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.

WØRPK Home Page