Appliance applications illustrate how to perform the necessary

thermal calculations using datasheet information supplied by

the semiconductor vendor.

Triacs are used to control ac mains loads in home appliances, and commercial and industrial equipment. In the majority of applications, the triac will dissipate sufficient power to make thermal considerations necessary. The size of heatsinks must be calculated, and the maximum junction temperature must be predicted. These thermal design procedures must be followed to ensure long-term reliability of the application.

The thermal design requires several stages of calculation involving power, thermal resistance and temperature rise, as illustrated by several triac (and one silicon-controlled rectifier; SCR) application examples. These include a vacuum cleaner, refrigerator compressor, washing machine and power tool designs.

### Calculating Triac Power

Triac power dissipation is influenced by the load current. Full sine-wave current (full-wave conduction) is assumed, as it presents the worst-case condition of maximum triac power dissipation. It also makes for the easiest calculations.

P = V_{O} × I_{TRIACAVG} + R_{S} × I_{TRIACRMS}^{2} (Eq. 1)

where P is the triac power (W), V_{O} is the triac knee voltage (V), I_{TRIAC}_{AVG} is the average load current (A), R_{S} is the triac slope resistance (Ω) and I_{TRIAC}_{RMS} is the root-mean-square (RMS) load current (A).

V_{O} and R_{S} are given in the NXP Semiconductors datasheets on the I_{TRIAC} / V_{TRIAC} curve. If the values are not available, they can be obtained from the I_{TRIAC} / V_{TRIAC} curve as described under the heading “Calculating V_{O} and R_{S}.” I_{TRIAC}_{AVG} is calculated from the application's RMS load current using Eq. 2. (This assumes full-wave conduction and sinusoidal load current, which will give worst-case power dissipation.) The value for I_{TRIAC}_{RMS} is measured in the application.

If half-wave conduction is necessary, as shown in **Fig. 1** for a SCR, here's how to calculate I_{TRIAC}_{RMS} and I_{TRIAC}_{AVG}:

### Calculating V_{O} and R_{S}

If values for V_{O} and R_{S} are not given in the datasheet, you will have to generate the data yourself. These can be derived from the device's datasheet, as shown in **Fig. 2**. First, make an enlarged photocopy of the I_{TRIAC} / V_{TRIAC} curve to increase accuracy. Second, in the graph of I_{TRIAC} versus the maximum V_{TRIAC} for T_{J}_{MAX}, draw a tangent through the point on the curve corresponding to the rated current of the triac. Third, the point where the tangent crosses the V_{TRIAC} axis gives V_{O}. In the fourth and final step, the slope of the tangent V_{TRIAC} / I_{TRIAC} gives R_{S}.

### Calculating T_{JMAX}

T_{J}_{MAX} is influenced by ambient temperature, triac power dissipation and the thermal resistance between junction and ambient. For this article, only the steady-state condition will be considered. In the short-term transient condition, transient thermal impedance (Z_{TH}) applies. This will always be lower than the steady-state thermal resistance (R_{TH}). The transient condition is more complicated to analyze and beyond the scope of this article.

T_{J} = T_{A} + P × R_{TH}_{J-A}, (Eq. 6)

where T_{J} is the junction temperature (°C), T_{A} is the ambient temperature (°C), P is the triac power (W) and R_{TH}_{J-A} is the junction-to-ambient thermal resistance (°C/W).

### Analysis of R_{THJ-A}

Thermal resistance is similar to electrical resistance, in that the total resistance can be broken down into several smaller resistances in series. For the most popular package (TO-220), R_{TH}_{J-A} is composed of the following resistances:

R_{TH}_{J-A} = R_{TH}_{J-MB} + R_{TH}_{MB-HS} + R_{TH}_{HS-A} (Eq. 7)

where R_{TH}_{J-MB} is the junction-to-mounting base thermal resistance (°C/W), R_{TH}_{MB-HS} is the mounting base-to-heatsink thermal resistance (°C/W) and R_{TH}_{HS-A} is the heatsink-to-ambient thermal resistance (°C/W).

