Assume, now, that a square-wave pulse of power or energy and duration time is applied to a P E real resistor with finite area of its resistive element. Assume also that the resistor thickness S satisfies (8). The power density of two-dimensional heat source in the model (4) can be calculated as the w following: Suppose that heat transfer on direction parallel to surface plane is negligible. Then the resistor’s resistor may be regarded as a portion of infinite that dissipates the same pulse power per “resistor” unit of surface area. Substitution of (9) into (4) yields an expression for the distribution of the temperature rise in the substrate in terms of the given parameters: Substitution of (9) into (6) yields an expression for the distribution of the temperature rise in the resistive film (z = 0) in terms of the given parameters: All discussed models are presented in the following table. Type of resistor load 2-dimensional 3-dimensional Comments resistive element resistive element Short-time pulse Heat remains inside resistive element (no heat transfer to ambiance) Medium-time pulse Heat remains inside resistor (no heat transfer to ambiance) Long-time pulse Heat transfer to ambiance is significant Steady state For comparison Physical phenomena related to pulse loading. 2.1. Burnout of resistive film. Suppose that chip resistor with bare and uniform (non-trimmed) thick-film resistive element (Fig. 3) is loaded by square-wave pulse. Fig.3 Suppose that resistor substrate is made of 96% alumina (typical substrate for thick-film resistor), and, therefore, = 24 W/(mK), = 8.8102 J/(kgK), = 3.72103 kg/m3, = 7.310-6 m2/s. Suppose K c a too that duration of applied pulse satisfies (8) where is resistor substrate thickness. Some example h values of and respective minimum values of calculated per (8) are presented in the table below: h Minimum alumina substrate thickness when solution (11) for infinite model is applicable , ms mm h,
Assume, now, that a square-wave pulse of power P or energy E and duration time is applied to a real resistor with finite area S of its resistive element. Assume also that the resistor thickness satisfies (8). The power density w of two-dimensional heat source in the model (4) can be calculated as the following: Suppose that heat transfer on direction parallel to resistor’s surface plane is negligible. Then the resistor may be regarded as a portion of infinite “resistor” that dissipates the same pulse power per unit of surface area. Substitution of (9) into (4) yields an expression for the distribution of the temperature rise in the substrate in terms of the given parameters: Substitution of (9) into (6) yields an expression for the distribution of the temperature rise in the resistive film (z = 0) in terms of the given parameters: All discussed models are presented in the following table. Type of resistor load 2-dimensional resistive element 3-dimensional resistive element Comments Short-time pulse Heat remains inside resistive element (no heat transfer to ambiance) Medium-time pulse Heat remains inside resistor (no heat transfer to ambiance) Long-time pulse Heat transfer to ambiance is significant Steady state For comparison Physical phenomena related to pulse loading. 2.1. Burnout of resistive film. Suppose that chip resistor with bare and uniform (non-trimmed) thick-film resistive element (Fig. 3) is loaded by square-wave pulse. Fig.3 Suppose that resistor substrate is made of 96% alumina (typical substrate for thick-film resistor), and, therefore, K = 24 W/(mK), c = 8.8102 J/(kgK), = 3.72103 kg/m3, a = 7.310-6 m2/s. Suppose too that duration of applied pulse satisfies (8) where h is resistor substrate thickness. Some example values of and respective minimum values of h calculated per (8) are presented in the table below: Minimum alumina substrate thickness when solution (11) for infinite model is applicable , ms h, mm