A method and system for measuring the noise power spectral density of a superconducting dynamic inductance detector KID

Abstract

The application provides a noise power spectral density measurement method and a measurement system of a superconducting dynamic inductance detector KID, a VNA is used to test the transmission coefficient frequency response curve of the whole measurement system near the KID resonance point; seven parameters are fitted in the frequency response curve to obtain the frequency response curve and the resonance circle of a single superconducting dynamic inductance detector; the transmission coefficient of the whole measurement system at the resonance point frequency and the non-resonance point frequency within a period of time is disturbed by the VNA, the transmission coefficient of the group of disturbances is calibrated by using seven parameters; the noise power spectral density and the noise equivalent power at the current resonance point and the non-resonance point frequency are calculated. Compared with the existing quadrature mixing method, the method does not need to do additional IQ calibration under the premise of achieving the same function, and is easy to implement; the power noise spectrum test result of the method is free from spurious interference, and the good electromagnetic interference resistance of the hardware ensures better data result readability.

Description

Technical Field

[0001] This invention relates to the field of terahertz signal detection technology, and in particular to a method and system for measuring the noise power spectral density of a superconducting dynamic inductive detector (KID). Background Technology

[0002] The Kinetic Inductor Detector (KID) is a microwave resonator based on a planar inductor and capacitor fabricated from a superconducting thin film. Its core circuitry mainly consists of a photon signal receiver and a microwave resonator. According to the KID's working principle, when a sufficiently powerful external signal is incident on the KID, the Cooper pairs on the surface of the superconducting thin film are broken, causing changes in the dynamic resistance and dynamic inductance of the microwave resonator, thus influencing its characteristics (Q-factor, amplitude, phase, etc.). The amplitude or phase of the microwave resonator is obtained through a readout circuit (which can be obtained via S...). 21 By analyzing the changes in parameters, the indirect measurement of the incident signal can be completed.

[0003] On the other hand, the resonant frequency, amplitude, and phase of the KID vary with temperature, incident power, and time, reflecting its inherent sensitivity information. The power spectral density (PSD) of the KID (including amplitude and phase) is typically characterized using a homodyne mixer. This measurement hardware system generally employs a quadrature IQ mixer. The signal generator output is split into two channels by a directional coupler. One channel uses a room-temperature adjustable attenuator, a low-temperature KID, a low-temperature low-noise amplifier, a room-temperature attenuator, and a room-temperature amplifier, respectively. This, along with the other direct-through channel, serves as the RF and LO signals at the input of the room-temperature quadrature IQ mixer. The difference frequency outputs I and Q signals, which are then filtered by a low-pass filter and impedance transformer before being input to an AD converter, converting the two time-domain signals into amplitude or phase noise power spectral densities in the frequency domain. A block diagram of the measurement system is shown below. Figure 1 As shown.

[0004] The main drawback of this method is that, due to the inherent amplitude and phase imbalance at the intermediate frequency (IF) I and Q outputs of quadrature mixers, which varies with frequency, data acquisition becomes inaccurate, leading to inaccurate noise power spectral density in post-processing. This also limits the input power measurement range of the entire Homodyne system. Therefore, self-calibration of the I and Q output imbalance of the IQ mixer is necessary. However, the calibration process for the IQ mixer is complex and requires two signal sources, increasing hardware costs. Summary of the Invention

[0005] Purpose of the invention: To propose a method for measuring the noise power spectral density of a superconducting dynamic inductive detector (KID), and further to propose a system for implementing the above measurement method, so as to solve the above-mentioned problems existing in the prior art.

[0006] Firstly, a noise power spectral density measurement method based on a superconducting dynamic inductive detector (KID) using a vector network analyzer (VNA) is proposed (hereinafter referred to as the VNA method). The steps are as follows:

[0007] S1. Build a noise power spectral density measurement system based on a vector network analyzer, and use the vector network analyzer to test the frequency response curve of the transmission coefficient of the entire measurement system near the KID resonant point of the superconducting dynamic inductor detector.

[0008] S2. Fit the following parameters into the frequency response curve of the transmission coefficient: system link gain, phase rotation angle, coaxial cable delay time, resonator quality factor, coupler quality factor, resonator resonant frequency, and phase angle to obtain the frequency response curve and resonant circle of a single superconducting dynamic inductor detector.

