Frequency-demultiplication OEO for stable millimeter-wave signal generation utilizing phase-locked frequency-quadrupling

Jingliang Liu; Anni Liu; Zhonghan Wu; Yiran Gao; Jian Dai; Yuanan Liu; Kun Xu

doi:10.1364/OE.26.027358

1. Introduction

The millimeter-wave (mmW) signal with inherent-wide bandwidth plays an increasingly prominent role in areas such as wireless communications [1,2], access networks [3], radar [4], and warfare systems [5]. In conventional electronic system, the phase noise will deteriorate rapidly when multiplying the low-frequency electrical signal into mmW range [6]. Besides, the mmW signal suffers serious propagation loss in the cable, causing the restriction of energy storage time. The microwave photonics technology [7–9] can be a superior method to generate the mmW signal and improve its storage time via optical fiber.

Various remarkable techniques based on microwave photonics have been proposed for the generation of mmW signals. One typical approach is called as microwave photonics frequency multiplying technique (MPFMT) [10]. By beating the optical carrier or its sidebands via a high-speed photodetector (PD), the generated radio-frequency (RF) signals will have a good coherence multiplying from the same local oscillator (LO) signal. The Mach-Zehnder modulator (MZM) can serve to implement frequency doubling [11–13]. The frequency-quadrupling can be achieved by suppressing the optical carrier and the first-order sidebands by using cascaded MZMs [14, 15] or dual-parallel MZMs [16, 17]. However, the spectral quality of the mmW signal is limited by the external LO, and the best parameter matching between the MZMs is also required. Another approach is the introduction of the optoelectronic oscillator (OEO) as a strategy to generate high-frequency RF signals with low phase noise [18, 19]. The stability of the OEO can be improved by incorporating a phase-locked loop (PLL) [20,21]. The mmW OEO is proposed to oscillate at mmW range without the limitation of phase noise in theory [22]; however, the system will still face severe challenges due to the bandwidth of the filter and the tuning range of the voltage-controlled phase shifter (VPS). Applying the OEO as the LO to the MPFMT system is an effective way to generate high quality mmW signals. However, the conventional OEO working at fundamental frequency would face the complex structure for the photonic-assisted frequency quadrupling and the narrow compensation range for the oscillation frequency drift.

In this paper, we present a frequency-demultiplication OEO (FD-OEO) with a PLL for the generation and stabilization of the mmW signal. The oscillation model of the FD-OEO is theoretically and mathematically analyzed. With the application of the electrical frequency divider (EFD), the OEO can keep sustaining when biasing the MZM at its maximum transmission point. Therefore, the proposed scheme can help to simplify the photonic-assisted frequency quadrupling structure and guarantee a sufficiently wide frequency compensation range. In our system, the device limitation for a higher frequency will be only the PD, which is reportedly capable of achieving an extremely high frequency [23,24]. Besides, we can obtain three coherent output frequencies with only one MZM, which will reduce the cost of the optoelectronic devices and improve the stability of the system. As a consequence, the generated PLL-locked mmW signal exhibits a good performance of frequency stability and phase noise. The stability of the PLL-locked 40-GHz signal has reached 1.71 × 10⁻¹¹ and 1.38 × 10⁻¹² at the average time of 1 s and 100 s, which is much lower than the free-running mmW signal. The single-sideband (SSB) phase noise of the PLL-locked 40-GHz signal is as low as −60 dBc/Hz and −103 dBc/Hz at 10-Hz and 10-kHz offset frequencies, respectively. Besides, the spurious level of the PLL-locked mmW signal reaches −97 dBc.

2. Setup and principle

The configuration of the proposed PLL-locked mmW generator is shown in Fig. 1. A continuous wave light from a laser diode is sent into a MZM, and then it is divided into two branches by an optical coupler. One branch is for the generation of the LO signal, and the other is for the generation of the mmW signal. In the FD-OEO loop, an EFD by 2 is used to recover the fundamental frequency of the OEO. After BPF, the PLL can work at the fundamental frequency and stabilize the phase of the whole system. Because of the suppression of the first-order sidebands of the MZM, the mmW signal can be obtained simply by suppressing the optical carrier with a tunable optical filter (TOF). Finally, the stable mmW signal will be recovered back to the electrical domain by the high-speed PD.

