### Test Latex Support

\section{Bar-Cohen and Rohsennow Solution}

Finned surfaces of various shapes, called heat sinks, are frequently used in the cooling of electronic devices. Energy dissipated by these devices is transferred to the heat sinks by conduction and from the heat sinks to the ambient air by natural or forced convection, depending on the power dissipation requirements. Natural convection is the preferred mode of heat transfer since it involves no moving parts, like the electronic components themselves. However, in the natural convection mode, the components are more likely to run at a higher temperature and thus undermine reliability. A properly selected heat sink may considerably lower the operation temperature of the components and thus reduce the risk of failure.

Natural convection from vertical finned surfaces of rectangular shape has been the subject of numerous studies, mostly experimental.

\begin{figure}[htp]
\centering
\includegraphics[width=3cm]{flow.eps}
\caption{Natural convection flow through a channel between two isothermal vertical plates.}
\label{flow}
\end{figure}

Natural convection flow through a channel formed by two parallel plates as shown in Fig \ref{flow} is commonly encountered in practice. When the plates are hot ($T_s > T_{\infty}$), the ambient fluid at $T_{\infty}$ enters the channel from the lower end, rises as it is heated under the effect of buoyancy, and the heated fluid leaves the channel from the upper end. The plates can be approximated as being isothermal ($T_s = constant$) in this case.

Boundary layers start to develop at the lower ends of opposing surfaces, and eventually merge at the midplane if the plates are vertical and sufficiently long. In this case, we will have fully developed channel flow after the merger of the boundary layers, and the natural convection flow is analyzed as channel flow. But when the plates are short or the spacing is large, the boundary layers of opposing surfaces never reach each other, and the natural convection flow on a surface is not affected by the presence of the opposing surface. In that case, the problem should be analyzed as natural convection from two in- dependent plates in a quiescent medium, using the relations given for surfaces, rather than natural convection flow through a channel.

\begin{figure}[htp]
\centering
\includegraphics[width=4cm]{fin.eps}
\caption{Various dimensions of a finned surface oriented vertically.}
\label{fin}
\end{figure}
\subsection{Heat Flow Transfer by Fin}
Bar-Cohen and Rohsenow (1984) \cite{Bar} have compiled the available data under various boundary conditions, and developed correlations for the Nusselt number and optimum spacing. The characteristic length for vertical parallel plates used as fins is usually taken to be the spacing between adjacent fins $S$, although the fin height $L$ could also be used. The Rayleigh number is expressed as

\label{eq:ra}
Ra_S=\dfrac{g\beta (T_S-T_{\infty})S^3}{\nu^2}Pr

\label{eq:nu}
Nu=\left[ \dfrac{576}{(Ra_SS/L)^2}+\dfrac{2.873}{(Ra_SS/L)^{0.5}}\right] ^{-0.5}

\label{eq:h}
h=Nuk/S

\label{eq:q}
\dot{Q}=hA(T_s-T_{\infty})

\subsection{Optimum Fin Spacing}
A question that often arises in the selection of a heat sink is whether to select one with closely packed fins or widely spaced fins for a given base area. A heat sink with closely packed fins will have greater surface area for heat transfer but a smaller heat transfer coefficient because of the extra resistance the additional fins introduce to fluid flow through the interfin passages. A heat sink with widely spaced fins, on the other hand, will have a higher heat transfer coefficient but a smaller surface area. Therefore, there must be an optimum spacing that maximizes the natural convection heat transfer from the heat sink for a given base area $WL$, where $W$ and $L$ are the width and height of the base of the heat sink, respectively, as shown in Fig. \ref{fin}. When the fins are essentially isothermal and the fin thickness t is small relative to the fin spacing S, the optimum fin spacing for a vertical heat sink is determined by Bar-Cohen and Rohsenow to be

\label{eq:optS}
S_{opt}=2.714\frac{L}{Ra_L^{0.25}}

\label{key}
Ra_L=\dfrac{g\beta(T_s-T_{\infty})L^3}{\nu^2}Pr

It can be shown by combining the three equations above that when $S = S_{opt}$, the Nusselt number is a constant and its value is 1.307,

Nu=\dfrac{hS_{opt}}{k}=1.307

\section{Discussion}
if fin distance is very big, that analysis as two independent plate:

\label{key}
Nu=\left[ 0.825+\dfrac{0.387Ra_L^{1/6}}{[1+(0.492/Pr)^{9/16}]^{8/27}}\right]^2

\begin{figure}[htp]
\centering
\includegraphics[width=10cm]{compare.eps}
\caption{Calculation Result compare}
\end{figure}

that shows when space become bigger, Bar-Cohen provide equation result will same as signal plate result. And it has max point.

I use matlab to solve the max flow rate will space change, the result not matched author provided equation \ref{eq:optS} result. use equation \ref{eq:optS} the fin space is
\begin{lstlisting}
Sopt = 9.5070
Nopt = 24.7467
Nuopt = 1.7343
\end{lstlisting}
Noticed the Nu is 1.7343, which not same as it said equal to a fix number 1.307.

But solve equations \ref{eq:ra} – \ref{eq:q} results is
\begin{lstlisting}
Sopt = 10.2079
Nopt = 23.4866
Nuopt = 1.2194
\end{lstlisting}

The optimum of fin space has some error of the original text book, that may cause it calculate the fin number as below:
\label{key}
N=W/(S+t)\simeq W/S

But the fin number should be calculate as
\label{key}
N=(W-t)/(S+t)+1

\begin{figure}[htp]
\centering
\includegraphics[width=10cm]{Nu.eps}
\caption{Nu number change with length with two calculation methods}
\end{figure}

Below Matlab code calculate the heat flow with given parameters.

% —————————————————————-
\begin{lstlisting}
%Cal Heat Sink Heat Flow
Ts=87;
Ta=45;
W=300;
L=330;
H=39.6;
N=21;
t=3;
% Air parameters, change them as need.
Pr=0.7177;
nu=0.00001995;
g=9.81;
k=0.02881;

%%The setting fin space is
S=(W-t)/(N-1)-t
A=H*L*2*N*1E-6;
beta=1/((Ts+Ta)/2+273);

%Ra number and Nu number
Ras=g*beta*(Ts-Ta)*(S/1000)^3/nu^2*Pr
RaL=g*beta*(Ts-Ta)*(L/1000)^3/nu^2*Pr
Nu_p=(576/(Ras*S/L)^2+2.873/(Ras*S/L)^0.5)^(-0.5)%Parallel Wall
Nu_s=(0.825+0.387*RaL^(1/6)/(1+(0.492/0.7202)^(9/16))^(8/27))^2%Signal Wall
%Heat transfer coff is

h_p=Nu_p*k/S*1000
h_s=k*Nu_s/L*1000

Q_p=h_p*A*(Ts-Ta)
Q_s=h_s*A*(Ts-Ta)

%Optimized fin space
Sopt=2.714*L/RaL^0.25
Nopt=(W-t)/(t+Sopt)+1
Nuopt=(576/(Ras*Sopt/L)^2+2.873/(Ras*Sopt/L)^0.5)^(-0.5)
\end{lstlisting}

\begin{thebibliography}{99}

\bibliographystyle{amsplain}
% 英文学术期刊中的文章
%\bibitem{paper:english} A. Charnes, W. W. Cooper and E. Rhodes. Measuring the efficiency of decision making units. {\it European Journal of Operaional Research}, 2(6), 429–444, 1978.
\bibitem{Bar}Bar-Cohen AA, Rohsenow WM. Thermally Optimum Spacing of Vertical, Natural Convection Cooled, Parallel Plates. {\it ASME. J. Heat Transfer}. 1984;106(1):116-123. doi:10.1115/1.3246622.
% 中文学术期刊中的文章
%\bibitem{paper:chinese} 韩松, 魏权龄. 资源配置的非参数~DEA~模型. {\it 系统工程理论与实践}, 22, 59–64, 2002.

