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Abstract
In order to obtain microwave signals with low spurs and low phase noise, we studied the residual phase noise of the frequency-conversion filtering oscillator and methods to improve its phase noise performance. We first analyze the influence of the dispersion of the intermediate frequency (IF) filter on the residual phase noise in the frequency conversion filtering process. Then, we use an electro-optic modulator to achieve up-conversion in the frequency conversion filtering and extend the intra-cavity delay with an optical fiber after the modulator. This allows the optoelectronic oscillator (OEO) to improve the phase noise performance while having a good suppression of spurs. The spurs suppression ratio of the proposed OEO is 80 dB with a fiber of about 1.6 km in the cavity. The phase noise of the proposed OEO is −130 dBc/Hz at 10 kHz offset from 10 GHz, which is 10 dB lower than our previous work.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The low-phase-noise microwave signal is widely used in communications, navigation, radar, and precise scientific measurements [1–6]. A direct method to obtain low phase noise signals is to use microwave resonators. The microwave resonator has a high-quality factor (Q-factor) when operating at a low frequency. However, as the carrier frequency increases, the Q-factor decreases. Therefore, the phase noise deteriorates when a high-frequency signal is generated with the microwave resonator. Another method is the multiplication frequency of a low-frequency signal generated by a high-performance quartz resonator. However, the phase noise of the frequency-multiplicated signal is proportional to the square of the multiplication factor. For some applications, the high-frequency microwave generated by this method still cannot meet the requirements. Optoelectronic oscillator (OEO) is one promotional method for generating high-frequency microwaves with low phase noise. Utilizing the ultra-low transmission loss of the optical fiber, the OEO resonator can achieve a very large Q-factor, which is also independent from the oscillating frequency.
By using long and low-loss fibers, a high Q-factor of the feedback loop can be achieved, thereby ensuring low phase noise. For example, an OEO of a 10-GHz microwave signal with a phase noise as low as −163 dBc/Hz at an offset frequency of 6 kHz was demonstrated with 16-km-long optical fiber in the cavity [7]. Although OEO has excellent phase noise performance, it also has some problems. The most troublesome problems are multimode oscillation and mode hopping. Since the optical fiber is filterless, all frequency components that satisfy self-sustained condition can oscillate in the cavity. Therefore, an extra radio frequency (RF) filter is usually required in the cavity to select the desired mode. But the bandwidth of the RF filter with a high center frequency is difficult to reach below MHz, which makes the single-mode filtering very difficult. When using long optical fibers in OEO, the large number of closely-spaced longitudinal modes make stable single-mode oscillation extremely difficult. Traditional methods of suppressing the side modes include multi-loop OEO, external oscillator injection locking, etc. [8,9]. A 60 dB suppression of the nearest-neighbor spur is demonstrated in dual injection locking OEO [10]. And the spurs suppression ratio of novel dual-loop OEO based on self-polarization-stabilization technique is 69 dB [11]. Even the multi-loop OEO can realize single-mode oscillation, but more than one loop will make the whole system more complex and sensitive to the environment. In addition, it makes the OEO lack of tunability. For external oscillator injection locking, it requires a signal source with the same frequency. In order to maintain low phase noise and suppress the side modes, it has high requirements on the phase noise performance of the external injection source.
In our previous work, we proposed a single-mode, low-phase-noise oscillation implemented by a hybrid radio-intermediate-frequency oscillator with photonic-delay-matched frequency conversion pair [12]. The demonstrated delay-matched frequency conversion pair results in an equivalent narrowband RF filter, which can suppress the undesired side modes while maintaining low phase noise performance. In this paper, we hope to further reduce the phase noise of OEO, while also ensuring a high spur suppression ratio. In our previous work, the delay of the cavity is mainly determined by the narrow intermediate frequency (IF) bandpass filter (BPF). In order to improve the phase noise performance of OEO, increasing the cavity delay is an easier and feasible method. In theory, you can reduce the bandwidth of the IF filter to obtain a larger delay in the cavity, thereby further reducing the phase noise of the generated microwave. However, it turns out that the phase noise cancellation of the local oscillator (LO) is only effective within the bandwidth of the IF BPF [13]. Recently, a single-mode oscillation was observed in a parity-time symmetric OEO with a tunable frequency. A photonic integrated microdisk resonator (MDR) is incorporated in an OEO to implement parity-time (PT) symmetry as well as frequency tuning [14].
