CHAPTER 7

7. Power amplifier.

Introduction

One of the important functions of the output stage of amplifiers are to provide high power and low output impedance so that the output signal could be delivered to the load without loss of gain.

Due to handling of large power, important parameters for the power amplifiers are different form small signal amplifiers, the most important being, efficiency, and linearity.

Inefficient large signal amplifier means large power will be dissipated in the transistors, which in turn will increase the internal junction temperature. The maximum junction temperature (ranging from to for silicon devices) if breached will destroy the transistors. Efficiency is also important to prolong the life of batteries in battery-powered circuits, to permit a smaller low-cost power supply or to forgo the need for cooling fans.

Linearity determines the goodness of the output stage design. None linearity will introduce large total harmonic distortion (THD).THD is the rms value of the harmonic components of the output signal, excluding the fundamental, expressed in a percentage of the rms of the fundamental. A high fidelity audio power amplifier features a THD of less than 1 %.

7.1. Classification of output stage.

Audio power amplifiers are classified primarily by the design of the output stage. Classification is based on the amount of time the output devices operate during each cycle of signal swing. It is also defined in terms of output bias current, (the amount of current flowing in the output devices with no signal).

Several class of power amplifier existed, such as Class A, B, AB, AB+B, C, D, T, G, H and other newer classes. The basic classes are A, B, AB, C and D. Class AB is actually a linearity improvement to class B. Class T is improvement to class D while Class G and H are improvements to increase the efficiency of class AB.

Class A

Class A amplifier as shown in Figure 7.1a operates with both devices conduct continuously for the entire cycle of signal swing. The Q point of the amplifier and its collector current waveform is shown in figure 7.1b and c. respectively. The bias current flows in the output devices at all times. The key ingredient of class A operation is that both devices are always on. Because of this, class A amplifiers are single-ended designs with only one type polarity output devices. Class A is the most inefficient of all power amplifier designs, averaging only around 20%. Because of this, class A amplifiers are large, heavy and run very hot. However, due to this type of operation, class A designs are inherently the most linear, with the least amount of distortion.

Figure 7.1a Class A power amplifier. and always conduct.

Figure 7.1b: DC load line of Class A

Figure 7.1c: The collector current waveform of class A amplifier Transistor conduction is of input cycle.

Class B

Class B circuit is shown in Figure 7.1d. Class B operation is the opposite of class A. Both output devices are never allowed to be on at the same time. Thus each output device is on for exactly one half of a complete sinusoidal signal cycle as shown in Figure 7.1e and f respectively. The bias is set so that current flow in a specific output device is zero when not stimulated with an input signal, i.e., the current in a specific output flows for one half cycle. The Q point and the collector current output waveform are shown in figure 7.1f and g respectively. Due to this operation, class B designs show high efficiency but poor linearity around the crossover region. This is due to the time it takes to turn one device off and the other device on, which translates into extreme crossover distortion. The Transfer characteristic and the cross over distortion are shown in Figure 7.1j and k respectively. This distortion, restricting class B designs to power consumption critical applications, e.g., battery operated equipment, such as 2-way radio and other communications audio.

Figure 7.1d: circuit of Class B operation.

Figure 7.1e: one half of class B amplifier. The npn transistor is on when input is positive.

Figure 7.1f: the other half of class B amplifier. Pnp transistor is switched on when the input is negative.

Figure 7.1h. Q point of Class B amplifier

Figure 7.1i: collector current waveform of Class B amplifier. Transistor conduction is exactly of input cycle.

Figure 7.1j: Transfer characteristic of class B amplifier.

Figure 7.1k: The dead band in the class B transfer characteristic results in cross over distortion in its output waveform.

