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Traditional microwave photonic systems cannot implement frequency up-conversion with phase tunable capability, which plays an important role for phase array beamforming. Here, a method that can implement both upconversion and downconversion with a broadband full-degree phase-shift capability by constructing an optical path with a Hilbert transform function is presented. Owing to the Hilbert transform path, the dual-drive Mach-Zehnder modulator (DMZM) bias information, which initially influences the amplitudes of the output signals, are transferred to their phases. As a result, the phase-shift capability of the output radio frequencies (RFs) and intermediate frequencies (IFs) can be achieved by simply adjusting the bias voltage of the DMZM without using an optical filter. Experimental results demonstrate that a 360° phase shift can be achieved when the IF signal below 4-GHz and the RF signal between 8 and 16-GHz are converted into each other.
© 2017 Optical Society of America
1. Introduction
In millimeter-wave phased-array beamforming networks and phase-coded radar systems, both wideband phase shifter and frequency converter are essential processing elements. On the one hand, a continuous full 360° tunable wideband phase shifter is a key component for phase-array beam pointing [1]. On the other hand, intermediate frequency (IF) signals should be upconverted into radio frequencies (RFs) at the transmitter, and RFs should be downconverted into IFs at the receiver [2], as Fig. 1 shows. Owing to the advantages of a large bandwidth, constant attenuation over the entire microwave frequency range, and electromagnetic interference immunity [3], both photonic-assisted microwave phase shifter and microwave mixer have been intensively studied and well developed. For example, many microwave photonic mixer schemes have been designed to achieve high conversion efficiency [4,5], high linearity [6], harmonic conversion [7], or high carrier-to-noise ratio [8]. Various microwave photonic phase shifters have also been proposed with emphasis on features such as phase shift range [9], phase deviation [5, 10], or operation bandwidth [11,12].
Fig. 1 Typical application of the proposed system on radio phase array beamforming (a) transmitter, (b) receiver. (VGA: variable gain amplifier, LNA: low noise amplifier).
All these schemes can only achieve either frequency conversion or phase shift. In fact, combining both functions into a simple compact configuration can not only simplify the structure of the entire system, but also improve its performance. Recently, microwave photonic solutions for frequency downconversion with phase-shift capability have been reported [13–15]. Phase-shift capability is achieved by filtering out and manipulating the phases of the first-order sidebands of the RF and local oscillator (LO) frequency using optical filter (OF). However, the bandwidth narrowness of OF limits their low operating frequency. More importantly, these method can-not combine a phase shift with frequency upconversion, which plays a more important role in phased-array beamforming networks at the transmitter.
In this paper, we theoretically and experimentally achieve a compact both photonic upconversion and downconversion approach with wideband phase-shift capability by adding an optical path in the Hilbert transform domain. Without using OF, the system can operate at the frequency as low as DC. In the proposed system, two dual-drive Mach-Zehnder modulators (DMZMs) are operated in two orthogonally polarized optical fields. The RF and LO signals are fed to either arm of each DMZM. After the photodetector, the output signals which stem from the two polarizations are then generated and combined in the electrical domain. The Hilbert transform domain is constructed, and the bias voltage information can be simply transferred to the phase of the output IF and RF signals by setting a 90° differences in the LO phase and a bias point between the DMZMs. Thus, the phase of the converted signal of the output frequency can be tuned accurately and easily by adjusting the DC bias of either DMZM. A proof-of-concept experiment is conducted. Both downconversion and upconversion with phase-shift capability is realized.
