In the realm of high-frequency electronics, Rogers Corporation’s circuit board materials have become a go-to choice for engineers and designers. These materials offer excellent electrical and thermal properties, making them ideal for applications ranging from telecommunications to aerospace. However, as frequencies increase and power densities rise, thermal management becomes a critical concern. This article delves into the methods and considerations for estimating temperature rise in Rogers high-frequency circuit boards when carrying direct or RF current.

Understanding Rogers High Frequency Materials

Before diving into temperature rise estimations, it’s crucial to understand the characteristics of Rogers’ high-frequency materials.

Key Properties of Rogers Materials

Rogers Corporation offers several product lines designed for high-frequency applications, including:

1. RO4000® Series
2. RT/duroid®
3. CLTE-XT™
4. AD Series

These materials are known for their:

• Low dielectric loss
• Stable dielectric constant over a wide frequency range
• Low thermal coefficient of dielectric constant
• Good thermal conductivity
• Excellent dimensional stability

Thermal Conductivity

Thermal conductivity is a key factor in heat dissipation. Rogers materials typically have thermal conductivity values ranging from 0.3 to 1.5 W/m·K, depending on the specific product. This property significantly influences how heat is distributed across the board.

Factors Affecting Temperature Rise

Several factors contribute to temperature rise in high-frequency circuit boards:

1. Current density
2. Frequency of operation
3. Trace geometry
4. Substrate thickness
5. Copper thickness
6. Ambient temperature
7. Presence of thermal vias or heat sinks

Current Density and Its Impact

Current density, measured in amperes per square meter (A/m²), is a primary driver of temperature rise. As current density increases, so does the heat generated in the conductor due to resistive losses.

Frequency Considerations

At high frequencies, additional phenomena come into play:

• Skin effect: Current tends to flow near the surface of conductors, effectively reducing the cross-sectional area and increasing resistance.
• Dielectric losses: The substrate material absorbs some energy, converting it to heat.

Methods for Estimating Temperature Rise

Several approaches can be used to estimate temperature rise in Rogers circuit boards:

1. Analytical calculations
2. IPC-2152 standard
3. Finite Element Analysis (FEA)
4. Empirical testing

Analytical Calculations

For simple cases, particularly with DC current, analytical methods can provide a good starting point. The basic equation for temperature rise (ΔT) due to power dissipation is:

ΔT = (P * θ) / A

Where:

• P is the power dissipated (W)
• θ is the thermal resistance (°C·m²/W)
• A is the area of heat dissipation (m²)

For a PCB trace, we can estimate the power dissipation using:

P = I² * R

Where:

• I is the current (A)
• R is the resistance of the trace (Ω)

The resistance R can be calculated based on the trace dimensions and the resistivity of copper.

IPC-2152 Standard

The IPC-2152 standard, “Standard for Determining Current-Carrying Capacity in Printed Board Design,” provides charts and equations for estimating temperature rise based on current, trace width, and copper thickness. While not specifically designed for high-frequency applications, it can serve as a useful reference point.

Finite Element Analysis (FEA)

FEA software allows for more complex and accurate simulations, taking into account:

• 3D geometry of the board and components
• Material properties of all elements
• Heat sources (including RF losses)
• Cooling mechanisms (conduction, convection, radiation)

Popular FEA tools for PCB thermal analysis include ANSYS, COMSOL Multiphysics, and Siemens Simcenter.

Empirical Testing

While simulation and calculations are valuable, empirical testing remains crucial, especially for high-frequency applications. Methods include:

• Infrared thermography
• Embedded temperature sensors
• Thermal test boards

Read more about:

• RF PCB
• Taconic PCB
• Rogers 3003
• Rogers 5880
• Arlon PCB

Estimating Temperature Rise for DC Current

For DC current, the process is relatively straightforward:

1. Calculate the resistance of the trace based on its dimensions and copper resistivity.
2. Determine the power dissipation using P = I² * R.
3. Estimate the area of heat dissipation, considering both the trace surface and the surrounding board area.
4. Use the thermal resistance of the Rogers material to calculate the temperature rise.