R_{TH}_{J-MB} is fixed and governed by the device as it is influenced by die size (refer to the relevant datasheet for the exact value). R_{TH}_{MB-HS} is controlled by the equipment manufacturer because it is governed by the mounting method (for example, with or without thermal grease, screw or clip-mounted, insulating pad material). R_{TH}_{HS-A} is governed by the application and is under the sole control of the equipment manufacturer. **Fig. 3** illustrates these thermal resistance components.

Note that there are some important caveats in the way the thermal resistance is specified because it depends on the package type and the practicality of isolating a metallic thermal reference point. For example, for plastic packages without a metal mounting base, the expression R_{TH}_{J-MB} + R_{TH}_{MB-HS} is replaced by a single parameter of R_{TH}_{J-HS}, since the heatsink is the nearest metallic reference point. Also, for low-power plastic packages where a heatsink would not be used, only R_{TH}_{J-LEAD} is specified, because the leads are the nearest metallic reference point. Most of the heat would be conducted through the leads to the pc board, with a little radiated directly from the package to ambient. Finally, for some surface-mount packages without a mounting base but with a solder point instead, R_{TH}_{J-MB} is replaced by R_{TH}_{J-SP}.

The **table** lists the NXP triac packages and the means of specifying their thermal resistance. It shows thermal resistance values where they are fixed by the package type or mounting method. If a thermal resistance is influenced by the triac die, the specification becomes specific to that particular device, so it will be given in the datasheet.

### Vacuum Cleaner Example

A triac is used in a discrete phase-control circuit to control the speed of a vacuum-cleaner motor. Confirm by calculating for worst-case conditions that the triac's T_{J}_{MAX} of 125°C will not be exceeded. For this application, the motor power equals 1.8 kW max, the ac mains supply equals 230 V_{RMS} and, therefore:

Max I_{TRIAC}_{RMS} = P / V = 1800 W / 230 V_{RMS} = 7.83 A.

The triac is fixed to an air-cooled heatsink, without thermal grease. Bleed air is allowed to flow through the heatsink at all times, even if the main airflow is blocked. The heatsink is double insulated. Absolute maximum heatsink temperature is 70°C.

A 12-A Hi-Com triac is recommended to cope with the inductive load and high inrush current. We will take as our example the BTA212-600B. Its I_{GATE} of 50 mA is well matched to the typical discrete gate trigger circuit.

From the datasheet, V_{O} = 1.175 V and R_{S} = 0.0316 Ω.

Using Eq. 1, P = V_{O} × I_{TRIAC}_{AVG} + R_{S} × I_{TRIAC}_{RMS}^{2} = 1.175 V × 7.05 A + 0.0316 Ω × (7.83 A)^{2} = 10.22 W.

Using Eq. 7, R_{TH}_{J-A} = R_{TH}_{J-MB} + R_{TH}_{MB-HS} + R_{TH}_{HS-A}.

From the datasheet, R_{TH}_{J-MB} = 1.5°C/W.

From the **table**, for the TO-220 package screw mounted without insulator and without heatsink compound, R_{TH}_{MB-HS} = 1.4°C/W.

R_{TH}_{HS-A} can be regarded as zero, since the maximum heatsink temperature is fixed at 70°C under worst-case airflow conditions. It can be regarded as an infinite heatsink with a temperature of 70°C. Therefore, R_{TH}_{J-A} = 1.5°C/W + 1.4°C/W + 0 = 2.9°C/W.

Using Eq. 6, T_{J}_{MAX} = T_{A} + P × R_{TH}_{J-A}

= 70°C + 10.22 W × 2.9°C/W

= 100°C.

This is below T_{J}_{MAX} of 125°C and, therefore, acceptable.

### Refrigerator Compressor Example

A triac is used in an electronic thermostat that controls the on-off switching of a refrigerator compressor. The triac gate is triggered from a microcontroller with 20-mA current sink capability. What maximum heatsink thermal resistance is allowed to keep the triac's junction temperature within its T_{J}_{MAX} of 125°C? Steady-state motor current equals 1.4 A_{RMS}. Maximum inrush current equals 17 A_{PK} in the first half cycle. Mains supply equals 230 V_{RMS}. A surface-mounted triac is required for direct soldering to the controller pc board. Maximum ambient temperature is 40°C.

