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")