[0009] S3. Use a vector network analyzer to collect the perturbation of the transmission coefficient of the entire measurement system at the resonant frequency and non-resonant frequency over a period of time. Use the seven parameters fitted in step S2 to calibrate the transmission coefficient of the perturbation, and mark the calibrated result on the resonant circle in step S2.

[0010] S4. Calculate the noise power spectral density and noise equivalent power at the current resonant and non-resonant frequencies.

[0011] In a further embodiment of the first aspect, the frequency response curve of the transmission coefficient of the entire measurement system in step S1 near the resonant point of the superconducting dynamic inductor detector is S 21 The power of the test receiver b2 at the second port of the vector network analyzer was measured as the ratio of the power of the reference receiver a1 at the first port.

[0012] S 21 =b2 / a1;

[0013] In the formula, b2 represents the power of the test receiver; a1 represents the power of the reference receiver;

[0014] The test receiver and the reference receiver share the same local oscillator, and each receiver contains I and Q signals; S 21 It is a complex number, with real and imaginary parts, which are converted to obtain amplitude and phase information.

[0015] In a further embodiment of the first aspect, the frequency response curve S of a single superconducting dynamic inductor detector is obtained by fitting seven parameters to the frequency response curve of the transmission coefficient. 21 The function expression for (f) is as follows:

[0016]

[0017] In the formula, a represents the system link gain; e iα Indicates the phase rotation angle; τ represents the coaxial cable delay time; Q r Q represents the resonator quality factor; c f represents the coupler quality factor; r Indicates the resonant frequency of the resonator; φ represents the phase angle;

[0018] By fitting the frequency response curve of the transmission coefficient using the above parameters, the effects of system gain, phase shift, link delay, and initial phase angle are eliminated, and the characteristic parameters of a single superconducting dynamic inductive detector are obtained.

[0019] In a further embodiment of the first aspect, step S3 further includes:

[0020] At the resonant and non-resonant frequencies, the vector network analyzer is set to single-frequency-time acquisition mode, and the acquisition frequency is set to either the resonant frequency or the non-resonant frequency.

[0021] Set the output power, number of sampling points, intermediate frequency bandwidth, and dwell time, and use a vector network analyzer to analyze S. 21 The real and imaginary parts are collected;

[0022] Using the system link gain, phase rotation angle, coaxial cable delay time, resonator quality factor, coupler quality factor, resonator resonant frequency, and phase angle from step S2, the transmission coefficient of the disturbance at the current resonant point noise and non-resonant point noise is calibrated, and the calibrated result is plotted on the resonant circle described in step S2.

[0023] In a further embodiment of the first aspect, the expression for calculating the current noise power spectral density psd(x) using the noise point in step S4 is as follows:

[0024] psd(x) = 2·(Fs·N)|x| 2 ;

[0025] In the formula, Fs is the sampling frequency, N is the total number of sampling points, and |x| is the Fourier transform amplitude value of the amplitude value of the calibrated transmission coefficient.

[0026] In a further embodiment of the first aspect, the expression for calculating the current noise equivalent power (NEP) using the noise point in step S4 is as follows:

[0027]

[0028] In the formula, S x The noise power spectral density represents the amplitude of the transmission coefficient of a superconducting dynamic inductive detector. τ represents the response of the transmission coefficient amplitude to radiated power, ω represents the angular frequency; qp τ represents the recombination time of quasiparticles; res This indicates the resonator response time.

[0029] Secondly, a noise power spectral density measurement system for a superconducting dynamic inductive detector (KID) is proposed, the system comprising:

[0030] Vector network analyzer;

[0031] Low-temperature Dewar; the Port1 port of the vector network analyzer is connected to the input terminal of the low-temperature Dewar via a first adjustable attenuator and a DC blocking device;

[0032] The cryogenic Dewar contains a second fixed attenuator electrically connected to the DC blocker, a KID electrically connected to the second fixed attenuator, and a first cryogenic low-noise amplifier electrically connected to the KID.

