電気電子回路のための熱力学

https://www.it-book.co.jp/books/075.html

```
import numpy as np
import matplotlib.pyplot as plt

# 定数
k_B = 1.38e-23  # ボルツマン定数 (J/K)

# 時間設定
t = np.linspace(0, 10, 500)  # 0から10秒まで500ポイント

# エネルギーの変化（例: キャパシタから抵抗器へのエネルギー変換）
initial_energy = 1.0  # 初期エネルギー (Joules)
energy = initial_energy * np.exp(-0.1 * t)  # エネルギーの減少（例: 指数関数的に減少）

# エントロピーの変化計算
def entropy_change(E_initial, E_final):
    return k_B * np.log(E_initial / E_final)

entropy_changes = entropy_change(initial_energy, energy)

# グラフ描画
plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plt.plot(t, energy, label='Energy')
plt.xlabel('Time (s)')
plt.ylabel('Energy (Joules)')
plt.title('Energy Over Time')
plt.grid()
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(t, entropy_changes, label='Entropy Change', color='r')
plt.xlabel('Time (s)')
plt.ylabel('Entropy Change (J/K)')
plt.title('Entropy Change Over Time')
plt.grid()
plt.legend()

plt.tight_layout()
plt.show()

```

```
import numpy as np
import matplotlib.pyplot as plt

# 定数
h = 6.626e-34  # プランク定数 (Js)
c = 3.0e8      # 光速 (m/s)
k_B = 1.38e-23 # ボルツマン定数 (J/K)

def planck_law(wavelength, T):
    """
    プランクの法則に基づく放射強度の計算
    :param wavelength: 波長 (m)
    :param T: 絶対温度 (K)
    :return: 放射強度 (W/m^3)
    """
    return (2 * h * c**2) / (wavelength**5) * 1 / (np.exp((h * c) / (wavelength * k_B * T)) - 1)

# 波長範囲
wavelength = np.linspace(1e-9, 2e-6, 500)  # 波長範囲 (m)

# 温度設定
temperatures = [3000, 4000, 5000]  # 絶対温度 (K)

# グラフ描画
plt.figure(figsize=(12, 8))

for T in temperatures:
    I = planck_law(wavelength, T)
    plt.plot(wavelength * 1e9, I, label=f'T = {T} K')  # 波長をnm単位に変換してプロット

plt.xlabel('Wavelength (nm)')
plt.ylabel('Intensity (W/m^3)')
plt.title("Blackbody Radiation Spectrum (Planck's Law)")
plt.legend()
plt.grid()
plt.show()

```

```
import numpy as np
import matplotlib.pyplot as plt

# 定数
length = 1.0  # 導体の長さ (m)
num_points = 100
x = np.linspace(0, length, num_points)

# 熱伝導率の設定 (W/mK)
k_conductor = 200  # 導体の熱伝導率 (例: 銅)
k_insulator = 0.1  # 絶縁体の熱伝導率 (例: ガラスウール)

# 温度分布の設定
T_left = 100  # 左端の温度 (°C)
T_right = 20  # 右端の温度 (°C)

# 温度勾配の計算
def temperature_distribution(x, T_left, T_right):
    return T_left - (T_left - T_right) * (x / length)

T_conductor = temperature_distribution(x, T_left, T_right)
T_insulator = temperature_distribution(x, T_left, T_right)

# 熱流の計算
def heat_flux(temperature, k):
    dT_dx = np.gradient(temperature, x)
    return -k * dT_dx

q_conductor = heat_flux(T_conductor, k_conductor)
q_insulator = heat_flux(T_insulator, k_insulator)

# グラフ描画
plt.figure(figsize=(12, 6))

# 温度分布
plt.subplot(1, 2, 1)
plt.plot(x, T_conductor, label='Conductor (k=200 W/mK)')
plt.plot(x, T_insulator, label='Insulator (k=0.1 W/mK)')
plt.xlabel('Position (m)')
plt.ylabel('Temperature (°C)')
plt.title('Temperature Distribution')
plt.legend()
plt.grid()

# 熱流
plt.subplot(1, 2, 2)
plt.plot(x, q_conductor, label='Conductor (k=200 W/mK)')
plt.plot(x, q_insulator, label='Insulator (k=0.1 W/mK)')
plt.xlabel('Position (m)')
plt.ylabel('Heat Flux (W/m²)')
plt.title('Heat Flux')
plt.legend()
plt.grid()

plt.tight_layout()
plt.show()


