Efficient Heat Dissipation: Copper Substrate PCB Benefits

copper substrate pcb

Printed Circuit Boards (PCBs) are the backbone of modern electronic devices, providing the foundation for electrical connectivity and component support. PCBs revolutionized the electronics industry by enabling the miniaturization and complexity of circuits, crucial for today’s advanced technology. Initially, PCBs were made using basic materials like phenolic and epoxy resins. However, as electronic devices evolved to become more powerful and compact, the need for better performance and durability led to the diversification of PCB materials.

One significant advancement in this field is the development of copper substrate PCBs. These PCBs use copper as the primary substrate material, offering superior thermal conductivity and electrical performance compared to traditional FR4 or CEM-1 materials. Copper substrate PCBs are particularly important in applications requiring efficient heat dissipation, such as high-power LEDs, power converters, and automotive electronics. This evolution highlights the ongoing innovation in PCB technology, driving the future of electronics forward.

What is a Copper Substrate PCB?


A Copper Substrate PCB is a type of printed circuit board that utilizes copper as the primary substrate material. This substrate forms the base layer upon which other materials and components are built, providing a robust foundation for electronic circuits.


Copper substrate PCBs are designed to leverage the exceptional thermal and electrical properties of copper. Unlike traditional PCBs, which typically use FR4 (a glass-reinforced epoxy laminate) or other resin-based materials, copper substrate PCBs offer significantly enhanced thermal conductivity. This feature is critical for applications where efficient heat dissipation is paramount, such as in high-power LEDs, power electronics, and RF applications.

The structure of a copper substrate PCB includes a thick copper base, a dielectric layer, and the circuit layer. The copper base acts as a heat sink, dissipating heat away from sensitive components, thereby improving reliability and performance. The dielectric layer provides electrical insulation while maintaining thermal conductivity, and the circuit layer forms the conductive pathways for electronic signals.

Distinguishing Copper Substrate, Copper Core, and Metal Core PCBs

  1. Copper Substrate PCBs:
  • Primary Material: Copper is used as the main substrate.
  • Applications: Ideal for high-thermal applications requiring efficient heat management.
  • Benefits: Superior thermal conductivity and mechanical strength.
  1. Copper Core PCBs:
  • Primary Material: Contains a core of copper within the PCB layers.
  • Applications: Used where specific sections of the PCB require enhanced thermal management.
  • Benefits: Targeted thermal control with the versatility of additional materials.
  1. Metal Core PCBs (MCPCBs):
  • Primary Material: Can include various metals such as aluminum, copper, or iron as the core.
  • Applications: Broad range including automotive, industrial power, and LED lighting.
  • Benefits: General improvement in heat dissipation and mechanical durability, with material choice depending on specific thermal and mechanical requirements.

While copper substrate PCBs utilize a full copper base for optimal thermal performance, copper core PCBs use copper selectively within the layers for targeted thermal benefits. Metal core PCBs, on the other hand, can use various metals for the core, providing a balance of thermal management and mechanical properties tailored to specific applications.

Pros and Cons of Copper Substrate PCBs


1. Excellent Thermal Conductivity Copper substrate PCBs are renowned for their superior thermal conductivity. Copper is one of the best conductors of heat, which means it can effectively dissipate heat away from critical components. This is particularly beneficial in applications involving high-power devices, such as LEDs, power transistors, and automotive electronics, where overheating can lead to failure or reduced performance.

2. Enhanced Electrical Performance Copper offers excellent electrical conductivity, allowing for efficient signal transmission and minimal loss of electrical power. This ensures that electronic devices perform reliably and consistently, even under high-stress conditions. The low electrical resistance of copper substrates contributes to improved performance in high-frequency and high-speed applications, making them ideal for advanced electronic systems.

3. Superior Mechanical Strength The mechanical strength of copper substrates is significantly higher than that of traditional PCB materials like FR4. This robustness ensures that the PCBs can withstand mechanical stress and strain during manufacturing, assembly, and operation. The durability of copper substrate PCBs makes them suitable for use in harsh environments and applications that demand high reliability, such as military and aerospace.

4. Better Heat Dissipation Copper substrate PCBs excel in heat dissipation, which is crucial for maintaining the stability and longevity of electronic components. Efficient heat dissipation helps in preventing thermal-induced failures and enhances the overall lifespan of the device. This makes copper substrate PCBs a preferred choice for high-power applications where thermal management is a critical concern.