[0033] The first low-temperature low-noise amplifier is connected to the output of the temperature dewar via an insulated cable; the output of the low-temperature dewar is connected to the Port2 port of the vector network analyzer via a combination of a second room-temperature attenuator and a second room-temperature low-noise amplifier.

[0034] In a further embodiment of the second aspect, the vector network analyzer has a built-in measurement sweep unit that is driven to test the frequency response curve of the transmission coefficient of the entire measurement system near the resonant frequency of the superconducting dynamic inductor detector.

[0035] In a further embodiment of the second aspect, the noise power spectral density measurement system further includes a measurement program calculation module for calculating KID-PSD; the measurement program calculation module includes a fitting unit, an acquisition unit, and a calculation unit;

[0036] The fitting unit is driven to fit the following parameters into the transmission coefficient frequency response curve: system link gain, phase rotation angle, coaxial cable delay time, resonator quality factor, coupler quality factor, resonator resonant frequency, and phase angle, to obtain the transmission coefficient frequency response curve and resonant circle of a single superconducting dynamic inductive detector.

[0037] The acquisition unit is driven to acquire the perturbation of the transmission coefficient at the resonant frequency and non-resonant frequency of the entire measurement system over a period of time. The seven parameters fitted by the fitting unit are used to calibrate the transmission coefficient of the perturbation and mark it on the resonant circle.

[0038] The computing unit is driven to calculate the current noise power spectral density and noise equivalent power.

[0039] Thirdly, a computer-readable storage medium is proposed, storing a computer program that causes a computer to perform the noise power spectral density measurement method as described in the first aspect.

[0040] Beneficial Effects: Compared to the existing Homodyne method, the proposed method for measuring the noise power spectral density of the superconducting dynamic inductive detector (KID) in this invention achieves the same functionality without requiring additional IQ calibration due to the imbalance between the two output channels of the IQ mixer. Therefore, the testing procedure is simpler than the Homodyne method, involves fewer instruments, and is easier to implement. Furthermore, because this method uses a vector network analyzer, it has high integration and reliability; the power noise spectrum test results are free from clutter interference; and the hardware's excellent electromagnetic interference resistance ensures better readability of the data results. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the existing KID-NEP measurement system based on the Homodyne method.

[0042] Figure 2 This is a schematic diagram of the KID-NEP measurement system based on the VNA method in an embodiment of the present invention.

[0043] Figure 3 This is a flowchart comparing the VNA method and the Homodyne method.

[0044] Figure 4 shows the frequency response (a) and the resonance circle diagram (b) of the original amplitude values ​​obtained by the VNA method and the Homodyne method.

[0045] Figure 5 The S-parameters obtained after fitting using the VNA and Homodyne methods are... 21 Amplitude-frequency response curve.

[0046] Figure 6 The KID resonance circle and the S-point of the resonance point are obtained by fitting seven parameters using the VNA and Homodyne methods. 21 Schematic diagram of perturbation over time.

[0047] Figure 7This is a comparison chart of the KID amplitude (AMP) noise spectrum and phase (PSD) noise spectrum measured by the VNA method and the Homodyne method.

[0048] Figure 8 This is a comparison chart of the KID amplitude NEP measured by the VNA method and the Homodyne method.

[0049] Figure 9 This is a flowchart of the noise power spectral density measurement method for the superconducting dynamic inductive detector KID in an embodiment of the present invention.

[0050] Among them, Figure 4 to Figure 8 The device under test is an 80nm thick Al film KID with a resonant frequency of 4197MHz and a test environment temperature of 80mK. Detailed Implementation

[0051] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0052] The amplitude or phase change information at the KID resonant frequency can be obtained by measuring the S in the transmission link. 21 To obtain the link transmission coefficient S of the entire measurement system, since the resonant frequency of the resonator is in the microwave band (e.g., 4–8 GHz), a vector network analyzer (VNA) is typically used in the experimental stage. 21 The data can be read out. Simultaneously, using a VNA, the resonant frequencies of all resonators within the broadband range, as well as their amplitude and phase variations with temperature, optical power, and time, can be obtained.

