Question:
Reference for part a:
You are designing a transmission line for use as an interconnect in a chip circuit. The printed circuit board substrate is made of high-quality 99.5% alumina (Al2O3) and the transmission line is made of annealed copper, both non-magnetic. The circuit will operate in air at room temperature at frequency = 20 kHz. Each line will generate electromagnetic wave radiation that will penetrate both the other line and the PCB. a) What is the loss tangent for: i. the PCB ii. the transmission line(s) For part a), you will need to locate materials property information, from either your textbook or from the given reference on D2L: Aluminum Oxide Al2O3 Material Properties. b) Write down the expressions you can use to evaluate the attenuation coefficient(s) for: i. the PCB ii. the transmission line(s) Use any approximations that are justified by part a) c) What is the expected EM wave penetration depth for: i. the PCB ii. the transmission lines Aluminum Oxide, Al2O3 Ceramic Properties Alumina is one of the most cost effective and widely used material in the family of engineering ceramics. The raw materials from which this high performance technical grade ceramic is made are readily available and reasonably priced, resulting in good value for the cost in fabricated alumina shapes. With an excellent combination of properties and an attractive price, it is no surprise that fine grain technical grade alumina has a very wide range of applications. Key Properties Hard, wear-resistant Excellent dielectric properties from DC to GHz frequencies Resists strong acid and alkali attack at elevated temperatures Good thermal conductivity Excellent size and shape capability High strength and stiffness Available in purity ranges from 94%, an easily metallizable composition, to 99.8% for the most demanding high temperature applications. Typical Uses Gas laser tubes Wear pads Seal rings High temperature electrical insulators High voltage insulators Furnace liner tubes Thread and wire guides Electronic substrates Ballistic armor Abrasion resistant tube and elbow liners Thermometry sensors Laboratory instrument tubes and sample holders Instrumentation parts for thermal property test machines Grinding media General Information Aluminum oxide, commonly referred to as alumina, possesses strong ionic interatomic bonding giving rise to it's desirable material characteristics. It can exist in several crystalline phases which all revert to the most stable hexagonal alpha phase at elevated temperatures. This is the phase of particular interest for structural applications and the material available from Accuratus. Engineering Properties* 94% Aluminum Oxide Mechanical SI/Metric Units of Measure gm/cc (lb/ft?) %(%) 3.69 (Imperial) (230.4) (0) 0 Density Porosity Color Flexural Strength white 330 (47) Elastic Modulus 300 MPa (lb/in?x103) GPa (lb/in2x106) GPa (lb/in2x106) GPa (lb/in2x106) Shear Modulus 124 165 Bulk Modulus Poisson's Ratio (43.5) (18) (24) (0.21) (304.5) 0.21 2100 MPa (lb/in2x103) Kg/mm2 1175 MPa.m 1/2 3.5 C (F) 1700 (3090) 18 Compressive Strength Hardness Fracture Toughness Kic Maximum Use Temperature (no load) Thermal Thermal Conductivity Coefficient of Thermal Expansion Specific Heat Electrical Dielectric Strength Dielectric Constant Dissipation Factor Loss Tangent Volume Resistivity W/mK (BTU.in/ft2.hrF) 10-61C (10-61F) J/KgK (Btu/lbF) 8.1 (125) (4.5) (0.21) 880 16.7 ac-kv/mm (volts/mil) @ 1 MHz @ 1 kHz 9.1 0.0007 (418) (9.1) (0.0007) @ 1 kHz ohm.cm - >1014 96% Aluminum Oxide Mechanical Units of Measure Si/Metric gm/cc (lb/ft3) 3.72 Density Porosity (Imperial) (232.2) (0) %(%) 0 Color white 345 Flexural Strength Elastic Modulus 300 MPa (lb/in2x103) GPa (lb/in2x106) GPa (lb/in2x106) GPa (lb/in2x106) Shear Modulus 124 (50) (43.5) (18) (25) (0.21) (304.5) Bulk Modulus 172 Poisson's Ratio 0.21 2100 MPa (lb/in2x103) Kg/mm2 1100 Compressive Strength Hardness Fracture Toughness Kic Maximum Use Temperature (no load) MPa.m 1/2 3.5 C (F) 1700 (3090) Thermal 25 Thermal Conductivity Coefficient of Thermal Expansion Specific Heat W/mK (BTU.in/ft2.hrF) 10-61C (10-61F) J/KgK (Btu/lbF) 8.2 (174) (4.6) (0.21) 880 14.6 (365) Electrical Dielectric Strength Dielectric Constant Dissipation Factor Loss Tangent Volume Resistivity ac-kv/mm (volts/mil) @ 1 MHz @ 1 kHz 9.0 0.0011 (9.0) (0.0011) @ 1 kHz ohm.cm >1014 Download 99.5% Alumina datasheet 99.5% Aluminum Oxide Mechanical SI/Metric Units of Measure gm/cc (lb/ft3) %(%) Density Porosity Color 3.89 (Imperial) (242.8) (0) 0 ivory 379 Flexural Strength (55) Elastic Modulus 375 MPa (lb/in2x103) GPa (lb/in2x106) GPa (Ib/in2x106) GPa (lb/in2x106) Shear Modulus 152 (54.4) (22) (33) Bulk Modulus 228 Poisson's Ratio 0.22 (0.22) 2600 (377) MPa (lb/in2x103) Kg/mm2 MPa.m 1/2 1440 4 C (F) 1750 (3180) 35 Compressive Strength Hardness Fracture Toughness Kic Maximum Use Temperature (no load) Thermal Thermal Conductivity Coefficient of Thermal Expansion Specific Heat Electrical Dielectric Strength Dielectric Constant Dissipation Factor Loss Tangent Volume Resistivity W/mK (BTU.in/ft?.hrF) 10-61C (10-61F) J/KgK (Btu/lbF) 8.4 (243) (4.7) (0.21) 880 16.9 ac-kv/mm (volts/mil) @ 1 MHz 9.8 (420) (9.8) (0.0002) @ 1 kHz 0.0002 @ 1 kHz ohm.cm >1014 You are designing a transmission line for use as an interconnect in a chip circuit. The printed circuit board substrate is made of high-quality 99.5% alumina (Al2O3) and the transmission line is made of annealed copper, both non-magnetic. The circuit will operate in air at room temperature at frequency = 20 kHz. Each line will generate electromagnetic wave radiation that will penetrate both the other line and the PCB. a) What is the loss tangent for: i. the PCB ii. the transmission line(s) For part a), you will need to locate materials property information, from either your textbook or from the given reference on D2L: Aluminum Oxide Al2O3 Material Properties. b) Write down the expressions you can use to evaluate the attenuation coefficient(s) for: i. the PCB ii. the transmission line(s) Use any approximations that are justified by part a) c) What is the expected EM wave penetration depth for: i. the PCB ii. the transmission lines Aluminum Oxide, Al2O3 Ceramic Properties Alumina is one of the most cost effective and widely used material in the family of engineering ceramics. The raw materials from which this high performance technical grade ceramic is made are readily available and reasonably priced, resulting in good value for the cost in fabricated alumina shapes. With an excellent combination of properties and an attractive price, it is no surprise that fine grain technical grade alumina has a very wide range of applications. Key Properties Hard, wear-resistant Excellent dielectric properties from DC to GHz frequencies Resists strong acid and alkali attack at elevated temperatures Good thermal conductivity Excellent size and shape capability High strength and stiffness Available in purity ranges from 