A TXI calculator is the definitive thermal derating and dissipation framework used for open-frame AC-DC power supplies (benchmarking against the ubiquitous XP Power TXI series and similar 60W-150W industrial modules). The direct answer to sizing your thermal management is calculating the required heatsink-to-ambient thermal resistance ($R_{\theta SA}$) using the master formula: $R_{\theta SA} = \frac{T_{C(MAX)} - T_{A}}{P_{DISS}} - R_{\theta CS}$. If your calculated $R_{\theta SA}$ is above 10 °C/W, you can run the supply bare; if it falls between 2 and 10 °C/W, you need a passive extruded aluminum heatsink; if it drops below 2 °C/W, you must add forced-air cooling.
What the TXI Calculator Actually Solves (and Its Core Assumptions)
Open-frame AC-DC converters lack an integrated metal enclosure to act as a heatsink. The TXI calculator framework solves the steady-state thermal equilibrium problem: matching the silicon's maximum allowable case temperature to the ambient environment by quantifying the heat rejected by the converter's efficiency losses.
This mathematical model relies on strict assumptions. If you violate them, your calculated thermal resistance will be useless, and your power supply will trigger its internal thermal shutdown (or worse, suffer catastrophic electrolytic capacitor venting).
- Steady-State DC Load: The formulas assume a constant continuous load, not a dynamic pulsed load. For pulsed loads, you must calculate transient thermal impedance ($Z_{\theta}$), which is outside the scope of this steady-state calculator.
- Airflow Conditions: Natural convection assumes an air velocity of $\le 0.1$ m/s. Forced convection assumes a minimum cross-flow of $1.0$ m/s (approx. 200 LFM).
- Altitude Derating: Air density drops at altitude, reducing convective heat transfer. These formulas assume operation below 2,000 meters. Above 2,000m, you must derate the maximum ambient temperature by 1°C for every 200m of additional elevation.
- Component Aging: Efficiency ($\eta$) degrades as electrolytic capacitors age and their Equivalent Series Resistance (ESR) rises. Always use the datasheet's minimum guaranteed efficiency at full load and high temperature, not the 'typical' peak efficiency.
The Master Formula: Symbol Definitions and Rearranged Forms
The thermal design of an open-frame supply requires two coupled equations. First, you determine how much heat the supply generates based on its efficiency. Second, you calculate the thermal resistance required to move that heat into the ambient air.
| Symbol | Parameter | Standard Unit | Realistic Magnitude |
|---|---|---|---|
| $P_{DISS}$ | Power Dissipated as Heat | Watts (W) | 5 W to 25 W |
| $P_{OUT}$ | Output Power Delivered to Load | Watts (W) | 50 W to 150 W |
| $\eta$ | Power Supply Efficiency | Decimal (e.g., 0.88) | 0.82 to 0.94 |
| $R_{\theta SA}$ | Heatsink-to-Ambient Thermal Resistance | °C/W | 1.5 °C/W to 15 °C/W |
| $T_{C(MAX)}$ | Maximum Allowable Case Temperature | °C | 85 °C to 95 °C |
| $T_{A}$ | Maximum Ambient Air Temperature | °C | 25 °C to 50 °C |
| $R_{\theta CS}$ | Case-to-Sink Thermal Resistance (TIM) | °C/W | 0.1 °C/W to 0.5 °C/W |
Equation 1 (Power Dissipation):
$P_{DISS} = P_{OUT} \times \left( \frac{1}{\eta} - 1 \right)$
Equation 2 (Thermal Resistance):
$R_{\theta SA} = \frac{T_{C(MAX)} - T_{A}}{P_{DISS}} - R_{\theta CS}$
Rearranged Forms
Depending on your design constraints, you will need to isolate different variables. Here are the algebraically rearranged forms for the TXI calculator framework:
- Solving for Maximum Output Power ($P_{OUT}$):
$P_{OUT} = \left[ \frac{T_{C(MAX)} - T_{A}}{R_{\theta SA} + R_{\theta CS}} \right] \times \left( \frac{\eta}{1 - \eta} \right)$ - Solving for Maximum Ambient Temperature ($T_{A}$):
$T_{A} = T_{C(MAX)} - [P_{DISS} \times (R_{\theta SA} + R_{\theta CS})]$ - Solving for Required Efficiency ($\eta$):
$\eta = \frac{P_{OUT}}{P_{OUT} + \left[ \frac{T_{C(MAX)} - T_{A}}{R_{\theta SA} + R_{\theta CS}} \right]}$
Unit Mistakes That Will Fry Your Power Supply
When punching numbers into a TXI calculator, three specific unit errors routinely lead to melted terminal lugs or nuisance thermal trips.
- The Percentage vs. Decimal Trap: Plugging $\eta = 89$ instead of $\eta = 0.89$ into Equation 1 will result in a negative power dissipation value. The math will tell you the supply is generating 'negative heat' (cooling the room), leading you to skip the heatsink entirely.
- Delta Celsius vs. Absolute Kelvin: Thermal resistance (°C/W) is based on a temperature difference ($\Delta T$). A difference of 40°C is identical to a difference of 40 K. Do not add 273.15 to your $T_{C(MAX)}$ and $T_{A}$ values before subtracting them. If you convert to Kelvin, you must convert both, and the 273.15 will cancel out during the subtraction step.
- Ignoring the TIM Layer ($R_{\theta CS}$): Assuming $R_{\theta CS} = 0$ because you bolted the supply directly to a chassis. Without a thermal interface material (TIM) like a Bergquist Sil-Pad or thermal compound, microscopic air gaps between the PCB and the chassis will add 1.0 to 2.0 °C/W of hidden resistance, invalidating your $R_{\theta SA}$ target.