\end{thebibliography}

### NATURAL CONVECTION:NATURAL CONVECTION FROM FINNED SURFACES AND PCBs

Natural convection flow through a channel formed by two parallel plates as shown in Fig. 20–16 is commonly encountered in practice. When the plates are hot (Ts > Too), the ambient fluid atToo enters the channel from the lower end, rises as it is heated under the effect of buoyancy, and the heated fluid leaves the channel from the upper end. The plates could be the fins of a finned heat sink, or the PCBs (printed circuit boards) of an electronic device. The plates can be approximated as being isothermal (Ts = constant) in the first case, and isoflux ( · = constant) in the second case.
Boundary layers start to develop at the lower ends of opposing surfaces, and eventually merge at the midplane if the plates are vertical and sufficiently long. In this case, we will have fully developed channel flow after the merger of the boundary layers, and the natural convection flow is analyzed as channel flow. But when the plates are short or the spacing is large, the boundary layers of opposing surfaces never reach each other, and the natural convection flow on a surface is not affected by the presence of the opposing surface. In that case, the problem should be analyzed as natural convection from two in- dependent plates in a quiescent medium, using the relations given for surfaces, rather than natural convection flow through a channel.

## Natural Convection Cooling of Finned Surfaces (Ts = constant)

Finned surfaces of various shapes, called heat sinks, are frequently used in the cooling of electronic devices. Energy dissipated by these devices is transferred to the heat sinks by conduction and from the heat sinks to the ambient air by natural or forced convection, depending on the power dissipation requirements. Natural convection is the preferred mode of heat transfer since it involves no moving parts, like the electronic components themselves. However, in the natural convection mode, the components are more likely to run at a higher temperature and thus undermine reliability. A properly selected heat sink may considerably lower the operation temperature of the components and thus reduce the risk of failure.

Natural convection from vertical finned surfaces of rectangular shape has been the subject of numerous studies, mostly experimental. Bar-Cohen and Rohsenow (1984) have compiled the available data under various boundary conditions, and developed correlations for the Nusselt number and optimum spacing. The characteristic length for vertical parallel plates used as fins is usually taken to be the spacing between adjacent fins S, although the fin heightL could also be used. The Rayleigh number is expressed as

A question that often arises in the selection of a heat sink is whether to select one with closely packed fins or widely spaced fins for a given base area (Fig. 20–17). A heat sink with closely packed fins will have greater surface area for heat transfer but a smaller heat transfer coefficient because of the extra resistance the additional fins introduce to fluid flow through the interfin passages. A heat sink with widely spaced fins, on the other hand, will have a higher heat transfer coefficient but a smaller surface area. Therefore, there must be an optimum spacing that maximizes the natural convection heat transfer from the heat sink for a given base area WL, where W and L are the width and height of the base of the heat sink, respectively, as shown in Fig. 20–18. When the fins are essentially isothermal and the fin thickness t is small relative to the fin spacing S, the optimum fin spacing for a vertical heat sink is determined by Bar-Cohen and Rohsenow to be

## Natural Convection Cooling of Vertical PCBs

Arrays of printed circuit boards used in electronic systems can often be modeled as parallel plates subjected to uniform heat flux · (Fig. 20–19). The plate temperature in this case increases with height, reaching a maximum at the upper edge of the board. The modified Rayleigh number for uniform heat flux on both plates is expressed as

Mass Flow Rate through the Space between Plates

As we mentioned earlier, the magnitude of the natural convection heat transfer is directly related to the mass flow rate of the fluid, which is established by the dynamic balance of two opposing effects: buoyancy and friction.

The fins of a heat sink introduce both effects: inducing extra buoyancy as a result of the elevated temperature of the fin surfaces and slowing down the fluid by acting as an added obstacle on the flow path. As a result, increasing the number of fins on a heat sink can either enhance or reduce natural convection, depending on which effect is dominant. The buoyancy-driven fluid flow rate is established at the point where these two effects balance each other. The friction force increases as more and more solid surfaces are introduced, seriously disrupting fluid flow and heat transfer. Under some conditions, the increase in friction may more than offset the increase in buoyancy. This in turn will tend to reduce the flow rate and thus the heat transfer. For that reason, heat sinks with closely spaced fins are not suitable for natural convection cooling.

When the heat sink involves closely spaced fins, the narrow channels formed tend to block or “suffocate” the fluid, especially when the heat sink is long. As a result, the blocking action produced overwhelms the extra buoy- ancy and downgrades the heat transfer characteristics of the heat sink. Then, at a fixed power setting, the heat sink runs at a higher temperature relative to the no-shroud case. When the heat sink involves widely spaced fins, the shroud does not introduce a significant increase in resistance to flow, and the buoyancy effects dominate. As a result, heat transfer by natural convection may improve, and at a fixed power level the heat sink may run at a lower temperature.

When extended surfaces such as fins are used to enhance natural convection heat transfer between a solid and a fluid, the flow rate of the fluid in the vicinity of the solid adjusts itself to incorporate the changes in buoyancy and friction. It is obvious that this enhancement technique will work to advantage only when the increase in buoyancy is greater than the additional friction introduced. One does not need to be concerned with pressure drop or pumping power when studying natural convection since no pumps or blowers are used in this case. Therefore, an enhancement technique in natural convection is evaluated on heat transfer performance alone.

The failure rate of an electronic component increases almost exponentially with operating temperature. The cooler the electronic device operates, the more reliable it is. A rule of thumb is that the semiconductor failure rate is halved for each 10°C reduction in junction operating temperature. The de- sire to lower the operating temperature without having to resort to forced convection has motivated researchers to investigate enhancement techniques for natural convection. Sparrow and Prakash have demonstrated that, under certain conditions, the use of discrete plates in lieu of continuous plates of the same surface area increases heat transfer considerably. In other experimental work, using transistors as the heat source, Çengel and Zing have demonstrated that temperature recorded on the transistor case dropped by as much as 30°C when a shroud was used, as opposed to the corresponding no- shroud case.

### Introduction

With thermal solutions becoming more challenging, there is a push for novel cooling ideas or materials to further mitigate thermal issues facing today’s electronics. In these design situations, the proven method of analytical calculations, modeling, and laboratory testing is sometimes bypassed in the search for a quick “cure-all” solution. Evolutionary progress is needed in the thermal industry of course. However, in a rush to implement new ideas/materials thorough testing should not be overlooked in determining thermal performance of a solution before implementation.

Table 1. Heatsink Geometry

The stated thermal properties of engineered graphite foams have been a motivator for their consideration as heat sink materials. Yet, the literature is void of true comparison of these materials against copper and aluminum. To address the issue of graphite foam as a viable material for heat sinks, a series of tests were conducted to compare thermal performance of geometrically identical heat sinks (Table 1) made of copper, aluminum, and graphite foam (Table 2). These tests were conducted in a research quality laboratory wind tunnel where the flow was unducted consistent with most typical applications. The results for the ducted and jet impingement flows, though similar to the unducted case, will be presented in a future article along with a secondary graphite foam material, “foam B”.

Table 2. Comparative Thermal and Physical Properties of Metals and Foams

### Test Procedure

Prior foam experimentation by Coursey and Boudreaux [1] utilized solder brazing to affix the foam heatsink to a heated component. This solder method was chosen to reduce the problematic interfacial resistance when using foams due to their porous nature. Directly bonding the heatsink to a component has two potential drawbacks. The first involves the high temperatures common in brazing, which could damage the electrical component itself. The other drawback of soldering involves the complication of replacement or rework of the component. Due to the low tensile strength of foam, (Table 2 [2]), a greater potential for heatsink damage occurs when compared to an aluminum or copper variant. If the heatsink is damaged, or if the attached component needs to be serviced, the bonding method increases the cost of rework.