1. Higher Cost Compared to Other Materials One of the primary drawbacks of copper substrate PCBs is their cost. Copper is a relatively expensive material, and the use of thick copper layers further increases the cost. This makes copper substrate PCBs more expensive than those made from traditional materials like FR4 or CEM-1. The higher cost can be a significant factor for cost-sensitive applications, where budget constraints are critical.

2. More Complex Manufacturing Process The manufacturing process for copper substrate PCBs is more complex and demanding compared to standard PCBs. The additional steps required to handle the thick copper layers and ensure proper bonding and insulation add to the manufacturing time and cost. This complexity can also lead to a higher rate of manufacturing defects if not managed properly, necessitating stringent quality control measures.

3. Potential Issues with Weight and Flexibility Copper substrate PCBs are heavier than those made from traditional materials due to the density of copper. This added weight can be a disadvantage in applications where weight is a critical factor, such as in portable or wearable electronics. Additionally, copper substrate PCBs are less flexible, making them unsuitable for applications that require flexible or bendable circuit boards. The rigidity of copper substrates limits their use in dynamic environments where flexibility is required.

While copper substrate PCBs offer unparalleled thermal and electrical performance, mechanical strength, and heat dissipation, these advantages come with trade-offs in terms of higher costs, manufacturing complexity, and limitations in weight and flexibility. The decision to use copper substrate PCBs should be based on a careful consideration of these factors in relation to the specific requirements of the application.

Cost Analysis of Copper Substrate PCBs

Factors Influencing Cost

1. Material Costs The primary factor influencing the cost of copper substrate PCBs is the price of copper itself. Copper is a relatively expensive raw material, and the cost increases with the thickness of the copper layer used in the PCB. Additionally, the quality and purity of copper can also affect the overall cost. High-grade copper ensures better performance but comes at a premium price.

2. Manufacturing Complexity Copper substrate PCBs require a more complex manufacturing process compared to traditional PCBs. The process involves additional steps such as precision etching, layering, and bonding of the thick copper substrate, which demands specialized equipment and expertise. This complexity increases both the time and cost of production. Moreover, ensuring the dielectric layer provides adequate insulation while maintaining thermal conductivity adds to the manufacturing challenges and costs.

3. Volume of Production The production volume significantly impacts the cost per unit of copper substrate PCBs. Larger production runs benefit from economies of scale, reducing the cost per unit. Conversely, small production batches can be quite expensive due to the initial setup costs and the higher relative expense of raw materials and manufacturing processes. Bulk ordering can mitigate some of the high costs associated with copper substrate PCBs.

4. Customization Requirements Customization can further drive up the costs of copper substrate PCBs. Custom specifications, such as unique shapes, sizes, or specific thermal properties, require tailored manufacturing processes and additional design considerations. Custom orders may also involve prototyping, which adds to the overall expense. The need for specialized components or additional layers to meet specific performance criteria can also elevate costs.

Comparative Cost

1. Comparison with Other Types of PCBs

  • FR4 PCBs: These are the most common and cost-effective type of PCBs, using a fiberglass-reinforced epoxy laminate. The cost of FR4 PCBs is significantly lower than copper substrate PCBs due to the cheaper material and simpler manufacturing process. However, they do not offer the same level of thermal and electrical performance.
  • Aluminum Core PCBs: These PCBs are also designed for better thermal management but use aluminum as the core material. While aluminum core PCBs are less expensive than copper substrate PCBs, they offer lower thermal conductivity and electrical performance. They are a middle-ground option for applications that need improved thermal management without the higher costs associated with copper.
  • CEM-1 and CEM-3 PCBs: These are cost-effective alternatives to FR4, made from composite materials. They are cheaper than copper substrate PCBs but also offer inferior performance in terms of thermal management and durability.

2. Cost-Benefit Analysis When conducting a cost-benefit analysis, the higher initial cost of copper substrate PCBs can be justified by their superior performance in certain applications. The benefits of using copper substrate PCBs include enhanced thermal conductivity, better electrical performance, and increased mechanical strength. These attributes can lead to longer lifespan and improved reliability of electronic devices, which can offset the higher upfront costs.