[0053] For KID noise power spectral density (PSD) measurement, the goal is to obtain the amplitude and phase spectrum changes near the KID resonant frequency. Previous techniques used a self-developed Homodyne system, involving expensive equipment such as signal sources and high-speed A / D converters. Furthermore, low-noise amplifiers and IQ mixers were required, and IQ imbalance had to be considered. To ensure accurate test results, complex IQ calibration procedures were necessary. Therefore, this paper proposes a VNA-based system and method for KID noise power spectral density measurement to replace the Homodyne system and address the aforementioned problems of existing technologies. VNAs are primarily used to test the S-parameters of ordinary microwave devices, rather than for long-term power spectrum information acquisition. We built a system specifically for KID testing applications, utilizing the single-frequency acquisition function of a modern commercial VNA. The VNA frequency was set at the KID resonant and non-resonant frequencies, and the perturbation of the transmission coefficient of the entire measurement system over a period of time was collected. After subsequent data processing, the KID noise power spectral density (PSD) was obtained. The test block diagram is shown in Figure 2. The VNA's Port 1 is connected to the input of the cryogenic Dewar via an adjustable attenuator and a DC blocker. The cryogenic Dewar includes a cryogenic attenuator, a KID (Knowledge Induction Device), and a cryogenic low-noise amplifier, and is connected to the room-temperature section via an insulated cable. The cryogenic Dewar output is then connected to the VNA's Port 2 via a combination of a room-temperature attenuator and a room-temperature amplifier. The following example details the specific process of obtaining the KID-PSD using the VNA method.

[0054] Example 1:

[0055] This embodiment discloses a specific process for obtaining KID-PSD using the VNA method, such as... Figure 9 As shown.

[0056] The first step is to sweep the frequency near the resonant point.

[0057] The purpose of frequency sweeping is to obtain the transmission coefficient S of a single KID. 21 Frequency response curve. Based on the VNA system architecture, S 21 The power of the test receiver b2 at port 2 can be measured by the ratio of the power of the reference receiver a1 at port 1, i.e., S. 21 =b2 / a1. The two receivers share the same local oscillator, and each receiver contains I and Q signals. S 21 It is a complex number, possessing both real and imaginary parts. Its amplitude and phase information can be determined through conversion.

[0058] The second step is seven-parameter fitting.

[0059] Theoretically, KID's own transmission coefficient S 21 The frequency response is as follows

[0060]

[0061] In the complex plane of real and imaginary parts, it is represented as a circle with an opening at the right end.

[0062] The vector network VNA method was used to measure the transmission parameters S of the entire measurement system. 21 It includes a KID, attenuator, amplifier, cable, etc. Near the resonant frequency, the total transmission coefficient S... 21 The following model can be used to represent it.

[0063]

[0064] The physical meanings of the seven parameters are: readout system link gain α; phase rotation angle e. iα Coaxial cable delay time τ, resonator quality factor Q r Coupler quality factor Q c Resonant frequency f r Phase angle φ. By selecting a series of S 21 By fitting the measured values ​​to the above seven parameters to eliminate the effects of system gain, phase shift, link delay, and initial phase angle, the resonant characteristic parameters of the KID itself can be obtained. After fitting, the KID's own frequency response S can be obtained. 21 And using the real-imaginary part form (resonance circle) and amplitude frequency response curve S 21 Represented in (dB) format.

[0065] The third step is to collect the transmission coefficient S at the KID resonant and non-resonant frequencies over a period of time. 21

[0066] Set the VNA to single-frequency time-of-flight (CW) acquisition mode. Depending on the acquisition requirements, set the CW freq to either the KID resonant frequency or the non-resonant frequency. Also, configure the output power, number of sampling points, intermediate frequency bandwidth, dwell time, and other parameters for VNA Port1. Finally, set the transmission coefficient S of the entire measurement system. 21 The real and imaginary parts are acquired. In reality, the actual sampling rate, number of sampling points, and intermediate frequency bandwidth of the VNA do not affect the PSD of the KID. Using the seven parameters obtained in the second step, the calibrated results are plotted on the resonant circle from the second step.

[0067] The fourth step is to calculate the noise power spectral density (PSD) and noise equivalent power (NEP) at the current resonant and non-resonant frequencies.