Class AB

The simplified circuit of class AB amplifier is shown in Figure 7.1l. It behave like a class B amplifier. Class AB operation allows both devices to be on at the same time (like in class A), but just barely. The output bias is set so that current flows in a specific output device appreciably more than a half cycle but less than the entire cycle., as shown in Figure 7.1m n. That is, only a small amount of current is allowed to flow through both devices, unlike the complete load current of class A designs, but enough to keep each device operating so they respond instantly to input voltage demands. Thus the inherent non-linearity of class B designs is eliminated as illustrated in the transfer characteristic plot in Figure 7.1o . It is this combination of good efficiency (around 50%) with excellent linearity that makes class AB the most popular audio amplifier design. Several circuits exist for the implementation of class B. Such circuits are shown in Figure 7.1p q and r.

Figure 7.1l Class AB amplifier.

Figure 7.1m. Q point of class AB amplifier. The devices are always “just on”

Figure 7.1n: collector current waveform of class AB amplifier. Transistor conduction is more than of input cycle.

Figure 71o: Transfer characteristic of Class AB. The elimination of dead zone removes the cross-over distortion.

Figure 7.1p : diode biased class AB amplifier

Figure 7.1q: Class AB amplifier biased using “VBE multiplier as its biasing circuit.

Figure 7.1r: Another circuit of class AB amplifier.

Class C

The circuit of class C is shown in Figure 7.1s. In Class C the transistor conducts for less then of input cycle. In Class C, the amplifying device is deliberately not operated linearly. Instead, it is operated as a switch in order to reduce resistance loss. The Q point is set at imaginary negative extension of the dc load line, as shown in Figure 7.1t. It requires the input to be larger than to switch on the transistor. In effect, the tank circuit makes the RF output sine wave--like a bell that is struck at a constant rate by a hammer. A shown in Figure 7.1u

The efficiency of a typical Class C amplifier is very high. As is the case with Class B operation, the distortion from Class C operation is so high that SSB operation is precluded. Only CW, FM or FSK operation is practical. The harmonic output level from a Class C amplifier is substantial. Extra filtering is usually needed to control harmonic radiation.

Figure 7.1s: Class C amplifier.

Figure 7.1t: Q point of Class C amplifier.

Figure 7.1u: collector waveform of class c, transistor conduct for less than of input cycle.

Class D

Class D does not stand for digital. The class D amplifier block diagram is as shown in Figure 7.1v while its detail is shown in Figure7.1w.The input is converted to a two-state (binary) representation of the audio waveform.

Figure 7.1v block diagram of Class D amplifier.

Figure 7.1w: complete working diagram of class D amplifier.

Class D facts

Class D is a power-amplifier principle which using Pulse Width Modulation (PWM) to achieve high efficiency. The PWM signal consists of square waves, which minimize the power losses in the output stage of the power amplifier.

The efficiency of Class D can be up to 95% at full power. This means that a Class D amplifier delivering 950W, only waste 50W in heat and consume 1000W. At normal music, the average power will be around 10dB down from full power. At such level the Class D efficiency will be around 80%. This is the value that can be compared with the Class AB efficiency of 20% or the Class H of 50% at normal music level.

The high efficiency is the only benefit for the Class D compared to Class A, AB and B. There are no benefits in the sonic quality for the Class D over the Class A, AB and B amplifier!

Class D drawbacks

The Class D power amplifier needs a recovery filter between the output stage and the load (loudspeaker) to filter out the audio signal from the PWM square wave signal. This filter can only be optimised for one load impedance, which means that it will create a non-flat frequency response for reactive loads. This will colour the sound.

The recovery filter has to be steep filter slope to reduce the radio interference, which will be conducted via the speaker cables. To create a steep filter it requires several reactive components, which destroy the damping factor at high frequencies. A steep filter also destroys the phase behaviour of the signal. Too much phase distortion minimizes the ability to compensate the output stage and filter with negative feedback.

Negative feedback is needed to minimize non-linearity that produce distortion and lower the output impedance to achieve a good damping factor.

The only way to use a simpler recovery filter in Class D power amplifiers is to increase the switch frequency. Most Class D amplifiers use frequencies from 200-500 kHz. A switch frequency around 3MHz (3000kHz) will be needed to get the same performance of the simpler filter. The problem is that there are no output transistors available today, which can switch at such high frequency at high power.