```
```
import numpy as np
import matplotlib.pyplot as plt

# 定数
length = 0.1  # ヒートシンクの長さ (m)
num_points = 100
x = np.linspace(0, length, num_points)

# パラメータ設定
k_source = 1000  # 発熱源の熱伝導率 (W/mK)
k_heatsink = 200  # ヒートシンクの熱伝導率 (W/mK)
k_pads = 5      # サーマルパッドの熱伝導率 (W/mK)
thickness_pads = 0.001  # サーマルパッドの厚さ (m)

# 温度分布の設定
T_source = 100  # 発熱源の温度 (°C)
T_ambient = 25  # 環境温度 (°C)

# ヒートシンクとサーマルパッドの温度分布
def temperature_distribution(x, T_source, T_ambient, k_material, thickness=0):
    if thickness > 0:
        # サーマルパッドの影響を含む場合
        x = np.linspace(0, length + thickness, num_points)
        return T_source - (T_source - T_ambient) * (x / (length + thickness))
    else:
        return T_source - (T_source - T_ambient) * (x / length)

T_source_only = temperature_distribution(x, T_source, T_ambient, k_source)
T_heatsink = temperature_distribution(x, T_source, T_ambient, k_heatsink)
T_pads = temperature_distribution(x, T_source, T_ambient, k_pads, thickness_pads)

# グラフ描画
plt.figure(figsize=(12, 6))

# 温度分布
plt.subplot(1, 2, 1)
plt.plot(x, T_source_only, label='Heat Source Only')
plt.plot(x, T_heatsink, label='Heatsink')
plt.plot(x, T_pads, label='Thermal Pads')
plt.xlabel('Position (m)')
plt.ylabel('Temperature (°C)')
plt.title('Temperature Distribution')
plt.legend()
plt.grid()

# 温度勾配（熱流のプロキシ）
def temperature_gradient(temperature, x):
    return np.gradient(temperature, x)

q_source_only = temperature_gradient(T_source_only, x)
q_heatsink = temperature_gradient(T_heatsink, x)
q_pads = temperature_gradient(T_pads, x)

# 熱流のプロット
plt.subplot(1, 2, 2)
plt.plot(x, q_source_only, label='Heat Source Only')
plt.plot(x, q_heatsink, label='Heatsink')
plt.plot(x, q_pads, label='Thermal Pads')
plt.xlabel('Position (m)')
plt.ylabel('Heat Flux (W/m²)')
plt.title('Heat Flux')
plt.legend()
plt.grid()

plt.tight_layout()
plt.show()


```


```

import numpy as np
import matplotlib.pyplot as plt

# 定数
length = 0.01  # 半導体デバイスの長さ (m)
width = 0.01   # 半導体デバイスの幅 (m)
thickness = 0.001  # 半導体デバイスの厚さ (m)
num_points = 100
x = np.linspace(0, length, num_points)
y = np.linspace(0, width, num_points)
X, Y = np.meshgrid(x, y)

# 材料特性
k = 150  # 熱伝導率 (W/mK) (例: シリコン)
T_ambient = 25  # 環境温度 (°C)
Q_dot = 1e5  # 発熱量 (W/m³) (例: 100W/cm³)

# 定常状態の温度分布を計算
def temperature_distribution(X, Y, k, Q_dot, T_ambient, length, width):
    # 熱伝導方程式の定常状態の解 (近似的な解)
    return T_ambient + (Q_dot / (k * length * width)) * X * (length - X)

T = temperature_distribution(X, Y, k, Q_dot, T_ambient, length, width)

# グラフ描画
plt.figure(figsize=(12, 6))

# 温度分布のプロット
plt.contourf(X, Y, T, cmap='hot', levels=50)
plt.colorbar(label='Temperature (°C)')
plt.xlabel('Length (m)')
plt.ylabel('Width (m)')
plt.title('Temperature Distribution in Semiconductor Device')
plt.grid()
plt.show()

