\circ} \mathrm{C} / \mathrm{W}\) and a mounting insulation of \(\theta_{C S}=0.8^{\circ} \mathrm{C} / \mathrm{W}\). What maximum power can be handled by the transistor at an ambient temperature of \(80^{\circ} \mathrm{C}\) ? (The junction temperature should not exceed \(200^{\circ} \mathrm{C}\).)

Short Answer

Expert verified
The transistor can handle a maximum power of approximately 42.86 W without exceeding the maximum allowable junction temperature of \(200^{\circ} C\).

Step by step solution

01

Understand the Role of Each Given Parameter

The given parameters in this exercise are the power rating of the transistor, which is 160W. This is the amount of power the transistor can handle. Next, the thermal resistances given are the heat sink thermal resistance \(\theta_{S A}\), junction-to-case thermal resistance \(\theta_{J C}\), and case-to-sink thermal resistance \(\theta_{C S}\). These values represent how much heat can be transferred from one component to the next. Finally, the ambient temperature and the maximum allowable junction temperature are also given.
02

Apply the Thermal Resistance Formula

Thermal resistance is the inverse of heat transfer. In this context, it can be used to calculate the maximum power that can be dissipated by the transistor. The thermal resistance from the junction to the ambient can be calculated by adding the thermal resistances of each component as follows: \(\Theta_{J A} = \theta_{J C} + \theta_{C S} + \theta_{S A}\). Substituting the given values, \(\Theta_{J A} = 0.5 + 0.8 + 1.5 = 2.8 \,^{\circ}C / W\).
03

Compute the Maximum Power

The maximum power dissipation can be computed from the difference between the maximum allowable temperature at the transistor junction and the ambient temperature, divided by the total thermal resistance. This can be mathematically represented as: \(P_{\max} = \frac{T_{\max} - T_{A}}{\Theta_{J A}}\). Substituting the given values, \(P_{\max} = \frac{200 - 80}{2.8} = 42.86 W\).

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