Fig. 1 Schematic configuration of the proposed mmW generation and stabilization. LD: laser diode; MZM: Mach-Zehnder modulator; DSF: dispersion shifted fiber; TOF: tunable optical filter; EDFA: Erbium-doped fiber amplifier; OSA: optical spectrum analyzer; PD: photodetector; EA: electrical amplifier; BPF: band-pass filter; EFD: electronic frequency divider; VPS: voltage-controlled phase shifter; PID: proportion integration differentiation regulator; EPD: electrical phase detector; FC: frequency counter; ESA: electrical spectrum analyzer.

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The FD-OEO needs an external injected signal to start the oscillation because of the insertion of the EFD. In this section, we will give the mathematical models for the oscillation of the FD-OEO by analyzing the open-loop small-signal gain with one small signal (section 2.1) and with another injected signal (section 2.2). As shown in Fig. 2, the open-loop model of the FD-OEO is consisted of the optical input, the RF voltage input, the PD, the EFD and the EAs. Besides, Fig. 3 is consisted of the experimental measurements of the EFD’s output and the OEO’s open-loop gain for both situations.

Fig. 2 Open loop model for the setup.

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Fig. 3 Experimental measurements of the EFD and the OEO loop. (a) The output of the EFD with one input signal; (b) The loop gain of the OEO with one input signal; (c) The output of the EFD with an extra injected-signal; (d) The loop gain of the OEO with an extra injected-signal.

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2.1. Small-signal open-loop gain model for single input signal

As shown in Fig. 2, assuming that the voltage input is V_in(t, ω) = |V_in| · cos(ωt). The input optical power is P₀. When the modulator is set at the maximum transmission point, the optical power from the MZM’s output port is related to V_in by:

P (t, ω) = (γ P_{0} / 2) {1 + η cos π [V_{in} (t, ω) / V_{π}]}

where γ is the insertion loss of the modulator, P₀ is the input optical power, V_π is its half-wave voltage, and η determines the extinction ratio of the modulator by (1 + η)/(1 − η). The MZM will work at the first-order sidebands suppression point. Only the doubling frequency will be converted to the electrical domain by the high-speed PD. After filtering the DC part, the voltage of the signal sent into the EFD can be expressed as:

V_{2} (t, ω) = V_{ph} η cos π [| V_{in} | / V_{π} cos (ω t)]

V_ph is the photo-voltage defined as V_ph = (γP₀ρ/2)RG₁ = I_phRG₁, with I_ph ≡ γP₀ρ/2 as the photocurrent. ρ and R is the responsivity and load impedance of the PD, respectively. G₁ is the loop gain until the EFD. Using the Bessel function, V₂(t, ω) can be expanded as:

V_{2} (t, ω) = V_{ph} η cos π [| V_{in} | / V_{π} cos (ω t)] = 2 V_{ph} η \sum_{n = 1}^{\infty} {(- 1)}^{n} J_{2 n} (π | V_{in} | / V_{π}) cos (2 n ω t)

According to the frequency demultiplication and experimental gain-performance of the EFD as shown in Fig. 3(a), we can apply the hard thresholding function [25,26] to define the transmission function of the EFD as F_H(V(t, ω), V_T) = V_H(t, ω/2){|V(t, ω)| > V_T} which can be written as:

F_{H} (V (t, ω), V_{T}) = {\begin{array}{l} V_{H} (t, ω / 2) & , | V (t, ω) | > V_{T} \\ 0 & , | V (t, ω) | < V_{T} \end{array}

The V(t, ω) is the input voltage signal. In Eq. (4), V_T means the threshold of the EFD. The output voltage of the EFD will be constant as |V_H| while the input signal is larger than its threshold. After passing the EFD, the final output can be expressed as:

