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Abstract
An approach to generating stable phase-locked dual-frequency microwave signals is proposed and demonstrated based on a dual-passband optoelectronic oscillator (OEO). Mode gain competition is broken by employing frequency mixing mutual injection effect to realize phase locking between the two oscillation signals, which is achieved by applying a single-tone signal to a microwave mixer in the OEO cavity. In addition, a dual-loop configuration with balanced detection is utilized to ensure a high side mode suppression ratio (SMSR) and ultra-low phase noise, which also enhances the stability of the generated signal. In the experiment, a phase-locked dual-frequency microwave signal at 9.9982 GHz and 10.1155 GHz is generated by using the proposed OEO scheme. The SMSR and the phase noise are 75 dB and –141 dBc/Hz@10 kHz, respectively. Additionally, the Allan deviation of the generated signal is in the order of 10−11@1 s. These parameters are superior to those based on the same OEO but with a single-loop configuration, which are also compared in detail.
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1. Introduction
The phase noise of microwave sources is crucial for the performance of radar, communication and measurement systems [1–7]. Developing microwave sources with more excellent phase noise performance is an eternal theme in the field of microwave technology [8–10]. Optoelectronic oscillators (OEOs) are recognized as a promising candidate to generate microwave signals with ultra-low phase noise. The most prominent advantage of an OEO lies in that its phase noise is frequency independent, which makes it competitive in generating high-frequency microwave signals with low phase noise [11–13]. In particular, an OEO loop without a bandpass filter can play the role of a broadband comb-like frequency-locked loop with an ultra-high quality factor, which can be used to generate widely-tunable microwave signals through employing a dual-frequency laser as the optical source [14]. Nevertheless, there is a random phase relationship among numerous longitudinal modes in an OEO cavity, which results in strong gain competition among oscillation modes. As a result, only a single dominant mode can oscillate at a time in general [15–17]. Considering that there are sufficient longitudinal mode resources in an OEO cavity, it is possible to utilize these resources to generate dual-frequency or even multi-frequency microwave signals with ultra-low phase noise, which will be useful for modern high-performance multi-band radar and wireless communication systems [18,19].
In the past few decades, significant efforts have been devoted to generating dual-frequency microwave signals by using OEOs [20–24]. In [20], an OEO-based dual-frequency microwave signal generator has been demonstrated by using a push-pull electro-optic Mach-Zehnder modulator (MZM) biased at its null transmission point. Nevertheless, this scheme can only be used to generate two single-tone microwave signals with a double frequency relationship. In [21], a dual-passband microwave photonic filter based on stimulated Brillouin scattering (SBS) has been employed in the OEO cavity to generate tunable dual-frequency microwave signals. Due to the large noise introduced by the SBS effect, the generated microwave signals are with high phase noise. In addition, the side mode suppression ratio (SMSR) is poor due to the indulgent mode gain competition in each passband of the microwave photonic filter. Polarization multiplexing [22,23] or parallel filters [24,25] have also been used in OEOs to select special longitudinal modes for generating tunable dual-frequency microwave signals. However, due to the lack of a phase-locking mechanism within the OEO cavity, the coherence of the generated dual-frequency microwave signals is poor. In recent years, mode-locking technique has been introduced into OEOs to establish a fixed phase relationship among the oscillation modes, which enables generating coherent microwave combs [26–30]. Nevertheless, due to the small frequency interval between neighboring teeth and the uncontrollable tooth number, it is difficult to extract out specific comb teeth. In [31], an external signal is injected into a dual-passband OEO to synchronize two dominant oscillation modes. Based on the injection locking effect, a coherent dual-frequency microwave signal with ultra-low phase noise is generated. However, in order to achieve a high SMSR, the loop gain must be carefully adjusted as the authors pointed out. Otherwise, the initially-generated oscillation in any one of the two passbands is generally with strong side modes. As a result, frequency mixing mutual injection not only occurs between the two dominant oscillation modes but also occurs between the unwanted side modes in the two passbands. Hence, if the loop gain is not properly set at the initial oscillation stage, the SMSR of the generated dual-frequency microwave signal will greatly deteriorate.