To avoid these problems it is possible to solder the foam heatsink to an aluminum or copper carrier plate. This foam and plate assembly could then be mounted to a component in a standard fashion. This carrier plate would also allow for sufficient pressure be applied to the interface material, ensuring low contact resistance.

In this study the heatsinks were clamped directly to the test component without a carrier plate for a standard across all three materials. A high performance thermal grease [3] was used as an interface material to fill the porous surface of the foam and reduce interfacial resistance compared to a bare joint.

A total of five J-type thermocouples were used during the testing, they were placed upstream of the heatsink to record ambient air temperatures, in the heater block, in the center of the heatsink base, at the edge of the heatsink base, and in the tip of the outermost fin.

A thin film heater was set at 10 watts during all testing, and the heat source area was 25 x 25 mm, or a quarter of the overall sink base area, Figure 1. To insulate the bottom of the heater both cardboard and FR-4 board were used, the estimated value of Ψjb is 62.5°C/W. Throughout testing the value of Ψjb was 36 – 92 times greater than that of Ψja.

Figure 1. Exploded view of the heatsink test assembly.

### Results

As expected, the traditional copper and aluminum heatsinks preformed similarly, the main difference being due to the higher thermal conductivity of copper, which reduced spreading resistance.

During low velocity flow conditions the lower heat transfer rate dictates that the convection thermal resistance makes up a large portion of the overall Θja. As flow speed increases, the convection resistance decreases, and the internal heatsink conduction resistance becomes more of a factor in the overall Θja value. This behavior is evident when comparing the different heatsink materials. The graphite heatsink thermal performance was only 12% lower than aluminum at low flow rates, while this performance difference increased to 25-30% as the flow rate increased (Table 3) .

Table 3. Specific Thermal Test Results

Due to the lack of a solder joint, the foam heatsink experienced a larger interfacial resistance when compared to the solid heatsinks. This difference can be seen when comparing ΨHEATER-BASE in Table 3. To decouple the effect of interfacial resistance ΨBASE-AIR can be calculated. When ignoring interfacial resistance in this manner foam performs within 1% of aluminum at 1.5 m/sec (300 lfm), and within 15% at 3.5 m/sec (700 lfm).

### Conclusion

Graphite foam derived heatsinks show promise in specific applications, but exhibit several drawbacks in the mainstream electronics cooling industry. Due to the fragile nature of graphite foam, unique precautions must be taken during the handling of the heatsink and its use. When coupled to a copper base plate, graphite foam can perform with acceptably small spreading resistances. However the lower thermal conductivity of the foam reduces thermal performance at high flow velocities when compared to a traditional copper heatsink.

The mechanical attachment needed to ensure acceptable thermal interface performance without soldering or brazing is also an issue that prevents a foam based heatsink from being explored in many mainstream applications. Despite these challenges the thermal performance to weight ratio of foam is very attractive and well suited to the aerospace and military industries were cost and ease of use come second to weight and performance.

### References

1. Coursey, J., Jungho, K., Boudreaux, P. “Performance of Graphite Foam Evaporator for use in Thermal Management,” Journal of Electronics Packaging, Vol.127, June 2005, pp. 127-134.
2. Klett, J., “High Conductivity Graphitic Foams,” Oak Ridge National Laboratory, July 18, 2003, pp.1-53.
3. Shin Etsu X23.

## The Importance of Fan Efficiency

Why is fan efficiency so important? As a general rule, successive generations of electronic enclosures such as personal computers, telecommunications cabinets, as well as system routers, pack increasing functionality into smaller and smaller spaces. Accompanying this trend is the need to remove ever higher levels of heat energy from within those enclosures. Thermal engineers will often force air through a system using fans to regulate the internal temperatures; however as the aerodynamic performance increases so will input power.
In modern day equipment racks it’s not uncommon for the total fan load to be a significant factor in the system’s power budget. Coupled with the advent of equipment efficiency legislation and a growing awareness of cost of ownership, fan efficiency is becoming a critical selection parameter. Engineers now need to gain an understanding of fan efficiency, balancing it against more familiar metrics such as airflow and noise.

## Understanding Fan Static Efficiency

Fan manufacturers typically provide static efficiency as the value of efficiency, while total efficiency includes the outlet velocity term. Fan total efficiency is calculated using total pressure. Static efficiency is calculated using only static pressure.
Positive static pressure is created as a fan moves air through a system. Negative static pressure is what all other components in the airflow path create as they resist air movement. Different fan types will generate different airflow values while creating a positive static pressure to balance the negative static pressure caused by system obstructions. The fan performance curve (see Fig 1) is a representation of the airflow (X axis) that a particular fan type produces to overcome given static pressure values (Y axis).
Total pressure is the summation of static pressure and outlet velocity pressure. Outlet velocity pressure does not contribute to a fans ability to remove system heat energy; therefore it’s not normally included in fan efficiency calculations.

## Calculating Fan Efficiency

As with any energy converter, efficiency is the ratio of input and output power:-
Fan efficiency = Pout / Pin
Fan input power (Pin) is:-
Pin (Watts) = V <Volts> x I <Amps>
Fan output power (Pout) or airpower using Metric units is:-
Pout (Watts) = Air pressure <m3/sec> x Air flow <Pascal’s>
Using standard units the formula becomes:-
Pout (Watts) = (Air pressure <inch H2O> x Air flow <cfm>) / 8.5
Example:-
A 48V fan drawing 1A working at an operating point of 200 cfm and 0.5 inch H2O
Pin = 48 x 1 = 48 W
Pout = (200 x 0.5) / 8.5 = 11.76 W
Fan efficiency = 11.76 / 48 = 0.245 or 24.5 %

## The Fan Efficiency Curve

Fan efficiency varies dramatically as a function of aerodynamic loading. Because airpower is the product of flow and pressure, a fan working in the free air condition (no backflow pressure) has zero pressure and thus is producing no airpower and by definition has zero efficiency. Similarly, a fan in the fully shut off condition (no flow) has zero flow and is also producing no airpower and zero efficiency. The peak efficiency of an axial fan typically occurs at a pressure point of 1/3rd the maximum pressure.
Figure 1 below represents a performance plot of a 120mm size axial fan with curves for both airflow and efficiency.

Figure 1: Pressure vs. Flow Curve – 120mm Axial Fan
As a general rule, fan efficiency increases with blade diameter and speed. Fan manufacturers are now focusing on higher efficiency fans, resulting in new designs with significantly increased peak efficiency compared to older designs.
Table 1 provides an indication of peak efficiency values for different standard axial fan sizes and the comparative improvement with newer generation designs.
Table 1: Axial Fans Typical Peak Efficiency

Form Factor Old New
40 x 40 10% 25%
60 x 60 14% 30%
80 x 80 16% 33%
92 x 92 18% 35%
120 x 120 24% 40%
172 round 35% 45%

## Fan Selection Taking Account of Efficiency

Historically, fans were chosen by finding a standard form factor to occupy the available space and then matching airflow performance against system requirement; typically using free flow as a figure of merit. This approach has the potential for missing significant power savings which could be realized by carefully matching fan efficiency to the system operating point.
In the example shown below, (Fig. 2), selecting the fan based upon free air performance would favor the high flow fan option. Overlaying the system resistance line on the performance curve shows the high flow fan would achieve the required performance of 110cfm at 0.48 inch H2O. However, comparing this fan efficiency at the operating point against an alternative lower free air flow fan design, it can be seen the second design would actually provide higher efficiency while still meeting the duty point.