```


```
import numpy as np
import matplotlib.pyplot as plt

# 定数
T0 = 25  # 基準温度 (°C)
T = np.linspace(-20, 100, 200)  # 温度範囲 (°C)

# トランジスタのパラメータ
V_BE0 = 0.7  # 基準温度でのベース-エミッタ電圧 (V)
alpha_BJT = 2.2e-2  # 温度係数 (V/°C)

# 抵抗のパラメータ
R0 = 1000  # 基準温度での抵抗 (Ω)
alpha_R = 0.0039  # 温度係数 (1/°C)

# トランジスタのベース-エミッタ電圧の計算
V_BE = V_BE0 - alpha_BJT * (T - T0)

# 抵抗値の計算
R = R0 * (1 + alpha_R * (T - T0))

# グラフ描画
plt.figure(figsize=(12, 6))

# トランジスタのベース-エミッタ電圧
plt.subplot(1, 2, 1)
plt.plot(T, V_BE, label='Base-Emitter Voltage (V)')
plt.xlabel('Temperature (°C)')
plt.ylabel('V_BE (V)')
plt.title('Transistor Base-Emitter Voltage vs Temperature')
plt.grid()
plt.legend()

# 抵抗値
plt.subplot(1, 2, 2)
plt.plot(T, R, label='Resistance (Ω)')
plt.xlabel('Temperature (°C)')
plt.ylabel('Resistance (Ω)')
plt.title('Resistor Resistance vs Temperature')
plt.grid()
plt.legend()

plt.tight_layout()
plt.show()


```



```
import numpy as np
import matplotlib.pyplot as plt

# 定数
length = 0.01  # デバイスの長さ (m)
width = 0.01   # デバイスの幅 (m)
thickness = 0.001  # デバイスの厚さ (m)
num_points = 100
x = np.linspace(0, length, num_points)
y = np.linspace(0, width, num_points)
X, Y = np.meshgrid(x, y)

# パラメータ設定
k_source = 1000  # 発熱源の熱伝導率 (W/mK)
k_heatsink = 200  # ヒートシンクの熱伝導率 (W/mK)
k_heatsink_with_pipes = 500  # ヒートシンク + ヒートパイプの熱伝導率 (W/mK)
k_fan_cooling = 150  # 冷却ファンの効果を反映させた熱伝導率 (W/mK)

T_ambient = 25  # 環境温度 (°C)
Q_dot = 1e5  # 発熱量 (W/m³)

# 温度分布の計算
def temperature_distribution(X, Y, k_material, Q_dot, T_ambient):
    return T_ambient + (Q_dot / (k_material * length * width)) * X * (length - X)

# 各シナリオの温度分布
T_source = temperature_distribution(X, Y, k_source, Q_dot, T_ambient)
T_heatsink = temperature_distribution(X, Y, k_heatsink, Q_dot, T_ambient)
T_heatsink_pipes = temperature_distribution(X, Y, k_heatsink_with_pipes, Q_dot, T_ambient)
T_fan = temperature_distribution(X, Y, k_fan_cooling, Q_dot, T_ambient)

# グラフ描画
plt.figure(figsize=(15, 10))

# 発熱源のみ
plt.subplot(2, 2, 1)
plt.contourf(X, Y, T_source, cmap='hot', levels=50)
plt.colorbar(label='Temperature (°C)')
plt.title('Heat Source Only')
plt.xlabel('Length (m)')
plt.ylabel('Width (m)')
plt.grid()

# ヒートシンク
plt.subplot(2, 2, 2)
plt.contourf(X, Y, T_heatsink, cmap='hot', levels=50)
plt.colorbar(label='Temperature (°C)')
plt.title('Heatsink')
plt.xlabel('Length (m)')
plt.ylabel('Width (m)')
plt.grid()

# ヒートパイプ付きヒートシンク
plt.subplot(2, 2, 3)
plt.contourf(X, Y, T_heatsink_pipes, cmap='hot', levels=50)
plt.colorbar(label='Temperature (°C)')
plt.title('Heatsink with Heat Pipes')
plt.xlabel('Length (m)')
plt.ylabel('Width (m)')
plt.grid()

# 冷却ファン効果
plt.subplot(2, 2, 4)
plt.contourf(X, Y, T_fan, cmap='hot', levels=50)
plt.colorbar(label='Temperature (°C)')
plt.title('Cooling Fan Effect')
plt.xlabel('Length (m)')
plt.ylabel('Width (m)')
plt.grid()

plt.tight_layout()
plt.show()