2. Topology and principle of operation
Figure. 2(a) shows the basic block diagram of our proposed wideband phase-shift microwave mixer. The system consists of a laser diode (LD), two DMZMs, a polarization maintaining optical coupler (POC), a polarization beam combiner (PBC), and a photodetector (PD). A continuous lightwave, which is provided by a distributed feedback-based LD, is divided into two parts by a 50:50 POC. Subsequently, the lightwaves are injected into each of the two DMZMs. Each arm of DMZM can be considered as a phase modulator. RF/IF signal and local oscillator (LO) signal are applied to either arm of each DMZM. The modulated optical field after each DMZM can be expressed as:
where P0 represents the optical power of the LD; ωO represents the angular frequency of the optical carrier; and are the modulation depth of the upper and lower arms, respectively (Vs and VLO is the amplitudes of the RF/IF signal and LO signal, Vπ is the the half-wave voltage for a single arm of a DMZM); ωs represents the angular frequency of the RF/IF signal; ωLO represents the angular frequency of the LO microwave signal; θ1 is the optical phase difference between the arms of DMZM1; θ2 is the optical phase difference between the arms of DMZM2; ϕ1 is the LO phase added to DMZM1; and ϕ2 is the LO phase added to DMZM2. We set . After combining in the PBC, the optical field can be expressed as uf (t) and us (t) represent the optical fields of the fast and the slow axes of the PBC,respectively. The output lightwaves of PBC are then sent to the PD for square-law detection. After filtering out the spurs by electrical filter, the detected microwave components of the upconverted signals and downconverted signals can be described by where R is the photodetector responsivity. Thus, we set and to construct a Hilbert transform path. Then, we obtainFig. 2 Microwave photonic mixer with phase-shift function, (a) diagram of proposed system using polarization multiplexing, and (b) diagram of proposed system using wavelength multiplexing. EF: electrical filter.
Fig. 3 Experimental block diagram of microwave photonic mixer with wideband phase shift (VNA: vector network analyzer).
As shown in Eq. (5), the phases of both the upconverted and downconverted signals can be varied by ϕ1 or θ1. However, ϕ1 can only be adjusted by an electrical phase shifter, which is usually a narrow-band device. That is, adjusting ϕ1 is not suitable for the purpose of wideband phase shift. Thus, ϕ1 is fixed. For simplification, we can take ϕ1 = 0. Instead, turning θ1 which related to the bias voltage of DMZM1 can achieve a wideband phase shift. Thus, Eq. (5) can be simplified to
We can observe that the phases of both the downconversion and upconversion signals can be varied fully [0°, 360°] by changing θ1 while the amplitude remains unchanged. The condition of can be realized by a DC voltage control circuit, and can be ensured by an electrical phase shifter for a constant LO frequency. For some specific applications, where LO is a wideband signal, a 90° electrical hybrid coupler can be used to keep this phase difference. Thus, the Hilbert transform path can be constructed easily. The bias point of DMZM1 can be changed by either the electrical voltage difference between the two arms of DMZM1 or change in optical wavelength because of internal path-length mismatch between the arms of the DMZM [16, 17]. Mathematically, the phase differences θ of DMZM1 can be expressed as:
where ΔnL = nup Lup − ndown Ldown is the internal path-length mismatch between the two arms of the DMZM; nx is the index refraction of x arm; Lx is the waveguide length of x arm; VDC is the bias voltage of the DMZM. For a certain optical wavelength, adjusting VDC can change θ. For a certain bias voltage, θ is proportional to the laser wavelength.Thus, the proposed phase-tunable microwave photonic mixer can be realized by wavelength multiplexing, as shown in Fig. 2(b). Two LDs with different wavelengths are used as the optical sources of the DMZMs, respectively. The two modulated lightwaves can be demodulated in the photodetector separately as a polarization-multiplexed structure. This structure has two benefits. First, a DC voltage conversion circuit is not required. Both DMZMs can be driven simply by the same DC voltage. Wavelength multiplexing not only provides a dimension to implement the Hilbert transform path, but also renders the DMZMs biased at the different bias points to ensure the bias differences. Second, the Hilbert transfer path is constructed in the wavelength dimension. Instead of a PBC, only an optical coupler is required to combine the two paths. Thus, polarization maintain devices are unnecessary, thereby reducing the cost of the system. However, this structure consumes more power than the previous structure because of the additional LDs. These benefits can traded off in specific applications. The two phase-shift methods can be used in different applications. For a phase-array radar, adjusting the DC voltage is more suitable, because of the fast speed. By contrast, the method of adjusting the wavelength is more suitable for a communication system in the I/Q modulation and demodulation process.