Figure 2: Pressure Vs. Flow Curve with Fan Efficiency and System impedance

## Benefits of Selecting High Efficiency Fans

Higher levels of power are required to cool the large amount of heat generated by today’s high end servers. As a result, more electrical power will be needed to be allocated to the system’s cooling components. In some instances, 25% or more of the total power budget for a high end rack system is allocated to the cooling fans.
Using high efficiency fans has a cascade effect on system design. Power supplies can be down sized saving weight and space and the fans power distribution network can be minimized.
The long term benefit of specifying high efficiency fans is a reduction of ownership costs. Large data centers can contain tens of thousands of servers with anywhere between 10 and 50 fans in each. A few percentage points improvement in the efficiency of every fan installed can quickly represent many thousands of dollars in annual energy savings.
High efficiency fans can be more costly than older fan types, and this can be seen as a deterrent. Engineers and purchasing managers should understand the wider implications of using these newer fan designs. System level savings can result from the lower power requirements and substantial energy savings can be realized by the end user.

Authored by:
Mr. Nigel D. Strike
Principal Engineer
NMB Technologies Corporation
A Minebea Group Company
Cool Tech R & D Facility
Tempe, Arizona, USA

### Thermal Analysis of a Low Noise Amplifier

LNA Design Series – part 13

From RF Design HQ

It is time to make sure that all transistors are going to operate reliably at maximum temperatures.  For this analysis you can use Avago’s AppCAD Design Assistant.  We used this tool early in this series to plot some gain, Noise Figure and circuit stability circles.  This time we will showcase its Device Thermal Calculator tool.

## 1. Thermal Analysis of the ATF-34143

### Operating Temperature

In the previous Thermal Analysis screenshot I’ve plugged in the numbers for the Bias Voltage (Vin), Bias Current (Iin), Input Power (Pin), Output Power (Pout), PCB Thermal Resistance (Θca), Junction or Channel Resistance (Θjc), and Ambient Temperature (Ta).

Figure: Device Max Temperature Warning

Hidden deep in the preferences menu is an option to enter a Device Maximum Temperature Warning.  For the ATF-34143 it is 160°C as entered.  In reality we should enter a much lower number depending on the reliability targets of the design.  For reference, below is an excerpt from the AD-A153 744 “Reliability Derating Procedures” specific to GaAs for example.

Figure: GaAs Fet Device Derating Levels

Figure: ATF-34143 Absolute Maximum Ratings

So far everything looks to be well within the maximum operating conditions in regards to Channel Temperature with a Channel Temperature of 87°C vs. a maximum of 160°C.

### Total Power Dissipation

If you read Note 4 in the Absolute Ratings listed above we should take into account a reduction in Power Dissipation capability due to the Source leads at temperatures above 40°C. To be safe, we will use the Case Temperature (Tcase) of 72°C that was calculated with the Device Thermal Calculator.  This results in a 192mW((72-40)/6=192) degradation in Total Power Dissipation capabilities of the ATF-34143.  This results in a Total Power Dissipation maximum of 533mW.  Our previous analysis calculated this value to be a worst case of 89mW at an ambient temperature of 70°C.  This means the device will be operating safely below it’s absolute maximum temperatures.

## 2. MGA-53543 Operating Temperature and Power Dissipation

Listed below are the Maximum Ratings we need to perform the analysis for the MGA-53543.

Figure: MGA-53543 Absolute Maximum Ratings

### Lead Temperature of the MGA-53543

When we consider Device Lead Temperature as specified in note 2 of the Absolute Maximum Ratings sections of the data sheet.  We only need to derate the Power Dissipation capability if we exceed a lead temperature of 96°C.  The analysis presented below shows that the case temperature will not exceed 77°C making the derating of the Power Dissipation unnecessary.

Thermal Analysis of the MGA-53543

### Thermal Results for the MGA-53543

• The Maximum Junction Temperature remains below 150°C at 130°C.
• The Total Power Dissipated at heat is 335mW with a maximum allowed of 400mW.

## 3. ATF-50189 Operating Temperature and Power Dissipation

If you remember in Part-11 during the board layout of the ATF-50189, we went through great lengths to ensure good placement of large headed screws.  This was to achieve a strong contact to the case for improved heat dissipation.  Since this is the most power hungry of the devices in this amplifier design, it will help make this amplifier reliable under stressful conditions.

ATF-50189 Absolute Maximum Ratings

The ATF-50189 is in a SOT-89 package and is best suited for high linearity amplifiers because of their low Thermal Resistance.  This device achieves a Channel Resistance of 29°C/W which makes achieving reliable performance possible.

ATF-50189 Thermal Analysis

In this analysis you may have noted that we also depend upon an improved PCB Thermal Resistance.  This is due to the large Screws that are placed near the SOT-89 package.  If we really need to improve upon the heat transfer we can always opt for some brass screws.  That will certain shunt the heat more effectively than stainless steel.

ATF-50189 Analysis Results

Power Dissipation = 914mW  (Max 2250mW)
Channel Temperature = 111°C (Max 150°C)

## Summary

This analysis shows that all of the devices are well suited to meet the rugged reliability requirements needed of this design specification as outlined in part-1.  In this analysis we entered the parameters and examined the results against the Absolute Maximums.  You can also use the AppCAD design tool to determine the target case temperature to achieve channel temperatures that will provide the desired reliability/deratings a given application may require.  Making this a good heat sink design specification tool as well.

This concludes the thermal analysis of the Low Noise Microwave Amplifier design.

### THERMAL DESIGN EXPLORATION FOR THE OPEN COMPUTE PROJECT

By Tom Gregory

The Open Compute Project Foundation is tackling a big challenge: how to scale computing infrastructure in the most efficient and economical way possible.

The Foundation, founded by Facebook, is fostering a rapidly growing community of engineers around the world whose mission is to design and enable the delivery of the most efficient server, storage and data centre hardware designs for scalable computing.

To achieve this aim the Open Compute Project Foundation provides a structure in which individuals and organisations can share their intellectual property with Open Compute Projects.

The University of Texas at Arlington (UTA) is one such organisation that is involved in the Open Compute Project. UTA wanted to investigate new cooling strategies to improve the thermal design of the Open Compute Project’s Intel-based servers. To assist this work the team at UTA turned to thermal simulation to help find a solution.

Two different methods were chosen to improve the server’s thermal design: one improved the ducting inside the server, while the other utilised warm water cooling. To assess these options UTA used the 6SigmaET software throughout their project to create, simulate and fine-tune their proposed solutions to the server’s thermal design issues.

Solution 1: Improved Ducting

The first server had a removable chassis cover with an integrated air ducting system. However, this ducting was only provided in the CPU1 region: this caused excessive flow bypass in the CPU0 region, resulting in warm air entering heat sink 1. The university decided to investigate whether modifications to the server’s ducting system would improve its thermal performance.

Physical experiments were conducted on the server to determine its system impedance, flow rates, total server power consumption, fan speeds and fan power consumption at various power levels. This experimental data was used to generate and calibrate a detailed CFD model of the server using 6SigmaET. It was solved using the KE turbulence model, and the CFD model was matched with the temperatures obtained from testing. The CFD model and experimental data showed good agreement (see figure 1), with a maximum error of 12%.

###### Fig. 1: Comparison of experimental temperature results and CFD temperature results for CPU0

The university then used 6SigmaET to improve the server’s ducting system parametrically. The key goal was to reduce flow bypass in the CPU0 region without causing a temperature rise in the CPU1 region (and an increase in fan power, which would increase total server power consumption). The calibrated CFD model was used to parameterize the size and location of the duct, and solved for each new design iteration to determine how the processor temperatures would be affected in each case. This process led to a final design for the improved ducting system. This design was prototyped, then tested in the same way as the original server.

###### Fig. 2: Temperature plots of the original server (top) and the server with improved ducting (bottom).

The test results were positive: fan power consumption was reduced by 23.4-40%, fan speeds by 22-26% and flow rate by 31.3-37.3%, while the server’s temperature stayed within the recommended range (see figure 2).

Solution 2: Liquid Cooling

The university then investigated whether a liquid-cooled system would improve the server’s thermal performance. To achieve a completely liquid-cooled system, the air-cooled heat sinks were replaced with liquid-cooled cold plates and the system was sealed from the ambient air to prevent gaseous and component contamination.