In this paper, we first analyze the influence of IF filters with different bandwidth on the phase noise performance of signal in frequency conversion filtering. For a narrower IF filter with a larger delay, the in-band dispersion makes it difficult to compensate for the delay difference of the two transmission paths with optical delay line. Thus, the phase noise from LO cannot be well eliminated. Then, we proposed an OEO scheme that ensures low phase noise performance and suppresses the spurs. In the proposed scheme, an equivalent filter with frequency conversion pair is used to suppress the side modes. After replacing the up-converting RF mixer with MZM, additional fiber was added to the cavity behind the modulator. Therefore, the cavity formerly composed entirely of RF devices is now replaced by a hybrid cavity of optical fibers and RF devices, so the length of the cavity is greatly increased. It should be noted that although the increase in cavity length makes the cavity mode interval smaller than the bandwidth of the IF filter, the structure still has a high suppression ratio for spurs. The reason is that, compared to wideband RF BPFs, IF filters with a narrower bandwidth change more sharply around the center frequency. The difference in gain will increase the loss of the spurs, which can play a role in suppressing the spurs. With the proposed scheme, the phase noise at 10 kHz and 100 kHz offset from 10-GHz carrier frequency can reach −130 dBc/Hz and −135 dBc/Hz, respectively. The spurs suppression ratio can reach 80 dB, which is 40 dB higher than the traditional OEO.
2. Principle and experiment
In this section, we first analyze the residual phase noise introduced during the frequency conversion filtering process using IF filters with different bandwidths. In the traditional OEO, the phase noise is mainly determined by two factors, namely the open loop noise-to-signal ratio of the link and the delay of the resonator [15]. The phase noise of an OEO is inversely proportional to the square of the cavity delay. Compared with reducing the open loop noise-to-signal ratio, increasing the delay in the cavity is a simpler and more feasible method to reduce the phase noise of an OEO. A low phase noise single-mode oscillator is demonstrated with the frequency conversion pair and a narrow IF BPF in [13]. The bandwidth of the IF BPF is 510 kHz, and its group delay at center frequency is about 1 µs. The cavity delay is mainly determined by the narrow-band BPF, which greatly limits the phase noise performance of the OEO. When offset from 10 GHz by 10 kHz and 100 kHz, the phase noise of the single-mode oscillator is −120 dBc/Hz and −125 dBc/Hz, respectively. In order to increase the cavity delay, the direct method is to use an IF filter that can provide a larger delay. To our theory, an IF BPF with a narrower bandwidth provides a larger group delay. However, we find the depression of the IF filter has a great influence on the phase noise performance of the oscillating signal. It is difficult to improve phase noise performance only by reducing the bandwidth of the IF filter.
The residual phase noise from frequency conversion pair can be expressed as
An IF filter with narrower bandwidth does provide a larger delay, but it also brings greater in-band dispersion. The dispersion of the IF filter will seriously affect the level of residual phase noise. Figure 1 shows the group delay of two filters that we used in our experiment. The IF filter centered at 20 MHz with a bandwidth of approximately 510 kHz is shown in Fig. 1(a). Figure 1(b) shows a bandpass filter with a center frequency of 124.8 MHz and a bandwidth of 80 kHz. For the first filter, the delay at center frequency is about 1 µs, and the delay variation is nearly flat, which is less than 10 ns in the range of 100 kHz near the center frequency. For the second filter, the delay at center frequency is about 8 µs. At 100 kHz offset from the center frequency, the delay is reduced by 6 µs compared to that of the center frequency. Compared with the wider IF filter, the narrower one has a larger delay difference at 100 kHz offset from the center frequency after using delay matched fiber. As a result, the residual phase noise from the LO will be higher, which will greatly affect the phase noise of the oscillating signal in the RF-IF oscillator.
Fig. 1. Amplitude-frequency characteristics and delay characteristics of the IF filter (a) 510-kHz bandwidth centered at 20 MHz, (b) 80-kHz bandwidth centered at 124.8 MHz.