In this paper, an OEO scheme to generate a phase-locked dual-frequency microwave signal with high SMSR and ultra-low phase noise is proposed and experimentally demonstrated. The phase of the two generated microwave signals is locked through using an externally-applied signal to achieve frequency mixing mutual injection in the OEO cavity. In addition, a dual-loop configuration with balanced detection is employed to maintain stable high SMSR and ultra-low phase noise performance. In the experiment, a dual-frequency microwave signal at 9.9982 GHz and 10.1155 GHz is generated, where the SMSR and the phase noise are measured to be 75 dB and –141 dBc/Hz@10 kHz, respectively. In addition, the Allan deviations of the generated dual-frequency microwave signal are in the order of 10−11@1s.
2. Operation principle
Figure 1 shows the schematic diagram of the proposed phase-locked dual-frequency OEO. In the OEO, a dual-passband filter (DBPF) is used to select two oscillation modes in different frequency bands. The frequencies of the two single-tone microwave signals generated in the OEO cavity are denoted by f1 and f2 (f2 > f1). The phase of the two signals is locked through frequency mixing mutual injection, which is achieved by inserting a microwave mixer into the OEO cavity and injecting a single-tone signal with a frequency of finj = f2–f1 into the intermediate-frequency (IF) port of the mixer. Figure 1(c) exhibits the operation principle of the frequency mixing mutual injection process. If the external injection signal source is turned off, only a single-tone microwave signal within any one of the two passbands can oscillate due to gain competition. After turning on the external injection signal source, the free-running oscillation at either f1 or f2 will generate a phase-locked duplicate at f1 + finj = f2 or f2–finj = f1, respectively, performing injection locking in the other passband. On this condition, dual-frequency oscillation at f1 and f2 will be established in the OEO cavity, which promotes frequency mixing mutual injection-induced phase locking, i.e., the duplicate at f1 + finj = f2 generated by the single-tone microwave signal at f1 performs phase locking on the one at f2, and vice versa. Hence, through properly adjusting the loop gain via tuning the variable optical attenuator (VOA) outside the OEO cavity, stable phase-locked dual-frequency oscillation with similar power can be built up. It should be noted that the DBPF is with two narrow passbands and high out-of-band suppression ratios. Hence, the intermodulation products at f3 = f1–finj and f4 = f2 + finj are filtered out by the DBPF, which cannot oscillate in the OEO cavity. In general, the width of any passband in the DBPF is more than two orders of magnitude larger than the free spectrum range (FSR) of the OEO cavity since a spool of long optical fiber is usually employed in the OEO cavity to ensure the low phase noise performance of the generated microwave signal. Hence, if the OEO cavity is with a single-loop architecture, the initially generated oscillation in any one of the two passbands is generally with strong side modes due to gain competition. As a result, frequency mixing mutual injection not only occurs between the two dominant oscillation modes but also occurs between the unwanted side modes in the two passbands. In such a case, the generated phase-locked dual-frequency microwave signal is generally with a small SMSR if the loop gain is not properly set at the initial oscillation stage. To solve this problem, a dual-loop configuration is employed in the proposed OEO as shown in Fig. 1(a). In the dual-loop configuration, a spool of long single-mode fiber (SMF), i.e., SMF1, is shared by the two loops to ensure low phase noise performance of the generated microwave signal, and another section of short SMF, i.e., SMF2, is inserted into any loop to induce vernier effect as depicted in Fig. 1(b). With assistance of the Vernier effect in the seemingly complex dual-loop architecture, the strict requirement for loop gain to obtain a high SMSR is alleviated. As a result, the stability of the generated dual-frequency microwave signal is also enhanced. It should be pointed out that, since the noise in the two radio-over-fiber (RoF) links is a stationary random process, the small delay difference between the two RoF links and the balanced photodetection help suppress the common mode noise induced by the active devices in the RoF links, which is beneficial for further improving the phase noise of the generated dual-frequency microwave signal.
Fig. 1. Schematic diagram of the proposed phase-locked dual-frequency OEO. (a) Architecture of the OEO. (b) Vernier effect based on the dual-loop configuration. (c) Operation principle of the frequency mixing mutual injection process. LD: laser diode; VOA: variable optical attenuator; MZM: Mach-Zehnder modulator; SMF: single-mode fiber; OC: optical coupler; BPD: balanced photodetector; EA: electrical amplifier; EC: electrical coupler; DBPF: dual-passband filter; MWS: microwave source.
