Temperature Rise Estimations in Rogers High Frequency Circuit Boards Carrying Direct or RF Current

High-frequency circuit boards are critical in modern electronics, particularly in telecommunications, aerospace, defense, and 5G applications. Rogers Corporation provides high-performance laminates such as RO4000®, RO3000®, RO4003C™, and RT/duroid® series that combine excellent electrical stability with low-loss characteristics. However, DC and RF currents flowing through these boards generate heat, and understanding the resulting temperature rise is crucial for ensuring reliability, signal integrity, and long-term device performance.

1. Factors Influencing Temperature Rise

The temperature rise in a high-frequency PCB depends on multiple interrelated factors:

• Material Thermal Conductivity: Laminates with higher thermal conductivity dissipate heat more effectively. Rogers materials range from ~0.2 W/m·K (PTFE-based RT/duroid) to ~0.8 W/m·K (RO4000 series).

• Trace Geometry: Wider and thicker copper traces reduce resistance and improve heat dissipation.

• Current Density: Higher currents increase resistive heating (I²R losses).

• Operating Frequency: RF currents introduce skin effect and dielectric losses, further raising local temperatures.

• Environmental Conditions: Ambient temperature, airflow, and cooling methods significantly impact thermal behavior.

2. Thermal Properties of Key Rogers Laminates

These properties help designers select laminates that balance electrical performance, signal integrity, and thermal management for high-frequency applications.

3. Calculating Temperature Rise

A. DC Current Heating

For direct current (DC), the temperature rise can be estimated using Joule heating:

ΔT=I2⋅RA⋅k⋅t\Delta T = \frac{I^2 \cdot R}{A \cdot k \cdot t}ΔT=A⋅k⋅tI2⋅R​

Where:

• $I$ = Current (A)

• $R$ = Trace resistance (Ω)

• $A$ = Cross-sectional area of the trace (m²)

• $k$ = Thermal conductivity of the laminate (W/m·K)

• $t$ = Thermal dissipation thickness (m)

This formula allows engineers to predict ΔT and optimize trace dimensions and laminate selection for minimal heating.

B. RF Current Heating

For high-frequency applications, RF currents are affected by skin effect, which concentrates current near the conductor surface and increases effective resistance:

RRF=RDC⋅δDCδRFR_{RF} = R_{DC} \cdot \sqrt{\frac{\delta_{DC}}{\delta_{RF}}}RRF​=RDC​⋅δRF​δDC​​​

Where:

• δRF=ρπfμ\delta_{RF} = \sqrt{\frac{\rho}{\pi f \mu}}δRF​=πfμρ​​ is the skin depth

• $\rho$ = Conductor resistivity

• $f$ = Operating frequency (Hz)

• $\mu$ = Permeability of the conductor

The RF resistance RRFR_{RF}RRF​ is then used in the Joule heating equation to calculate temperature rise under alternating current conditions.

4. Example Calculation

Consider a RO4003C PCB with a 1 oz copper trace carrying a 2 A RF current at 2 GHz:

Material Parameters:

• Thermal Conductivity: k = 0.62 W/m·K

• Skin Depth: δ ≈ 1.4 μm

Trace Parameters:

• Width: 0.5 mm

• Thickness: 35 μm

Temperature Rise Estimation:

1. Calculate effective RF resistance considering skin effect.

2. Apply Joule heating formula to determine ΔT.

3. Confirm results with empirical measurements or simulation for high accuracy.

5. Mitigation Strategies for Temperature Rise

Designers can reduce temperature rise and improve PCB reliability using several techniques:

• Increase Trace Width or Thickness: Lowers current density and resistance.

• Use Heat Sinks or Thermal Vias: Enhances heat dissipation.

• Select High-Thermal-Conductivity Laminates: RO4000 or RO4350B for critical layers.

• Improve Ventilation: Incorporate forced airflow or optimized enclosure design.

• Use Copper Pours and Thermal Pads: Spread heat efficiently across the PCB.

6. Verification and Testing

Temperature rise estimations should always be validated through:

• Infrared Thermal Imaging: Detect hot spots in operating circuits.

• Thermocouples or RTDs: Measure temperatures at critical points.

• Load Testing: Simulate worst-case conditions to ensure thermal stability.

Empirical methods complement theoretical calculations and ensure real-world reliability.