For applications involving high-power components or where thermal management is critical, the additional investment in copper substrate PCBs can prevent costly failures and maintenance issues, leading to long-term savings. In contrast, for low-power applications where thermal management is less critical, the cost savings from using FR4 or aluminum core PCBs might outweigh the benefits of copper substrates.

While the cost of copper substrate PCBs is higher due to factors such as material costs, manufacturing complexity, production volume, and customization requirements, their superior performance characteristics can justify the investment in the right applications. A careful cost-benefit analysis should be conducted to determine whether the advantages of copper substrate PCBs align with the specific needs and budget constraints of the project.

Copper Core PCBs and Metal Core PCBs

Definition and Differences

Explanation of Copper Core PCBs Copper core PCBs are a type of metal core PCB that specifically uses copper as the core material. The core layer of copper provides superior thermal conductivity and heat dissipation compared to other materials. This design helps to manage heat in high-power applications, preventing overheating and ensuring the longevity and reliability of the electronic components.

Comparison with Other Metal Core PCBs

  • Aluminum Core PCBs: These PCBs use aluminum as the core material. While aluminum also provides good thermal conductivity and is lighter and cheaper than copper, it does not match copper’s thermal performance. Aluminum core PCBs are commonly used in LED lighting and consumer electronics where moderate thermal management is sufficient.
  • Iron Core PCBs: Iron cores are less common and are used in applications where weight is less of a concern and high mechanical strength is needed. Iron has inferior thermal conductivity compared to both copper and aluminum, making it less ideal for high-thermal applications.
  • Copper vs. Other Metals: Copper core PCBs stand out due to their superior thermal conductivity, which is significantly higher than that of aluminum and iron. This makes copper cores more effective in dissipating heat, which is crucial in high-power and high-frequency applications. However, copper is heavier and more expensive than aluminum, factors that might influence the choice depending on the specific requirements of the application.

Applications and Benefits

Specific Use Cases for Copper Core PCBs

  • High-Power LED Lighting: Copper core PCBs are used extensively in high-power LED lighting solutions where efficient heat dissipation is critical to maintain performance and longevity.
  • Power Converters and Amplifiers: These devices generate significant heat and benefit from the superior thermal management provided by copper cores, ensuring stable operation and extending component life.
  • Automotive Electronics: The harsh environments and high thermal loads in automotive applications, such as in powertrain and lighting systems, make copper core PCBs an ideal choice.
  • RF and Microwave Circuits: High-frequency applications demand excellent thermal performance and electrical properties, both of which are well supported by copper core PCBs.
  • Industrial Power Equipment: Industrial applications that involve high currents and voltages benefit from the robust thermal and mechanical properties of copper core PCBs.

Advantages Over Other Metal Core Options

  • Superior Thermal Conductivity: Copper has one of the highest thermal conductivities of any metal, significantly outperforming aluminum and iron. This makes copper core PCBs the best option for applications requiring efficient heat management.
  • Enhanced Electrical Performance: The excellent electrical conductivity of copper reduces losses and enhances the overall performance of electronic circuits, particularly in high-frequency and high-power applications.
  • Mechanical Strength: Copper core PCBs offer superior mechanical strength, making them more durable and reliable in environments subject to mechanical stress and vibrations.
  • Thermal Expansion: Copper has a relatively low coefficient of thermal expansion, reducing the risk of thermal fatigue and mechanical failure in electronic components, particularly during temperature fluctuations.

While copper core PCBs are more expensive and heavier than their aluminum counterparts, they provide unmatched thermal and electrical performance. These attributes make copper core PCBs the preferred choice for applications that demand high reliability and efficiency in thermal management. Their specific use cases in high-power LED lighting, power converters, automotive electronics, RF and microwave circuits, and industrial power equipment illustrate the critical role copper core PCBs play in advanced electronic designs.

Double-Sided Metal Core PCBs


Explanation of Double-Sided Metal Core PCBs
Double-sided metal core PCBs (MCPCBs) are a type of PCB that incorporates a metal core, typically made of materials like aluminum or copper, positioned between two layers of circuitry. Unlike single-sided MCPCBs, which have circuitry on only one side, double-sided MCPCBs feature conductive pathways on both the top and bottom layers. The metal core acts as a heat sink, effectively dissipating heat away from the components on both sides of the board, thereby enhancing thermal management.