Class D power amplifier suffers from bad reliability, as the high switch frequency makes the positive and negative transistors to cross conduct. Special timing circuits have to be used to solve the problem. However, these circuits produce crossover distortion. A full bridge Class D is a solution that can be reliable for reactive loads. A bridged Class D power amplifier can’t be bridged as a conventional Class AB, H or Class TD, as the Class D is already bridged. The exception is if the two bridged channels has separate power supplies.

A Class D amplifier needs a regulated power supply or some kind of ripple compensation. The power supply rejection used to be bad (<60dB) due to the low negative feedback around the Class D amplifier. A PWM modulated signal is very sensitive for power supply ripple, as the ripple will be multiplied with the audio signal and create intermodulation distortion.

Figure 7.1x shows the graphic diagram of major cause of imperfection of class D amplifier.

Figure 7.1x: source of imperfection of class D amplifier.

Class T

The block diagram of Class T is shown in Figure 7.1y. Class T (Tripath) is similar to class D with these exceptions: This class does not use analog feed back like its class D cousin. The feedback is digital and is taken ahead of the output filter, avoiding the phase shift of this filter. Because class D or T amplifier distortion arises from timing errors, the class T amplifier feeds back timing information. The other distinction is that this amplifier uses a digital signal processor to convert the analog input to a PWM signal and process the feedback information. The processor looks at the feedback information and makes timing adjustments. Because the feedback loop does not include the output filter, the class T amplifier is inherently more stable and can operate over the full audio band. Most listeners can not hear the difference between class T and good class AB designs. Both

class D and T designs share one problem: they consume extra power at idle. Because the high frequency waveform is present at all times, even when there is no audio present, the amplifiers generate some residual heat. Some of these amplifiers actually turn off in the absence of music, and can be annoying if there is too much delay turning back on.

Figure 7.1y: block diagram of class T amplifier.

Class G

Class G operation involves changing the power supply voltage from a lower level to a higher level when larger output swings are required. There have been several ways to do this. The simplest involves a single class AB output stage that is connected to two power supply rails by a diode, or a transistor switch. The design is such that for most musical program material, the output stage is connected to the lower supply voltage, and automatically switches to the higher rails for large signal peaks. Another approach uses two class AB output stages, each connected to a different power supply voltage, with the magnitude of the input signal determining the signal path. Using two power supplies improves efficiency enough to allow significantly more power for a given size and weight. Class G is becoming common for pro audio designs.

Class H

Class H operation takes the class G design one step further and actually modulates the higher power supply voltage by the input signal. This allows the power supply to track the audio input and provide just enough voltage for optimum operation of the output devices. The efficiency of class H is comparable to class G designs.

7.2. Analysis of power amplifier.

Analysis of power amplifier is to determine the important parameters, such as output power and power conversion efficiency. Analysis of THD is more complex.

Class A

Let analyse the class A power amplifier as shown in ‘Figure 7.2a.

The power conversion efficiency of an output stage is defined as

Since the output waveform is sinusoid, with peak voltage of with load

impedance of

Since the current in is constant and the average current in is equal to (sinusoidal current sitting on ) The average power drawn from the power supply is

Combining the relevant equation,

Since and the maximum efficiency is obtained when

giving the maximum efficiency of

Figure 7.2a. Class A amplifier.

Worked example 1

For the circuit in Figure 7.2b, calculate: The power delivered to the load, the average power drawn from the supplies and the power conversion efficiency if

and .

Figure 7.2b:

Solution

Since it’s a common collector circuit

Maximum output current is 100mA, hence maximum peak output

voltage is 10V.

= =

= =

Worked example 2

For the class A amplifier in Figure 7.2c calculate the output power, the power drawn from the supply and the conversion efficiency, given that ,

and provides maximum output signal.

Figure 7.2c common emitter class A amplifier.

