Introduction

High-frequency circuit boards are essential components in modern electronic systems, particularly in telecommunications, aerospace, and defense applications. Rogers Corporation is a leading manufacturer of high-performance circuit materials specifically designed for these demanding applications. When current flows through these circuit boards—whether direct current (DC) or radio frequency (RF) current—heat is generated due to various loss mechanisms. Understanding and accurately estimating the resulting temperature rise is crucial for ensuring reliable operation and preventing premature failure of electronic systems.

Theoretical Background of Heat Generation

The temperature rise in circuit boards is primarily caused by resistive losses (I²R losses) when current flows through conductive traces. For DC currents, the heat generation is relatively straightforward, governed by Joule’s heating law. However, for RF currents, additional loss mechanisms come into play, making temperature estimation more complex.

When RF current flows through a circuit board, losses occur due to:

1. Conductor losses – Resistive losses in the copper traces
2. Dielectric losses – Energy dissipated within the substrate material
3. Radiation losses – Energy converted to electromagnetic radiation

Rogers high-frequency materials are specifically engineered to minimize these losses, particularly at microwave and millimeter-wave frequencies. Materials such as RO4000® series, RT/duroid®, and CLTE™ offer low dielectric losses (characterized by low dissipation factor or tanδ) and stable electrical properties across frequency and temperature ranges.

DC Current Temperature Rise Estimation

For direct current applications, the temperature rise can be estimated using thermal resistance models. The key equation is:

ΔT = P × Rth

Where:

• ΔT is the temperature rise above ambient (°C)
• P is the power dissipated (watts)
• Rth is the thermal resistance (°C/W)

The power dissipated is calculated using P = I²R, where I is the current and R is the resistance of the trace. The resistance depends on the trace dimensions (width, thickness) and the resistivity of copper, which may vary slightly with temperature.

The thermal resistance depends on multiple factors:

• Circuit board substrate thermal conductivity
• Copper thickness and width
• Presence of thermal vias
• Proximity to ground planes
• Board thickness
• Air circulation around the board

Rogers materials typically have thermal conductivities ranging from 0.2 to 0.7 W/m·K, which is relatively low compared to ceramic substrates but higher than many conventional FR-4 materials.

RF Current Temperature Rise Estimation

For RF currents, the situation becomes more complex due to frequency-dependent effects. The estimation process requires consideration of:

1. Skin effect – At high frequencies, current flows primarily near the surface of conductors, effectively increasing resistance
2. Dielectric loss factor – Energy dissipated in the substrate material
3. Impedance matching – Mismatches can create standing waves, concentrating power at specific locations

The power dissipation for RF signals can be calculated using:

P = Pin × (1-|S21|²-|S11|²)

Where:

• Pin is the input power
• S21 is the transmission coefficient (power delivered to load)
• S11 is the reflection coefficient (power reflected back to source)

This calculation accounts for both the power transmitted through the circuit and the power reflected due to impedance mismatches.

Read more about:

• Rogers 4350B
• Rogers 4003c
• Rogers 5880
• Rogers 3003

Empirical Methods for Temperature Estimation

While theoretical calculations provide a foundation, empirical methods often yield more accurate temperature rise estimations for specific board configurations:

1. Reference designs – Using documented temperature rises from similar designs
2. Thermal modeling software – Finite element analysis (FEA) tools that account for material properties and boundary conditions
3. Infrared thermal imaging – Direct measurement of operating temperatures under various load conditions

Rogers Corporation provides thermal data sheets and application notes for their materials, which can serve as valuable references for temperature rise estimation.

Critical Factors Affecting Temperature Rise

Several key factors significantly impact temperature rise in Rogers high-frequency circuit boards:

Substrate Material Properties

Different Rogers materials exhibit varying thermal characteristics:

• RT/duroid® 5880 has a thermal conductivity of approximately 0.20 W/m·K
• RO4350B™ offers improved thermal conductivity around 0.62 W/m·K
• TC350™ is specifically designed for thermal management with conductivity up to 1.0 W/m·K

Copper Thickness and Trace Width

Wider traces and thicker copper layers provide lower resistance paths for current flow, reducing power dissipation. Standard copper thicknesses range from 1/2 oz (17.5 μm) to 2 oz (70 μm) for Rogers materials, with custom thicknesses available for high-current applications.

Thermal Management Techniques

Several techniques can be employed to mitigate temperature rise:

• Thermal vias – Connecting to internal ground planes or heat sinks
• Copper pours – Increasing the effective copper area for heat spreading
• Thermally conductive adhesives – Improving heat transfer to enclosures or heat sinks
• Forced air cooling – Enhancing convection cooling around the board

Practical Estimation Approach

A systematic approach to estimating temperature rise includes:

1. Calculate the DC resistance of the trace using dimensions and material properties
2. For RF applications, calculate the effective resistance accounting for skin effect
3. Determine power dissipation using appropriate equations for DC or RF current
4. Estimate thermal resistance based on board construction and cooling methods
5. Calculate temperature rise using ΔT = P × Rth
6. Apply safety factors to account for uncertainties

Case Studies

Example 1: DC Power Distribution Trace

Consider a 50 mil (1.27 mm) wide, 1 oz copper trace on RO4350B carrying 2 amperes of DC current. The trace resistance is approximately 0.02 ohms per inch. For a 3-inch trace:

• Total resistance = 0.06 ohms
• Power dissipation = (2 A)² × 0.06 Ω = 0.24 watts
• With a thermal resistance of approximately 30°C/W for this configuration
• Temperature rise = 0.24 W × 30°C/W = 7.2°C above ambient

Example 2: RF Power Amplifier Output Line

For a 50-ohm microstrip line on RT/duroid 6010 carrying 5 watts of RF power at 10 GHz:

• Insertion loss ≈ 0.2 dB/inch (primarily from conductor and dielectric losses)
• For a 2-inch line, total loss ≈ 0.4 dB or approximately 9% of power
• Power dissipation = 5 W × 0.09 = 0.45 watts
• With a thermal resistance of approximately 25°C/W for this configuration
• Temperature rise = 0.45 W × 25°C/W = 11.25°C above ambient

Verification Methods

Temperature rise estimations should always be verified using:

1. Thermal imaging cameras to identify hot spots
2. Thermocouples or RTDs placed at critical locations
3. Temperature-sensitive paint or labels for visual indication
4. Load testing under worst-case operating conditions

Conclusion

Accurate estimation of temperature rise in Rogers high-frequency circuit boards requires understanding both the electrical and thermal properties of the materials involved. While DC current temperature rise calculations are relatively straightforward, RF applications demand consideration of additional frequency-dependent effects. By using a combination of theoretical calculations, empirical data, and verification measurements, engineers can ensure that their high-frequency designs maintain acceptable operating temperatures.

As operating frequencies continue to increase and electronic packaging becomes more compact, thermal management will remain a critical aspect of high-frequency circuit design. Rogers Corporation continues to develop materials with improved thermal properties while maintaining excellent electrical characteristics, enabling the next generation of high-performance RF and microwave systems.