```

```

import numpy as np
import matplotlib.pyplot as plt

# 定数
length = 0.02  # MOSFETの長さ (m)
width = 0.02   # MOSFETの幅 (m)
num_points = 100
x = np.linspace(0, length, num_points)
y = np.linspace(0, width, num_points)
X, Y = np.meshgrid(x, y)

# パラメータ設定
Q_dot = 1e5  # MOSFETの発熱量 (W/m³)
T_ambient = 25  # 環境温度 (°C)

# MOSFETとヒートシンクの熱伝導率
k_mosfet = 100  # MOSFETの熱伝導率 (W/mK)
k_heatsink = 200  # ヒートシンクの熱伝導率 (W/mK)

# 温度分布の計算
def temperature_distribution(X, Y, k_material, Q_dot, T_ambient):
    return T_ambient + (Q_dot / (k_material * length * width)) * X * (length - X)

# MOSFETの温度分布
T_mosfet = temperature_distribution(X, Y, k_mosfet, Q_dot, T_ambient)

# ヒートシンク付きMOSFETの温度分布
T_heatsink = temperature_distribution(X, Y, k_heatsink, Q_dot, T_ambient)

# グラフ描画
plt.figure(figsize=(12, 8))

# MOSFETの温度分布
plt.subplot(1, 2, 1)
plt.contourf(X, Y, T_mosfet, cmap='hot', levels=50)
plt.colorbar(label='Temperature (°C)')
plt.title('MOSFET Temperature Distribution')
plt.xlabel('Length (m)')
plt.ylabel('Width (m)')
plt.grid()

# ヒートシンク付きMOSFETの温度分布
plt.subplot(1, 2, 2)
plt.contourf(X, Y, T_heatsink, cmap='hot', levels=50)
plt.colorbar(label='Temperature (°C)')
plt.title('MOSFET with Heatsink Temperature Distribution')
plt.xlabel('Length (m)')
plt.ylabel('Width (m)')
plt.grid()

plt.tight_layout()
plt.show()

```

```
import numpy as np
import matplotlib.pyplot as plt

# 定数
k_B = 1.38e-23  # ボルツマン定数 (J/K)

# 計算するパラメータ
temperatures = [300, 350, 400]  # 温度 (K)
resistances = [1000, 5000, 10000]  # 抵抗値 (Ω)
bandwidth = 1e6  # 帯域幅 (Hz)

# ノイズパワーの計算
def calculate_noise_power(T, R, B):
    S_V = 4 * k_B * T * R
    P = S_V * B
    return P

# ノイズパワーの計算とプロット
plt.figure(figsize=(12, 8))

for R in resistances:
    noise_powers = [calculate_noise_power(T, R, bandwidth) for T in temperatures]
    plt.plot(temperatures, noise_powers, label=f'R = {R} Ω')

plt.xlabel('Temperature (K)')
plt.ylabel('Noise Power (W)')
plt.title('Johnson-Nyquist Noise Power vs Temperature')
plt.legend()
plt.grid()
plt.yscale('log')  # ノイズパワーのスケールを対数に設定
plt.show()


```


```
import numpy as np
import matplotlib.pyplot as plt

# 定数
R = 1000  # 抵抗 (Ω)
C = 1e-6  # キャパシタ (F)
V_in = 5  # 入力電圧 (V)
I = V_in / R  # 抵抗に流れる電流 (A)
P = I**2 * R  # 抵抗で発生する熱量 (W)
T_ambient = 25  # 環境温度 (°C)

# 時間設定
t_max = 100  # 最大時間 (s)
dt = 1  # 時間ステップ (s)
time = np.arange(0, t_max, dt)

# 温度変化の計算
def temperature_change(time, P, R, C, T_ambient):
    # 簡単なモデルとして、発熱量を時間にわたって均等に拡散する
    T = T_ambient + P * R / (R * C) * (1 - np.exp(-time / (R * C)))
    return T

# 温度分布の計算
temperature = temperature_change(time, P, R, C, T_ambient)

# グラフ描画
plt.figure(figsize=(12, 6))
plt.plot(time, temperature, label='Temperature of Resistor')
plt.xlabel('Time (s)')
plt.ylabel('Temperature (°C)')
plt.title('Temperature Change of Resistor in RC Circuit')
plt.legend()
plt.grid()
plt.show()