A heat exchanger was incorporated to cool the air inside the server, as the remaining components are not directly liquid cooled. A combination of warm water and recirculated air would be used to cool the server. This solution required custom ducting to direct the recirculated air over the server’s DIMMs (dual in-line memory modules), PCH (Platform Controller Hub), hard drive (HDD) and other heat generating components.

A range of candidate ducts were designed, with the goal of ensuring adequate airflow through the system and keeping component temperatures within the server’s critical limits. These designs were modelled and simulated in 6SigmaET, and the results used to determine the optimum duct design.

A prototype was created from this design, which was then subjected to thermal testing. It was tested with water inlet temperatures from 27.5-45°C in increments of 2.5°C. The server was exercised computationally at idle, 40%, 60%, 80% and 100% CPU loading, and one test was performed with maximum CPU and memory power levels to provide continuous heat dissipation.

###### Fig. 3: CFD simulation showing airflow velocity through the improved system.

The thermal testing results showed a correlation between the server’s performance and the increased water inlet temperatures. The server’s cooling power consumption, radiator fan speeds, CPU temperatures and IT power consumption increased as the water temperature increased. However, the CPU temperatures remained below the critical die temperature of 80°C throughout the experiment.

The prototyped duct regulated the air flow through the DIMMs, HDD and other auxiliary components as expected, maintaining component temperatures below critical. The university concluded that there was ample incentive to operate at higher water temperatures, up to 45°C.

###### Fig. 4: DIMM temperatures from experimental tests. A4-A7 are closer to the internal radiator fan. A0-A3 are further from the fan, and are affected by pre-heat from the other DIMMS. The modified design maintains component temperatures below critical, up to 45°C

Conclusions

Both projects used thermal simulation to analyse airflow and temperatures in the original server and determine where improvements could be made. This allowed the university to create and test a range of designs, iteratively improve them, and determine which performed best. The design with the best results was then prototyped and physically tested, with good agreement between the CFD model and the experimental results. Thermal simulation using 6SigmaET reduced the time and cost of the design stage, and meant that a wide range of potential solutions could be investigated.

This case study gives a perfect demonstration of how thermal simulations give engineers a unique visual representation of the temperature and airflow inside equipment. This insight allows them to make better engineering decisions. Even in the context of a global mission like the Open Compute Project, these details matter and can make a big difference.

Tom Gregory is 6SigmaET Product Specialist at Future Facilities -http://www.6sigmaet.info/

### General aspects on fan selection and layout

By Dr. Ing. Walter Angelis

### Introduction and Description of Fan Types

Small ventilators are generally called fans. Depending on the geometrical design of the impeller, various constructional types are distinguished to indicate the main direction of the airflow. Here are the descriptions of the most important types of fans:

Axial Fans

Axial fans are characterized by their typical impeller form, which resembles a propeller (Figure 1). The air flows through the impeller essentially in parallel to the axis, giving rise to the nomenclature employed. The blade geometry required for different versions is generally calculated with a computer; e.g., using a CAD system. Axial fans for electronic cooling are usually equipped complete with an outer housing and an electric motor integrated into the impeller hub. This compact construction enables equipment installation in a minimum of space.

Figure 1. Impeller of an axial fan.

The appearance of the impeller in a radial fan is somewhat similar to that of a water wheel (Figure 2). Air intake occurs in an axial direction. The air passes through the impeller radially. Depending on whether the exhaust angle of the blade is greater or less than 90

o

forward or backward curved

. A special type of the impeller is the so-called

drum rotor

, which is equipped with a large number of short, forward-curved blades. In radial fans for electronic cooling, the drive motor is conventionally located in the suction area of the fan. This reduces the flow rate to a certain extent, but enables a compact design to be realized.

Mixed-Flow Fans

Since mixed-flow fans are rather similar in appearance to axial designs, they are often termed “semi-axial” fans. In mixed-flow fans, air is drawn into a mixed-flow impeller axially and exhausted diagonally. Mixed-flow fans therefore represent an intermediate solution between axial and radial design. As a result, the mixed-flow fan can generate a higher pressure for the same overall dimensions and speed than an axial fan, although it cannot achieve the pressure values of a radial fan.

### Curve Representation with Dimensionless Parameters

By considering the physical laws for transferring model measurement results to similar versions (termed “similarity mechanics”), characteristic fan curves may be represented in a dimensionless manner. The pressure increase and the flow rate are referred appropriately to the rational velocity u at the perimeter, the outer diameterD of the impeller, and the density p of the fluid medium resulting in the dimensionless parameters “pressure figure” and “volume figure” :

The parameters are also particularly suited for comparing versions of different designs, dimensions and speed with one another. Figure 3 illustrates this comparison for typical characteristic curves of the various designs, making the special advantages apparent. Particularly appropriate for application are:

• Radial fans for high increase in pressure and low flow rates
• Mixed-flow fans for medium pressure and medium flow rates
• Axial fans for high flow rates and low increase in pressure

Figure 3. Comparison of normalized curves for various fan designs.

### Noise Properties

Since many electronic units are located in the immediate vicinity of operating personnel, noise emissions should be as low as possible. The fan used must be optimized to reduce intolerable noise. For these reasons, the noise performance represents a device criterion for selecting a fan.

Sound is propagated in air by pressure waves. The effective value of the pressure changes is expressed relatively as sound pressure level in decibels (dB). The so-called A weighting curve is commonly employed today. The sound pressure level obtained is correspondingly expressed in dB(A).

Since the sound pressure level varies with the distance and direction to a device, its suitability as magnitude for judgement is only limited. By contrast, the sound power level comprises entire sound emissions; the procedure for determining this level from sound pressure measurements is contained in the German DIN 45635 Part 38.

### Characteristic Acoustical Curve

The sound radiation of a fan changes with its operating state, so that the DIN sound power level is only conditionally indicative for applications in which the fan does not operate under optimum conditions. The above mentioned pressure chamber enables the sound pressure level to be determined in relation to the pressure increase or the flow rate resulting in a “characteristic acoustical curve” of the fan.

Figure 4 depicts this characteristic for an axial fan and a radial fan, whereby the sound pressure level measured at a distance of 1 m from the intake side of the fan is depicted as a function of the flow rate.

Figure 4. Sound pressure level characteristic; comparison between axial and radial fan.For axial designs, a sharp increase in noise is particularly noticeable when the flow rate is excessively restricted. The axial fan enters as operating range in which the air flow no longer follows the contour of the impeller hub, resulting in additional noise.

### Conclusions

For cooling of electronics devices, besides less relevant types of fans, three major types of fans are used: Axial, Radial and Mixed-Flow. The appropriate applications for these three types are the following:

• Axial fans for low increase in pressure and high flow rates
• Radial fans for high increase in pressure and low flow rates
• Mixed-flow fans for medium increase in pressure and medium flow rates

The differentiation between these types, depending on flow rate and pressure increase, can be made with the help of the dimensionless parameters.

The ideal blade geometry, based on the specific flow rate, pressure increase and rpm of rotor, is usually designed by a computer. For this point of operation and the ideal blade geometry you can achieve the highest aerodynamic efficiency. This point of highest aerodynamic efficiency matches approximately the point of minimal noise generation. For this reason the smallest noise generation can only be achieved for the given point of operation.

### Reference

Harmsen, S.: Equipment Fans for Electronic Cooling Function and Behaviour in Practical Application, verlag moderne industrie, 1991.

### Thermal Resistance

INTRODUCTION

Generally, the life of a device would decrease to half, and the failure rate would double whenever Junction Temperature, Tj, goes up by 10°C. Moreover, when Tj exceeds 175°C, a device has the possibility of breaking.Therefore, it is necessary to keep Tj in the proper temperature range, which is the lower the better, and a heat design should be done under the condition of the range of 80-100℃.In fact, it is difficult for IC packages that handle high power to keep Tj in this range. Therefore, it is common to make Tj the 80% of a maximum permissible temperature.A value of a thermal resistance is dependent on a chip, a layout of a leadframe, a board, and so forth. It means even if sizes of the IC packages are the same and layouts of leadframes are different, thermal resistances are not the same.