Mathematically, the input dual-frequency microwave signal of the electro-optic MZM is written as
Furthermore, the injection locking range of an OEO can be written as [32–35]
3. Experimental results
In the experiment, a distributed-feedback laser diode (INNO-9317-DFBM-PM) at 1310 nm and with an output optical power of 17 dBm is used to generate the continuous-wave (CW) light. The optical power of the CW light injected into the OEO cavity is finely adjusted by using a VOA to maintain a stable loop gain. The feedback dual-frequency microwave signal is loaded onto the CW light via a 40 Gb/s 1310-nm electro-optic MZM (Exail, MX1300-LN-40). The modulated optical signal first propagates through, and is then split into two branches by using a 3-dB optical coupler. A section of SMF with a length of 0.3 km is inserted into one branch to introduce Vernier effect. The optical signals from the two branches are detected by using a high-speed BPD (YINUO BPD) with an operation bandwidth of 22 GHz. Two electrical amplifiers (YINUO LNA) with identical operation frequency range from 2 GHz to 20 GHz and small-signal gain of 33 dB are employed to compensate for the loop loss. Frequency mixing injection locking is achieved by using a microwave mixer (Marki M1-0212) whose IF, LO and RF ports are with operation frequency ranges from DC to 2 GHz, 2 GHz to 12 GHz and 2 GHz to 12 GHz, respectively. The externally-injected single-tone signal is provided by using a tunable microwave signal source (R&S SMB100A, 100 kHz-12.75 GHz). A customized DBPF (MDP10G-20 M/10.1G-20-4083) with passband center frequencies of 10 GHz and 10.1 GHz, and 3-dB passband widths of 44 MHz and 49 MHz, respectively, are utilized to achieve mode selection in the OEO. An electrical coupler (GTPD-COMB50 G, DC-50 GHz) is used to provide a feedback signal in the OEO cavity and output the generated dual-frequency microwave signal. The spectra and the temporal waveforms of the generated dual-frequency microwave signal are measured by using an electrical spectrum analyzer (R&S FSU50, 20 Hz-50 GHz) and a high-speed real-time oscilloscope (Tektronix DP75002SX, 33 GHz, 100 GSa/s), respectively. The phase noise and the Allen deviation of the generated microwave signals are measured by using a phase noise analyzer (R&S FSWP50, 1 MHz-50 GHz).
Firstly, the open-loop frequency response of the OEO without external signal injection is measured by using a vector network analyzer (Keysight N5235A, 10 MHz-50 GHz). In the measurement, the output port of the vector network analyzer is connected to the RF input port of the MZM, and the input port of the vector network analyzer is connected to the output port of the electrical coupler. Figure 2(a) and (b) show the measured open-loop frequency responses of the OEO based on single-loop and dual-loop configurations, respectively. Thereinto, the single-loop configuration is realized by disconnecting one optical input port of the BPD. It can be seen from Fig. 2 that, compared with the single-loop configuration, there is a fine comb-like filtering in the two passbands of the DBPF for the dual-loop configuration due to the Vernier effect, where the effective FSR is measured to be 625.6 kHz. This fine comb-like filtering characteristic is beneficial for suppressing side modes at the initial oscillation stage and also the final stable dual-frequency oscillation state.
Fig. 2. Open-loop frequency responses of the OEO based on (a) single-loop configuration and (b) dual-loop configuration.
The OEO loop is then closed by connecting the output port of the electrical coupler to the RF input port of the MZM. The external injection signal is not turned on. Hence, there is a strong gain competition between the longitudinal modes in the two passbands of the DBPF, resulting in oscillating only in a single passband. Figure 3(a) and (b) show the spectra of the generated microwave signals based on single-loop and dual-loop configurations, respectively. It can be seen from Fig. 3 that, compared with the single-loop configuration, the SMSR of the generated microwave signal from the OEO based on the dual-loop configuration is enhanced from 34.2 dB to 78 dB. Hence, the dual-loop configuration is beneficial for enhancing the SMSR of the dual-frequency OEO.