Applications and Use Cases

Where and Why They Are Used

  • LED Lighting Systems: Double-sided MCPCBs are widely used in LED applications where efficient heat dissipation is critical. The ability to manage heat from components on both sides of the PCB allows for higher power densities and improved performance of LED systems.
  • Power Electronics: In devices like power converters and inverters, where high currents generate significant heat, double-sided MCPCBs provide the necessary thermal management to ensure reliable operation.
  • Automotive Electronics: These PCBs are used in automotive applications such as LED headlights, powertrain electronics, and infotainment systems. The harsh operating conditions and the need for high reliability in automotive electronics make double-sided MCPCBs an ideal choice.
  • Industrial Control Systems: In industrial environments, where equipment operates under high power and potentially harsh conditions, double-sided MCPCBs offer robust thermal management and enhanced durability.
  • Telecommunications: High-frequency and high-power telecommunications equipment benefit from the superior thermal and electrical performance of double-sided MCPCBs, ensuring stable and reliable signal transmission.


Improved Thermal Management

  • Effective Heat Dissipation: The metal core in double-sided MCPCBs acts as an efficient heat sink, dissipating heat away from both sides of the PCB. This prevents overheating of components, reducing the risk of thermal-induced failures and extending the lifespan of the electronic devices.
  • High Power Density: The ability to manage heat from both sides allows for higher component densities and power ratings, which is particularly beneficial in compact or high-power applications.
  • Thermal Stability: Double-sided MCPCBs offer better thermal stability, which is crucial in maintaining consistent performance in applications subjected to fluctuating temperatures.

Increased Electrical Performance

  • Enhanced Conductivity: The metal core, especially when made of copper, provides excellent electrical conductivity. This reduces resistance and enhances the overall electrical performance of the PCB.
  • Reduced Signal Loss: The superior electrical properties of the metal core help in minimizing signal loss and interference, which is essential for high-frequency applications.
  • Mechanical Strength: The metal core adds mechanical strength to the PCB, making it more resistant to physical stresses and vibrations. This is particularly important in applications where the PCB is exposed to harsh environmental conditions or mechanical impacts.

Double-sided metal core PCBs combine the benefits of effective thermal management and superior electrical performance. They are particularly suited for applications that demand high power density, reliable heat dissipation, and robust mechanical properties. From LED lighting and power electronics to automotive systems and industrial controls, double-sided MCPCBs offer the enhanced performance and durability required in advanced electronic designs.

Best Substrate Materials for PCBs

Common Substrate Materials

1. FR4 (Flame Retardant 4) FR4 is the most widely used PCB substrate material. It is a fiberglass-reinforced epoxy laminate that offers good mechanical strength, electrical insulation, and thermal resistance. Its cost-effectiveness and versatility make it suitable for a wide range of applications, from consumer electronics to industrial equipment.

2. CEM-1 (Composite Epoxy Material 1) CEM-1 is made from a combination of woven glass fabric and paper with epoxy resin. It is less expensive than FR4 and provides decent mechanical and electrical properties. CEM-1 is typically used in single-layer PCBs for low-cost applications like simple consumer electronics.

3. CEM-3 (Composite Epoxy Material 3) CEM-3 is similar to FR4 but uses a woven glass fabric with non-woven glass core. It offers better performance than CEM-1, with improved mechanical strength and electrical insulation. CEM-3 is often used for double-sided PCBs where moderate performance is needed at a lower cost than FR4.

4. Polyimide Polyimide substrates are known for their high thermal stability, excellent mechanical properties, and good electrical insulation. They can withstand high temperatures, making them suitable for aerospace, military, and high-temperature industrial applications. Polyimide is also flexible, making it ideal for flexible and rigid-flex PCBs.

5. PTFE (Polytetrafluoroethylene) PTFE, commonly known by the brand name Teflon, is used in PCBs that require high-frequency performance due to its excellent dielectric properties. It offers low signal loss, high thermal resistance, and good chemical resistance. PTFE is used in RF, microwave, and high-speed digital applications, but it is more expensive and challenging to process.

Material Selection Criteria

1. Thermal Conductivity The ability of the substrate material to conduct heat is crucial for applications involving high-power components. Materials with high thermal conductivity, such as copper and aluminum, are preferred in these cases to ensure efficient heat dissipation and prevent overheating.