Example Calculation:

Let’s consider a 50 mm long, 1 mm wide trace on RO4350B material with 1 oz copper thickness, carrying 2A DC.

1. Trace resistance: R ≈ 8.9 mΩ (calculated based on trace dimensions)
2. Power dissipation: P = 2² * 0.0089 = 0.0356 W
3. Dissipation area: A ≈ 100 mm² (assuming some spread beyond the trace)
4. Thermal resistance: θ ≈ 0.5 °C·in²/W (from Rogers datasheet, converted to metric)
5. Temperature rise: ΔT = (0.0356 * 0.5) / (100 * 10^-6) ≈ 178°C

This simplified calculation suggests a significant temperature rise, highlighting the importance of proper thermal management even for DC applications.

Estimating Temperature Rise for RF Current

Estimating temperature rise for RF current is more complex due to additional factors:

• Skin effect
• Dielectric losses
• Radiation losses

Skin Effect Considerations

At high frequencies, current flows primarily near the surface of the conductor, effectively increasing its resistance. The skin depth (δ) can be calculated as:

δ = √(ρ / (π * f * μ))

Where:

• ρ is the resistivity of copper
• f is the frequency
• μ is the magnetic permeability

For frequencies above 1 GHz, the skin depth in copper is less than 2 μm, significantly increasing the effective resistance.

Dielectric Losses

The loss tangent (tan δ) of the Rogers material determines the dielectric losses. These losses contribute to overall heating and can be significant at high frequencies.

The power loss in the dielectric (Pd) can be estimated as:

Pd = 2π * f * C * V² * tan δ

Where:

• f is the frequency
• C is the capacitance of the structure
• V is the voltage
• tan δ is the loss tangent of the material

Radiation Losses

At high frequencies, some power is lost through radiation. While this doesn’t directly contribute to board heating, it reduces the overall efficiency and can indirectly affect thermal performance.

Practical Approach to RF Temperature Rise Estimation

For RF applications, a combination of methods is often most effective:

1. Use analytical methods to get a baseline estimate.
2. Employ specialized RF simulation software (e.g., Ansys HFSS, CST Microwave Studio) to model EM fields and losses.
3. Use thermal simulation software to convert RF losses into temperature distributions.
4. Validate results through empirical testing.

Thermal Management Strategies

Once temperature rise has been estimated, various strategies can be employed to manage thermal issues:

1. Increase copper weight: Thicker copper reduces resistance and improves heat spreading.
2. Widen traces: Increases the cross-sectional area, reducing current density.
3. Use thermal vias: Helps conduct heat to other layers or a ground plane.
4. Implement heat sinks: Increases the surface area for heat dissipation.
5. Forced air cooling: Improves convection cooling.
6. Use of thermally conductive materials: Fills air gaps and improves heat transfer.

Case Study: High-Power RF Amplifier Board

Consider a high-power RF amplifier operating at 2.4 GHz on a Rogers RO4350B substrate. The amplifier outputs 50W of RF power, with an efficiency of 60%.

Approach:

1. Calculate total power dissipation: 50W * (1/0.6 – 1) = 33.3W
2. Use EM simulation to determine current distribution and losses in traces.
3. Apply thermal simulation to estimate temperature distribution.
4. Validate through infrared thermography.

Results might show hotspots near the amplifier output, requiring strategies like:

• Increasing copper thickness on output traces
• Adding thermal vias under the amplifier
• Implementing a heat sink on the amplifier and critical trace areas

Conclusion

Estimating temperature rise in Rogers high-frequency circuit boards carrying direct or RF current is a complex but crucial aspect of high-frequency design. While analytical methods provide a starting point, the complexity of high-frequency effects often necessitates advanced simulation techniques and empirical validation.

Key takeaways:

1. Consider both conductive and dielectric losses, especially at high frequencies.
2. Use a combination of analytical, simulation, and empirical methods for accurate estimations.
3. Implement appropriate thermal management strategies based on your estimations.
4. Always validate your designs through testing, especially for critical high-frequency applications.

As frequencies and power levels continue to increase, thorough thermal analysis and management will remain essential for ensuring the reliability and performance of high-frequency circuits built on Rogers materials.