An 8-A Hi-Com triac is recommended to cope with the inductive load and startup current. A suitable triac is the BTA208S-600E, which uses the DPAK package. Its I_{GATE} of 10 mA is well matched to the drive capability of the microcontroller.

From the datasheet, V_{O} = 1.264 V and R_{S} = 0.0378 Ω.

Using Eq. 1, P = V_{O} × I_{TRIAC}_{AVG} + R_{S} × I_{TRIAC}_{RMS}^{2} = 1.264 V × 1.26 A + 0.0378 Ω × (1.4 A)^{2} = 1.67 W.

Using Eq. 6, T_{J}_{MAX} = T_{A} + P × R_{TH}_{J-A}.

T_{J}_{MAX} = 125°C, T_{A} = 40°C and P = 1.67 W.

Rearranging the equation gives:

R_{TH}_{J-A} = (T_{J} - T_{A}) / P = (125°C - 40°C) / 1.67 W = 51°C/W.

Using Eq. 7, R_{TH}_{J-A} = R_{TH}_{J-MB} + R_{TH}_{MB-HS} + R_{TH}_{H-SA}.

From the datasheet, R_{TH}_{J-MB} = 2°C/W. We need to find R_{TH}_{MB-A}.

Rearranging the equation gives:

R_{TH}_{MB-A} = R_{TH}_{J-A} - R_{TH}_{J-MB} = 51°C/W - 2°C/W = 49°C/W.

This is effectively the heatsink thermal resistance, since the pc board is the heatsink in this case. As an approximate guide, this thermal resistance can be obtained with a copper pad area of 500 mm^{2} (refer to the NXP application note “Surface Mounted Triacs and Thyristors,” document order number 9397 750 02622).

Please note that the actual thermal resistance will be reduced by other, nondissipating components in close proximity to the triac, while it will be increased by any components that dissipate power. It is essential to measure the prototype to discover the true thermal performance.

### Vertical-Axis Washing Machine Example

The washing machine uses a reversing induction motor that's controlled by two triacs. Will the triacs' T_{J}_{MAX} of 125°C be exceeded if they are operated without a heatsink?

Full load motor power equals 300 W. The ac mains supply equals 230 V_{RMS}. Therefore:

Max I_{TRIAC}_{RMS} = P / V = 300 W / 230 V_{RMS} = 1.3 A.

An isolated triac package is required, and the maximum ambient temperature is 40°C. Calculations are as follows:

This application requires 1000-V triacs to withstand the high ac mains voltage that the motor imposes across them. A three-quadrant design is mandatory for maximum immunity to spurious triggering. The BTA208X-1000C is recommended. It is an 8-A Hi-Com triac with I_{GATE} of 35 mA. It uses the SOT186A all-plastic package.

From the datasheet, V_{O} = 1.216 V and R_{S} = 0.0416 Ω.

Using Eq. 1, P = V_{O} × I_{TRIAC}_{AVG} + R_{S} × I_{TRIAC}_{RMS}^{2} = 1.216 V × 1.17 A + 0.0416 Ω × (1.3 A)^{2} = 1.49 W.

Using Eq. 6, T_{J} = T_{A} + P × R_{TH}_{J-A}.

We already know that T_{A} = 40°C and P = 1.49 W.

From the datasheet, R_{TH}_{J-A} for the SOT186A package in free air is 55°C/W.

Therefore, T_{J} = 40°C + 1.49 W × 55°C/W = 122°C. This is below the T_{J}_{MAX} of 125°C. Therefore, the triacs can be operated without heatsinks.

A heavy-duty electric drill uses a universal (brush) motor whose speed is controlled by a half-wave phase-control circuit. Calculate the maximum power dissipation in the SCR and calculate the heatsink thermal resistance required to maintain the junction temperature below T_{J}_{MAX}.

Peak motor current during normal running = 5 A. A surface-mounted triac is required for mounting within the trigger switch. Maximum ambient temperature is 50°C.