We compared the residual phase noise introduced by equivalent frequency filtering using IF filters with different bandwidths after delay matching. The principle of equivalent filtering with delay-matched fiber is shown in Fig. 2. Two IF filters mentioned above are used for comparison. The input RF signal is first down-converted by an external LO with an RF mixer. After the IF amplifier and IF filter, the IF signal is mixed with the same LO, which is recovered from the delay-matched photonic link. An RF filter is added before the output to suppress other frequency components introduced by the frequency conversion process. For the two IF filters mentioned above, the length of the delay-matched fiber is 200 m and 1.6 km, respectively. The input RF signal generated by a commercial microwave source is fixed at 10 GHz. For the two IF filters with different center frequencies, the frequencies of LO are 10.02 GHz and 10.1248 GHz, respectively. The phase noise of the LO and the 10-GHz RF signal before and after the equivalent filter is shown in Fig. 3. In addition, we also calculated the residual phase noise of the output signal based on the frequency delay characteristics of the IF filter and the phase noise of LO. The delay matching set in the calculation is the same as that used in the experiment. The difference between the phase noise of LO and the residual phase noise is the phase noise suppression ratio, which can be easily seen in Fig. 3. For the wider IF filter, when the offset frequency is less than 100 kHz, the phase noise suppression ratio is greater than 30 dB. As the offset frequency increases to 300 kHz, the suppression ratio drops to 0 dB. However, for the narrower IF filter, the phase noise suppression ratio is close to 0 dB at 60 kHz offset from the center frequency. Because the phase noise of the input signal is lower than that of the LO, we can see that the phase noise of the output signal is lower than the LO when the suppression ratio is greater than 0 dB. As the suppression ratio drops below 0, the phase noise of the output is gradually increasing and finally 6 dB higher than that of LO. The phase noise of the output signal obtained from the experimental measurement corresponds well with the theoretical calculation result. If the narrower BPF is used in the hybrid radio-intermediate-frequency oscillator, although a larger intra-cavity delay can be obtained, the additional phase noise caused by the frequency conversion filtering will make the oscillating signal worse and cannot obtain a low phase noise output.
Fig. 3. Residual phase noise caused by equivalent filtering with IF filter of (a) 510-kHz bandwidth centered at 20 MHz, (b) 80-kHz bandwidth centered at 124.8 MHz.
Instead of using a narrower bandwidth IF filter to provide a larger delay, we use a method of adding optical fiber in the cavity to increase the cavity delay. In this paper, we propose an OEO scheme which can achieve a good phase noise performance as well as suppress the spurs. The schematic of the proposed OEO is shown in Fig. 4. In the proposed oscillator, the oscillating RF signal is first down-converted to the IF signal by an external LO with an RF mixer. After the down-conversion, the IF signal is amplified and the filtered with a narrowband IF BPF. The filtered IF signal is then sent to the RF input of the Mach-Zehnder modulator (MZM) in order to recover RF oscillating in the following process. About the optical path, the same LO is modulated on the optical carrier with the first MZM. After the optical fiber SMF1, the IF signal and the LO are mixed by the second MZM to recover the oscillation signal. We should note that the proposed OEO also uses two sections of fiber, but its principle is different from that of dual-loop OEO. In the proposed OEO, the SMF1 is outside the cavity and provides a matching delay to minimize the residual phase noise of the LO, and the SMF2 is located in the loop to increase the Q-factor of the cavity. While the two sections of fiber in a dual-loop OEO constitute a two-tap finite impulse response (FIR) filter to suppress the spurs.
In our experiment, the LO is generated by a commercial microwave source. After a 3-dB RF power splitter, the RF power to the mixer is about 16 dBm. The conversion loss caused by the RF mixer is about 7 dB. The other part is sent to the RF input of the first MZM. The length of delay-matched fiber (SMF1) is 200 meters, which corresponds to the delay of the IF filter. The frequency of the LO is 10.02 GHz. The home-made IF BPF is the same as the one used above, which is centered at 20 MHz. After filtering, the IF signal is sent to the RF input of the second MZM. As for the optical part, the optical power of the laser is 14 dBm. The LO is modulated on the optical carrier with the first MZM. A polarization controller is placed in front of the second MZM to align the polarization to the modulator. After the second MZM, an extra optical fiber of about 1.6 km is added in the loop. Then, the optical power incident on the PD (DSC 40S) is about −2 dBm. The low optical power incident on PD and the use of an electro-optic modulator for up-conversion result in large losses. Therefore, several amplifiers are used in the loop. The gains of the IF and RF amplifiers are 20 dB and 50 dB, respectively. After the RF amplifier, the recovered RF signal is filtered by an RF filter which is centered at 10 GHz, with a bandwidth of 10 MHz. The output of the OEO is spilt into two parts, one is for phase noise measurement (Agilent E5052A + E5053B) and the other part is sent to an electrical spectrum analyzer (Agilent N9030A).
Except for the proposed OEO, we also demonstrated the RF-IF oscillator in [12] for comparison. The IF filter is the same one used in the proposed OEO. Because the cavity length is largely increased in the proposed OEO, its phase noise should be reduced compared with the RF-IF oscillator. In addition, the spurs are also greatly suppressed compared with the traditional OEO when the same length of fiber is used in the loop. We demonstrate a traditional OEO with about 1.6 km of optical fiber in the cavity. And an RF BPF centered at 10 GHz with 10-MHz bandwidth is used to select modes. In the case of almost the same cavity length, the phase noise of the proposed OEO has not deteriorated, but the spurs have been greatly suppressed.
