# Superconducting Sub-Terahertz Oscillator with Continuous Frequency Tuning
## 3 Results and Discussion
### Measurements of the FFO Radiation  
In practice, the most accurate measurements of Rd are made by recording spectra of the FFO emission line; the measuring technique is described in the papers [28,39,67]. The oscillator under study was part of an integrated microcircuit also comprising a small SIS junction with an area of about 1.5 \(\upmu\)m\({}^{2}\) to monitor the radiation of the FFO, and specially designed matching and tuning elements. The superconducting microcircuit was mounted  
Figure 8: Amplitude of the wave after propagation in the line and reflection from the end normalized to the initial amplitude versus frequency for simulated structures.  
inside a helium cryostat equipped with the necessary electronics for DC and microwave measurements. The SIS junction located on the same chip with the FFO was also used as a harmonic mixer (HM) with a very high harmonic number up to 50. The emission from the FFO under testing and the signal from the reference synthesizer (which is at room temperature, \(f_{synth}\) = 10-20 GHz met at the harmonic mixer. At the output of the HM, a signal appeared at the intermediate frequency (\(IF\)) \(f_{IF}\), equal to the difference between the frequency of the \(FFO\), \(f_{FFO}\), and the nth harmonic of the reference synthesizer \(f_{synth}\).  
\[f_{FFO}=n\cdot f_{synth}\pm f_{IF} \tag{9}\]  
Next, the output HM signal traveled to a cryogenic high electron mobility transistors (HEMT) amplifier, then to a warm IF amplifier that was at room temperature. Thus, the signal from a superconducting local oscillator was downconverted and recorded by a spectrum analyzer. By using this technique, it was possible to record FFO IVCs and determine FFO differential resistance with very high accuracy by using Josephson relation: FFO frequency can be measured by a spectrum analyzer with an accuracy of about 1 MHz that corresponds to 2 nV precision for voltage reading. By measuring the FFO bias current for two points with a certain frequency shift (e.g., 500 MHz, which corresponds to a voltage shift of about 1 nV), the R\({}_{\rm d}\) value can be determined. The results are presented in Figure 9a,b for two FFO frequencies.  
By using a technique based on an integrated harmonic mixer described above [17; 28; 39; 67], it was possible to the measure free-running linewidth of the FFO at each point, providing frequency stabilization to compensate for low-frequency noise temperature fluctuations. The results are presented in Figure 10, which shows down-converted emission spectra measured in two points, marked in Figure 9 by labels \"A\" and \"B\"; the linewidth varies from 4 MHz to 12 MHz due to the change in the value of R\({}_{\rm d}\) using a specially developed technique [28; 39; 67]. Dependence of the FFO linewidth versus frequency is shown in Figure 11. The linewidth does not exceed 12 MHz at all operating points, making FFO phase locking PLL possible [28; 39; 67]; phase-locked spectra of the FFO are shown in Figure 10, along with free-running FFO spectra. Thus, the proposed approach ensured the smooth tuning of the oscillator frequency and provided the possibility for phase locking of the FFO for any frequency at a constant bias current.  
Figure 9: Dependencies of the FFO differential resistance Rd on FFO frequency recorded for the Nb-AlN-NbN junction by spectra measuring technique in two frequency ranges; near 365 (**a**) and 515 GHz (**b**). Experimental points are connected by lines as a guide for the eye.