[0068] Typically, the transmission coefficient S of KID itself at the resonant frequency is used. 21The noise characteristics are measured by the fluctuation of amplitude or phase (frequency) over time. It is usually characterized by the noise power spectral density (PSD), which reflects the frequency distribution of noise signal power within a unit bandwidth, measured in W / Hz. According to the Wiener-Khinchin theorem, if a signal can be considered a stationary random process, then the power spectral density is the Fourier transform of the signal's autocorrelation function. Calculating the power spectrum requires first performing autocorrelation on the signal, followed by an FFT operation. Using the above method, the acquired VNA signal at the resonant point S... 21 The real and imaginary parts of the time-domain signal are converted into amplitude or phase noise in the frequency domain.

[0069] For KID (Knowledge, Indication, and Distance) sensors, the sensitivity is typically measured using Noise Equivalent Power (NEP). NEP is generally defined as the detectable power at a signal-to-noise ratio of 1 and a bandwidth of 1 Hz, with units of [unit missing]. According to the formula

[0070]

[0071] Where S x dX / dP represents the noise power spectral density of the physical quantity to be measured, such as amplitude and phase, in W / Hz. rad For the acquired quantities (such as ADC acquisition voltage, S...) 21 The response rate to radiated power. For NEP measurements in dark environments, the KID chip temperature is typically used as an intermediate physical quantity to calculate the Noise Equivalent Temperature (NET). This is then converted to NEP using the theoretical relationship between ambient temperature and received power.

[0072] In summary, both the VNA and Homodyne methods can obtain the power spectral density (PSD) of KID, and consistent results can be obtained after data processing. A comparison of the workflow is provided below. Figure 3 As shown.

[0073] Example 2:

[0074] This embodiment uses an 80nm thick Al film KID at an ambient temperature of 80mK as an example, selecting its resonant frequency of 4197.5MHz. For comparison, both the VNA and Homodyne methods are used to obtain the PSD and NEP. The feasibility of the method is demonstrated by comparing the consistency of the results. The testing apparatus for the Homodyne and VNA methods are shown in [link to documentation]. Figure 1 and Figure 2As shown. Adjust the room temperature adjustable attenuator at the Dewar input to 50dB, so that the power at the KID input is approximately -70dBm. Connect the Dewar output to a room temperature amplifier with a passband gain of approximately 30dB.

[0075] Step 1: For the VNA method, sweep the frequency near the resonant frequency using a VNA to obtain S. 21 The amplitude and phase are then converted into real and imaginary parts, as shown by the gray lines in the figure.

[0076] Set the VNA to the default sweep mode, with a center frequency of 4197.5MHz, a sweep bandwidth of 2MHz, an IF bandwidth of 100Hz, a sweep point count of 2000, and an output power of 0dBm.

[0077] For the Homodyne method, a separate IQ calibration of the Homodyne system is required first, as detailed below. Figure 1 In this process, the first signal source frequency is set to the resonant frequency of KID and connected to the LO terminal of the IQ mixer through a coupler and a DC blocker. The second signal source frequency is set to the first signal source frequency - 10kHz and connected to a Homodyne 3dB attenuator and low-noise amplifier at the output of the cryogenic Dewar, finally entering the RF terminal of the IQ mixer. Using the sampled values ​​from the discrete ADC data acquisition module, the relationship curve (IQ ellipse) between the I and Q signal values ​​at the mixer output is plotted. Then, after least squares fitting, the imbalance parameters of the IQ mixer itself (I / Q path DC offset, IQ path amplitude, and phase offset angle) are obtained. The IQ ellipse is calibrated to become a perfect circle.

[0078] After IQ calibration, connect the output of the cryogenic Dewar back to the input of the Homodyne system, set the frequency range and number of sweep points to be the same as the VNA settings, perform a frequency sweep on the Homodyne system, and after IQ calibration of the collected IQ data, obtain the output power curve and the resonant circle of IQ reception, as shown by the black line in Figure 4.

[0079] The second step is seven-parameter fitting.

[0080] After seven-parameter fitting, KID's own transmission coefficient S 21 Frequency response curves and resonant circle curves are as follows: Figure 5 and Figure 6 As shown in the figure, gray represents the VNA method and black represents the Homodyne method. It can be seen that after seven-parameter fitting, the transmission coefficient S of KID obtained by the two methods is... 21 The amplitude curve and the resonance circle have a high degree of overlap.