94%, an easily metallizable composition, to 99.8% for the most demanding high temperature applications. Typical Uses Gas laser tubes Wear pads Seal rings High temperature electrical insulators High voltage insulators Furnace liner tubes Thread and wire guides Electronic substrates Ballistic armor Abrasion resistant tube and elbow liners Thermometry sensors Laboratory instrument tubes and sample holders Instrumentation parts for thermal property test machines Grinding media General Information Aluminum oxide, commonly referred to as alumina, possesses strong ionic interatomic bonding giving rise to it's desirable material characteristics. It can exist in several crystalline phases which all revert to the most stable hexagonal alpha phase at elevated temperatures. This is the phase of particular interest for structural applications and the material available from Accuratus. Engineering Properties* 94% Aluminum Oxide Mechanical SI/Metric Units of Measure gm/cc (lb/ft?) %(%) 3.69 (Imperial) (230.4) (0) 0 Density Porosity Color Flexural Strength white 330 (47) Elastic Modulus 300 MPa (lb/in?x103) GPa (lb/in2x106) GPa (lb/in2x106) GPa (lb/in2x106) Shear Modulus 124 165 Bulk Modulus Poisson's Ratio (43.5) (18) (24) (0.21) (304.5) 0.21 2100 MPa (lb/in2x103) Kg/mm2 1175 MPa.m 1/2 3.5 C (F) 1700 (3090) 18 Compressive Strength Hardness Fracture Toughness Kic Maximum Use Temperature (no load) Thermal Thermal Conductivity Coefficient of Thermal Expansion Specific Heat Electrical Dielectric Strength Dielectric Constant Dissipation Factor Loss Tangent Volume Resistivity W/mK (BTU.in/ft2.hrF) 10-61C (10-61F) J/KgK (Btu/lbF) 8.1 (125) (4.5) (0.21) 880 16.7 ac-kv/mm (volts/mil) @ 1 MHz @ 1 kHz 9.1 0.0007 (418) (9.1) (0.0007) @ 1 kHz ohm.cm - >1014 96% Aluminum Oxide Mechanical Units of Measure Si/Metric gm/cc (lb/ft3) 3.72 Density Porosity (Imperial) (232.2) (0) %(%) 0 Color white 345 Flexural Strength Elastic Modulus 300 MPa (lb/in2x103) GPa (lb/in2x106) GPa (lb/in2x106) GPa (lb/in2x106) Shear Modulus 124 (50) (43.5) (18) (25) (0.21) (304.5) Bulk Modulus 172 Poisson's Ratio 0.21 2100 MPa (lb/in2x103) Kg/mm2 1100 Compressive Strength Hardness Fracture Toughness Kic Maximum Use Temperature (no load) MPa.m 1/2 3.5 C (F) 1700 (3090) Thermal 25 Thermal Conductivity Coefficient of Thermal Expansion Specific Heat W/mK (BTU.in/ft2.hrF) 10-61C (10-61F) J/KgK (Btu/lbF) 8.2 (174) (4.6) (0.21) 880 14.6 (365) Electrical Dielectric Strength Dielectric Constant Dissipation Factor Loss Tangent Volume Resistivity ac-kv/mm (volts/mil) @ 1 MHz @ 1 kHz 9.0 0.0011 (9.0) (0.0011) @ 1 kHz ohm.cm >1014 Download 99.5% Alumina datasheet 99.5% Aluminum Oxide Mechanical SI/Metric Units of Measure gm/cc (lb/ft3) %(%) Density Porosity Color 3.89 (Imperial) (242.8) (0) 0 ivory 379 Flexural Strength (55) Elastic Modulus 375 MPa (lb/in2x103) GPa (lb/in2x106) GPa (Ib/in2x106) GPa (lb/in2x106) Shear Modulus 152 (54.4) (22) (33) Bulk Modulus 228 Poisson's Ratio 0.22 (0.22) 2600 (377) MPa (lb/in2x103) Kg/mm2 MPa.m 1/2 1440 4 C (F) 1750 (3180) 35 Compressive Strength Hardness Fracture Toughness Kic Maximum Use Temperature (no load) Thermal Thermal Conductivity Coefficient of Thermal Expansion Specific Heat Electrical Dielectric Strength Dielectric Constant Dissipation Factor Loss Tangent Volume Resistivity W/mK (BTU.in/ft?.hrF) 10-61C (10-61F) J/KgK (Btu/lbF) 8.4 (243) (4.7) (0.21) 880 16.9 ac-kv/mm (volts/mil) @ 1 MHz 9.8 (420) (9.8) (0.0002) @ 1 kHz 0.0002 @ 1 kHz ohm.cm >1014