Solution

=

Maximum output signal =

=

Power conversion efficiency,

Class B /AB

Let analyse the class B amplifier in Figure 7.2d. Analysis of class AB would be similar.

Figure 7.2d Class B amplifier.

With

The current drawn form the supplies are unidirectional as shown in Figure 7.2e.

Figure 7.2e: current waveform drawn from the supplies.

For the unidirectional current.

=

Conversion efficiency, =

when

With that

Power dissipated by the output power transistors is

Power dissipated in each transistor is

For maximum

Maximum power dissipated by each transistor, (also the minimum power rating

required for the power transistor ) is

Note: For circuits with biasing current.

Worked example 3

For the circuit in Figure 7.2f, calculate the output power, the power drawn from the supplies and the conversion efficiency, , when the input signal .

Figure 7.2f: Class AB power amplifier.

Solution

Average output power

= 2.39A

Power drawn from the supplies.

=

Power conversion efficiency,

Minimum power rating of the transistor is equivalent to L

2

2CC

dmxR

VP

Worked example 4

For the circuit in Figure 7.2g, calculate the output power, the power drawn from the supplies and the conversion efficiency, , when the input signal .

Figure 7.2g: Single rail class AB power amplifier.

Solution

Average output power

Power drawn from the supplies.

=

Power conversion efficiency,

Minimum power rating of the transistor is equivalent to L

2

2CC

dmxR

VP

7.3. Power Amplifier heat sinking

7.3.1. Introduction

With the increase in heat dissipation from microelectronics devices and the reduction in overall form factors, thermal management becomes a more important element of electronic product design.

Performance reliability and life expectancy of electronic equipment are inversely related to the component temperature of the equipment. A reduction in the temperature corresponds to an exponential increase in the reliability and life expectancy of the device. Thus controlling the device operating temperature within the limits set by the device design engineers, is necessary to maintain high reliability and life expectancy of the equipment.

Heat sinks are devices that enhance heat dissipation from a hot surface, usually the case of a heat generating component, to a cooler ambient, usually air. In most situations, heat transfer across the interface between the solid surface and the coolant air is the least efficient within the system, and the solid-air interface represents the greatest barrier for heat dissipation. A heat sink lowers this barrier mainly by increasing the surface area that is in direct contact with the coolant. This allows more heat to be dissipated and/or lowers the device operating temperature. The primary purpose of a heat sink is to maintain the device temperature below the maximum allowable temperature specified by the device manufacturers.

7.3.2. Thermal Circuit

The common terms in the concept of thermal circuit relevant to heat sinking are:

Q: total power or rate of heat dissipation in Watts, represent the rate of heat dissipated by the electronic component during operation. For the purpose of selecting a heat sink, the maximum operating power dissipation is used.

: maximum junction temperature of the device in °C. Allowable values range from 115°C in typical microelectronics applications to as high as 180°C for some electronic control devices. In special and military applications, 65°C to 80°C are not uncommon.

: case temperature of the device in °C. Since the case temperature of a device depends on the location of measurement, it usually represent the maximum local temperature of the case.

: sink temperature in °C. Again, this represents the maximum temperature of a heat sink at the location closest to the device.

: ambient air temperature in °C.

Using temperatures and the rate of heat dissipation, a quantitative measure of heat transfer efficiency across two locations of a thermal component can be expressed in terms of thermal resistance , defined as

Were is the temperature difference between the two locations. The unit of thermal resistance is in °C/W, indicating the temperature rise per unit rate of heat

dissipation. This thermal resistance is analogous to the electrical resistance , given by Ohm's law:

With V being the voltage difference and I the current.

Figure 1: Thermal resistance circuit

Consider a simple case where a heat sink is mounted on a device package as shown in Fig 4. Using the concept of thermal resistance, a simplified thermal circuit of this system can be drawn, as also shown in the figure. In this simplified model, heat flows serially from the junction to the case then across the interface into the heat sink and is finally dissipated from the heat sink to the air stream.