2. Electrical Insulation Good electrical insulation is necessary to prevent short circuits and ensure reliable performance. Substrate materials should have high dielectric strength and low dielectric loss to maintain signal integrity, especially in high-frequency applications.

3. Mechanical Properties Mechanical strength and durability are important factors, particularly for PCBs that will be subjected to physical stress or harsh environments. Materials should have high tensile strength, good impact resistance, and the ability to withstand thermal cycling without degrading.

4. Cost The cost of the substrate material is a significant consideration, particularly for mass-produced consumer electronics. While high-performance materials like polyimide and PTFE offer superior properties, they are also more expensive. Balancing performance requirements with cost constraints is essential for selecting the right substrate material.

Why Copper is Often Preferred

Superior Thermal and Electrical Properties Copper is often preferred in PCBs for its exceptional thermal and electrical properties. It has one of the highest thermal conductivities among common metals, which allows for efficient heat dissipation. This is crucial in high-power applications, such as LED lighting, power electronics, and automotive systems, where managing heat is vital to maintaining performance and reliability.

Copper also offers excellent electrical conductivity, which minimizes signal loss and resistance. This enhances the overall electrical performance of the PCB, making it suitable for high-frequency and high-speed applications. The combination of thermal and electrical properties makes copper a superior choice for substrates in advanced and demanding electronic designs.

Selecting the best substrate material for PCBs involves considering factors like thermal conductivity, electrical insulation, mechanical properties, and cost. While materials like FR4, CEM-1, CEM-3, polyimide, and PTFE each have their advantages and use cases, copper stands out for its superior thermal and electrical properties. This makes copper an ideal choice for high-performance and high-reliability applications.

Why is Copper Used in PCBs?

Thermal and Electrical Conductivity

How Copper Improves Performance

  1. Thermal Conductivity: Copper is highly efficient at conducting heat, making it an excellent choice for applications requiring effective heat dissipation. In PCBs, copper helps to transfer heat away from critical components, preventing overheating and ensuring optimal performance. This is particularly important in high-power applications, where excessive heat can lead to component failure.
  2. Electrical Conductivity: Copper is also one of the best conductors of electricity, offering low resistance to the flow of electrical current. This property minimizes signal loss and ensures efficient transmission of electrical signals across the PCB. Copper traces and planes provide reliable electrical connections, reducing impedance and improving the overall electrical performance of the circuit.

Durability and Reliability

Copper’s Impact on the Longevity of PCBs

  • Mechanical Strength: Copper is a relatively strong and durable metal, enhancing the mechanical integrity of PCBs. Copper traces and planes resist deformation and withstand mechanical stresses during manufacturing, assembly, and operation. This durability contributes to the longevity of PCBs, reducing the risk of damage or failure over time.
  • Corrosion Resistance: Copper has excellent corrosion resistance, particularly when protected by a layer of solder mask or other protective coatings. This resistance to oxidation and corrosion ensures the reliability and stability of copper-based PCBs, even in harsh environments or under prolonged exposure to moisture and contaminants.


Ease of Working with Copper in PCB Production

  • Etching: Copper is easily etched using chemical processes, allowing for precise patterning of traces and planes on the PCB surface. This enables the fabrication of intricate and densely packed circuits with high precision and accuracy.
  • Plating: Copper can be selectively plated onto the substrate to create conductive pathways and connections. Electroplating techniques ensure uniform deposition of copper layers, facilitating the creation of complex multilayer PCBs with reliable electrical connections.
  • Soldering: Copper surfaces readily bond with solder, providing strong and durable connections between components and traces. This facilitates the assembly process and ensures the integrity of electrical connections, even under thermal cycling and mechanical stress.

Copper is used in PCBs primarily for its exceptional thermal and electrical conductivity, which improve the performance and reliability of electronic devices. Its mechanical strength, corrosion resistance, and ease of manufacturability further contribute to the longevity and quality of copper-based PCBs. Whether in high-power applications, high-frequency circuits, or demanding environmental conditions, copper remains a preferred choice for achieving superior performance and durability in PCB designs.

Substrate Materials Used in PCBs

Detailed Analysis

1. FR4 (Flame Retardant 4)

  • Explanation: FR4 is a fiberglass-reinforced epoxy laminate widely used in PCB fabrication. It offers good mechanical strength, electrical insulation, and thermal resistance.
  • Advantages: Cost-effective, versatile, good mechanical properties, widely available.
  • Disadvantages: Limited thermal conductivity, prone to moisture absorption, relatively high dielectric constant.