Fig. 3. Spectra of the generated microwave signals based on (a) single-loop configuration and (b) dual-loop configuration.
Then, a single-tone signal at 117.1 MHz and 117.3 MHz is injected into the mixer to achieve frequency mixing mutual injection in the OEO based on single-loop and dual-loop configurations, respectively. On this condition, a stable dual-frequency microwave signal is generated. It should be pointed out that the frequency difference of the two injection signals is mainly attributed to the frequent mode hopping in the single-loop OEO, where the 200-kHz frequency difference is approximately 6 times the FSR of the single-loop OEO, i.e., ∼33.3 kHz. Figure 4(a) and (b) exhibit the spectra of the generated dual-frequency microwave signals based on single-loop and dual-loop configurations, respectively. In the single-loop configuration, although frequency mixing mutual injection process is established, it not only occurs between the two dominant oscillation modes but also occurs between the unwanted side modes in the two passbands. Hence, the generated dual-frequency microwave signal is with a small SMSR of only about 45 dB. Similar result can also be found in [30]. In the dual-loop configuration, due to the fine comb-like filtering characteristic induced by the Vernier effect, the SMSR of the generated dual-frequency microwave signal is enhanced to beyond 75 dB.
Fig. 4. Spectra of the generated dual-frequency microwave signals based on (a) single-loop configuration and (b) dual-loop configuration.
The stability of the generated dual-frequency microwave signals is measured. Figure 5 shows the measured Allan deviations of the signals based on single-loop and dual-loop configurations. It can be seen from Fig. 5 that the Allan deviations of the two single-tone microwave signals for the dual-loop configuration are in the order of 10−11@1 s, which are nearly one order lower than those for the single-loop configuration. This improvement is attributed to the fact that the dual-loop configuration greatly enlarges the effective FSR and also the frequency mixing mutual injection locking range, which is beneficial for enhancing the long-term stability of the dual-frequency microwave signal, as analyzed in Section 2.
Fig. 5. Allan deviations of the generated dual-frequency microwave signals based on single-loop and dual-loop configurations.
Figure 6 presents the phase noise curves of the generated dual-frequency microwave signal based on dual-loop configuration, together with that of the microwave signal generated without external signal injection. It can be seen from Fig. 6 that the phase noise curves of the two single-tone microwave signals are nearly identical with each other, and also with that of the microwave signal generated without external signal injection. The phase noise sensitivity of the employed phase noise analyzer for a signal at 10 GHz is –133 dBc/Hz@1 kHz and –152 dBc/Hz@10 kHz. Hence, the measured phase noise of –115 dBc/Hz@1 kHz and –141 dBc/Hz@10 kHz is reliable, since it is far higher than the phase noise sensitivity of the analyzer. It should be noted that there is an inevitable measurement uncertainty of the phase noise [36]. According to the specifications of the analyzer, the phase noise measurement uncertainty in the frequency offset range of 10 mHz to 1 MHz is less than 1.2 dB (σ=0.4 dB). Hence, the phase noise of the generated dual-frequency microwave signal is believed to be better than –113.8 dBc/Hz@1 kHz and –139.8 dBc/Hz@10 kHz at least. To evaluate the coherence between the two single-tone microwave signals, the generated dual-frequency microwave signal is split into two branches via another 3-dB electrical coupler. Then, the two duplicates are sent to another mixer outside the OEO cavity to obtain an IF signal with its frequency identical to that of the injection signal. Figure 6 also presents the phase noise of the injection signal and the IF signal from the mixer. It can be seen from Fig. 6 that the phase noise curve of the IF signal approaches that of the injection signal in the frequency offset range from 10 Hz to 13 kHz, while it approaches that of the dual-frequency microwave signal in the frequency offset range from 13 kHz to 10 MHz. Compared with the generated dual-frequency microwave signal, the phase noise of the IF signal from the mixer is improved by 52 dB at the frequency offset of 10 Hz, indicating that the two single-tone microwave signals in the generated dual-frequency microwave signal are phase-locked. It should be pointed out that the phase noise deterioration of the IF signal relative to the injection signal is attributed to the additional phase noise of the RoF links.