The thermal resistance between the junction and the case of a device is defined as

This resistance is specified by the device manufacturer. Although the value of a given device depends on how and where the cooling mechanism is employed over the package, it is usually given as a constant value. It is also accepted that is beyond the user's ability to alter or control.

Similarly, case-to-sink and sink-to-ambient resistance are defined as

respectively. Here, represents the thermal resistance across the interface between the case and the heat sink and is often called the interface resistance. This value can be improved substantially depending on the quality of mating surface finish and/or the choice of interface material. is heat sink thermal resistance.

Obviously, the total junction-to-ambient resistance is the sum of all three resistances:

7.3.3. Required Heat-Sink Thermal Resistance

To begin the heat sink selection, the first step is to determine the heat sink thermal resistance required to satisfy the thermal criteria of the component. By rearranging the previous equation, the heat sink resistance can be easily obtained as

In this expression, , Q and are provided by the device manufacturer, and

and are the user defined parameters.

The ambient air temperature for cooling electronic equipment depends on the operating environment in which the component is expected to be used. Typically, it ranges from 35 to 45°C, if the external air is used and from 50 to 60°C, if the component is enclosed or is placed in a wake of another heat generating equipment.

The interface resistance depends on the surface finish, flatness, applied mounting pressure, contact area and, of course, the type of interface material and its thickness. Precise value of this resistance, even for a give type of material and thickness, is difficult to obtain, since it may vary widely with the mounting pressure and other case dependent parameters. However, more reliable data can be obtained directly from material manufacturers or from heat sink manufacturers. Typical values for common interface materials are tabulated in Table 1. and Table 2

Table 1: Thermal properties of interface materials1

InterfaceThickness

(in)

,

Dry joint n/a n/a 2.9 9.9

Thermal Grease 0.003 0.7 0.9 8.1

Thermal compound

0.005 1.2 0.8 7.9

elastomer 0.010 5.0 1.8 8.9

Adhesive Film 0.009 0.7 2.7 0.6

Table 2: Thermal properties of interface materials1

Material Conductivity Thickness Resistance

W/in °C inches in2 °C/W

There-O-Link Thermal Compound 0.010 0.002 0.19

High Performance Thermal Compound

0.030 0.002 0.07

A-Dux (Thin film) 0.008 0.004 0.48

1080 Ther-A-Grip (double sided tape) 0.010 0.002 0.21

1081 Ther-A-Grip (double sided tape) 0.019 0.005 0.26

A-Phi 220 @ 20psi (gap fillers) 0.074 0.020 0.27

1897 in Sil-8 (pads) 0.010 0.008 0.81

With all the parameters on the right side of the expression identified, it becomes the required maximum thermal resistance of a heat sink for the application. In other words, the thermal resistance value of a chosen heat sink for the application has to be equal to or less than value for the junction

temperature to be maintained at or below the specified .

7.3.4. Heat-Sink Selection

In selecting an appropriate heat sink that meets the required thermal criteria, one needs to examine various parameters that affect not only the heat sink performance itself, but also the overall performance of the system. The choice of a particular type of heat sink depends largely to the thermal budget allowed for the heat sink and external conditions surrounding the heat sink. It is to be emphasized that there can never be a single value of thermal resistance assigned to a given heat sink, since the thermal resistance varies with external cooling conditions.

When selecting a heat sink, it is necessary to classify the air flow as natural, low flow mixed, or high flow forced convection. Natural convection occurs when there is no externally induced flow and heat transfer relies solely on the free buoyant flow of air surrounding the heat sink. Forced convection occurs when the flow of air is induced by mechanical means, usually a fan or blower. There is no clear distinction on the flow velocity that separates the mixed and forced flow regimes. It is generally accepted in applications that the effect of buoyant force on the overall heat transfer diminishes to negligible level (under 5%) when the induced air flow velocity excess 1 2 m/s (200 to 400 lfm).