The SCR is air-cooled by the motor cooling fan. The BTH151S-650R is chosen for its high repetitive surge guarantee for the repetitive overload conditions it will have to face. It is rated at 12 A_{RMS} and comes in the SOT428 (DPAK) package.

Using Eq. 3, I_{TRIAC}_{AVG} = I_{PK} / π = 5 / π = 1.59 A.

Using Eq. 5, I_{TRIAC}_{RMS} = I_{PK}/2 = 5/2 = 2.5 A.

From the datasheet, V_{O} = 1.06 V and R_{S} = 0.0304 Ω.

Using Eq. 1, P = V_{O} × I_{TRIAC}_{AVG} + R_{S} × I_{TRIAC}_{RMS}^{2} = 1.06 V × 1.59 A + 0.0304 Ω × (2.5 A)^{2} = 1.88 W.

Using Eq. 6, T_{J} = T_{A} + P × R_{TH}_{J-A}.

We already know that T_{A} = 50°C and P = 1.88 W and, in this case, T_{J} = T_{J}_{MAX} = 125°C.

Rearranging the equation gives:

R_{TH}_{J-A} = (T_{J} - T_{A}) / P = (125°C - 50°C) / 1.88 W = 39.9°C/W.

Using Eq. 7, R_{TH}_{J-A} = R_{TH}_{J-MB} + R_{TH}_{MB-HS} + R_{TH}_{HS-A}.

From the datasheet, R_{TH}_{J-MB} = 1.8°C/W. We need to find R_{TH}_{MB-A}.

Rearranging the equation gives:

R_{TH}_{MB-A} = R_{TH}_{J-A} - R_{TH}_{J-MB} = 39.9°C/W - 1.8°C/W = 38.1°C/W.

A maximum heatsink thermal resistance of 38°C/W will keep T_{J} at or below 125°C. This heatsink thermal resistance covers the steady-state condition and is easily achievable with a small degree of airflow through the switch module.

Package Type | Thermal Resistance Specification | Value (°C/W) |
---|---|---|

SOT54 (TO-92) | R_{TH}_{J-LEAD}R _{TH}_{J-A} (free air) | 60 150 |

SOT78 (TO-220) | R_{TH}_{J-MB}R _{TH}_{MB-HS} (clip, with grease, no insulator)R _{TH}_{MB-HS} (screw, with grease, no insulator)R _{TH}_{MB-HS} (clip, no grease, no insulator)R _{TH}_{MB-HS} (screw, no grease, no insulator)R _{TH}_{MB-HS} (clip, with grease, 0.1-mm mica insulator)R _{TH}_{MB-HS} (clip, with grease, 0.25-mm alumina insulator)R _{TH}_{MB-HS} (screw, with grease, 0.05-mm mica insulator)R _{TH}_{MB-HS} (screw, no grease, 0.05-mm mica insulator)R _{TH}_{J-A} (free air) | See datasheet 0.30 0.5 1.4 1.4 2.2 0.8 1.6 4.5 60 |

SOT82 | R_{TH}_{J-MB}R _{TH}_{MB-HS} (clip, with grease, no insulator)R _{TH}_{MB-HS} (clip, no grease, no insulator)R _{TH}_{MB-HS} (clip, with grease, 0.1-mm mica insulator)R _{TH}_{MB-HS} (clip, no grease, 0.1-mm mica insulator)R _{TH}_{J-A} (free air) | See datasheet 0.4 2.0 2.0 5.0 100 |

SOT186A (plastic TO-220) | R_{TH}_{J-HS} (with grease)R _{TH}_{J-HS} (no grease)R _{TH}_{J-A} (free air) | See datasheet See data sheet 55 |

SOT223 | R_{TH}_{J-SP}R _{TH}_{J-A} (free air, minimum pad area, FR4 pc board) | See datasheet 150 typical |

SOT404 (D ^{2}PAK) | R_{TH}_{J-MB}R _{TH}_{J-A} (free air, minimum pad area, FR4 pc board) | See datasheet 55 typical |

SOT428 (DPAK) | R_{TH}_{J-MB}R _{TH}_{J-A} (free air, minimum pad area, FR4 pc board) | See datasheet 75 typical |