DEFINITIONS

The thermal resistance of a IC package is calculated by the difference between Tj and the ambient Temperature, Ta, under the condition that the IC package dissipates electric power of 1W. Here are three expressions of the thermal resistance, and each term of expressions are defined in Table1 and Fig.1.

Fig.1 Thermal resistances of a IC package
Table1 Definitions
Item Definitions
θja thermal resistance between Tj and Ta
ψjt thermal resistance between Tj and Tc1
θjc thermal resistance between Tj and Tc2
θca thermal resistance between Tc and Ta
Tj junction temperature
Ta ambient temperature
Tc1 temperature of the top surface of IC package
Tc2 temperature of the bottom surface of IC package
Pd maximum permissible power

Estimation of Tj when ψjt is known

Tj can be estimated by following order

1. Power, P, is calculated by operating current and voltage.
2. Tc1 is measured by using a thermometer like a radiation thermometer and thermocouples.
3. Tj is calculated by Tc1, and ψjt which is shown in Table 3.

Tj=ψjt×P + Tc1Note) θja and ψｊt in Table 3 are measured values based on JEDEC with no wind.Each value is dependent on a chip, a layout of a leadframe, a board, and so forth.

Measurement of Thermal Resistance

The measurement of thermal resistance is based on JEDEC.

[Test board]The outline of the measurement board is shown in Fig.2, which is based on JEDEC.

Fig.2 Measurement board

Note)

• Board material : FR-4
• Board dimension:
• ( 2-layer board ) 114.3×76.2mm,Thickness 1.57mm
• ( 4-layer board with Cu foil 1,2 ) 114.3×76.2mm,Thickness 1.6mm
• Cu foil dimension : 74.2×74.2mm (Thickness 35µm) are applied to 4-layer board, as Cu foil 1, 2.
[Chip for measurement of Thermal Resistance]A chip is composed of elements of a resistance and a diode. The resistance is used for heating, and the diode is for a sensor of temperature. We have three kinds of size, because thermal resistance is dependent on a chip size.

Fig.3 Image of the chip

[Measurement of K factor]Tj cannot be measured directly. However, by a character of a forward voltage, V F of a diode is dependent on temperature. Therefore, Tj is known during a measurement by measuring VF.However, dependency of diode which called K-factor, K, should be measured first.

[JEDEC chamber]

• JEDEC chamber with no wind condition (still air) is adopted.The ambient temperature is measured with thermocouples at the position that is located 25.4mm below the center of the IC package.
• Fig.4 JEDEC chamber
[Measurement circuit]Fig.5 Measurement circuit
[Measurement procedure]

1. VF0 is measured by giving the diode with a current (1mA), IM, at the ambient temperature.
2. A Voltage, VH, is given to the resistance in the chip until temperature at upper surface of the IC package, which is measured with a radiation thermometer, is saturated. After confirming the saturation, IH is read.
3. VFSS is measured by giving the diode with a current, IM.

Fig.6 Timing of measurement

Note) VH is measured at three points, the voltage of Tstg-max, Vstg-max, and lower and higher than Vstg-max.

[Calculation]θja an ψjt are calculated from the following Table 2.

Table 2 Thermal resistance calculation

[The Permissible Regions of Dissipated Power]Pd is the maximum permissible power at Ta=25°C.Pd is dependent on the ambient temperture, which is shown in Fig.7.

Fig.7 The maximum permissible power

Thermal Resistance of each package

There are typical measured value based on JEDEC with no wind. Each value is dependent on a chip, a layout of a leadframe, a board, and so forth.

Table 3 Thermal resistance of each package
PKG 2 layer board 4 layer board
Tj:125°C Tj:150°C Tj:125°C Tj:150°C
θja ψjt Pd@Ta=25°C θja ψjt Pd@Ta=25°C
(°C/W) (°C/W) mW (°C/W) (°C/W) mW
DMP8 235 47 425 530 175 40 570 710
DMP14 195 47 510 640 150 40 665 830
DMP16 195 47 510 640 150 40 665 830
DMP20 150 37 665 830 120 33 830 1040
SOP8 JEDEC(EMP8) 180 34 555 690 125 29 800 1000
SOP16 JEDEC(EMP16-E2) 110 21 905 1135 70 18 1425 1785
SOP8 165 26 605 755 110 23 905 1135
SOP14 125 21 800 1000 80 17 1250 1560
SOP22 120 18 830 1040 85 14 1175 1470
SOP28 155 37 645 805 125 33 800 1000
SOP40-K1 135 37 740 925 105 33 950 1190
SSOP8 270 42 370 460 210 36 475 595
SSOP8-A3 215 36 465 580 155 15 645 805
SSOP10 270 42 370 460 210 36 475 595
SSOP14 225 38 440 555 180 33 555 690
SSOP16 210 35 475 595 160 26 625 780
SSOP20 185 34 540 675 140 26 710 890
SSOP20-B2 200 34 500 625 150 26 665 830
SSOP20-C3 130 13 765 960 85 9 1175 1470
SSOP32 110 20 905 1135 70 14 1425 1785
SSOP44 110 20 905 1135 70 14 1425 1785
TSSOP54-N1 105 10 950 1190 75 9 1330 1665
HSOP82) 160 28 625 780 50 12 2000 2500
HTSSOP24-P12) 115 14 865 1085 45 7 2220 2775
MSOP8(TVSP8) 215 27 465 580 160 23 625 780
MSOP10(TVSP10) 215 27 465 580 160 23 625 780
MSOP8(VSP8) 210 33 475 595 155 25 645 805
MSOP10(VSP10) 210 33 475 595 155 25 645 805
SC-88A 355 89 280 350 260 73 380 480
SC-82AB 365 89 270 340 255 72 390 490
SOT-23-5 260 70 380 480 195 60 510 640
SOT-23-6 245 70 405 510 175 60 570 710
SOT-89-31)2) 200 67 500 625 130 65 765 960
QFP32-J2 115 17 865 1085 90 15 1110 1385
QFP44-A1 95 17 1050 1315 75 15 1330 1665
QFP48-P1 65 17 1535 1920 50 15 2000 2500
LQFP48-R3 75 9 1330 1665 45 5 2220 2775
LQFP52-H2 85 11 1175 1470 65 11 1535 1920
QFP56-A1 105 17 950 1190 80 15 1250 1560
QFP64-H1 70 17 1425 1785 50 15 2000 2500
LQFP64-H2 65 6 1535 1920 50 5 2000 2500
QFP100-U1 55 5 1815 2270 45 5 2220 2775
TO-252-31)2) 105 17 950 1190 40 12 2500 3125
PLCC28 55 10 1815 2270 35 7 2855 3570
EPFFP6-A22) 370 59 270 335 220 53 450 565
EPFFP10-C42) 295 64 335 420 160 55 625 780
PCSP12-C3 240 40 415 520 140 33 710 890
PCSP20-CC 225 40 440 555 140 33 710 890
PCSP20-E3 225 40 440 555 130 33 765 960
PCSP24-ED 205 40 485 605 115 26 865 1085
PCSP32-F7 225 24 440 555 115 17 865 1085
PCSP32-G32) 205 24 485 605 115 17 865 1085
PCSP32-GD2) 205 24 485 605 115 17 865 1085
EPCSP32-L22) 210 29 475 595 95 16 1050 1315
DFN6-J1 (SON6-J1) 345 88 285 360 260 69 380 480
DFN4-F1 (ESON4-F1)2) 300 52 330 415 110 27 905 1135
DFN6-H1 (ESON6-H1)2) 280 42 355 445 110 26 905 1135
DFN8-U1 (ESON8-U1)2) 280 43 355 440 110 26 905 1135
DFN8-V1 (ESON8-V1)2) 215 16 465 580 70 8 1425 1785
DFN8-W2 (ESON8-W2)2) 195 21 510 640 60 8 1665 2080
QFN24-T1/T2 150 22 665 830 75 15 1330 1665
EQFN12-E22) 285 52 350 435 105 27 950 1190
EQFN12-E42) 285 52 350 435 105 27 950 1190
EQFN14-D72) 295 53 335 420 95 26 1050 1315
EQFN16-G22) 255 43 390 490 100 26 1000 1250
EQFN12-JE2) 215 22 465 580 80 10 1250 1560
EQFN16-JE2) 180 21 555 690 70 11 1425 1785
EQFN18-E72) 220 33 450 565 90 22 1110 1385
EQFN26-HH2) 160 15 625 780 60 7 1665 2080
EQFN24-LK2) 145 13 685 860 65 8 1535 1920
Notes
1) Thermal resistance values (θja,ψjt) are measured with the 2-layer board having 100mm2 copper foil, which is based on JEDEC.
2) Thermal resistance values (θja,ψjt) are measured with the 4-layer board having thermal via holes, which is also based on JEDEC.