The measured phase noise is shown in Fig. 5(a). The phase noise of the proposed OEO is about −130 dBc/Hz at 10-kHz offset, and −135 dBc/Hz at 100-kHz offset. We can see that the phase noise of the proposed OEO and the traditional OEO is almost identical when the offset frequency is smaller than 100 kHz. In the proposed OEO, when the offset frequency is smaller than 1 kHz, the phase noise performance is slightly higher than that of the traditional OEO and the RF-IF oscillator, which is mainly due to the flicker noise from additional amplifiers used to compensate for the large loss [8, 9,16,17]. Compared with the RF-IF oscillator, the phase noise of the proposed OEO is much improved between 1 kHz and 100 kHz. The improvement in phase noise performance is mainly due to the increase in cavity length. When the offset frequency exceeds 100 kHz, several peaks appear in the phase noise spectrum. These peaks are caused by the side modes which are not completely suppressed. For the proposed OEO, the phase noise increases after the offset frequency exceeds 100 kHz. We believe that the increase in noise floor is a possible reason for the deterioration of the phase noise at high offset frequency. The large loss resulted from the up-conversion using an electro-optic modulator causes the noise floor to increase, which has an impact on the oscillating signal. By increasing the optical power of the laser, the loss can be effectively compensated to reduce the noise floor. Another possible reason is the dispersion of the IF filter. In Fig. 1(a), when the offset frequency exceeds 100 kHz, the group delay of the IF filter decreases rapidly. This will make the originally accurate delay-matched structure imbalance, and the decrease of the phase noise suppression ratio will eventually make the oscillating signal worse. In terms of long-term stability, the proposed scheme improves the mode-hopping problem that is prone to occur in traditional OEO because a narrow-band IF filter is used. But the use of optical fiber makes additional temperature control measures need to be adopted to improve long-term stability.
Fig. 5. (a) Phase noise of the proposed OEO, traditional OEO and RF-IF oscillator (b) Spectrum of the proposed OEO and the traditional OEO with a span of 0.8 MHz. The inset shows the electrical spectrum of the proposed OEO with a frequency range of 10 MHz.
The inset in Fig. 5(b) shows the electrical spectrum of the proposed OEO with a frequency range of 10 MHz. The signal frequency is centered around 10 GHz, which is determined by the RF filter. For the traditional OEO, the spurs suppression is about 40 dB, while the proposed OEO can reach 80 dB in Fig. 5(b). Unlike previous RF-IF oscillator that used an IF filter to provide intracavity delay only, the cavity length of the proposed OEO is more flexible. The FSR in our experiment is about 125 kHz, and it is smaller than the bandwidth of the IF filter. Although it is said that the narrow-band IF filter will quickly reduce the gain near the oscillation frequency, which can suppress the side mode to a certain extent. But because the bandwidth of the IF filter is larger than the mode interval, it is difficult to completely eliminate the spurs. Nevertheless, the proposed structure also plays a role in the suppression of spurs, and the spurs suppression ratio is increased by 40 dB. However, when the offset frequency exceeds the bandwidth of the IF filter, its phase noise performance is limited by that of the LO. If an IF filter with wider bandwidth is employed, the influence of LO at higher offset frequency can be further reduced. But increasing the bandwidth of the IF filter will result in a reduction in spurs suppression ratio. As a result, a narrow IF filter and a LO having low noise at high offset frequency are recommended.
3. Conclusion
In conclusion, we studied the effect of the group delay of the IF filter on the residual phase noise in the frequency-converted oscillator. The large group delay would increase the residual phase noise introduced by the frequency conversion filtering process while increasing the cavity delay. Compared with the method that used a narrower bandwidth IF filter to obtain lower phase noise, we proposed a scheme of OEO which can both suppress the spurs and obtain a high phase noise performance. In the proposed OEO, spurs suppression was achieved using a narrowband filter by frequency conversion filtering. Different from the previous work, the intracavity delay was not only determined by the narrowband BPF. By increasing the length of the fiber within the cavity, the phase noise of the OEO can be further reduced. In our experiment, we generated a signal centered at 10 GHz with phase noise of −130 dBc/Hz at 10-kHz offset, −135 dBc/Hz at 100-kHz offset. The spurs suppression ratio of the proposed structure can reach 80 dB without deteriorating the phase noise performance, which is 40 dB higher than the traditional OEO that we demonstrated.
Funding
National Key Research and Development Program of China (2018YFA0701902); National Natural Science Foundation of China (61671071, 61675031).
Disclosures
The authors declare no conflicts of interest.
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