V_{3} = G_{2} F_{H} (V_{2} (t, ω), V_{T}) = G_{2} V_{H} (t, ω / 2) {| V_{2} (t, ω | > V_{T}}

Therefore, the final small signal open loop gain G_s can be expressed as:

\begin{array}{l} G_{s} = {\frac{d V_{3}}{d V_{in}} |}_{| V_{in} | = 0} & = G_{2} {\frac{d F_{H}}{d V_{2}} \frac{d V_{2}}{d V_{in}} |}_{| V_{in} | = 0} & = 0 \end{array}

The small signal gain will be fairly less than unity because of the application of the EFD, which also accords with experimental data from Fig. 3(b). As a result, the FD-OEO is difficult to start the oscillation by itself.

2.2. Small-signal gain when injecting another signal

The oscillation of the FD-OEO will start by employing another signal with power higher than the threshold of the EFD. Besides, the oscillation will keep sustaining after removing the injected signal. By injecting a large signal with voltage V_E = |V_E| cos(ωt + Δωt) and a small signal V_in = |V_in| cos(ωt) with the frequency interval Δω, we can get the input signal as:

\begin{array}{l} V_{input} = | V_{E} | / V_{π} cos (ω t + Δ ω t) + | V_{in} | / V_{π} cos (ω t) \\ \begin{array}{l} = [| V_{E} | / V_{π} cos (Δ ω t) + | V_{in} | / V_{π}] cos (ω t) - | V_{E} | / V_{π} sin (ω t) sin (Δ ω t) \end{array} \end{array}

The final output from PD can be simply expressed as:

\begin{array}{l} V_{2} (t, ω) = V_{ph} η cos [α cos (ω t) - β sin (ω t)] \\ \begin{array}{l} = V_{ph} η cos [α cos (ω t)] cos [β sin (ω t)] + V_{ph} η sin [α cos (ω t)] sin [β sin (ω t)] \end{array} \end{array}

where α = π |V_E| /V_π cos(Δωt) + π |V_in | /V_π and β = π |V_E| /V_π sin(Δωt).

While |V_in | ≪ |V_E| and Δω ≪ ω, the final form of the V₂ can be transformed with Bessel function ignoring the higher orders as:

\begin{array}{l} V_{2} (t, ω) = V_{ph} η [J_{0} (α) + 2 \sum_{n = 1}^{\infty} {(- 1)}^{n} J_{2 n} (α) cos (2 n ω t)] \cdot [J_{0} (β) + 2 \sum_{n = 1}^{\infty} J_{2 n} (β) cos (2 n ω t)] \\ \begin{array}{l} + V_{ph} η {- 2 \sum_{k = 1}^{\infty} {(- 1)}^{k} J_{2 k - 1} (α) cos [(2 k - 1) ω t]} \cdot {2 \sum_{k = 1}^{\infty} J_{2 k - 1} (β) sin [(2 k - 1) ω t]} \end{array} \\ \begin{array}{l} \approx 2 V_{ph} η [(1 - \frac{α^{2}}{4}) \frac{β^{2}}{8} - (1 - \frac{β^{2}}{4}) \frac{α^{2}}{8}] cos (2 ω t) + \frac{V_{ph} η α β}{2} \end{array} sin (2 ω t) \end{array}

By unfolding Eq. (9), the V₂ can be expressed as:

\begin{array}{l} V_{2} (t, ω) = 2 V_{ph} η \frac{{(π | V_{E} | / V_{π} sin (Δ ω t))}^{2} - {(π | V_{E} | / V_{π} cos (Δ ω t) + π | V_{in} | / V_{π})}^{2}}{8} cos (2 ω t) \\ \begin{array}{l} + \frac{V_{ph} η (π | V_{E} | / V_{π} cos (Δ ω t) + π | V_{in} | / V_{π}) π | V_{E} | / V_{π} sin (Δ ω t)}{2} \end{array} sin (2 ω t) \end{array}

As shown in Eq. (10), the power ratio of the frequency component 2ω + Δω will be linear which is between the doubling of the two input signals. By retaining the part of frequency 2ω + Δω, we can get:

