What is Rogers board?

Key Features of Rogers board

Low Dielectric Constant and Dissipation Factor

One of the main advantages of Rogers board is its low dielectric constant (Dk) and dissipation factor (Df). Dielectric constant measures a material’s ability to store electrical energy, while dissipation factor indicates the amount of energy lost as heat. Lower values of Dk and Df result in faster signal propagation, reduced signal loss, and improved signal integrity. Typical values for Rogers materials range from 2.2 to 10.2 for Dk and 0.0009 to 0.0025 for Df, depending on the specific product.

Excellent Thermal and Mechanical Stability

Rogers board exhibits excellent thermal and mechanical stability, ensuring consistent performance over a wide temperature range. These materials have a low coefficient of thermal expansion (CTE), which closely matches that of copper. This minimizes stress on the copper traces during temperature fluctuations, reducing the risk of delamination and improving the board’s longevity. Additionally, Rogers materials have high glass transition temperatures (Tg), ranging from 280°C to 425°C, allowing them to withstand lead-free soldering processes.

Controlled Impedance

Achieving controlled impedance is crucial for high-speed digital and RF applications to ensure proper signal transmission and minimize reflections. Rogers board materials have tightly controlled dielectric constants, allowing for more precise impedance control compared to FR-4. This enables designers to create transmission lines with specific impedance values, such as 50Ω or 75Ω, by adjusting the trace width and spacing.

Low Moisture Absorption

Moisture absorption can negatively impact a PCB’s electrical and mechanical properties, leading to signal degradation and reduced reliability. Rogers board materials have low moisture absorption rates, typically less than 0.1% by weight, which helps maintain stable performance even in humid environments. This is particularly important for outdoor applications or devices exposed to varying environmental conditions.

Popular Rogers Board Materials

Rogers Corporation offers a range of high-performance materials tailored for different applications. Some of the most popular Rogers board materials include:

RO4003C

RO4003C is a hydrocarbon ceramic laminate with a dielectric constant of 3.38 and a dissipation factor of 0.0027 at 10 GHz. It offers excellent electrical properties, making it suitable for high-frequency applications up to 77 GHz. RO4003C is compatible with standard FR-4 fabrication processes and has a low Z-axis CTE for improved plated through-hole reliability.

RO4350B

RO4350B is a low-loss, high-performance laminate with a dielectric constant of 3.48 and a dissipation factor of 0.0037 at 10 GHz. It is designed for applications requiring both high-frequency performance and mechanical stability. RO4350B has a low Z-axis CTE and is CAF (Conductive Anodic Filament) resistant, making it suitable for multilayer designs.

RO3003

RO3003 is a ceramic-filled PTFE composite with a dielectric constant of 3.0 and a dissipation factor of 0.0010 at 10 GHz. It offers the lowest dielectric loss among Rogers materials, making it ideal for applications requiring ultra-low-loss performance. RO3003 has a low moisture absorption rate and is compatible with standard PTFE fabrication processes.

Material Dielectric Constant (Dk) @ 10 GHz Dissipation Factor (Df) @ 10 GHz Thermal Conductivity (W/m/K) Z-axis CTE (ppm/°C)
RO4003C 3.38 0.0027 0.71 46
RO4350B 3.48 0.0037 0.69 50
RO3003 3.00 0.0010 0.50 17

Applications of Rogers Board

Rogers board materials find applications in various industries and products that require high-frequency, high-speed, and low-loss performance. Some common applications include:

Wireless Communication

Rogers materials are widely used in wireless communication systems, such as 5G networks, cellular base stations, satellite communication, and radar systems. These applications demand high-frequency performance, low signal loss, and consistent electrical properties over a wide temperature range. Rogers board enables the design of compact, reliable, and high-performance RF and microwave circuits.

Automotive Radar

Advanced driver assistance systems (ADAS) and autonomous vehicles rely on high-frequency radar sensors for object detection, collision avoidance, and navigation. Rogers materials, particularly the RO3000 series, are well-suited for automotive radar applications due to their low dielectric loss, stable performance over temperature, and compatibility with high-volume manufacturing processes.

High-Speed Digital

As data rates continue to increase, high-speed digital applications such as high-performance computing, data centers, and telecommunications require PCB materials that can handle fast rise times and minimize signal distortion. Rogers board materials, such as RO4000 series, offer controlled impedance, low loss, and low skew, enabling the design of high-speed digital circuits with improved signal integrity.