Worked Problem 1: Convection-Cooled TXI100 at High Ambient
Scenario: You are deploying an open-frame 100W supply (nominal 24V @ 4.16A) in an enclosed industrial control panel. The ambient temperature inside the panel reaches 50°C. You are relying on natural convection (no heatsink, no fan). The bare PCB-to-air thermal resistance ($R_{\theta SA}$) is approximately 12 °C/W. The supply's guaranteed minimum efficiency at this load and temperature is 88% ($\eta = 0.88$). The maximum allowable case temperature ($T_{C(MAX)}$) is 85°C.
Goal: Calculate the maximum safe output power ($P_{OUT}$) you can draw without triggering thermal shutdown.
- Identify Knowns:
$T_{C(MAX)} = 85°C$
$T_{A} = 50°C$
$R_{\theta SA} = 12 °C/W$
$R_{\theta CS} = 0 °C/W$ (bare board, no TIM)
$\eta = 0.88$ - Calculate Maximum Allowable Power Dissipation ($P_{DISS}$):
Rearranging Equation 2 to solve for $P_{DISS}$:
$P_{DISS} = \frac{T_{C(MAX)} - T_{A}}{R_{\theta SA} + R_{\theta CS}}$
$P_{DISS} = \frac{85 - 50}{12 + 0} = \frac{35}{12} = 2.916 \text{ W}$ - Calculate Derated Output Power ($P_{OUT}$):
Using the rearranged Equation 1:
$P_{OUT} = P_{DISS} \times \left( \frac{\eta}{1 - \eta} \right)$
$P_{OUT} = 2.916 \times \left( \frac{0.88}{1 - 0.88} \right)$
$P_{OUT} = 2.916 \times \left( \frac{0.88}{0.12} \right) = 2.916 \times 7.333 = 21.38 \text{ W}$
Result: Despite being a '100W' power supply, at 50°C ambient with no heatsink, you must derate the output to 21.3 W. This perfectly illustrates why open-frame supplies require aggressive thermal management in high-temperature enclosures. For deeper context on natural convection limits, refer to CUI Inc's thermal management guidelines for open-frame supplies.
Worked Problem 2: Sizing a Heatsink for a 24V 4A Load
Scenario: Your load strictly requires 75W (24V @ 3.125A). The control panel ambient is a manageable 40°C. You will mount the supply to a chassis using a 0.5mm thick thermal pad ($R_{\theta CS} = 0.2 °C/W$). The supply efficiency at 75W is 89% ($\eta = 0.89$). $T_{C(MAX)}$ remains 85°C.
Goal: Determine the maximum allowable $R_{\theta SA}$ to specify a heatsink.
- Calculate Power Dissipation ($P_{DISS}$):
$P_{DISS} = P_{OUT} \times \left( \frac{1}{\eta} - 1 \right)$
$P_{DISS} = 75 \times \left( \frac{1}{0.89} - 1 \right)$
$P_{DISS} = 75 \times (1.1236 - 1) = 75 \times 0.1236 = 9.27 \text{ W}$ - Calculate Required Heatsink Thermal Resistance ($R_{\theta SA}$):
$R_{\theta SA} = \frac{T_{C(MAX)} - T_{A}}{P_{DISS}} - R_{\theta CS}$
$R_{\theta SA} = \frac{85 - 40}{9.27} - 0.2$
$R_{\theta SA} = \frac{45}{9.27} - 0.2 = 4.854 - 0.2 = 4.65 \text{ °C/W}$
Result: You must source a heatsink with a thermal resistance of 4.65 °C/W or lower. When searching distributor catalogs like DigiKey's heatsink selection guides, you will filter for board-level or chassis-mount extruded aluminum profiles in the 3.0 to 4.5 °C/W range to provide a 15% safety margin.
Decision Path: Convection, Heatsink, or Forced Air?
Once your TXI calculator outputs the target $R_{\theta SA}$, use this decision matrix to terminate your design process and select the physical hardware. Do not over-engineer; match the cooling method to the thermal resistance magnitude.
| Calculated $R_{\theta SA}$ Requirement | Cooling Method | Hardware Implementation |
|---|---|---|
| > 10.0 °C/W | Natural Convection (Bare) | No heatsink required. Ensure 20mm clearance above and below the PCB for air circulation. |
| 2.1 to 10.0 °C/W | Passive Heatsink | Extruded aluminum fin array bolted to the PCB or chassis. Apply thermal pad (e.g., Bergquist Sil-Pad 900P). |
| ≤ 2.0 °C/W | Forced Air (Active) | Passive heatsink combined with a DC brushless fan providing minimum 1.0 m/s (200 LFM) cross-flow. |
The Concrete Default Pick
If your calculation lands in the passive heatsink zone (like our Worked Problem 2 requiring 4.65 °C/W), do not waste time evaluating complex liquid cold plates or vapor chambers. Select a standard 100x100x15mm extruded aluminum chassis heatsink, such as the Wakefield-Vette SA1250 series (or equivalent Aavid Thermalloy board-level extrusion), which natively provides ~4.0 °C/W in natural convection. Apply a 0.5mm Bergquist Sil-Pad 900P thermal interface material between the supply's aluminum baseplate and the heatsink, torque the mounting M3 screws to 0.4 Nm in a star pattern to ensure uniform TIM compression, and your thermal design is complete.
