Impedance Calculator

The ImpedanceCalculator computes characteristic impedance from electromagnetic field data. It uses voltage and current path integrals, and it supports three calculation methods.

Method	Required integrals	Formula
V and I	Voltage and current	`Z0 = V / I`
P and V	Voltage only	`Z0 = abs(V)^2 / (2 * conjugate(P))`
P and I	Current only	`Z0 = 2 * P / abs(I)^2`

P is the complex power flow through the cross-section.

Basic Usage

from flex_rf.tidy3d import (
    AxisAlignedCurrentIntegral,
    AxisAlignedVoltageIntegral,
    ImpedanceCalculator,
)

voltage_integral = AxisAlignedVoltageIntegral(
    center=(0, 0, 0),
    size=(0, 0, 2),
    sign="+",
    extrapolate_to_endpoints=True,
    snap_path_to_grid=True,
)

current_integral = AxisAlignedCurrentIntegral(
    center=(0, 0, 0),
    size=(4, 2, 0),
    sign="+",
    snap_contour_to_grid=True,
)

z_calculator = ImpedanceCalculator(
    voltage_integral=voltage_integral,
    current_integral=current_integral,
)

impedance = z_calculator.compute_impedance(mode_data)

With Mode Solver Data

The impedance calculator is commonly used with mode solver results to determine the characteristic impedance of transmission-line modes.

from flex_rf import web
from flex_rf.tidy3d import GridSpec, ModeSimulation

mode_sim = ModeSimulation(
    size=(10, 10, 0),
    grid_spec=GridSpec.auto(wavelength=0.3),
    structures=[...],
    monitors=[mode_monitor],
    freqs=[1e9, 2e9, 3e9],
)

mode_sim_data = web.run(mode_sim, task_name="mode_solver")
z0 = z_calculator.compute_impedance(mode_sim_data.modes)

Voltage And Current Output

Set return_voltage_and_current=True to retrieve impedance, voltage, and current together.

z0, voltage, current = z_calculator.compute_impedance(
    mode_data,
    return_voltage_and_current=True,
)

Single Integral Calculation

If only the voltage or current integral is provided, the calculator uses the complex power flow automatically.

z_calc_v = ImpedanceCalculator(
    voltage_integral=voltage_integral,
    current_integral=None,
)

z_from_v = z_calc_v.compute_impedance(mode_data)

z_calc_i = ImpedanceCalculator(
    voltage_integral=None,
    current_integral=current_integral,
)

z_from_i = z_calc_i.compute_impedance(mode_data)

Compatible Data

The impedance calculator and path integral classes work with several field-data containers:

Data object	Use
`ModeSolverData`	Mode profiles from a 2D mode solver.
`FieldData`	Frequency-domain monitor fields.
`FieldTimeData`	Time-domain monitor fields.
`MicrowaveModeSolverData`	Microwave mode solver data with transmission-line quantities.

Phase Convention

Flex RF follows the Tidy3D physics phase convention e^{-i omega t}. Some RF simulation tools and textbooks use e^{i omega t}. This affects calculated S-parameters and impedance values. Use complex conjugation to convert between the two conventions.

import numpy as np

z_engineering = np.conjugate(z_physics)
z_physics = np.conjugate(z_engineering)

Page	Why open it
Path Integrals	Define the voltage and current integrals used by the calculator.
RF Mode Analysis	Configure impedance calculation directly in a mode spec.