[0081] The third step is to collect the transmission coefficient S at the KID resonant and non-resonant frequencies over a period of time. 21

[0082] For the VNA method, the VNA is set to single-frequency time-of-flight acquisition mode (CW mode). The CW frequency is set to the KID resonant frequency obtained in the seven-parameter fitting step two, the output power is 0 dBm, the number of sampling points is set to 20,000, the intermediate frequency bandwidth (IF bandwidth) is set to 200 kHz, and the total VNA sampling time is set to 20,000 points. The dwell time is set to 1 µs, and the actual sampling frequency is 250 kHz. After setting these parameters, the VNA is used to sample the S... 21 The real and imaginary parts are collected. Using the seven parameters obtained in the second step, the resonant and non-resonant points S are analyzed. 21 The data is calibrated using seven parameters, and the noise points are plotted on the resonance circle from the second step, as shown in the figure.

[0083] For the Homodyne method, the I and Q signals acquired over a long period at the KID resonant point also require IQ calibration and seven-parameter fitting. The ADC sampling rate is set to 200k Samples / s, with 20,000 sampling points. A low-pass filter is connected to the ADC front end to limit the sampling bandwidth; in reality, the filter's cutoff frequency does not affect the detector's PSD.

[0084] Step 4: Resonance Point PSD, NEP

[0085] Based on the third step, the transmission coefficient S of the VNA at the resonant point is collected. 21 The time-domain signal, including its real and imaginary parts, is analyzed using 20,000 points per iteration, for a total of 500 data points. After a long period of time-domain acquisition, the signal is fitted with seven parameters, followed by autocorrelation and Fourier transform to convert it into the amplitude or phase noise power spectral density (PSD) in the frequency domain. In Matlab, the `pwelch` function can be used to estimate the signal's power spectral density. Specifically, the power spectral density formula is: psd(x) = 2·(Fs·N)|x| 2 Where Fs is the sampling frequency, N is the total number of sampling points, and |x| is the amplitude value after Fourier transform. Experiments show that the actual sampling rate, number of sampling points, and intermediate frequency bandwidth of the VNA do not affect the PSD of the KID.

[0086] The noise power spectral density (PSD) of this KID was measured using VNA and Homodyne methods, such as Figure 7 As shown. Regarding the amplitude noise spectrum, frequencies less than <10 4 Within Hz, the results of both methods are the same. However, for frequencies >10 Hz... 4In terms of Hz, the Homodyne method (black) yielded better results than the VNA method (gray); in terms of phase noise spectrum measurement, the VNA measured below -85dBc / Hz, while the Homodyne method measured below -90dBc / Hz, with the VNA result being 4dB higher than the Homodyne result.

[0087] On the other hand, due to the high integration and good EMC design considerations of VNA, the PSD results measured by the homodyne method (black curve) have less clutter interference.

[0088] Temperature variation testing revealed that the temperature-voltage responsivity (dA / dT) of the tested KID in dark conditions was 0.381, a value derived from the KID's inherent characteristics. Further, the NEP results of the KID can be calculated using two methods, as follows: Figure 8 As shown. At a frequency offset of 1 kHz, the Homodyne method yields the NEP as... The VNA method yields the NEP as follows: Therefore, the NEP of KID measured by the two methods differs by a factor of 2.4, which is precisely due to the 4 dB difference in PSD measured by the two methods. However, the difference is within one order of magnitude, and its impact on the accuracy of the true value of KID sensitivity is limited (NEP is less than...).

[0089] Example 3:

[0090] This embodiment proposes a noise power spectral density measurement system for a superconducting dynamic inductive detector, see [link to documentation]. Figure 2 The measurement system consists of a vector network analyzer, a cryogenic Dewar, and peripheral circuitry.

[0091] The Port1 port of the vector network analyzer is connected to the input of the cryogenic Dewar via a first adjustable attenuator and a DC blocking device. The cryogenic Dewar includes a second fixed attenuator electrically connected to the DC blocking device, a KID electrically connected to the first attenuator, and a first low-noise amplifier electrically connected to the KID. The cryogenic Dewar is connected to the room temperature section via an insulated cable. The output of the cryogenic Dewar is connected to the Port2 port of the vector network analyzer via a combination of a second attenuator and a second low-noise amplifier.

