## Abstract

A photonic approach to measuring microwave frequency with digital results is proposed and experimentally demonstrated. In the proposed approach, *N* photonic phase-shifted filters with a phase shift increment of *π/N* in the transmission responses are designed. The filters are then employed to process the single optical sideband generated by applying a microwave signal to a single sideband suppressed-carrier (SSB-SC) modulation module, to perform frequency-to-amplitude conversion and analog-to-digital conversion simultaneously. After the implementation of power detection and decision operation to the filtered optical sideband, an *N-*bit result in the form of the circular code is obtained, which indicates the frequency of the microwave signal. A proof-of-concept experiment is performed to verify the proposed approach and a 5-bit circular code is generated to indicate microwave frequency up to 40 GHz.

©2011 Optical Society of America

## 1. Introduction

Microwave signal characterization is of critical importance in various fields such as electronic warfare receivers, radars, and next-generation wideband communications. As for microwave signal characterization, parameters of interest include frequency, amplitude, direction of arrival, modulation format, pulse descriptor word, and so on. Among these parameters, frequency is one of the most significant parameters to be measured [1,2]. A variety of techniques for frequency measurement have been proposed, which can be categorized by analog results or digital outputs. With the rapid development of digital signal processing, it is desirable to realize digital frequency measurement that shows a series of advantages such as robustness of digital signal processing, easy and simple storage of digital data, and compatibility to other digital setups [3].

In both analog techniques and digital techniques aforementioned, a large instantaneous bandwidth for “wide-open” operation is highly required, for the bandwidth coverage for microwave/millimeter-wave signals ranges from 0 to 300 GHz in electronic warfare and radars [3]. Conventional electronic methods cannot offer such a large instantaneous bandwidth, however, microwave photonics provides a promising way to solve this issue [4–7] due to the inherent feature of photonics in large instantaneous bandwidth. Recently, various photonic approaches have been proposed to measure the frequency of microwave signals. Microwave frequency can be discriminated from two frequency-dependent microwave power functions [8–12] or two responses of microwave photonic filters [13–16]. By using optical channlization [17,18], optical mixing [19–21], or optical comb/edge filters [22–25], frequency measurement could be realized as well. In most of these photonic approaches analog results are derived, however, digital results are preferred according to the advantages of digital signal processing.

In the paper, a photonic approach with digital results is proposed for microwave frequency measurement. By using an array of phase-shifted filters, a digital circular code is generated to indicate the microwave frequency.

## 2. Principle

The apparatus for the proposed measurement approach is shown in Fig. 1 . An incoming microwave signal is applied to externally modulate the light wave from a CW laser. Under the condition of single sideband suppressed-carrier (SSB-SC) modulation, a single optical sideband is generated and is coupled into photonic phase-shifted filters and a reference branch. The phase-shifted filters, which are the key components of the apparatus, have isomorphic transmission responses with an identical free spectral range ($FSR$) but different phase shifts. To understand the operation of the proposed system, we start from the discussions on the transmission responses of the phase-shifted filters.

Firstly, it is well known that the transmission response of a two-tap delay-line interferometer (i.e., a comb filter) can be expressed as $F(f)=[1+\mathrm{cos}(2\pi f/FSR+{\theta}_{0})]/2$, where $f$ is the optical frequency, $FSR$ is the free spectral range, and ${\theta}_{0}$ is the initial phase. As the frequency of the laser is set to be the reference value (i.e., ${f}_{0}$) of the optical frequency coordinate, the transmission response can be rewritten as $F({f}_{m})=[1+\mathrm{cos}(2\pi {f}_{m}/FSR+{\theta}_{0})]/2$, where ${f}_{m}=f-{f}_{0}$ is the microwave frequency to be measured and also the offset frequency from the optical carrier. A number of comb filters with discrete phase shifts following a linear distribution as $\Delta {\theta}_{k}=(k-1)\pi /N$ are designed, to meet the requirement of the circular encoding. Namely, a phase shift increment of $\pi /N$ is introduced to the transmission responses. Therefore, the transmission response of the *k*-th filter is derived as

*k*-th filter and that of the reference branch, an optical power ratio can be derived as

Based on the power ratio, an analog-to-digital conversion can be done. For the *k*-th filter, the output bit is labeled as “1” if the power ratio is not less than 0.5; otherwise, the bit is encoded as “0”. Therefore, we obtain an *N*-bit circular-code result which indicates the frequency value. An unambiguous measurement range of full $FSR$ and a resolution of $FSR/(2N)$ are realized. Note that the function of the phase-shifted filters is twofold, to perform frequency-to-amplitude conversion and analog-to-digital conversion.

A demonstration of the above principle is clearly shown in Fig. 2
when *N* = 8. From Eqs. (1) and (3), eight phase-shifted transmission responses or eight power ratios are present. The $FSR$ is divided into sixteen sub-ranges, each of which corresponds to a resolution of $FSR/16$ in the frequency domain or to a relative phase shift of $\pi /8$ in the phase domain. Then 8-bit digits in the form of the circular code [25] are obtained for all sub-ranges as the threshold is specified as 0.5 for the decision operation.

## 3. Experiment and results

An experiment for obtaining digital measurement results is performed. To begin with, five phase-shifted filters are designed using a single high-birefringence (Hi-Bi) element. As shown in Fig. 3(a)
, a Hi-Bi element in conjunction with five branches is employed. When the optical sideband is linearly polarized at an angle of 45° with respect to one principal axis of the Hi-Bi element, identical *FSRs* are achieved for all five branches or filters, due to the use of the same differential group delay. On the other hand, at each branch an independent polarization controller is used to adjust the polarization angle and the initial phase of the optical sideband. Thus phase-shifted transmission responses are generated at the outputs of the five branches.