The next step is to determine the required volume of a heat sink.. Table 3 shows approximate ranges of volumetric thermal resistance of a typical heat sink under different flow conditions.

Table 3: Range of volumetric thermal resistance

Flow condition

m/s (lfm)

Volumetric Resistance

cm3 °C/W (in3 °C/W)

natural convection 500-800 (30-50)

1.0 (200) 150-250 (10-15)

2.5 (500) 80-150 (5-10)

5.0 (1000) 50-80 (3-5)

The volume of a heat sink for a given low condition can be obtained by dividing the volumetric thermal resistance by the required thermal resistance. Table 3 is to be used only as a guide for estimation purposes in the beginning of the selection process. The actual resistance values may vary outside the above range depending on many additional parameters, such as actual dimensions of the heat sink, type of the heat sink, flow configuration, orientation, surface finish, altitude, etc. The smaller values shown above correspond to a heat sink volume of approximately 100 to 200 cm3 (5 to 10 in3) and the larger ones to roughly 1000 cm3 (60in3).

The above tabulated ranges assume that the design has been optimized for a given flow condition. Although there are many parameters to be considered in optimizing a heat sink, one of the most critical parameters is the fin density. In a planar fin heat sink, optimum fin spacing is strongly related to two parameters: flow velocity and fin length in the direction of the flow. Table 4 may be used as a guide for determining the optimum fin spacing of a planar fin heat sink in a typical application.

Table 4: Fin spacing (in mm) versus flow and fin length

Fin length, mm

Flow condition m/s (lfm) 75 150 225 300

Natural convection 6.5 7.5 10 13

1.0 (200) 4.0 5.0 6.0 7.0

2.5 (500) 2.5 3.3 4.0 5.0

5.0 (1000) 2.0 2.5 3.0 3.5

The average performance of a typical heat sink is linearly proportional to the width of a heat sink in the direction perpendicular to the flow, and approximately proportional to the square root of the fin length in the direction parallel to the flow. For example, an increase in the width of a heat sink by a factor of two would increase the heat dissipation capability by a factor of two, whereas and increase

the heat dissipation capability by a factor of 1.4. Therefore , if the choice is available, it is beneficial to increase the width of a heat sink rather than the length of the heat sink. Also, the effect of radiation heat transfer is very important in natural convection, as it can be responsible of up to 25% of the total heat dissipation. Unless the component is facing a hotter surface nearby, it is imperative to have the heat sink surfaces painted or anodized to enhance radiation.

7.3.5. Heat sink materials

The following materials are commonly used for heatsinks:

a. Aluminium. It has a thermal conductivity of 205W/mK, which is good (as a comparison: steel has about 50W/mK). The production of aluminium heatsinks is inexpensive; they can be made using extrusion Due to its softness, aluminium can also be milled quickly; die-casting and even cold forging are also possible (see part 2 of this guide for more information about production methods). Aluminium is also very light (thus, an aluminium heatsink will put less stress on its mounting when the unit is moved around).

b. Copper's thermal conductivity is about twice as high as aluminium - almost 400W/mK. This makes it an excellent material for heatsinks; but its disadvantages include high weight, high price, and less choice as far as production methods are concerned. Copper heatsinks can be milled, die-cast, or made of copper plates bonded together; extrusion is not possible.

To combine the advantages of aluminium and copper, heatsinks can be made of aluminium and copper bonded together. Here, the area in contact with the heat source is made of copper, which helps lead the heat away to the outer parts of the heatsink. The first heatsink for PC CPUs with an embedded copper piece was the Alpha P7125 (for first-generation Slot A Athlon CPUs). Keep in mind that a copper embedding is only useful if it is tightly bonded to the aluminium part for good thermal transfer. This is not always the case, especially not with inexpensive coolers. If the thermal transfer between the copper and the aluminium is poor, the copper embedding may do more harm than good.

Alpha P7125 base plate

The copper plate helps spread heat across the base plate.

AVC heatsink with copper core

The copper core helps the heat move to the upper parts of the heatsink.