Fig. 6. Phase noise curves of the generated dual-frequency microwave signal based on dual-loop configuration, the microwave signal generated without external signal injection, the injection signal, and the IF signal obtained through mixing the dual-frequency microwave signal.
In order to further evaluate the long-term phase stability of the dual-frequency microwave signal, two sections of temporal waveforms are recorded by using the high-speed real-time oscilloscope, where the recording time interval between the two temporal waveforms is 100 s. Figure 7 shows the cross-correlation result of the two temporal waveforms, which exhibits stable periodicity. This result indicates that the two single-tone microwave signals have excellent phase stability, and can maintain long-term synchronous oscillation. Furthermore, it can be seen from Fig. 7 that the minimum value of the normalized amplitude in the cross-correlation result is not zero, which is attributed to the unequal power of the two single-tone microwave signals.
Fig. 7. Cross-correlation result of two temporal waveforms with a recording time interval of 100 s for the generated dual-frequency microwave signal.
The dual-frequency microwave signal generation process under frequency mixing mutual injection locking is also measured. Figure 8 shows the time-frequency diagram of the generated microwave signal after turning on the external injection signal source, which is obtained by performing a short-term Fourier transform on the recorded temporal waveform. It can be seen from Fig. 8 that only a single-tone microwave signal at 10.1155 GHz oscillates in the OEO cavity without injection. Once the injection signal at 117.3 MHz is applied to the mixer, another single-tone microwave signal at 9.9982 GHz appears due to frequency mixing injection. After about 135.87 µs, i.e., 85 cycles in the OEO cavity, the two single-tone microwave signals maintain stable oscillation under frequency mixing mutual injection locking.
Fig. 8. Time-frequency diagram of the generated microwave signal after turning on the external injection signal source.
Finally, the performance of the generated phase-locked dual-frequency microwave signal is compared with that of the dual-frequency microwave signal generated by using commercial instruments. Figure 9(a), (b) and (c) show the spectra of the dual-frequency microwave signals generated by using the proposed dual-frequency OEO, two synchronized microwave sources (R&S SMB100A, 100 kHz-40 GHz) and an arbitrary waveform generator (Keysight M8194A, 120 GSa/s), respectively. Figure 10 exhibits the corresponding phase noise curves. The results indicate that the spurious suppression ratio of the dual-frequency microwave signal generated by using the proposed OEO is much better than that generated by using the arbitrary waveform generator. In addition, the phase noise performance is much better than that of the other two commercial instruments.
Fig. 9. Spectra of the dual-frequency microwave signals generated by using (a) the proposed dual-frequency OEO, (b) two synchronized microwave sources, and (c) an arbitrary waveform generator.
Fig. 10. Phase noise curves of the dual-frequency microwave signals generated by using the proposed dual-frequency OEO, two synchronized microwave sources, and an arbitrary waveform generator.
4. Conclusion
In summary, we have proposed and demonstrated an OEO to generate phase-locked dual-frequency microwave signals. The gain competition between the two oscillation signals is broken by injecting a single-tone signal into the OEO cavity to introduce frequency mixing mutual injection effect, and finally to achieve phase locking between the two oscillation modes. The adoption of a dual-loop configuration in the OEO cavity not only suppresses the unwanted side modes but also enhances the stability of the dual-frequency microwave signal oscillation. In addition, the use of balanced detection helps suppress common mode noise in the RoF links, ensuring ultra-low phase noise performance of the generated dual-frequency microwave signals. In the experiment, a phase-locked dual-frequency microwave signal at 9.9982 GHz and 10.1155 GHz was generated, where the SMSR and the phase noise were measured to be about 75 dB and –141 dBc/Hz@10 kHz, respectively. In addition, the Allan deviation of the generated dual-frequency microwave signal was in the order of 10−11@1s. The proposed OEO scheme can be used to generate pure phase-locked dual-frequency microwave signals with ultra-low phase noise in the high-frequency range, which will be useful for modern high-performance dual-band radar and wireless communication systems.
Funding
National Natural Science Foundation of China (62305046, 61927821); Fundamental Research Funds for the Central Universities (ZYGX2020ZB012).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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