```

```
import numpy as np
import matplotlib.pyplot as plt

# Parameters
length = 1.0  # Length of the semiconductor material (m)
nx = 100  # Number of spatial points
dx = length / (nx - 1)  # Spatial step size
alpha = 1e-5  # Thermal diffusivity (m²/s)
dt = 1.0  # Time step size (s)
nt = 100  # Number of time steps
initial_temp = 300  # Initial temperature (K)
heat_source_pos = length / 2  # Position of the heat source (m)
heat_source_temp = 600  # Temperature of the heat source (K)

# Initialize temperature array
T = np.ones(nx) * initial_temp

# Time stepping
for n in range(nt):
    T_new = T.copy()
    for i in range(1, nx - 1):
        T_new[i] = T[i] + alpha * dt / dx**2 * (T[i + 1] - 2 * T[i] + T[i - 1])
    
    # Apply heat source (boundary condition)
    T_new[int(heat_source_pos / dx)] = heat_source_temp
    
    T = T_new

# Spatial grid
x = np.linspace(0, length, nx)

# Plot temperature distribution
plt.figure(figsize=(10, 6))
plt.plot(x, T, label=f'Temperature distribution at t = {nt * dt} s')
plt.xlabel('Position (m)')
plt.ylabel('Temperature (K)')
plt.title('Temperature Distribution in a Semiconductor Material')
plt.legend()
plt.grid()
plt.show()


```


```

# Given parameters
Vin = 12  # Input voltage in volts
Vout = 5  # Output voltage in volts
I = 0.1  # Output current in amperes (100mA)
theta_JA = 60  # Thermal resistance in °C/W
TJ_max = 125  # Maximum junction temperature in °C
TA = 25  # Ambient temperature in °C

# Calculate power dissipation
PD = (Vin - Vout) * I

# Calculate junction temperature
TJ = TA + theta_JA * PD

# Calculate the maximum permissible ambient temperature
TA_max = TJ_max - theta_JA * PD

# Print the results
print(f"Power Dissipation (PD): {PD:.2f} W")
print(f"Junction Temperature (TJ): {TJ:.2f} °C")
print(f"Maximum Permissible Ambient Temperature (TA_max): {TA_max:.2f} °C")

# Additional calculation for doubled current
I_doubled = 2 * I
PD_doubled = (Vin - Vout) * I_doubled
TA_max_doubled = TJ_max - theta_JA * PD_doubled

print(f"\nWith Doubled Current (I = {I_doubled} A):")
print(f"Power Dissipation (PD): {PD_doubled:.2f} W")
print(f"Maximum Permissible Ambient Temperature (TA_max): {TA_max_doubled:.2f} °C")



