In high-frequency circuit designs, managing temperature rise is crucial for ensuring optimal performance and reliability. Rogers’ high-frequency circuit boards, such as those made with RO4000, RO3000, or RT-duroid laminates, exhibit excellent thermal and electrical properties. However, the combination of DC or RF currents and environmental conditions can lead to localized temperature increases that need to be estimated and mitigated.

1. Factors Influencing Temperature Rise

The temperature rise in a high-frequency circuit board is determined by several factors:

1. Material Thermal Conductivity: Rogers laminates have varying thermal conductivities depending on their composition (e.g., PTFE-based, ceramic-filled).
2. Trace Geometry: Wider and thicker traces dissipate heat more effectively.
3. Current Density: Higher current densities result in increased resistive heating.
4. Operating Frequency: RF currents introduce additional losses due to the skin effect.
5. Environmental Conditions: Ambient temperature, cooling mechanisms, and air circulation.

2. Thermal Properties of Rogers Laminates

Material	Thermal Conductivity (W/m·K)	Dielectric Constant (Dk)
RO4000 Series	0.62 – 0.80	~3.5
RO3000 Series	0.5 – 0.6	~3.0
RT-duroid 5870/5880	0.20 – 0.25	2.2 – 2.33

3. Calculating Temperature Rise

A. DC Current Heating

The temperature rise (ΔT\Delta TΔT) due to DC current can be approximated 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:

• III = Current (A)
• RRR = Resistance of the trace (Ω)
• AAA = Cross-sectional area of the trace (m²)
• kkk = Thermal conductivity of the laminate (W/m·K)
• ttt = Thermal dissipation thickness (m)

B. RF Current Heating

For RF currents, skin effect increases resistance:RRF=RDC⋅δDCδRFR_{RF} = R_{DC} \cdot \sqrt{\frac{\delta_{DC}}{\delta_{RF}}}RRF​=RDC​⋅δRF​δDC​​​

Where:

• δRF\delta_{RF}δRF​ = Skin depth at RF frequency (δ=ρπfμ\delta = \sqrt{\frac{\rho}{\pi f \mu}}δ=πfμρ​​)
• ρ\rhoρ = Resistivity of the conductor
• fff = Frequency (Hz)
• μ\muμ = Permeability of the conductor

Temperature rise under RF conditions is then calculated using the modified resistance RRFR_{RF}RRF​ in the Joule heating equation.

4. Example Calculation

For a RO4003C laminate with a 1 oz copper trace carrying a 2 A RF current at 2 GHz:

1. Material Parameters:
   • Thermal Conductivity: k=0.62 W/m\cdotpKk = 0.62 \, \text{W/m·K}k=0.62W/m\cdotpK
   • Skin depth: δ≈1.4 μm\delta \approx 1.4 \, \mu\text{m}δ≈1.4μm
2. Trace Parameters:
   • Width: 0.5 mm0.5 \, \text{mm}0.5mm
   • Thickness: 35 μm35 \, \mu\text{m}35μm
3. Temperature Rise:
   • Estimate resistance with skin effect: RRFR_{RF}RRF​.
   • Calculate ΔT\Delta TΔT based on heat dissipation properties.

5. Mitigation Strategies

1. Increase Trace Width/Thickness: Reduces current density and lowers resistance.
2. Use Heat Sinks: Adds thermal mass to dissipate heat.
3. Optimize Laminate Selection: Use laminates with higher thermal conductivity for better heat management.
4. Improve Ventilation: Enhances heat dissipation through air or forced cooling.

Estimating and managing temperature rise in high-frequency circuit boards is essential for reliable performance. By understanding the thermal and electrical characteristics of Rogers laminates and applying proper design techniques, temperature effects can be minimized, enhancing the durability and functionality of the circuit.