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Thermal Impedance

+++ date = "2017-04-13" image = "pcbpic.jpg" description = "Thermal Impedance and Thermal Resistance" categories = ["Thermal", "Learning"] title = "Thermal Impedance and Thermal Resistance" slug = "Thermal Impedance and Thermal Resistance" tags = ["TIM"] +++

热阻

热阻(thermal resistance),\(R\),单位是\(°C/W\),它代表在单位时间内当有单位热能量通过物体时,物体两端的温度差。

\[R=(T_1-T_2)/Q=\Delta T/Q\]

应用已知热阻计算温度差\(\Delta T=RQ\)

导热率

导热率(thermal conductivity),\(k\),单位是\(W/(m·°C)\),是材料的固有特性。

根据Fourier's law有

\[Q=\frac {kA\Delta T}{t}\]

因此可以计算某一特定形状物体的热阻:

\[R=\frac{t}{kA}\]

⧸⧸从上式可以看出材料的导热率\(k\)越大,接触面积越大\(A\),热阻越小;厚度或间隙\(t\)越大,热阻越大。⧸⧸从上式可以看出物体的热阻\(R\)不仅和其本身的导热率\(k\)相关,还和参与热传导的面积\(A\)及厚度\(t\)相关。材料的导热率\(k\)越大,接触面积越大\(A\),热阻越小;厚度或间隙\(t\)越大,热阻越大。⧸⧸

接触热阻

接触热阻(thermal contact resistance),这里将接触热阻标记为\(R_c\),单位是\(m^2·°C/W\)

⧸⧸两个互相接触的固体表面,实际上接触仅仅发生在一些离散的面积元上,在未接触的界面之间的间隙常常充满了空气,热量将以传导的方式穿过这种气隙层,这种情况与固体表面完全接触相比,增加了传递热阻。接触热阻等于两个交界表面温度之差除以热流量。接触热阻单位是:\(m^2·K/W\)

需要注意的是,接触热阻的单位和我们前面说的热阻的单位是不一样的。我们可以认为,接触热阻等热阻乘以面积,因此接触热阻的大小与接触面积无关。

Since \(T_c\) and \(T_s\) 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°".

temperature fluctuation as a function of the current conduction angle T and current waveform

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.

Z th to case \(Z th\(j-c\) ) and to heatsink Z th\(j-s\) of a discrete 100 A thyristor

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

For more information, please read:

Heat Transfer in Power Semiconductor Devices

Cooling Methods for Power Semiconductor Devices

⧸⧸两个互相接触的固体表面,实际上接触仅仅发生在一些离散的面积元上,在未接触的界面之间的间隙常常充满了空气,热量将以传导的方式穿过这种气隙层,这种情况与固体表面完全接触相比,增加了传递热阻。接触热阻等于两个交界表面温度之差除以热流量。

需要注意的是,接触热阻的单位和我们前面说的热阻的单位是不一样的。我们可以认为,接触热阻等热阻乘以面积:

\[R_c=RA=\frac{t}{k}\]

因此接触热阻的大小与接触面积无关。注意对于接触面而言,上式中的\(k\)实际上是不存在的,因为接触面并不是一个特定的物理实体。⧸⧸

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