```

```
import numpy as np
import matplotlib.pyplot as plt

# Define the parameters
initial_temp = 25  # Initial ambient temperature in Celsius
theta_ja = 60  # Thermal resistance in °C/W
power_dissipation = 0.7  # Power dissipation in W

# Different thermal management strategies (percent temperature reduction)
strategies = {
    "No Heatsink": 0,
    "Heatsink 1 cm": 0.12,
    "Heatsink 2 cm": 0.19,
    "Increased PCB Layers": 0.07,
    "Increased Copper Thickness": 0.06,
    "Heatsink with Higher Emissivity": 0.12,
    "Drain-Frame Vias": 0.12,
    "Peripheral Vias": 0.10
}

# Calculate the junction temperature for each strategy
temps = {}
for strategy, reduction in strategies.items():
    temp_increase = theta_ja * power_dissipation
    temp_with_strategy = initial_temp + temp_increase * (1 - reduction)
    temps[strategy] = temp_with_strategy

# Plotting
plt.figure(figsize=(10, 6))
plt.barh(list(temps.keys()), list(temps.values()), color='skyblue')
plt.xlabel('Junction Temperature (°C)')
plt.title('Effect of Thermal Management Strategies on Junction Temperature')
plt.axvline(125, color='r', linestyle='--', label='Max Safe Junction Temperature (125°C)')
plt.legend()
plt.grid(True)
plt.show()
```


```

# 基本的な定数の定義
T_A = 25  # 周囲温度 (°C)
T_C = 40  # ケース温度 (°C)
P_D = 0.7  # 消費電力 (W)

# θJAを使ったジャンクション温度の計算
theta_JA = 60  # θJA (°C/W)
T_J_theta_JA = T_A + theta_JA * P_D

# ΨJTを使ったジャンクション温度の計算
psi_JT = 5  # ΨJT (°C/W)
T_J_psi_JT = T_C + psi_JT * P_D

# 過渡熱抵抗を使った温度上昇の計算
transient_Rth = 40  # 過渡熱抵抗 (°C/W) at 1ms
delta_T_transient = transient_Rth * P_D

# 結果の表示
print(f"TJ using θJA: {T_J_theta_JA:.2f} °C")
print(f"TJ using ΨJT: {T_J_psi_JT:.2f} °C")
print(f"Temperature rise using transient Rth: {delta_T_transient:.2f} °C")

```


```
# Basic Constants Definition (基本的な定数の定義)
Tj = 100  # Junction Temperature (ジャンクション温度) in °C
Ta = 25   # Ambient Temperature (周囲温度) in °C
Tc_top = 40  # Case Temperature at the top (パッケージマーク面中央温度) in °C
Tc_bot = 35  # Case Temperature at the bottom (パッケージ裏面温度) in °C
Pd = 1.5  # Power Dissipation (消費電力) in W

# θJA Calculation: Thermal resistance between Junction Temperature (Tj) and Ambient Temperature (Ta)
# θJAの計算: ジャンクション温度 Tj と 周囲温度 Ta の間の熱抵抗
theta_JA = (Tj - Ta) / Pd

# ΨJT Calculation: Thermal parameter between Junction Temperature (Tj) and Case Temperature at the top (Tc_top)
# ΨJTの計算: ジャンクション温度 Tj と パッケージマーク面中央温度 Tc(top) の間の熱パラメータ
psi_JT = (Tj - Tc_top) / Pd

# θJC Calculation: Thermal resistance between Junction Temperature (Tj) and Case Temperature at the bottom (Tc_bot)
# θJCの計算: ジャンクション温度 Tj と パッケージ裏面 Tc(bot) の間の熱抵抗
theta_JC = (Tj - Tc_bot) / Pd

# Displaying Results (結果の表示)
print(f"θJA: {theta_JA:.2f} °C/W (°C per Watt)")
print(f"ΨJT: {psi_JT:.2f} °C/W (°C per Watt)")
print(f"θJC: {theta_JC:.2f} °C/W (°C per Watt)")