[0092] The vector network analyzer has a built-in measurement frequency sweep unit, which is driven to sweep frequencies near the resonant frequency of the superconducting dynamic inductor detector to obtain the transmission coefficient S of the measurement system. 21 Frequency response curve.

[0093] Additionally, a measurement program module for calculating KID-PSD is required; the measurement program calculation module consists of three parts: a fitting unit, an acquisition unit, and a calculation unit.

[0094] The fitting unit is driven to fit the following parameters to the frequency response curve of the transmission coefficient near the KID resonant frequency of the entire measurement system: system link gain, phase rotation angle, coaxial cable delay time, resonator quality factor, coupler quality factor, resonator resonant frequency, and phase angle, to obtain the frequency response curve of the transmission coefficient near the resonant point of a single dynamic inductor detector and the resonant circle.

[0095] The acquisition unit uses the single-frequency point acquisition function of the vector network analyzer to acquire the frequency noise of the resonant point and the transmission coefficient S21 of the non-resonant point frequency of the entire system as a function of time. After seven-parameter fitting and calibration, the data is marked on the resonant circle.

[0096] The noise power spectral density measurement system proposed in this embodiment can realize the noise power spectral density measurement method disclosed in Embodiments 1 and 2 above.

[0097] In summary, compared to the traditional homodyne method, the VNA method offers higher commercial integration, lower cost, and higher reliability; simultaneously, the hardware's excellent immunity to electromagnetic interference ensures better readability of the data results. Furthermore, the VNA method eliminates the need for additional IQ calibration due to imbalance in the two output channels of the IQ mixer, requiring fewer instruments and being easier to implement while achieving equivalent test results.

[0098] Table 1 compares the noise power spectral density (PSD) test performance of the two methods for KID. For details, please refer to the above embodiments and... Figure 7 , Figure 8 .

[0099] Table 1 Comparison of noise power spectrum test results for KID using the two methods

[0100]

[0101] In summary, the differences between the VNA method and the Homodyne method are:

[0102] ① Regarding the method of acquiring the transmission coefficient frequency response curve of KID, the VNA method can directly obtain the transmission coefficient S by frequency sweeping. 21 The frequency response curve is the ratio of the input and output power values ​​before and after passing through the entire measurement system. In the Homodyne method, the signal source sweeps the frequency, and the Homodyne system converts the IQ amplitude values ​​at different frequency points acquired by the ADC into... It has been processed.

[0103] ②Because the I and Q outputs of the IQ quadrature mixer in the Homodyne system are unbalanced, IQ calibration is required. The VNA method does not require IQ calibration, saving a lot of manpower and material costs.

[0104] ③ The settings for noise acquisition at resonant and non-resonant points differ. VNA uses a single-frequency-point time-varying acquisition mode (CW mode). This requires setting the total acquisition time, number of sampling points, and IF bandwidth. Homodyne requires setting the sampling rate, number of sampling points, and a low-pass filter before IQ sampling. However, these settings do not affect the PSD results of KID.

[0105] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for measuring the noise power spectral density of a superconducting dynamic inductive detector (KID), characterized in that... Includes the following steps: S1. Build a noise power spectral density measurement system based on a vector network analyzer, and use the vector network analyzer to test the frequency response curve of the transmission coefficient of the entire measurement system near the resonant point of the superconducting dynamic inductor detector. S2. Fit the following parameters into the frequency response curve of the transmission coefficient: system link gain, phase rotation angle, coaxial cable delay time, resonator quality factor, coupler quality factor, resonator resonant frequency, and phase angle to obtain the frequency response curve and resonant circle of a single superconducting dynamic inductor detector. S3. Use a vector network analyzer to collect the perturbation of the transmission coefficient of the entire measurement system at the resonant frequency and non-resonant frequency over a period of time. Use the seven parameters fitted in step S2 to calibrate the transmission coefficient of the perturbation, and mark the calibrated result on the resonant circle in step S2. S4. Calculate the noise power spectral density and noise equivalent power at the current resonant and non-resonant frequencies.