V_{2} (t, ω) = \frac{V_{ph} η π^{2} | V_{in} V_{E} |}{{2 V_{π}}^{2}} \cdot cos (2 ω + Δ ω) t

With the injected signal, the frequency 2ω + Δω will be converted to ω with linear gain when passing the EFD, as shown in Fig. 3(c) and Eq. (12):

F_{H} (V_{in} (t, 2 ω + Δ ω), V_{T}) = {\begin{array}{l} G_{H} | V_{in} | cos (ω t) & , | V_{E} | > V_{T} \\ 0 & , | V_{E} | < V_{T} \end{array}

The final output from port 3 can be expressed as: V₃ = G₂F_H(V₂(t, ω), V_T).

According to the Bessel equation and its Taylor expansion, the final small-signal gain of the open loop FD-OEO can be expressed as:

\begin{array}{l} G_{s} = {\frac{d V_{3}}{d V_{in}} |}_{| V_{in} | = 0} & = G_{2} {\frac{d F_{H}}{d V_{in}} |}_{| V_{in} | = 0} & = G_{2} G_{H} {\frac{d V_{2}}{d V_{in}} |}_{| V_{in} | = 0} & = \frac{G_{2} G_{H} V_{ph} η π^{2} | V_{E} |}{{2 V_{π}}^{2}} \end{array}

The final open-loop small-signal gain of the FD-OEO is described in Eq. (13). It is a constant power related to the loop amplifiers. There are two power limitations of the close loop, the input of the EFD and the loop gain after the EFD. By adjusting the amplifiers after the EFD, the gain of the small signal is easy to be higher than unity as shown in Fig. 3(d). In our scheme, the small-signal gain limitation is not the normal modality because of the frequency conversion of doubling and demultiplication.

2.3. The sustainment of the FD-OEO after disconnecting the injected signal

By adjusting the gain of the FD-OEO, it can oscillate after injecting an external signal. After oscillating from noise, higher harmonics of the oscillation will be generated by the nonlinear effect of the modulator or the amplifiers, which will decrease the gain of the loop. The gain of the oscillation frequency will decrease according to higher harmonics in accordance with Bessel function, till the gain is slightly less than unity, and the oscillation will be stable. The EFD will work continually while the input power is over its threshold. Thus, the oscillation will be sustained after removing the external source. The injected signal can be treated as the gain-switch for the FD-OEO loop but not the gain compensation for the loop. In other words, it can only affect the starting but not the persistence of the oscillation. Besides, the frequency and the phase noise of the external signal will not influence the oscillation signal. To prove it, we choose a free-running voltage controlled oscillator (VCO) as the injected signal, whose frequency is about 9.994 GHz and out of the bandwidth of the BPF in the loop.

In consequence, by employing an EFD in the OEO loop, we can achieve the oscillation without optical first-order sidebands. At the same time, other electrical devices can work efficiently at the fundamental frequency.

2.4. Frequency stabilization of the system

The frequency stability constitutes one of the most important indexes for application of the generated mmW signals. With inherent advantage of phase noise performance at high frequency, OEO can be locked to a stable frequency reference by employing a PLL [20,21]. As a result, the OEO signal can act as the LO signal with low phase noise and high stability at high frequencies.

As illustrated in Fig. 1, the frequency stabilization setup of the FD-OEO consists of an OEO loop, a phase-locked circuit and a stable reference source. After the EFD, the frequency is converted to the 10-GHz fundamental frequency. Therefore, the devices in the PLL can operate at the fundamental frequency efficiently.

For the phase control, we implement a VPS in the PLL, which utilizes the OEO loop as a VCO. The phase drift of the OEO signal will be detected from the electrical phase detector (EPD) by mixing with a stable reference source. The proportion integration differentiation (PID) regulator can generate the servo-control signal according to the input error signal. With the feedback servo-control signal from the PID regulator, the phase difference between the 10-GHz OEO signal and the input microwave reference can be always adjusted to a certain constant in the phase-locked state. As a result, the outputs of the OEO will inherit the stability from the stable reference signal. By employing the stable 10-GHz OEO signal as the LO signal, the generated mmW signal will perform good stability as well.