Equation. (6) suggests that both upconversion and downconversion components have the same amplitude factor which is correlated with Bessel function of the first order of parameter of β2. Thus, the conversion efficiency and dynamic range are the same as those in [14]. To prove this point, we perform an experiment, and its results demonstrate that the maximum conversion efficiency occurs at β2 = 1.84. This result agrees well with the given principle. If the proposed microwave photonics phase-tunable mixer is transmitted over some length of fiber, it will mainly affected by dispersion, such as polarization mode dispersion (PMD) and chromatic dispersion (CD). On one hand, the two paths operate at different polarization state. That is to say, the system can be treated as a polarization multiplexing system. Therefore, the PMD will damage the matching relation on the dimension of delay and further impact the accuracy of phase shift and the flatness of the amplitude response. However, this kind of mismatch can be completely compensated by adjusting an optical delay line which is placed in either path. On the other hand, traditional power fading induced by CD is existed in our system. Mathematically, the detected frequency converted signal after transmitted over fiber with a length of L can be expressed as:
where D is the chromatic dispersion of the fiber. From the Eq. (8), we can find that of the downconverted signal and upconverted will induce different power fading due to their frequency differences. For the case of D = 17ps/nmkm, ωo = 193.45T Hz, the up-converted signal with frequency of 16-GHz will be completely extinguished at a fiber length of 14.3km. In down-conversion, considering, the IF signal with of 4-GHz will be completely extinguished at a fiber length of 229.5km.3. Experimental results
The experimental setup of the microwave photonic mixer with phase-shift function is shown in Fig. 3. A tunable laser (Southern Photonics, TLS150D) provides a polarization-maintaining lightwave with a power of 15-dBm at 1550.43 nm. The laser output is then injected into a commercial dual-polarization Dual-Drive Mach-Zehnder modulator (DP-DMZM, Fujitsu, FTM7980EDA). This modulator comprises 3dB coupler, two DMZM modulators, polarization rotator followed by the polarization beam combiner. In this modulator, the optical carrier is split equally into the two DMZM. The half-wave voltage of each arm is measured to be 3.2V@DC and calculated to be 5.4V@12-GHz by the S21 curve in the datasheet. Port 1 of a vector network analyzer (VNA, Agilent 8722es), which represents RF/IF signal, is divided equally into two parts by an electrical power divider. The divided signals drive the upper arms of the two DMZMs. The lower arms of the DMZMs are driven by the LO signal provided by a microwave source (Agilent, E8267D) with a frequency of 12-GHz. The phase of the LO signal added to DMZM2 is shifted by 90° by an electrical phase shifter. The power of the VNA is set to be 5 dBm. The LO modulation depth is set to 1.84 to obtain the maximum conversion efficiency. The DC bias voltage of DMZM2 is set to 1.6V higher than the bias voltage of DMZM1 by a DC source to ensure the 90° bias point difference between the DMZMs. Due to the constant relationship between θ1 and θ2,the bias voltage of DMZM2 will change accordingly. Consequently, a Hilbert transform path is established. The output lightwaves of the DMZMs are combined by a polarization-maintaining combiner in the integrated modulator and then output through a single mode fiber. The optical power before the PD (Agere Systems, R2860D) is 6-dBm. The responsivity of the PD is 0.8 A/W.
Considering the traditional path is bias at the quadrature point, we have . Due to the 90° bias difference relationship θ2 = 0. So, the optical carrier of the Hilbert transfer path is suppressed, as Fig. 4(b) shows. According Eq. (9), ωs and ωLO components can be observed in Fig. 4(c). While the ωIF and ωRF components can be seen in Fig. 4(d). Electrical power of these components for each of the path will be changed according to the θ1. After combining the both paths together, electrical spectrum is shown in Fig. 4(e). When we adjust the θ1, electrical power of all these components can be keep constant, while their phases can be change continually. Figure. 4(e) shows the dynamic range performance. It can be see that the spur free dynamic range (SFDR) is measured to be 101.3dB.
Fig. 4 (a)/(b) Optical spectrum of traditional path and Hilbert transfer path when , θ2 = 0.(c)/(d) Electrical spectrum of traditional path and Hilbert transfer path when , θ2 = 0. (e) Electrical spectrum when combing both paths. (f) Dynamic range performance of the proposed system. (IMD3: third order intermodulation distortion.)