```


```

import numpy as np

# Constants
thermal_conductivity = 200  # Thermal conductivity (W/(m·K)) for conduction example
thickness = 0.01  # Thickness (m) for conduction example
area = 0.01  # Area (m^2) for conduction example
temperature_diff_conduction = 50  # Temperature difference (K) for conduction example

# Conduction Heat Transfer (伝導)
def conduction_heat_transfer(thermal_conductivity, thickness, area, temperature_diff):
    return thermal_conductivity * area * temperature_diff / thickness

# Convection Heat Transfer (対流)
def convection_heat_transfer(h, area, temperature_diff):
    return h * area * temperature_diff

# Radiation Heat Transfer (放射)
def radiation_heat_transfer(sigma, emissivity, area, temp1, temp2):
    return sigma * emissivity * area * (temp1**4 - temp2**4)

# Thermal Resistance (熱抵抗) Calculations
def thermal_resistance_conduction(thermal_conductivity, thickness, area):
    return thickness / (thermal_conductivity * area)

def thermal_resistance_convection(h, area):
    return 1 / (h * area)

def thermal_resistance_radiation(sigma, emissivity, area, temp1, temp2):
    return 1 / (sigma * emissivity * area * (temp1**4 - temp2**4))

# Example Parameters
thermal_conductivity = 200  # W/(m·K)
thickness = 0.01  # m
area = 0.01  # m^2
temperature_diff_conduction = 50  # K

# Convection Parameters
h = 10  # Heat transfer coefficient (W/(m^2·K))
temperature_diff_convection = 50  # K

# Radiation Parameters
sigma = 5.67e-8  # Stefan-Boltzmann constant (W/(m^2·K^4))
emissivity = 0.9  # Emissivity
temp1 = 350  # K
temp2 = 300  # K

# Calculations
conduction_heat_transfer_rate = conduction_heat_transfer(thermal_conductivity, thickness, area, temperature_diff_conduction)
convection_heat_transfer_rate = convection_heat_transfer(h, area, temperature_diff_convection)
radiation_heat_transfer_rate = radiation_heat_transfer(sigma, emissivity, area, temp1, temp2)

# Thermal Resistances
theta_conduction = thermal_resistance_conduction(thermal_conductivity, thickness, area)
theta_convection = thermal_resistance_convection(h, area)
theta_radiation = thermal_resistance_radiation(sigma, emissivity, area, temp1, temp2)

# Display Results
print(f"Conduction Heat Transfer Rate: {conduction_heat_transfer_rate:.2f} W")
print(f"Convection Heat Transfer Rate: {convection_heat_transfer_rate:.2f} W")
print(f"Radiation Heat Transfer Rate: {radiation_heat_transfer_rate:.2f} W")
print(f"Thermal Resistance (Conduction): {theta_conduction:.2f} °C/W")
print(f"Thermal Resistance (Convection): {theta_convection:.2f} °C/W")
print(f"Thermal Resistance (Radiation): {theta_radiation:.2f} °C/W")

```

```
# Constants
Tch_max = 150  # Maximum channel temperature (°C)
Ta = 25        # Ambient temperature (°C)
Pd = 1.5       # Power dissipation (W)

# Thermal resistances
theta_i = 1.0  # Internal thermal resistance (°C/W)
theta_b = 3.0  # External thermal resistance (°C/W)
theta_s = 0.5  # Insulator thermal resistance (°C/W)
theta_c = 0.3  # Contact thermal resistance (°C/W)
theta_f = 0.2  # Heat sink thermal resistance (°C/W)

# Calculate thermal resistance
Rth_ch_a_case1 = theta_i + (theta_b * (theta_s + theta_c + theta_f)) / (theta_b + theta_s + theta_c + theta_f)
Rth_ch_a_case2 = theta_i + theta_b
Rth_ch_a_case3 = theta_i + theta_s + theta_c + theta_f

# Maximum power dissipation calculations
Pd_max_case1 = (Tch_max - Ta) / Rth_ch_a_case1
Pd_max_case2 = (Tch_max - Ta) / Rth_ch_a_case2
Pd_max_case3 = (Tch_max - Ta) / Rth_ch_a_case3

# Display results
print(f"Maximum Power Dissipation (Case 1): {Pd_max_case1:.2f} W")
print(f"Maximum Power Dissipation (Case 2): {Pd_max_case2:.2f} W")
print(f"Maximum Power Dissipation (Case 3): {Pd_max_case3:.2f} W")
```

```
# Pulse parameters
P0 = 2.0  # Peak power during pulse (W)
T1 = 0.1  # Pulse width (s)
T = 0.5   # Period of the pulse train (s)

# Transient thermal resistance (example values, typically obtained from datasheet)
def transient_thermal_resistance(T_pulse):
    # Example linear approximation
    return 0.5 * T_pulse + 0.2

# Calculate peak temperature for a single pulse
Tch_peak_single_pulse = transient_thermal_resistance(T1) * P0 + Ta

# Calculate peak temperature for repeated pulses
Rth_ch_a = Rth_ch_a_case1  # Using Rth_ch-a from Case 1 as an example
Tch_peak_repeated_pulses = P0 * (T1 / T * Rth_ch_a + (1 - T1 / T) * (transient_thermal_resistance(T + T1) - transient_thermal_resistance(T) + transient_thermal_resistance(T1))) + Ta

# Display results
print(f"Peak Temperature for a Single Pulse: {Tch_peak_single_pulse:.2f} °C")
print(f"Peak Temperature for Repeated Pulses: {Tch_peak_repeated_pulses:.2f} °C")


```