3. Experiment results and discussion

The proposed PLL-locked mmW signal generation has been theoretically analyzed above. In order to demonstrate its feasibility, an experiment has been carried out based on the setup shown in Fig. 1. In the OEO loop, the laser diode (New Focus, TLB-6700) with the wavelength settled at 1550nm is injected into the MZM (EOspace, 40-GHz bandwidth) which is biased at the maximum transmission point for the suppression of the optical first-order sidebands. 3-km dispersion shifted fiber is inserted to improve the quality factor of the oscillation loop for lower phase noise. PD 1 (U2T, 0.5 A/W responsivity and 40-GHz bandwidth) is utilized for recovering the 20-GHz doubling signal. The 10-GHz fundamental signal will be recovered back after the EFD (RF Bay, FPS-2-20). RF amplifiers are employed in the electrical path to compensate the gain loss from the optical link. The center frequency and the linewidth of the BPF are 10.001 GHz and 3.7 MHz. In the PLL, the generated OEO signal is divided partly into the EPD for the generation of the error signal. After the servo control of the VPS (PMI, 5 GHz 18 GHz), the OEO signal will be phase locked to the stable reference source 2 (Agilent E8257D). A VCO (9.994 GHz) is used to start the oscillation of the FD-OEO as microwave source 1. For the generation of the mmW signal, a TOF (Finisar) is used to suppress the carrier of the optical signal divided from the output of the MZM. After the TOF, an EDFA (Amonics, AEDFA-PA-30-B-FA) with 5-dBm output power is utilized to compensate the power loss. The two second-order sidebands with 40-GHz spacing will be converted into the microwave domain by the high-speed PD 2 (U2T, 0.5 A/W responsivity and 40-GHz bandwidth).

3.1. Frequency conversion of the system

As illustrated in Figs. 4 and 5(a) (dash curve), the optical first-order sidebands will be suppressed by biasing the MZM at the maximum transmission point. As described in Eq. (2), the input of the EFD only contains the doubling frequency. On account of the frequency demultiplication of the EFD, the fundamental frequency can be recovered to modulate the MZM. The full-span electrical spectrum of the generated fundamental-frequency and doubling-frequency signals are shown in Figs. 5(b) and 5(c).

Fig. 4 The specific frequency conversion of the proposed scheme.

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Fig. 5 Optical and electrical spectrum. (a) Dash curve, the optical spectra without the TOF; line curve, the optical spectra after filtering; (b),(c) and (d) The electrical spectrum for 10 GHz, 20 GHz and 40 GHz, respectively.

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The frequency quadrupling can be simply achieved by suppressing the optical carrier, as shown in Fig. 4. Especially, the sideband is 20-GHz far from the optical carrier. We choose an easy way to suppress the optical carrier by using the TOF, which is stable for tuning. The band-pass width of the TOF is about 30 GHz. The rejection ratio of the optical carrier is about 27 dB, as shown in Fig. 5(a) (line curve). After the high-speed PD, the mmW signal can be generated 23 dB higher than the third harmonic, as shown in Fig. 5(d).

As a consequence, the scheme will output three signals with multiplying relationship at the same time. As shown in Fig. 5, the generated three signals have independent full-span spectrum with similar quality inherited from the OEO loop.

3.2. Stability of the mmW signal

A frequency counter (Agilent 53152A with the minimum resolution of 1 Hz) is utilized to record a series of frequency measurements. To characterize the stability by using the Allan deviation (ADEV), the frequency deviation from the mean Δf / f, is plotted with different averaging times to obtain the ADEV. Figure 6(a) shows the ADEV of the free-running and PLL-locked signals for 10 GHz and 40 GHz. The PLL-locked mmW signal exhibits a stability of 1.71 × 10⁻¹¹ and 1.38 × 10⁻¹² at the average time of 1 s and 100 s, which is much lower than that of the free-running mmW signal.

