Network Conversions

This module provides functions to convert between the two network topologies. These conversions are mathematically equivalent and preserve the network’s impedance characteristics.

cauer_to_foster(cauer_network)

Converts a CauerNetwork to an equivalent FosterNetwork.

The conversion uses symbolic partial fraction expansion of the Cauer network’s impedance function $Z(s)$ to find the poles and residues, which map directly to the R and C values of the Foster network.

• cauer_network: CauerNetwork - The Cauer network to convert.
• Returns: FosterNetwork - The equivalent Foster network.

foster_to_cauer(foster_network)

Converts a FosterNetwork to an equivalent CauerNetwork.

The conversion uses symbolic continued fraction expansion (Cauer II form) on the Foster network’s impedance function $Z(s)$.

• foster_network: FosterNetwork - The Foster network to convert.
• Returns: CauerNetwork - The equivalent Cauer network.

Round-Trip Conversion Example

A robust way to test the conversions is to perform a round-trip (e.g., Cauer -> Foster -> Cauer) and verify that the final parameters match the original ones.

1. Define an original Cauer network

   import numpy as np
   from thermal_network.networks import CauerNetwork, FosterNetwork
   from thermal_network.conversions import cauer_to_foster, foster_to_cauer
   
   original_cauer = CauerNetwork(r=[0.1, 0.5, 1.2], c=[0.3, 0.8, 2.0])

2. Convert to Foster and back to Cauer

   intermediate_foster = cauer_to_foster(original_cauer)
   final_cauer = foster_to_cauer(intermediate_foster)

3. Check if the result is identical to the original

   print(f"Original Cauer R: {original_cauer.r}")
   print(f"Final Cauer R:    {np.round(final_cauer.r, 6)}")
   assert np.allclose(original_cauer.r, final_cauer.r)
   
   print(f"Original Cauer C: {original_cauer.c}")
   print(f"Final Cauer C:    {np.round(final_cauer.c, 6)}")
   assert np.allclose(original_cauer.c, final_cauer.c)