### Categorized |Power Design, Thermal Management

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Posted on 19 December 2019

# Thermal Impedance and Thermal Resistance

Thermal impedance is defined as a quotient of the time function of a temperature difference divided by the impressed power dissipation. In the datasheets this value is given as a function of time in the form of a diagram.

$Z_{th}(t) = \frac {T_1(t) - T_2(t)}{P}$

The static upper range value is the actual thermal resistance. This is indicated in the datasheets in the form of a characteristic. Depending on the choice of temperature detection points, distinctions are made. For example:

• Zth(j-c) / Rth(j-c)    : junction-case
• Zth(c-s) / Rth(c-s)   : case-heatsink
• Zth(s-a) / Rth(s-a)  : heatsink-ambient
• Zth(j-a) / Rth(j-a)   : junction-ambient

Since Tc and Ts depend on the position of the detection point, their shares of the total thermal resistance may vary. The total thermal resistance, however, is always calculated as follows (this also applies to Zth):

$R_{th(j-c)} + R_{th(c-s)} + R_{th(s-a)} = R_{th(j-a)}$

Thermal resistance may be used to calculate true constant quantities, as well as average temperatures of periodic functions. Normally, however, the current conducted through a semiconductor device and, consequently, the power losses, are time dependent parameters. In line rectifiers, the losses and temperatures vary within the bounds of the line frequency around a mean value. The virtual junction temperature Tj is higher under peak load than under direct current load or if calculated with a mean power loss PFAV /PTAV and Rth . The temperature fluctuation range depends on the current waveform and the current flow time within a cycle. With help of the thermal impedance, the effective junction temperature Tj(t) can be calculated for any given duration of power dissipation. The datasheets of older components still contain auxiliary values. This is owing to the restricted methods of calculation at that time. These values should enable the user to factor in the load dependent power loss and temperature fluctuation based on the operating frequency. Although not correct from a physics point of view, the static resistance Rth is used as a mathematical aid and is multiplied by a corrective factor in order to project the mean temperature to the maximum temperature value (Figure 1). The resulting value Rth, which is given either as a pure operand or in the form of a diagram, applies to the given current waveform and the lead angle for a frequency range of 40…60 Hz. In other words, Rec120 stands for "rectangular current with a current flow time of 120°".

Figure 1. Rth(j-c) of a discrete 100A thyristor multiplied by a corrective factor to calculate the temperature fluctuation as a function of the current conduction angle Θ and current waveform

Similar auxiliary parameters are, for example, the thermal pulse impedance Zth(p) and the thermal supplementary impedance Zth(z).

$Z_{th(p)} = Z_{th} + Z_{th(z)}$

The thermal impedance is used to calculate the temperature change at a specified point in time after power dissipation has been in effect. For this purpose, the mean on-state power dissipation PTAV is normally averaged over one line frequency cycle. This temperature rise is also superposed by a fluctuation at operation frequency. This fluctuation can be calculated analytically using the thermal impedances for individual pulses and pulse sequences. Although not correct from a physics point of view, the thermal impedance is indicated with a supplementary value in former datasheets in order to infer the maximum temperature from the average dissipated power. For example, Figure 2 gives such supplementary impedances for different current conduction angles and waveforms.

Figure 2. Zth to case (Zth(j-c)) and to heatsink (Zth(j-s)) of a discrete 100 A thyristor and mathematical auxiliary parameter Zth(z) to calculate the temperature fluctuation at line frequency for different current conduction angles and waveforms

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