Fitting resonators¶

General usecase¶

• Import your data as a complex number, make sure your magnitude is linear
• Select the correct measurement type between 'reflection', 'hanger' and 'transmission'

Read the SQIL-core documentation to learn about all the options.

In [7]:

import sqil_core as sqil
import numpy as np

path = r"Z:\Projects\BottomLoader\data\20250612_AQUA_skinny\2025-06-12\00000-pulsed_onetone_2025-06-12T205752"
measurement = "transmission"

freq, data = sqil.extract_h5_data(path, ["ro_freq", "data"])

# Quick fit to estimate parameters
params = sqil.resonator.quick_fit(freq, data, measurement)
# Full fit
fit_res = sqil.resonator.full_fit(freq, data, measurement, *params)

# Plot
x_fit = np.linspace(freq[0], freq[-1], np.max([len(freq), 1000]))
sqil.resonator.plot_resonator(freq, data, x_fit, fit_res.predict(x_fit))

# Print results
sqil.resonator.print_resonator_params(fit_res.params, measurement)

import sqil_core as sqil import numpy as np path = r"Z:\Projects\BottomLoader\data\20250612_AQUA_skinny\2025-06-12\00000-pulsed_onetone_2025-06-12T205752" measurement = "transmission" freq, data = sqil.extract_h5_data(path, ["ro_freq", "data"]) # Quick fit to estimate parameters params = sqil.resonator.quick_fit(freq, data, measurement) # Full fit fit_res = sqil.resonator.full_fit(freq, data, measurement, *params) # Plot x_fit = np.linspace(freq[0], freq[-1], np.max([len(freq), 1000])) sqil.resonator.plot_resonator(freq, data, x_fit, fit_res.predict(x_fit)) # Print results sqil.resonator.print_resonator_params(fit_res.params, measurement)

| Param     | Value       |
|-----------|-------------|
| fr        | 7.46257 GHz |
| Q_tot     | 5074        |
| kappa_tot | 1.471 MHz   |

For extra information on your fit run

In [8]:

fit_res.summary();

fit_res.summary();

reduced χ²  2.720e-11             GREAT (or overfitting)
nrmse       5.960e-03-1.300e-04j  GREAT
| Param   |   Fitted value |    STD error |   % Error |
|---------|----------------|--------------|-----------|
| a       |    0.000711667 |    1.566e-06 |      0.22 |
| alpha   |   -0.666959    |    0.01078   |     -1.62 |
| tau     |   -5.40365e-08 |    8.397e-11 |     -0.16 |
| Q_tot   | 5074.46        |   16.21      |      0.32 |
| fr      |    7.46257e+09 | 2285         |      0    |

Fitting with a background¶

The magnitude background can create problems for the fit, so we need a way to account for it.

In [9]:

import sqil_core as sqil
import numpy as np
import matplotlib.pyplot as plt

path = r"Z:\Projects\BottomLoader\RT_measurement\20241212_cavities\2024-12-12\00082-cavity_check_2024-12-12T174140"
measurement = "hanger"

[freq], [mag_db], [phase] = sqil.extract_h5_data(path, ["frequency", "mag", "phase"])
linmag = 10 ** (mag_db / 20)
data = linmag * np.exp(1j * phase)
freq = freq


plt.figure(figsize=(4,2))
plt.title("Magnitude")
plt.plot(freq, linmag, '.-')
plt.show()

import sqil_core as sqil import numpy as np import matplotlib.pyplot as plt path = r"Z:\Projects\BottomLoader\RT_measurement\20241212_cavities\2024-12-12\00082-cavity_check_2024-12-12T174140" measurement = "hanger" [freq], [mag_db], [phase] = sqil.extract_h5_data(path, ["frequency", "mag", "phase"]) linmag = 10 ** (mag_db / 20) data = linmag * np.exp(1j * phase) freq = freq plt.figure(figsize=(4,2)) plt.title("Magnitude") plt.plot(freq, linmag, '.-') plt.show()

Find a way to estimate your background. It's recommended to use a simple fit, linear or at most polynomial.
It could be helpful to take a wider shot of your data.

IMPORTANT: The background can be ANY array of the same size as the frequency, so it can be completely arbitrary.

In [10]:

# Estimate the linear background from the last few points
[y0, m] = sqil.estimate_linear_background(freq, linmag, cut_from_back=True)

plt.figure(figsize=(4, 2))
plt.title("Magnitude")
plt.plot(freq, linmag, ".-")
plt.plot(freq, m * freq + y0, "-.", color='tab:green')
plt.show()

# Estimate the linear background from the last few points [y0, m] = sqil.estimate_linear_background(freq, linmag, cut_from_back=True) plt.figure(figsize=(4, 2)) plt.title("Magnitude") plt.plot(freq, linmag, ".-") plt.plot(freq, m * freq + y0, "-.", color='tab:green') plt.show()

Then cut the data closer to the resonance. Don't be afraid to get quite close.
Remmeber to also cut the background!

In [11]:

cut = slice(300, 600)
freq, data = freq[cut], data[cut]

# After cutting the data don't forget to define
# the background on the newly cut frequency
mag_bg = m * freq + y0

plt.figure(figsize=(4, 2))
plt.title("Magnitude")
plt.plot(freq, np.abs(data), ".-")
plt.plot(freq, mag_bg, "-.", color="tab:green")
plt.show()

cut = slice(300, 600) freq, data = freq[cut], data[cut] # After cutting the data don't forget to define # the background on the newly cut frequency mag_bg = m * freq + y0 plt.figure(figsize=(4, 2)) plt.title("Magnitude") plt.plot(freq, np.abs(data), ".-") plt.plot(freq, mag_bg, "-.", color="tab:green") plt.show()

In [12]:

# Quick fit to estimate parameters
params = sqil.resonator.quick_fit(freq, data, measurement, mag_bg=mag_bg)
# Full fit
fit_res = sqil.resonator.full_fit(freq, data, measurement, *params, mag_bg=mag_bg)

# Print results
sqil.resonator.print_resonator_params(fit_res.params, measurement)

# Plot
sqil.resonator.plot_resonator(freq, data, freq, fit_res.predict(freq), mag_bg=mag_bg)

# Quick fit to estimate parameters params = sqil.resonator.quick_fit(freq, data, measurement, mag_bg=mag_bg) # Full fit fit_res = sqil.resonator.full_fit(freq, data, measurement, *params, mag_bg=mag_bg) # Print results sqil.resonator.print_resonator_params(fit_res.params, measurement) # Plot sqil.resonator.plot_resonator(freq, data, freq, fit_res.predict(freq), mag_bg=mag_bg)

| Param     | Value       |
|-----------|-------------|
| fr        | 7.74145 GHz |
| Re[Q_ext] | 824         |
| Q_int     | 3564        |
| Q_tot     | 2237        |
| kappa_ext | 9.39 MHz    |
| kappa_int | 2.172 MHz   |
| kappa_tot | 3.461 MHz   |