Impedance Calculation

These functions calculate the impedance of a given network model. These are convinience functions for validation and plotting.

foster_impedance_time_domain()

foster_impedance_time_domain(network, t_values)

Calculates the time-domain thermal impedance Z_th(t) for a Foster network, which represents the transient temperature response to a unit power step.

The impedance is calculated as:

Z_th(t) = Σ_i R_i · (1 - e^-t/τ_i)

where τ_i = R_i · C_i.

Parameters:

• network: FosterNetwork - The Foster network model.
• t_values: array-like - An array of time points at which to calculate the impedance.
• Returns: np.ndarray - An array of thermal impedance values.

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Frequency Domain Impedance Z(s)

For frequency-domain analysis, the impedance Z(s) is calculated at complex frequency points s = jω.

Foster

foster_impedance_freq_domain()

foster_impedance_freq_domain(network, s_values)

Computes the complex impedance for a Foster network as the sum of parallel RC branches:

Z(s) = Σ_i R_i / (1 + s R_i C_i)

Parameters:

• network: FosterNetwork - The Foster network model.
• s_values: array-like - An array of complex frequency points.
• Returns: np.ndarray - An array of complex impedance values.

Cauer

cauer_impedance_freq_domain()

cauer_impedance_freq_domain(network, s_values)

Computes the complex impedance for a Cauer network using its continued fraction representation, which reflects the ladder structure of the network.

Parameters:

• network: CauerNetwork - The Cauer network model.
• s_values: array-like - An array of complex frequency points.
• Returns: np.ndarray - An array of complex impedance values.

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Example

import numpy as np
from thermal_network.networks import FosterNetwork
from thermal_network.impedance import foster_impedance_time_domain, foster_impedance_freq_domain

# Define the network and data points
net = FosterNetwork(r_values=[0.7, 0.3], c_values=[1.0, 10.0])
time_data = np.logspace(-1, 2, 5)
freq_data = np.logspace(-1, 2, 5) * 1j  # s = jw

# Time-domain impedance
z_time = foster_impedance_time_domain(net, time_data)
print(f"Time-domain Z(t): {np.round(z_time, 3)}")

# Frequency-domain impedance
z_freq = foster_impedance_freq_domain(net, freq_data)
print(f"Frequency-domain |Z(s)|: {np.round(np.abs(z_freq), 3)}")