Thermal Resistance depending on area of Cu foil

There are typical values by mounting on five kinds of boards, “PAT.1” through “PAT.5”, shown in Table 4 and Table 5.Those are 2-layer boards based on JEDEC. However, they do not have any thermal via holes.

Fig.8 Thermal Resistance depending on area of Cu foilTable 4 Image of Cu foil

 TO-252 SOT-89 SOT-23-5 SOT-23-6 PAT.1 PAT.2 PAT.3 PAT.4 PAT.5 –
 SC-88A SC-82AB PAT.1 PAT.2 PAT.3 PAT.4
 TO-252 SOT-89 SOT-23-5 SOT-23-6 SC-88A SC-82AB PAT.1 100mm2 PAT.2 225mm2 PAT.3 400mm2 PAT.4 600mm2 1600mm2 PAT.5 1225mm2 –

### Estimating Natural Convection Heat Transfer Coefficient on a Flat Plate

Although most of the emphasis today in the electronics cooling community is devoted to extending forced convection cooling capability, many applications still depend upon natural convection cooling. Basically, natural convection cooling combined with radiation is what results when a fan is not used in the cooling design to move air. Instead, movement of the air is induced by density differences resulting from the heat dissipated by the electronic components. An obvious advantage of natural convection, or “free” convection as it is sometimes called, is that the expense of incorporating a fan is avoided. Of course the penalty associated with this method of cooling is lower heat transfer coefficients.

To estimate the surface temperatures of components mounted on a card or board we sometimes approximate the surface as a flat plate. We can then use dimensionless natural convection correlations to estimate the natural convection heat transfer coefficient [1]. These correlations take the form,

where

 cp = Specific heat constant pressure gc = Gravitational acceleration Gr = Grashof number (dimensionless) h = Heat transfer coefficient k = Thermal conductivity of air L = Height or length of plate Nu = Nusselt number (dimensionless) Pr = Prandtl number (dimensionless) Ra = Rayleigh number (dimensionless) Ta = Temperature of ambient air Ts = Temperature of heated surface T = Temperature difference from surface to air B = Coefficient of thermal expansion for air = Density of air = Dynamic viscosity of air

The value of constant C and exponent n will depend upon the orientation of the heated surface as given in Table 1.

Table 1. Value of Constant C and Exponent n

 Plate Dimensionless Correlation (1) C n Simplified Formula for h C n Vertical .59 .25 1.42 .25 Horizontal (heated) .54 .25 1.32 .25 Horizontal (heated) .27 .25 .59 .25

Thermophysical properties of air for use in equations 1 and 2 may be found in any basic heat transfer textbook [2]. The values of air properties to be used should be at the mean film temperature, which is defined as the average of the surface temperature and the free air temperature away from the plate.

The problem in using these correlations is that we usually have an idea of the power being dissipated and want to calculate a surface temperature so that we can estimate some component internal temperature. Since we do not know the surface temperature a priori, we must guess a temperature to obtain the air properties and T to use in the correlations to calculate h.Fortunately, there is a simplified formula for air, which gives the heat transfer coefficient for natural convection of air over a flat plate [1]. This formula is of the form,

Although this formula also depends upon surface temperature, Ts, if we combine it with the Newton rate equation,

after a little algebraic manipulation we can obtain an expression for Ts as a function of the heat dissipation, q, from the plate surface,

A comparison of the value of natural convection h for a 100 mm square plate calculated using dimension-less equation 2 versus the simplified dimensional equation 3 is shown in Figure 1. These results show that the simplified formula underpredicts h by 3 to 6 % for the vertical plate and the horizontal plate with heated side up. For the case of a horizontal plate with the heated side down the simplified formula underpredicts h by 13 to 15 %.

Figure 1. Heat transfer coefficient plotted against surface temperature.The equations presented here are valid only for laminar natural convection. In most electronic cooling applications it is unlikely that turbulent natural convection will be encountered. It should also be noted that both the dimensionless equation and the simplified dimensional equation are valid only if there are no surfaces nearby to interfere with development of the natural convection boundary layer. The effect of nearby surfaces on natural convection heat transfer is a topic for future columns.

References
1. McAdams, W.H., Heat Transmission, 3rd ed., McGraw-Hill, New York, NY, 1954.
2. Incropera, F.P., and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, John Wiley and Sons, New York, NY, 1985.

### Thermal Characterization of IC Packages

Abstract: Thermal characterization of packages is critical for the performance and reliability of IC applications. This article describes the standard thermal package properties: thermal resistance (known as “theta” or Θ), ΘJA, ΘJC, and ΘCA. Thermal calculations and references for more information on thermal management are provided.

#### Introduction

Thermal management should be considered during package selection to ensure high product reliability. All ICs generate heat when power is applied to them. Therefore, to maintain the device’s junction temperature below the maximum allowed, effective heat flow from the IC through the package to the ambient is essential. This article helps designers and customers understand basic IC thermal-management concepts. In discussing package heat transfer, it defines important terms for thermal characterization, which begin with thermal resistance and its various “theta” representations. The article also provides thermal calculations and data to ensure proper junction (die), case (package), and board temperature.

#### The Importance of Thermal Resistance

Thermal management of semiconductors involves thermal resistance, which is an important figure of merit describing the heat transfer properties of material. In calculations, thermal resistance is identified as “Theta,” derived from the Greek word for heat, “thermos.” It is thermal resistance that particularly interests us.

The thermal resistance of an IC package is the measure of the package’s ability to transfer heat generated by the IC (die) to the circuit board or the ambient. Given the temperatures at two points, the amount of heat flow from one point to the other is completely determined by the thermal resistance. By knowing the thermal resistance of a package, one can calculate the IC’s junction temperature for a given power dissipation and its reference temperature.

The Maxim website (Manufacturing, Layout, Production, QA/Reliability, Procurement) provides information about commonly used thermal-resistance values for ICs.

#### Definitions

The following section defines Theta (Θ) and Psi (Ψ), standard terms used in thermal characterization of IC packages.

ΘJA is the thermal resistance from junction to ambient, measured as °C/W. Ambient is regarded as thermal “ground.” ΘJA depends on the package, board, airflow, radiation, and system characteristics. Generally, the effects of radiation are negligible. ΘJA values are listed for natural convention conditions (no forced air) only.

ΘJC is the thermal resistance from junction to case. Case is a specified point on the outside surface of the package. ΘJC depends on the package materials (the lead frame, mold compound, die attach adhesive) and on the specific package design (die thickness, exposed pad, internal thermal vias, and thermal conductivity of the metals used).

For leaded packages, the ΘJC reference point on the case is where pin 1 emerges from the plastic. For standard plastic packages, ΘJC is measured at the corner of pin 1. It is measured at the center of the exposed-pad surface for exposed-pad packages. The ΘJC measurement is done by attaching the package directly to an “infinite heat sink,” usually a liquid-cooled copper block which can absorb any amount of heat flow with no thermal resistance. The measurement represents the transfer of heat from the die to the package surface purely by conduction.