Aerospace and Defense

Aerospace and defense applications often require PCBs that can withstand harsh environments, including extreme temperatures, vibration, and moisture. Rogers materials, with their excellent thermal and mechanical stability, low moisture absorption, and CAF resistance, are well-suited for these demanding applications. They are used in avionics, radar systems, satellite communication, and military electronics.

Designing with Rogers Board

When designing with Rogers board materials, there are several factors to consider to ensure optimal performance and manufacturability:

Material Selection

Choosing the right Rogers material depends on the specific application requirements, such as frequency range, dielectric constant, loss tangent, and thermal properties. Designers should consult the material datasheets and work with their PCB fabricator to select the most suitable material for their project.

Stack-up Design

Proper stack-up design is crucial for achieving the desired electrical performance and impedance control. Designers should consider factors such as layer count, dielectric thickness, copper weight, and ground plane placement. Rogers Corporation provides stack-up design tools and guidelines to assist designers in creating optimal stack-ups for their applications.

Impedance Control

Achieving controlled impedance is essential for high-frequency and high-speed digital applications. Designers should use impedance calculation tools to determine the appropriate trace width and spacing for the desired impedance value. It is important to work closely with the PCB fabricator to ensure that the designed impedance can be consistently manufactured.

Manufacturing Considerations

Rogers board materials may require specialized fabrication processes compared to traditional FR-4. Designers should communicate their requirements clearly with the PCB fabricator and ensure that they have experience working with Rogers materials. Some key manufacturing considerations include:

  • Copper surface preparation: Rogers materials may require special surface treatments, such as reverse treat electroless copper (RTEC), to improve adhesion and reliability.
  • Drilling and routing: Due to the unique properties of Rogers materials, modified drilling and routing parameters may be necessary to avoid delamination or other defects.
  • Solder mask application: Some Rogers materials may require special solder mask formulations or application processes to ensure proper adhesion and coverage.
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Frequently Asked Questions (FAQ)

1. Can Rogers board be used for lower frequency applications?

While Rogers materials are primarily designed for high-frequency applications, they can also be used for lower frequency applications that require superior electrical or mechanical properties compared to FR-4. However, the cost of Rogers materials may be higher than traditional PCB substrates, so designers should consider the specific requirements and cost-benefit analysis for their project.

2. Are Rogers materials compatible with lead-free soldering processes?

Yes, Rogers materials are compatible with lead-free soldering processes. They have high glass transition temperatures (Tg), typically above 280°C, which allows them to withstand the higher temperatures required for lead-free soldering without delamination or other defects.

3. How do I select the right Rogers material for my application?

Selecting the right Rogers material depends on several factors, including the frequency range, dielectric constant, loss tangent, thermal properties, and mechanical requirements of your application. Review the material datasheets and consult with Rogers Corporation or your PCB fabricator to determine the most suitable material for your specific needs.

4. Can Rogers board be used in multilayer PCB designs?

Yes, Rogers materials can be used in multilayer PCB designs. Some materials, such as RO4350B, are specifically designed for multilayer applications and offer good CAF (Conductive Anodic Filament) resistance. However, designers should work closely with their PCB fabricator to ensure proper stack-up design, material compatibility, and manufacturing processes for multilayer Rogers boards.

5. Are there any special handling or storage requirements for Rogers materials?

Rogers materials should be stored in a cool, dry place, away from direct sunlight and sources of heat or humidity. Some materials may be more sensitive to moisture absorption than others, so it is important to follow the manufacturer’s recommendations for storage and handling. When handling Rogers laminates, it is essential to wear gloves to prevent contamination and maintain the material’s electrical properties.

Conclusion

Rogers board materials offer superior electrical and mechanical properties compared to traditional FR-4 PCBs, making them ideal for high-frequency, high-speed, and low-loss applications. With their low dielectric constant, low dissipation factor, excellent thermal and mechanical stability, and controlled impedance, Rogers materials enable designers to create high-performance PCBs for demanding applications in telecommunications, automotive, aerospace, and defense industries.

When designing with Rogers board, it is crucial to select the right material, create an optimal stack-up, ensure controlled impedance, and consider manufacturing requirements. By working closely with Rogers Corporation and experienced PCB fabricators, designers can leverage the full potential of Rogers materials and create reliable, high-performance electronic products.

As technology continues to advance and the demand for high-frequency and high-speed applications grows, Rogers board materials will play an increasingly important role in enabling the next generation of electronic devices and systems.

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