Fig. 6 Stability test of the generated signals. (a) The ADEV of the generated 10 GHz and 40 GHz with or without PLL; (b) Frequency drift of the PLL-locked and free-running mmW signals.

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We also set the electrical spectrum analyzer (ESA) at the “max-hold” mode with 70-kHz span to measure the frequency drift for 10 minutes. As shown in Fig. 6(b), the frequency drift of the generated mmW signal at 40 GHz with or without the PLL compensation is measured. The frequency drift of the free-running mmW signal is about 22 kHz (green curve). In contrast, the PLL-locked mmW signal keeps stable (blue curve). Such experimental results confirm that the PLL-locked mmW will have a better stability comparing with the free-running mmW signal.

3.3. Electronic spectrum and phase noise of the mmW signal

Figures 7(a) and 7(b) illustrate the measured electrical spectrum of the PLL-locked and free-running mmW signals with the span of 5 MHz, and the insets show the zoom-in view in a span of 50 kHz, respectively.

Fig. 7 (a) Spectra for free-running mmW signal; (b) Spectra for PLL-locked mmW signal.

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Figure 8 illustrates the phase noise performance of the PLL-locked 10-GHz (red curve), 20-GHz (yellow curve), 40-GHz mmW signal (blue curve) and the free-running mmW signal (greed curve) from 10-Hz to 10-MHz offset frequencies. They are measured by the ESA (Keysight N9030B). It displays that the phase noise of the PLL-locked mmW signal has a great improvement comparing with the free-running mmW signal for offset frequencies from 10 Hz to 1 kHz. The SSB phase noise of the PLL-locked mmW signal is as low as −60 dBc/Hz at 10-Hz offset frequency which is 35 dB lower than the free-running mmW signal. Although the EDFA would introduce significant amplitude noise and phase noise, the SSB phase noise is lower than −103 dBc/Hz at 10-kHz offset frequency. The PLL-locked mmW signal also has a spurious level of −97 dBc. These experimental results reveal that the PLL-locked mmW signal has great improvement of phase noise and frequency stability. The ultimate PLL-locked mmW signal combines the phase noise performance from the PLL at low offset frequencies and from the OEO signal at high offset frequencies.

Fig. 8 Comparison of phase noise for the system.

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4. Conclusion

In this paper, we propose a novel scheme for the PLL-locked frequency-quadrupling generation of mmW signals by employing the FD-OEO. The oscillation model of the new-type FD-OEO was theoretically and mathematically studied. By introducing the EFD in the OEO loop, the system can work without the optical first-order sidebands. The proposed scheme will help to simplify the photonic-assisted frequency quadrupling process. Besides, the application of the PLL for the FD-OEO can stabilize the whole system more effectively with three coherent signals generated simultaneously. The stability of the generated 40-GHz signal has reached 1.38 × 10⁻¹² at the average time of 100 s, which is much lower than the free-running one. The measured SSB phase noise of the generated mmW signal is as low −60 dBc/Hz and −103 dBc/Hz at 10-Hz and 10-kHz offset frequencies, respectively. Besides, the spurious level reaches −97 dBc.

Funding

National Natural Science Foundation of China (NSFC) Program (61501051, 61625104 and 61431003); BUPT Excellent Ph.D. Students Foundation (CX2018215); Fundamental Research Funds for the Central Universities; Fund of State Key Laboratory of Information Photonics and Optical Communications (BUPT No. IPOC2017ZT01); BUPT Ph.D. Students Short Term Exchange Program.

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Frequency-demultiplication OEO for stable millimeter-wave signal generation utilizing phase-locked frequency-quadrupling

Abstract

1. Introduction

2. Setup and principle

2.1. Small-signal open-loop gain model for single input signal

2.2. Small-signal gain when injecting another signal

2.3. The sustainment of the FD-OEO after disconnecting the injected signal

2.4. Frequency stabilization of the system

3. Experiment results and discussion

3.1. Frequency conversion of the system

3.2. Stability of the mmW signal

3.3. Electronic spectrum and phase noise of the mmW signal

4. Conclusion

Funding

References

Cited By

Figures (8)

Equations (13)

Optics Express