For the investigation of the amplitude and phase response of the frequency conversion system, the output signal is reconverted into the original frequency. An electrical mixer and the same LO signal are used for reconversion process. First, the VNA is calibrated in through mode while our system is connected. The phase responses of both the downconverted signals and upconverted signals are presented in Fig. 5. Figure. 5(a) shows the measured phase response of the downconverted signal with a 45° phase shift step. The measurements are taken over a frequency ranging from 8 to 16 GHz. Flat phase responses for all the phase shifts are obtained. Adjusting the voltage of DMZM1 stepwise by approximately 0.8 V, shift the phases of the output signal stepwise by 45°. This reslut is in good agreement with our theoretical analysis. Figure. 5(b) shows the frequency upconversion performance. For the upconversion, the VNA provided IF signal frequency sweep range is set to be 0 – 4 GHz which is limited by the IF frequency range of the electrical mixer. Clearly, full 360° tunable flat-phase response is also achieved. The phase deviation is measured to be ±2°. It should be noted that the frequency range of the IF port of the electrical mixer is DC-4GHz. This measurement device limit the measured RF range in our experiment. The bandwidth of the system should limited by the electrical element which has a narrower bandwidth than the optical element. However, commercial 90° hybrid coupler with frequency up to 67-GHz has been produced (Marki Microwave, QH-0867). This bandwidth is comparable to most of the commercial modulator. In this case, the broadband performance can also be obtained.
Fig. 5 Experimentally measured phase response of proposed system at different DC biases for (a) downconverted signal, (b) upconverted signal.
The amplitude responses of both downconversion and upconversion are measured. Using the same experimental setting, Fig. 6(a) and 6(b) show that ±2 dB power variations are obtained for both downconversion and upconversion configurations. These results are acceptable for most applications. Flat power responses with little ripple are obtained when the output phase is swept by a step of 45°. This result proves that the DC voltage of DMZM1 can only affect the phase but not the amplitude for both the downconverted and upconverted signals. To evaluate the system stability, we operate the system in a laboratory environment and sweep the time from 0 to 200 s. Figure. 6(c) shows the phase stability for different phase shifts when an RF signal with frequency of 12.5-GHz is downconverted into 500-MHz. As demonstrated by Fig. 6(d), a similar stability can be obtained with the upconversion configuration, when the IF signal with a frequency of 500-MHz is upconverted into 12.5-GHz. Stability can be maintained when the phases are tuned.
Fig. 6 (a) Power responses of downconverted signal for different phase shifts, (b) power responses of upconverted signal for different phase shift, (c) phase shifts of downconverted signal when time is swept from 0 to 200s, and (d) phase shift of upconverted signal when the time is swept from 0 to 200s.
4. Conclusion
In conclusion, a photonic scheme that can simultaneously achieve a microwave mixer and a wideband microwave phase shifter is proposed and experimentally demonstrated. With the addition of a Hilbert transform path, the DMZM bias information, which initially influences the amplitudes of the output signals, is transferred to their phases. Therefore, the phases of both the upconverted and downconverted signals can be tuned by simply adjusting the bias voltage. In the experiment, flat tunable full 360° phase-shift capability is achieved when the IF signals below 4-GHz are upconverted into an RF frequency between 12 to 16-GHz. A similar performance is obtained during the downconversion process. Therefore, the proposed method could be applied to the front end for phased-array beamforming networks or vector modulation for communication systems.
5. Appendix
In this Appendix, the Eq. (4) is proved and the complete expression of the signal output the PD is given. The detected signal of different polarization is independent. So, the detected signal from the fast axes can be expressed as:
Detected signal from the slow axes can be expressed as:
Due to the relation of , ϕ1 = 0 and , Equation (10) can be expressed as:
The detected signals stem from the two polarizations will add and the ultimate output electrical signal given by
Equation. (12) indicates that there will be ωs, ωLO and second harmonics of ωs at the output of PD. It should be noted that these spur components are not close to the required downconverted or upconverted signal. So, electrical filters can be used to remove them in real applications.
Funding
National Basic Research Program of China (2014CB340102); National Natural Science Foundation of China (NSFC) (61427813, 61690195, 61531003); Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications); Youth research and innovation program of BUPT.
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