Thermal Calculator

1. Thermal Basics

Proper thermal management is crucial for semiconductor reliability and performance. Heat flow follows a path from the junction through various thermal resistances to the ambient environment.

Junction temperature (Tj)
Case temperature (Tc)
Heat sink temperature (Ts)
Ambient temperature (Ta)

2. Thermal Energy Calculations

How to calculate thermal energy in different scenarios:

Energy Type	Formula	Units
From Temperature	Q = m × c × ΔT	Joules (J)
From Kinetic Energy	Q = KE × efficiency	Joules (J)

3. Thermal Resistance

Thermal resistance represents the opposition to heat flow:

Tj = Ta + (P × θja)
θja = θjc + θcs + θsa
where:
θja: Junction to ambient
θjc: Junction to case
θcs: Case to sink
θsa: Sink to ambient

3. Power Dissipation

Power dissipation considerations:

Maximum power rating
Temperature derating
Safe operating area
Thermal runaway prevention

4. Heat Sink Selection

Heat sink requirements calculation:

Required thermal resistance
Surface area and fin design
Mounting considerations
Air flow requirements

5. Thermal Conductivity Calculations

How to calculate thermal conductivity and related parameters:

Parameter	Formula	Units
Thermal Conductivity	k = (Q × L)/(A × ΔT)	W/(m·K)
R-Value	R = L/(k × A)	m²·K/W

6. Thermal Expansion Analysis

Calculating thermal expansion in different materials:

Linear Expansion:
- ΔL = α × L × ΔT
- α: Linear expansion coefficient
- L: Original length
- ΔT: Temperature change
Material Coefficients:
- Steel: 11-13 × 10⁻⁶/°C
- Aluminum: 23-24 × 10⁻⁶/°C
- Copper: 16-17 × 10⁻⁶/°C
- Glass: 8-9 × 10⁻⁶/°C

7. Thermal Equilibrium

How to calculate thermal equilibrium temperature:

System Type	Formula	Example
Two Bodies	Tf = (m₁c₁T₁ + m₂c₂T₂)/(m₁c₁ + m₂c₂)	Metal-water system
Multiple Bodies	Tf = Σ(mᵢcᵢTᵢ)/Σ(mᵢcᵢ)	Complex systems

8. Thermal Efficiency

How to calculate thermal efficiency in different systems:

System Type	Formula	Typical Range
Heat Engine	η = (Qh - Qc)/Qh	30-60%
Rankine Cycle	η = Wnet/Qin	35-45%

9. Thermal Boundary Layer

Calculating thermal boundary layer thickness:

Laminar Flow:
- δt = 5x/√(Rex × Pr)
- Rex: Reynolds number
- Pr: Prandtl number
- x: Distance from leading edge
Key Parameters:
- Flow velocity
- Fluid properties
- Surface temperature
- Heat transfer coefficient

10. Thermal Time Constant

Understanding thermal response time:

Parameter	Formula	Application
Time Constant	τ = R × C	Transient response
Temperature Rise	T(t) = Tf(1 - e^(-t/τ))	Dynamic behavior

11. Thermal Stress Analysis

How to calculate thermal stress in materials:

Parameter	Formula	Considerations
Thermal Stress	σ = E × α × ΔT	Material properties
Strain Energy	U = (σ²/2E) × V	Volume effects

12. PCB Thermal Design

PCB thermal calculations and considerations:

Via Thermal Resistance:
- Rth = L/(k × A × N)
- N: Number of vias
- A: Via cross-section
- k: Copper conductivity
Thermal Relief Design:
- Spoke width calculation
- Air gap spacing
- Copper thickness
- Connection angle

13. Thermal Noise Calculations

Understanding thermal noise in electronic systems:

Parameter	Formula	Notes
Noise Voltage	Vn = √(4kTRB)	Johnson noise
Noise Power	Pn = kTB	Available power

8. Design Guidelines

Best practices for thermal design:

Temperature margin (20% typical)
Power derating with temperature
Proper component spacing
Air flow optimization
Thermal measurement points
Worst-case analysis

Understanding Thermal Management