2. CEM-1 (Composite Epoxy Material 1)

  • Explanation: CEM-1 consists of woven glass fabric and paper with epoxy resin. It is less expensive than FR4 but offers lower mechanical strength and thermal stability.
  • Advantages: Lower cost, suitable for single-layer PCBs in low-cost applications.
  • Disadvantages: Lower mechanical strength and thermal stability compared to FR4.

3. CEM-3 (Composite Epoxy Material 3)

  • Explanation: CEM-3 uses a woven glass fabric with a non-woven glass core and epoxy resin. It offers better mechanical strength and thermal stability than CEM-1.
  • Advantages: Better mechanical strength and thermal stability than CEM-1, suitable for double-sided PCBs.
  • Disadvantages: Not as widely available as FR4, higher cost compared to CEM-1.

4. Polyimide

  • Explanation: Polyimide substrates offer high thermal stability, excellent mechanical properties, and good electrical insulation. They can withstand high temperatures and are flexible, making them ideal for flexible and rigid-flex PCBs.
  • Advantages: High thermal stability, good electrical insulation, flexibility.
  • Disadvantages: Higher cost, limited availability, challenging to process.

5. PTFE (Polytetrafluoroethylene)

  • Explanation: PTFE, or Teflon, is used in PCBs requiring high-frequency performance due to its excellent dielectric properties. It offers low signal loss, high thermal resistance, and good chemical resistance.
  • Advantages: Low signal loss, high thermal resistance, chemical resistance.
  • Disadvantages: Higher cost, challenging to process, limited availability.

Trends and Innovations

Emerging Materials and Future Trends in PCB Substrates

  • High-Frequency Materials: With the increasing demand for high-frequency applications in telecommunications and data communication, there is a growing need for substrates with low dielectric loss and high-frequency performance.
  • Thermal Management Solutions: As electronic devices become more compact and powerful, there is a greater emphasis on thermal management. Emerging materials with enhanced thermal conductivity, such as metal matrix composites and ceramics, are being explored for their potential to improve heat dissipation in PCBs.
  • Flexible and Stretchable Substrates: The rise of wearable electronics and flexible displays has spurred research into flexible and stretchable substrate materials. Innovations in materials like elastomers and nanocomposites are paving the way for PCBs that can conform to irregular shapes and withstand mechanical deformation.
  • Environmentally Friendly Materials: As sustainability becomes a priority, there is a shift towards environmentally friendly substrate materials. Bio-based resins, recycled materials, and non-toxic alternatives are gaining traction as manufacturers seek to reduce their environmental footprint.

The choice of substrate material for PCBs depends on various factors such as cost, performance requirements, and application-specific considerations. While traditional materials like FR4 and CEM-3 remain popular due to their cost-effectiveness and reliability, emerging materials offer opportunities for improved performance and innovation in PCB design. Trends such as high-frequency materials, thermal management solutions, flexible substrates, and environmentally friendly materials are shaping the future of PCB substrates, driving advancements in electronic device design and manufacturing.

FAQs About Copper Substrate PCB

What is copper base PCB?

A copper base PCB, also known as a copper substrate PCB, is a type of printed circuit board where copper serves as the primary substrate material. This design offers superior thermal conductivity and is commonly used in applications requiring efficient heat dissipation.

What is the best substrate for PCB?

The best substrate for PCB depends on the specific requirements of the application. However, materials like FR4 (fiberglass-reinforced epoxy laminate), polyimide, and ceramic are commonly used due to their excellent thermal stability, mechanical strength, and electrical insulation properties.

Why is copper used in PCBs?

Copper is used in PCBs primarily for its exceptional thermal and electrical conductivity. It efficiently dissipates heat away from critical components, preventing overheating and ensuring optimal performance. Additionally, copper offers good mechanical strength and durability, contributing to the reliability of PCBs.

What substrate material is used in PCB?

PCBs can be made from various substrate materials, including FR4, CEM-1, CEM-3, polyimide, and PTFE (polytetrafluoroethylene). Each material has its advantages and is chosen based on factors such as thermal conductivity, electrical insulation, mechanical properties, and cost.