The SSB-SC modulation is implemented via the use of a carrier suppression setup in conjunction with an optical pass filter having a very narrow transition band. The optical filter removes the + 1^{st} or the −1^{st} sideband and a single optical sideband is generated after the external modulation [25]. A microwave signal with its frequency sweeping within the range of 14~40 GHz, is applied to the modulation module. Here the upper boundary is limited by the bandwidth of the modulator and the lower one is limited by the SSB-SC modulation. The optical powers detected at the outputs of the five branches and the reference branch, are depicted in Fig. 3(b).

After a power comparison, five power ratios shown in Fig. 3(c) are derived, indicating five phase factors as $-3\pi \text{/}5$, $-2\pi \text{/}5$, $-\pi \text{/}5$, $0$, and $\pi \text{/}5$. Like the use of another five phase factors of $-4\pi \text{/}5$, $-3\pi \text{/}5$, $-2\pi \text{/}5$, $-\pi \text{/}5$, and $0$, a phase shift increment of $\pi \text{/}5$ is observed as well. To clarify the analog-to-digital conversion in a simple way, the power ratios in linear scale are shown in Fig. 4 . By setting 0.5 as the decision threshold, 5-bit digital results in the form of the circular code [26] are achieved. The full $FSR$ (i.e., 44 GHz) is divided into ten sub-ranges and each sub-range covers a measurement range of 4.4 GHz. For example, “00011” covers the sub-range of 24.2~28.6 GHz. More importantly, in the measurement range of 14~40 GHz, the experimental data (circles) are highly consistent with the theoretical trends (solid lines) and the digital results agree well with the values of the input frequencies. Therefore digital circular-code results are experimentally verified within the range of 14~40 GHz.

Due to the limit on the measurement range of the experiment setup, the experimental results cannot cover all the sub-ranges. However, seven sub-ranges out of ten have already been covered, indicating that the measurement ambiguity within a measurement range of $FSR/2$ in the previous photonic approaches [22,23] is effectively eliminated. Then a measurement range of 44 G and a resolution of 4.4 GHz would result as an effective SSB-SC modulation module is realized.

## 4. Discussions

The encoding efficiency, the sensitivity, and the stability of the proposed approach and of the experiment are discussed here with more details.

Digital circular-code results with a code length of *2N* are generated in the proposed approach and the experiment, which is regarded as a simple and minimum-error encoding way. On the one hand, compared with the Gray code or the natural binary code with a code length of *2 ^{N}*, the encoding efficiency here is lower. For instance, the number of effective bits for the 5-bit circular-code results in the experiment is 3.32. On the other hand, the circular code is much easier to be implemented for the digital frequency measurement since the phase-shifted filters with identical

*FSRs*can be designed using the same Hi-Bi element. While for the Gray code or the natural binary code results, filters with several exactly multiplied

*FSRs*are required, which are more practically difficult to develop.

The sensitivity and the dynamic range are mostly determined by the half-wave voltage of the employed electro-optic modulator (MPZ-LN). To ensure measurement errors to be less than 0.2 GHz, the minimum power of the microwave signal should be greater than –40.2 dBm while ${V}_{\pi}=7V$. Meanwhile, the maximum power should be less than −5.6 dBm to make sure that the 2^{nd} sidebands are too small to be detected by the optical power-meter. Thus the dynamic range of the frequency measurement is 34.6 dB.

The stability of the experiment setup would suffer from the drift of the phase shifts under the influence of environment. For simplicity, we investigate the influence of the temperature on the stability of the phase shifts. The discrete phase shifts are set by detecting the optical power at the output of each filter, when no external modulation is implemented. For instance, a maximum power or half maximum power corresponds to a phase shift of 0 or $\pi /3$, respectively. In order to avoid encoding errors, in the experiment setup a drift less than 0.01π should be ensured such that a temperature stability of $\pm 2.6K$is required. This temperature stability can be achieved using a commercially available temperature controller. Also, the wavelength of the laser source can be synchronously tuned to compensate the drift of all the phase shifts using the feedback from temperature change, to enable a stable frequency measurement. In addition, the stability of the phase-shifted filters can be improved using other solutions, such as the use of a photonic-crystal fiber with low temperature-dependent birefringence coefficient or the use of the photonic integrated circuits or commercial tunable interferometers.

## 5. Summary

In conclusion, with the use of photonic phase-shifted filters, an approach having digital circular-code results has been proposed and verified for microwave frequency measurement. When the discrete phase shifts of the *N* transmission responses are specified as $(k-1)\pi /N$, *N*-bit circular codes were generated. The measurement range and the resolution were $FSR$ and $FSR/(2N)$, respectively. An experiment with 5-bit circular-code outputs was implemented to measure the frequency up to 40 GHz. In addition, the stability, the sensitivity, and the encoding efficiency are discussed.

## Acknowledgments

The work was supported by National Natural Science Foundation of China (61101053, 71090402/G01), “973” Project (2012CB315704), Research Fund for the Doctoral Program of Higher Education of China (20100184120007, Funding for Priority Areas), and Fundamental Research Funds for the Central Universities (SWJTU09CX033, SWJTU10ZT05).

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