Thermalright heatsink (prototype) with large heat pipe in the centre

A heat pipe provides substantially better thermal transfer than a solid piece of copper.

c. Silver has an even higher thermal conductivity than copper, but only by about 10%. This does not justify the much higher price for heatsink production - however, pulverized silver is a common ingredient in high-end thermal compounds.

7.3.6. Heat Sink Types

Heat sinks can be classified in terms of manufacturing methods and their final form shapes. The most common types of air-cooled heat sinks include:

a. Stampings: Copper or aluminium sheet metals are stamped into desired shapes. they are used in traditional air cooling of electronic components and offer a low cost solution to low density thermal problems. They are suitable for high volume production, because advanced tooling with high speed stamping would lower costs. Additional labour-saving options, such as taps, clips, and interface materials, can be factory applied to help to reduce the board assembly costs.

Heat sink by stamping

b. Extrusion: These allow the formation of elaborate two-dimensional shapes capable of dissipating large heat loads. They may be cut, machined, and options added. A cross-cutting will produce omni-directional, rectangular pin fin heat sinks, and incorporating serrated fins improves the performance by approximately 10 to 20%, but with a slower extrusion rate. Extrusion limits, such as the fin height-to-gap fin thickness, usually dictate the flexibility in design options. Typical fin height-to-gap aspect ratio of up to 6 and a minimum fin thickness of 1.3mm, are attainable with a standard extrusion. A 10 to 1 aspect ratio and a fin thickness of 0.8" can be achieved with special die design features. However, as the aspect ratio increases, the extrusion tolerance is compromised.

Extruded heatsink with classic design,

c. Bonded/Fabricated Fins: Most air cooled heat sinks are convection limited, and the overall thermal performance of an air cooled heat sink can often be improved significantly if more surface area can be exposed to the air stream. These high performance heat sinks utilize thermally conductive aluminium-filled epoxy to bond planar fins onto a grooved extrusion base plate. This process allows for a much greater fin height-to-gap aspect ratio

of 20 to 40, greatly increasing the cooling capacity without increasing volume requirements.

Bonded fin

d. Castings: Sand, lost core and die casting processes are available with or without vacuum assistance, in aluminium or copper/bronze. this technology is used in high density pin fin heat sinks which provide maximum performance when using impingement cooling.

Die-cast heatsinks made of aluminium and copper

e. Folded Fins: Corrugated sheet metal in either aluminium or copper increases surface area and, hence, the volumetric performance. The heat sink is then attached to either a base plate or directly to the heating surface via epoxying or brazing. It is not suitable for high profile heat sinks on account of the availability and fin efficiency. Hence, it allows high performance heat sinks to be fabricated for applications.

Thermalright "bonded fin" heatsink

Figure 2 shows the typical range of cost functions for different types of heat sinks in terms of required thermal resistance.

Figure 2: Cost versus required thermal resistance

The performance of different heat sink types varies dramatically with the air flow through the heat sink. To quantify the effectiveness of different types of heat sinks, the volumetric heat transfer efficiency can be defined as

where, m is the mass flow rate through the heat sink, c is the heat capacity of the fluid, and is the average temperature difference between the heat sink and the ambient air. The heat transfer efficiencies have been measured for a wide range of heat sink configurations, and their ranges are listed in Table 5.

Table 5 Range of heat transfer efficiencies

Heat sink type range, %

Stamping & flat plates 10-18

Finned extrusions 15-22

Impingement flow Fan heat sinks 25-32

Fully ducted extrusions 45-58

Ducted pin fin, Bonded & folded fins 78-90

The improved thermal performance is generally associated with additional costs in either material or manufacturing, or both

7.3.7. Thermal Performance Graph

Performance graph typical of those published by heat sink vendors are shown in Fig. 3. The graphs are a composite of two separate curves which have been combined into a single figure. It is assumed that the device to be cooled is

properly mounted, and the heat sink is in its normally used mounting orientation with respect to the direction of air flow. The first plot travelling from the lower left to the upper right is the natural convection curve of heat sink temperature rise,

, versus Q. The natural convection curves also assume that the heat sink is painted or anodized black. The curve from the upper left to lower right is the forced convection curve of thermal resistance versus air velocity. In forced convection, is linearly proportional to Q, hence is independent of Q and becomes a function only of the flow velocity. However, the natural convection phenomenon is non-linear, making it necessary to present as a function of Q.

