Thermal Via Array Resistance

Rarray = Rsingle / n

Quick answer

This calculator solves R_array = R_single / n for Array Thermal Resistance. With Single Via Thermal R 44 °C/W, Number of Vias 0.5, the result is 88 °C/W. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Array Thermal Resistance (°C/W)
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Formula

R_array = R_single / n

Description

Thermal vias are plated through-holes placed under a heat-generating component to conduct heat from the top copper layer to a large ground plane on an inner or bottom layer. Vias in parallel reduce the total thermal resistance by a factor of n. A typical 0.3 mm diameter plated via with 25 µm copper plating through a 1.6 mm board has a thermal resistance of about 70-100°C/W. An array of 20 such vias reduces this to about 3.5-5°C/W, making it practical for thermal management of QFN and BGA packages with exposed thermal pads.

Variables

  • R_array — Combined thermal resistance of the via array (°C/W)
  • R_single — Thermal resistance of one via (°C/W)
  • n — Number of vias in the array

Practical Notes

Via thermal resistance depends on diameter, plating thickness, and board thickness. Filled and capped vias (via-in-pad) have lower thermal resistance than open vias. Via-in-pad requires VIPPO (Via In Pad Plated Over) process to prevent solder wicking during assembly. For best thermal performance, place vias on a regular grid with 1-1.2 mm pitch directly under the thermal pad. Solder-filled vias have significantly lower thermal resistance than air-filled ones.

Symbols and units

Symbol Meaning Default unit Accepted units
Rarray Array Thermal Resistance °C/W °C/W
Rsingle Single Via Thermal R °C/W °C/W
n Number of Vias — —

Step by step

  1. 1. What you know: Single Via Thermal R 44 °C/W, Number of Vias 0.5
  2. 2. The relation: R_array = R_single / n
  3. 3. Substitute: Rsingle = 44 °C/W, n = 0.5
  4. 4. Result: Array Thermal Resistance = 88 °C/W

Worked examples

Minimum range

Given: Single Via Thermal R 0.22 °C/W, Number of Vias 0.025

Result: Array Thermal Resistance = 8.8 °C/W

Low range

Given: Single Via Thermal R 2.2 °C/W, Number of Vias 0.25

Result: Array Thermal Resistance = 8.8 °C/W

Typical

Given: Single Via Thermal R 44 °C/W, Number of Vias 0.5

Result: Array Thermal Resistance = 88 °C/W

High range

Given: Single Via Thermal R 220 °C/W, Number of Vias 0.8

Result: Array Thermal Resistance = 275 °C/W

Maximum range

Given: Single Via Thermal R 2200 °C/W, Number of Vias 8

Result: Array Thermal Resistance = 275 °C/W

Solving for each variable

Solve for Array Thermal Resistance

Single Via Thermal R 0.22 °C/W, Number of Vias 0.025 → 8.8 °C/W

Solve for Single Via Thermal R

Array Thermal Resistance 0.1 °C/W, Number of Vias 0.025 → 0.0025 °C/W

Solve for Number of Vias

Array Thermal Resistance 0.1 °C/W, Single Via Thermal R 0.22 °C/W → 2.2

How Array Thermal Resistance changes with Single Via Thermal R

Single Via Thermal R (input) Array Thermal Resistance (result)
4.4 °C/W 8.8 °C/W
11 °C/W 22 °C/W
22 °C/W 44 °C/W
33 °C/W 66 °C/W
44 °C/W 88 °C/W
66 °C/W 132 °C/W
88 °C/W 176 °C/W
176 °C/W 352 °C/W
308 °C/W 616 °C/W
440 °C/W 880 °C/W

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Frequently asked questions

How do you calculate Thermal Via Array Resistance?

Use R_array = R_single / n. With Single Via Thermal R 44 °C/W, Number of Vias 0.5, Array Thermal Resistance works out to 88 °C/W.

What is the formula for Thermal Via Array Resistance?

The formula is R_array = R_single / n. Thermal vias are plated through-holes placed under a heat-generating component to conduct heat from the top copper layer to a large ground plane on an inner or bottom layer.

How do you find Single Via Thermal R when you know the other values?

Rearrange for Single Via Thermal R: with Array Thermal Resistance 0.1 °C/W, Number of Vias 0.025, Single Via Thermal R is 0.0025 °C/W.

How do you find Number of Vias when you know the other values?

Rearrange for Number of Vias: with Array Thermal Resistance 0.1 °C/W, Single Via Thermal R 0.22 °C/W, Number of Vias is 2.2.

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