**Semiconductor Heat Dissipation and Heat Sink Calculations**

**(with
a motor control H-Bridge design example)**

Ralph Wallio, WØRPK WØRPK at netINS.net

**IMPORTANT NOTE**

This discussion was written a couple of years ago. SOLUTIONS CUBED has since replaced these older modules with units using much more efficient MOSFET technology complete with heat sinks. See http://www.solutions-cubed.com/.

I
recently acquired a pair of MINI-MOD MOTOR MIND H-Bridge modules from SOLUTIONS
CUBED. These modules include PIC 16C620 processors which allow a master
controller to communicate H-Bridge motor commands via a serial data stream. The
MOTOR MIND uses an ALLEGRO A3952SW H-Bridge device with specifications allowing
motor voltage up to 30V, continuous motor current of 2A, and maximum power
dissipation of 3.5W when the device is operated without a heat sink in a 25dC
ambient environment or 10W when a heat sink holds tab temperature below 125dC (http://www.allegromicro.com/).

A seemingly simple application question about whether this device has the guts
to drive a 12V D.C. motor which draws 1.8A under design load has evolved into a
significant educational process. ALLEGRO includes very little power and heat
dissipation discussion in their device specification documents but NATIONAL
does offer LMD18200 Application Note 694 which includes a substantial segment
on power dissipation calculations. This discussion is based on NATIONAL's
contribution (http://www.national.com/design/index.html).

Worst case approximations of H-Bridge Total Power Dissipation (Ptot) requires
views of three contributors, Quiescent Power Dissipation (Pq), Conductive Power
Dissipation (Pcond) and Switching Power Dissipation (Psw),

**Ptot = Pq + Pcond + Psw**

**Quiescent Power Dissipation, Pq**

(Device power consumption under quiescent, no load, conditions)

Pq = Logic Supply Voltage x Logic Supply Current + Load supply Voltage x Load
Supply Current (under no load conditions)

Logic Vcc = 5V

Logic Icc(brake) = 40mA

Load Vbb = 12V (for the design example)

Load Ibb(off) = 6.5mA

**Pq = 5V x 40mA + 12V x 6.5mA = 0.28W**

**Conductive Power Dissipation, Pcond**

(Power dissipation of load current switches (two required). The equivalent
series resistance of the H-Bridge is approximately twice the on-resistance of
one switch.)

Pcond = 2 x Irms^2 x Rds(on)

Irms = worst case value of RMS load current = 1.8A (for the design example)

Rds(on) = ON resistance of each power switch at operating junction temperature

ALLEGRO specifications include Output Saturation Voltage, the
collector-to-emitter voltage drop, Vce(sat), for both source and sink drivers.
Worst case, 1.8V, occurs with maximum load current of 2A. Vce(sat) can be
converted to ON resistance using Rds(on) = Vce(sat)/Irms = 1.8V/2A = 0.9 Ohms.

**Pcond = 2 x 1.8A^2 x 0.9 = 5.8W**

**Switching Power Dissipation, Psw**

(Switching power dissipation is the combination of energy dissipated by
switches and protection diodes during the ON/OFF switching action.)

Psw = (Eon + Eoff) x F

Eon = (Vs Io Ton)/2 + Vs Qrr + Vs Io Trr

Eoff = (Vs Io Toff)/2

Vs = Load supply voltage = 12V

Io = Load peak current = 1.8A

Ton = Switch turn on time = 2.9uS

Toff = Switch turn off time = 0.7uS

Qrr = Protection diode recovered charge = 150 nanocoulombs

Trr = Diode reverse recovery time = 100nS

F = Operating frequency of H-Bridge = 15.625KHz

Eon = (12V x 1.8A x 2.9uS)/2 + 12V x 150nC + 12V x 1.8A x 100nS = 35.28-06
Watt-Seconds

12V x 1.8A x 0.7uS

Eoff = (12V 1.8A 0.7uS)/2 = 7.56-06 Watt-Seconds

**Psw = (35.28-06 + 7.56-06) x 15625Hz =
0.67W**

Approximate Total Power Dissipation, Ptot, can now be totaled,

**Ptot = Pq + Pcond + Psw = 0.28W + 5.8W
+ 0.67W = 6.75W**

Note that Pcond contributes 5.8/6.75=86% of the total. It appears we can
reasonably eliminate most of the design work by estimating Ptot as Pcond/.85
and thereby deal only with Irms and Rds(on) or Vce(sat).

The answer to the first question is YES, it is reasonable to drive a 12V motor
drawing 1.8A with the ALLEGRO A3952SW H-Bridge device. A second question now
surfaces, when dissipating 6.75W, what heat sinking methods can be used to
remove heat from the H-Bridge device? WAKEFIELD ENGINEERING,

manufacturer of a robust line of "Thermal Management Solutions",
(read, "heat sinks"), offers a significant thermal design technical
discussion in their current catalog. This discussion applies the concept of
THERMAL RESISTANCE, resistance to the flow of heat from a source, the
semiconductor junction, through the package or case, through a heat sink to the
ambient environment. WAKEFIELD's methods are used in this discussion (http://www.wakefield.com/).

We can quickly prove a heat sink will be required. Beyond ALLEGRO's graphed
specification that operation without a heat sink is limited to 3.5W of power
dissipation in a 25dC ambient environment, we can use the temperature rise
specification for the A3952SW package of 36dC/Watt. Starting at 25dC, and
dissipating 6.75W, that is 25dC + (36dC/Watt x 6.75W) = 268dC, well over the
maximum allowable junction temperature of 150dC.

We need to select a heat sink which will keep the tab and junction well below
150dC. For this we will need to establish an ambient environment and for this
exercise we will use 25dC, normal room temperature. We will also need the
device junction-to-tab thermal resistance which is specified as 2.0dC/Watt. We
also will need to specify a tab-to-sink thermal resistance which could be as
low as 0.09dC/Watt but installation methods may set a practical limit of
0.50dC/Watt. Finally, we will need to set a desired maximum junction
temperature and for this exercise we will use 100dC, 2/3 of maximum (a
reasonably conservative constraint).

Thermal Resistance from junction to heat sink equals the sum of Thermal
Resistances from junction to tab and from tab to heat sink,

TRjs = TRjt + TRts = 2.0dC/Watt + 0.50dC/Watt = 2.5dC/Watt

Therefore change in junction Temperature (with a reasonable heat sink) is the
product of power dissipation and Thermal Resistance,

Delta Tj = 6.75W x 2.5dC/Watt = 16.9dC

Maximum heat sink temperature is calculated by subtracting junction temperature
change from desired maximum junction temperature,

MAX Ts = MAX Tt - DELTA Tj = 100dC - 16.9dC = 83.1dC

Finally, we calculate the allowable heat sink temperature rise when it is loaded
with 6.75W of power dissipation,

Delta Ts @ 6.75W = MAX Ts - Ta = 83.1dC - 25dC = 58.1dC

Consulting the WAKEFIELD catalog, we select the smallest, lightest, least
expensive product that will meet calculated requirements. WAKEFIELD makes
numerous cast, stamped and extruded heat sink designs. They provide thermal
performance specifications for both natural convection and forced convection
using blowers. Consulting the natural convection specifications, a product is
found that will dissipate 7.5W with a temperature rise of 58dC, our design
requirement. A 680-75A maximum efficiency omnidirectional heat sink is often
used with TO-3 (now known as type TO-204AA) and TO-220 devices but can be
ordered blank, with no holes. As it happens, heat sinks from this product line
are already available from lab stock and will be used for this project.