Figure 3: Typical performance graphs

One can use the performance graphs to identify the heat sink and, for forced convection applications, to determine the minimum flow velocity that satisfy the thermal requirements. If the required thermal resistance in a force convection application is 8 °C/W, for example, the above sample thermal resistance versus flow velocity curve indicates that the velocity needs to be at or greater than 2.4 m/s (470 lfm). For natural convection applications, the required thermal resistance can be multiplied by Q to yield the maximum allowable The temperature rise of a chosen heat sink must be equal to or less than the maximum allowable at the same Q.

The natural convection curves assume an optional orientation of the heat sink with respect to the gravity. The flow velocity in the forced convection graph represents the approach flow velocity without accounting for the effect of flow bypass. There have been a limited number of investigations2,3 on the subject of flow bypass. These studies show that flow bypass may reduce the performance of a heat sink by as much as 50% for the same upstream flow velocity. For further consultation on this subject, readers are referred to the cited references.

When a device is substantially smaller than the base plate of a heat sink, there is an additional thermal resistance, called the spreading resistance, that needs to be considered I the selection process. Performance graphs generally assume that the heat is evenly distributed over the entire base area of the heat sink, and therefore, do not account for the additional temperature rise caused by a smaller heat source. This spreading resistance could typically be 5 to 30% of the total heat sink resistance, and can be estimated by using the simple analytical expression developed in Reference 4.

Another design criterion that needs to be considered in the selection of a heat sink, is the altitude effect. While the air temperature of an indoor environment is normally controlled and is not affected by the altitude change, the indoor air pressure does change with the altitude. Since many electronic systems are installed at an elevated altitude, it is necessary to derate the heat sink performance mainly due to the lower air density caused by the lower air pressure at higher altitude. Table 6 shows the performance derating factors for typical heat sinks at high altitudes. For example, in order to determine the actual thermal performance of a heat sink at altitudes other than the seal level, the thermal resistance values read off from the performance graphs should be divided by the derating factor before the values are compared with the required thermal resistance.

Table 6: Altitude derating factors

Altitude m Factor

0, sea level 1.00

1000 0.95

1500 0.90

2000 0.86

3000 0.80

3500 0.75

References

a. Aavid Engineering, Inc., EDS #117, Interface Materials, January 1992.

b. R.A. Wirtz, W. Chen, and R. Zhou, Effect of Flow Bypass on the Performance of Longitudinal Fin Heat Sinks, ASME Journal of Electronic Packaging",Vol.~116,pp.~206-211,1994.

c. S. Lee, Optimum Design and Selection of Heat Sinks, Proceedings of 11th IEEE Semi-Therm Symposium, pp. 48-54, 1995.

d. S. Song, S. Lee, and V. Au, Closed Form Equation for Thermal Constriction/Spreading Resistances with Variable Resistance Boundary Condition, Proceedings of the 1994 IEPS Technical Conference, pp. 111-121, 1994.

7.3.8. Worked example.

Worked example 1

What maximum power can a silicon transistor ( ) dissipate into free

air at an ambient temperature of

solution

Worked example 2

A 180-W silicon power transistor operated with heat sink ( ) and

mounting insulation of . What is the maximum power the transistor

could handle at ambient temperature of when and

Solution

=

Worked example 3

A power transistor need to dissipate a power of 60W at . A range of

heatsinks from to and a range of mounting

insulations form to is available. What is the power

rating and of the transistor required if, , derating factor is

.

Solution.

The minimum power rating of the transistor is 180W (at )

reasonable is