2. The noise power spectral density measurement method according to claim 1, characterized in that, The frequency response curve of the transmission coefficient of the entire measurement system near the resonant point of the superconducting dynamic inductor detector described in step S1. 21 The power of the test receiver b2 at the second port of the vector network analyzer was measured as the ratio of the power of the reference receiver a1 at the first port. S 21 =b2 / a1; In the formula, b2 represents the power of the test receiver; a1 represents the power of the reference receiver; The test receiver and the reference receiver share the same local oscillator, and each receiver contains I and Q signals; S 21 It is a complex number, with real and imaginary parts, which are converted to obtain amplitude and phase information.

3. The noise power spectral density measurement method according to claim 2, characterized in that, Step S3 further includes: At the resonant and non-resonant frequencies, the vector network analyzer is set to single-frequency-time acquisition mode, and the acquisition frequency is set to either the resonant frequency or the non-resonant frequency. Set the output power, number of sampling points, intermediate frequency bandwidth, and dwell time, and use a vector network analyzer to analyze S. 21 The real and imaginary parts are collected; Using the system link gain, phase rotation angle, coaxial cable delay time, resonator quality factor, coupler quality factor, resonator resonant frequency, and phase angle from step S2, the transmission coefficient of the disturbance at the current resonant point noise and non-resonant point noise is calibrated, and the calibrated result is plotted on the resonant circle described in step S2.

4. The noise power spectral density measurement method according to claim 1, characterized in that, The expression for the current noise power spectral density psd(x) calculated using noise points in step S4 is as follows: ； In the formula, Fs is the sampling frequency, N is the total number of sampling points, and |x| is the Fourier transform amplitude value of the amplitude value of the calibrated transmission coefficient.

5. The noise power spectral density measurement method according to claim 1, characterized in that, The expression for the current noise equivalent power NEP calculated using noise points in step S4 is as follows: ； In the formula, The noise power spectral density represents the amplitude of the transmission coefficient of a superconducting dynamic inductive detector. This represents the response of the transmission coefficient amplitude value to radiated power. Indicates angular frequency; Indicates the recombination time of quasiparticles; This indicates the resonator response time.

6. A noise power spectral density measurement system for a superconducting dynamic inductive detector (KID), characterized in that, include: Vector network analyzer; the vector network analyzer has a built-in measurement sweep unit, which is driven to test the frequency response curve of the transmission coefficient of the entire measurement system near the resonant frequency of the superconducting dynamic inductor detector. Low-temperature Dewar; the Port1 port of the vector network analyzer is connected to the input terminal of the low-temperature Dewar via a first adjustable attenuator and a DC blocking device; The cryogenic Dewar contains a second fixed attenuator electrically connected to the DC blocker, a KID electrically connected to the second fixed attenuator, and a first cryogenic low-noise amplifier electrically connected to the KID. The first low-temperature low-noise amplifier is connected to the output of the temperature dewar via an insulated cable; the output of the low-temperature dewar is connected to the Port2 port of the vector network analyzer via a combination of a second room-temperature attenuator and a second room-temperature low-noise amplifier. A measurement program calculation module for calculating KID-PSD; the measurement program calculation module includes a fitting unit, an acquisition unit, and a calculation unit; The fitting unit is driven to fit the following parameters into the transmission coefficient frequency response curve: system link gain, phase rotation angle, coaxial cable delay time, resonator quality factor, coupler quality factor, resonator resonant frequency, and phase angle, to obtain the transmission coefficient frequency response curve and resonant circle of a single superconducting dynamic inductive detector. The acquisition unit is driven to acquire the perturbation of the transmission coefficient at the resonant frequency and non-resonant frequency of the entire measurement system over a period of time. The seven parameters fitted by the fitting unit are used to calibrate the transmission coefficient of the perturbation and mark it on the resonant circle. The computing unit is driven to calculate the current noise power spectral density and noise equivalent power.

7. A computer-readable storage medium storing a computer program, characterized in that, The computer program causes the computer to perform the noise power spectral density measurement method as described in any one of claims 1-5.

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