Note that ΘJC considers only the resistance of heat flow paths to the surface of the package. For this reason ΘJC is always smaller than ΘJA. Thus, ΘJC represents a specific, conductive, heat-path thermal resistance, whereas ΘJA represents conductive, convective, and radiative heat paths.

ΘCA is thermal resistance from case to ambient. ΘCA includes thermal resistances for all heat paths from outside the package to ambient.

Given the above definitions, we see that:

ΘJA = ΘJC + ΘCA

ΘJB is thermal resistance from junction to board. ΘJB quantifies the junction-to-board thermal path and is typically measured on the board adjacent to the package near pin 1 (< 1mm from the package edge). ΘJB includes thermal resistance from two sources: from the IC’s junction to a reference point on the package bottom, and through the board under the package.

To measure ΘJB, convection from the top of the package is blocked and a cold plate is attached to the board’s far side opposite the package location. See Figure 1 below.

Figure 1. Illustration of the process for measuring ΘJB.

ΨJB is the junction-to-board thermal-characterization parameter, measured in units of °C/W. The JESD51-12, Guidelines for Reporting and Using Package Thermal Information, clarifies that thermal-characterization parameters are not the same as thermal resistances. Instead, ΨJB measures component power flowing through multiple thermal paths rather than a single direct path, as in thermal resistance, ΘJB. Thus, ΨJB thermal paths include convection from the top of the package, a fact that makes ΨJB more useful for customer applications. Refer to the JEDEC standards JESD51-8 and JESD51-12 for more detailed specifications on this parameter.

Designers can determine ΘJB and ΨJB values by thermal modeling or direct measurement. In either case, follow these steps:

1. Control the power dissipation conditions appropriate for ΘJB or ΨJB.
2. Determine the die temperature, typically using a diode on chip.
3. Determine the PCB temperature at < 1mm from the package’s edge.
4. Determine the power dissipation.

ΨJT is the characterization parameter that measures temperature change between the junction temperature and the temperature of the top of the package. ΨJT is useful for estimating the junction temperature when the temperature on top of the package and the power dissipation are known.

### Junction Temperature

TJ = TA + (ΘJA × P)

Where:

 TJ = junction temperature TA = ambient temperature, and P = power dissipation in Watts

TJ can also be calculated by using ΨJB or ΨJT values as.

TJ = TB + (ΨJB × P)

Where:
TB = board temperature measured within 1mm of the package

TJ = TT + (ΨJT × P)

Where:
TT = temperature measured at the center of the top of package.

Note: product data sheets specify the maximum allowable junction temperature for each device.

### Maximum Allowable Power Dissipation

Pmax = (TJ-max – TA) / ΘJA

Maxim listings of maximum allowable power assume an ambient temperature of +70°C and a maximum allowable junction temperature of +150°C.

### Deration Function

This function describes how much the power dissipation must be reduced for each °C of ambient temperature over +70°C. The deration function is expressed in mW/°C.

Deration function = P / (TJ – TA)

Where:
TA is typically +70°C (commercial)

And:
TJ is the maximum allowable junction temperature, typically +150°C.

To find the maximum allowable power when the ambient temperature is above +70°C (for example, +85°C in the extended temperature range), proceed as follows:

Pmax85C = Pmax70C – (Deration Function × (85 – 70))

#### Thermal Characterization and Measurement Conditions

The thermal performance of an IC package must be measured with JEDEC-standard methodologies and equipment. Characterizations run with application-specific boards can yield different results. It is also understood that the JEDEC-defined configurations do not represent typical real-world systems. Instead, the JEDEC configurations allow standardized thermal analysis and measurements for consistency; they are most useful for comparing the thermal figures of merit among package variations.

JEDEC specifications are available at: JEDEC. Note that the JEDEC standards cover different thermal applications.

### JEDEC Specification Titles

JESD51: Methodology for the Thermal Measurement of Component Packages (Single Semiconductor Device)
JESD51-1: Integrated Circuit Thermal Measurement Method—Electrical Test Method (Single Semiconductor Device)
JESD51-2: Integrated Circuit Thermal Test Method Environmental Conditions—Natural Convection (Still Air)
JESD51-3: Low Effective Thermal Conductivity Test Board for Leaded Surface Mount Packages
JESD51-4: Thermal Test Chip Guideline (Wire Bond Type Chip)
JESD51-5: Extension of Thermal Test Board Standards for Packages with Direct Thermal Attachment Mechanisms
JESD51-6: Integrated Circuit Thermal Test Method Environmental Conditions—Forced Convection (Moving Air)
JESD51-7: High Effective Thermal Conductivity Test Board for Leaded Surface Mount Packages
JESD51-8: Integrated Circuit Thermal Test Method Environmental Conditions—Junction-to-Board
JESD51-9: Test Boards for Area Array Surface Mount Package Thermal Measurements
JESD51-10: Test Boards for Through-Hole Perimeter Leaded Package Thermal Measurements.
JEDEC51-12: Guidelines for Reporting and Using Electronic Package Thermal Information.

#### Summary of JEDEC Thermal, Multilayer Test-Board Specification JESD51-7

High Effective Thermal Conductivity Test Board for Leaded Surface Mount Packages

The thermal test board described in the JESD51-7 specification is most appropriate for Maxim IC applications.

Material: FR-4
Layers: two signals (front and backside) and two planes (internal)
Finished thickness: 1.60 ±16mm
Metal thickness:

• Front and backside: 2oz copper (0.070mm finished thickness)
• Two internal planes: 1oz. copper (0.035mm finished thickness)

Dielectric layer thickness: 0.25mm to 0.50mm
Board size: 76.20mm x 114.30mm ±0.25mm for packages less than 27mm on a side

### Component Side Trace Design

Traces should be laid out so that the test device is centered on the board. Traces must extend at least 25mm from the edge of the package body. Trace widths shall be 0.25 ±10% for 0.5mm or greater pitch packages. For packages with finer pitches, the trace width shall equal the lead width. Trace pattern and trace termination requirements are specified in JESD51-7.

### Backside Trace Design

Component side traces terminated with through-hole vias can be connected to the edge connector by traces or by wire (22 AWG or smaller, copper wire). JESD51-7 specifies the current limits for different wire sizes.

Power and ground planes must be unbroken except for via isolation clearance patterns. The planes must not be present within 9.5mm of the edge connector pattern.

A critical requirement for thermal performance in exposed-pad (EP) packages (such as QFNs, DFNs (dual flat pack no-leads), and EP-TQFPs) is the design of thermal vias under the exposed pad solder joint. In a typical thermal-characterization board design there is an array of 4, 9, or 16 thermal vias connecting to the nearest ground plane. The thermal improvement becomes asymptotic above 25 vias. Understanding the direct relationship between board thermal vias and system thermal performance is critical. Refer to JESD51-5 for board-design enhancements for exposed-pad packages.

### Solder Coverage

When customers characterize their board soldering processes, they should target 90% or better coverage under the solder joint. When the solder joint voids approach 50% or more, the resulting disconnection of thermal vias will have a catastrophic effect on thermal resistance.

#### Thermal Modeling

FLOTHERM® and other thermal-analysis software programs allow accurate package and system thermal predictions. When appropriate thermal models are combined with empirical data, the user can have high confidence that the results accurately reflect real-world applications.

Electrical design tools such as PSPICE or Cadence® toolscan be used to make simple thermal models of packages. The package elements are represented as resistors connecting to the board in a resistor network. When the package model is confirmed to agree with empirical data, then the model can be used to predict package variations, including: die sizes, exposed pad sizes, fused leads, or the number of grounds connected to planes. These “what if” models give a reasonably accurate prediction of customized configurations.