The power rating of monolithic microwave integrated circuits (MMIC) is continuously going up. And the life of an MMIC component due to thermal related failure is directly related to the hot spot temperature on the die. Hence, circuit designers need to carefully design the interface between the MMIC component and the ambient to minimize the thermal related failure or increase the mean-time to failure (MTTF) of MMIC devices. In this article, we provide a simple method for thermal design of a printed circuit board (PCB). More accurate calculation requires performing thermal analysis using any of the finite element software such as ANSYS and COSMOS.

Thermal resistance is defined as the ratio of temperature rise to the power dissipated and is expressed in °C/W. Manufacturers of MMIC components provide the thermal resistance from junction to case (▸_jc). Figure 1 shows the cross section of an MMIC component, which contributes to heat rise.

A packaged MMIC component consists of a semiconductor die (or chip) mounted on a lead frame. The die is attached to the lead frame using conductive epoxy or solder. Electrical connections from the die to lead frame are done using wire bonding. To protect the die from the harsh environment, it is covered with a plastic molding compound.

The thermal resistance of the hot spot on the die to ambient consists of a series of thermal resistances:

• Hot spot on the die to bottom of die (θ _die)
• Conductive epoxy (θ_ce)
• Lead frame (θ_lf)
• Solder on PCB (θ_sl)
• Top of PCB to bottom surface (θ_PCB)
• PCB to ambient (θ _{PCB -A})

Out of the six factors, the sum of the first three is popularly called ▸_jc, thermal resistance from junction to case, and supplied by the component manufacturers. The contribution of solder (▸_sl) is small and not covered here.

This design tip explains the method of computing thermal resistance of the PCB (θ_PCB). For example, with Mini-Circuits' monolithic amplifier ERA-5XSM, the PCB layout for an amplifier must consider both the electrical requirements of the parts (proper line impedance, bypassing, etc.) and the thermal requirements. Via holes play an important part in providing good electrical and thermal path to ground.

Thermal resistance is defined as (Eq. 1):

where:

l= length (m),

A= Area in m²

k= Thermal conductivity (W/m-K).

For an unfilled via (Eq. 2):

where:

d_o= outer diameter of the via (m) and

d_i= inner diameter of the via (m).

Substituting Equation 2 into Equation 1, the thermal resistance of a single copper via can be calculated as (Eq. 3):

From the above equation it is seen that, thermal resistance will decrease as the

• length of the via decreases
• via diameter (d_o) increases
• copper thickness in the via increases

For ERA-5XSM, the data sheet provides a suggested PCB layout as reproduced in Figure 2. It consists of 12 via holes of 0.02-inch diameter (d_o) under DUT. Using 0.002-inch copper thickness, the inside diameter of the via hole is 0.016 inches (d_i). Also assuming 0.002-inch thickness of copper on top and bottom of the PCB, the length of the via is 0.034 inches (which is “l” in Eq. 1 and Eq. 3). Thermal conductivity of copper is 384 W/m-K. Substituting these parameters in Equation 3, thermal resistance of a 20-mil diameter unfilled via hole is 30.8 °C/W. For 12 via holes, the thermal resistance is calculated as if they are in parallel, which is 2.6 °C/W. This is a first-order approximation, as it does not consider the spatial distribution of the vias.

Figure 3 shows thermal simulation using ANSYS power dissipation of 1 W. Hence the temperature rise indicated in Figure 3 is also the thermal resistance, which reads as 2.35 °C/W, which is close to 2.6 °C/W calculated.

Hence manual calculation of the thermal resistance as shown can be used as a first-order approximation.

Power dissipation in an ERA-5XSM amplifier is 0.3185 W (device voltage multiplied by operating current).

There is an additional thermal resistance from PCB to ambient. The measured temperature rise of ERA-5XSM on the test board is around 11 °C. So one can calculate the thermal resistance from PCB to ambient as:

θ_PCB-A = (temperature rise)/Power dissipated = (11)/0.3185

= 34.5 °C/W

Hence the total thermal resistance is:

θ_jA = θ_jc + θ_sl + θ_PCB + θ_PCB-A = 133 °C + 0 °C + 2.6 °C + 34.5 °C = 170.1 °C/W

Hence T_jmax = Junction temperature at the die hot spot

= Max ambient temperature +θ_jA * Pd (Power dissipated)

Assuming a max ambient temperature of 85 θC, for ERA-5XSM, the example under consideration,

T_jmax = 85 °C + 170.1 °C * 0.3185 = 139.2 °C.

Figure 4 shows the MTTF vs. junction temperature for ERA-5XSM. At the calculated junction temperature, the MTTF is around 200 years.

For the PDF version of this article, click here.

1. Radha Krishna Setty, Kelvin Kiew and Harvey Kaylie, “Commercial-off-the-shelf MMIC components offer high reliability,” RF Design, February 2005, pp. 12-16.

2. www.minicircuits.com/applications.html, “Hela-10: High Ip3, Wide Band, Linear Power Amplifier.”

3. D.R. Pitts and L.E. Sissom, “Heat Transfer,” Schaum's Outline series, McGraw-Hill Publications.

Radha P.N. Setty is director of engineering at Mini-Circuits, Brooklyn, N.Y.

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