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untitled IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 18, SEPTEMBER 15, 2008 1521 Reduced Cost Photonic Instantaneous Frequency Measurement System Niusha Sarkhosh, Member, IEEE, Hossein Emami, Lam Bui, Member, IEEE, and Arnan Mitchell, Member, IEEE Abstract—A wideband photonic instantaneous frequency mea- surement system is proposed and practically demonstrated. This system employs only a low-frequency inexpensive photodetector and thus the system cost is reduced. Index Terms—Frequency measurement, microwave photonics. I. INTRODUCTION I NSTANTANEOUS frequency measurement (IFM) is im-portant for modern radar warning receivers, providing ini- tial threat classification of incoming signals and suggesting fre- quency ranges to focus processing resources. Traditional IFM receivers have been implemented simply using interferometers formed from hybrid couplers and delay lines [1][2]. The bandwidth of such implementations can be limited due to unwanted radiation and dispersion occurring inside radio-frequency (RF) devices [3], [4]. On the other hand, microwave photonics has been suggested as a means of increasing the bandwidth of signal processing sys- tems [5]–[8]. Broadband, low-noise optical modulators up-con- vert the RF signal to the optical domain where it is photonically processed and transmitted via optical fiber. Broadband photode- tectors then down-convert it to the RF domain. Photonics could offer advantages for broadband IFM systems. A recent photonics IFM was demonstrated using broadband high-performance photodetectors. However, banks of these devices would be prohibitively expensive [5]. In this letter, an alternate photonic IFM approach using low- cost low-frequency photodetectors is proposed and practically demonstrated, measuring frequencies from 1 to 10 GHz. II. IFM CONCEPT Fig. 1 shows a possible IFM system [1][2]. An RF tone is di- vided into two equal portions. One portion is delayed relative to the other by time . The two RF tones are then multiplied to- gether and the result is low-pass filtered. The output is a voltage proportional to , which varies with input RF frequency. This system can, therefore, be used to achieve a low- cost wideband IFM receiver; however, practical implementation of such a system would require broadband delays and mixers which can be challenging in the RF domain. Manuscript received April 2, 2008; revised May 28, 2008. The authors are with the Micro Electronics and Material Technology Center, School of Electrical and Computer Engineering, Royal Mel- bourne Institute of Technology, Melbourne, Victoria 3001, Austalia (e-mail:
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2008.927895 Fig. 1. Block diagram of an electrical IFM system. III. PHOTONIC IFM The system of Fig. 1 exhibits direct current (dc) output which is proportional to the RF frequency to be measured. Photonics can enable a broad frequency detection range and low-cost pho- todetectors could be used to reduce the total system cost. A. Photonic IFM System Configuration Fig. 2 shows the experimental setup of the proposed photonic IFM system. An RF signal generator produces a single RF tone which is divided equally into two portions using a Wilkinson power divider feeding two arms of the IFM system. These two arms are labelled the optical path and the RF path on Fig. 2. The RF tone in the optical path is input to a Mach–Zehnder modu- lator (MZM1) biased at quadrature . MZM1 modulates an optical carrier with wavelength of produced by a laser diode. The modulated carrier then traverses a fiber patch cord and ex- periences an optical delay. The second portion of the RF tone in the RF path is delayed using a length of co-axial cable, and is input to a second modulator (MZM2) (biased at ) modulating the optical carrier a second time. The twice-modulated signal is then detected by a photodetector. The output of the photode- tector is then low-pass filtered and measured by a digital volt- meter. Having conceived a photonic IFM system configuration, we now develop a theoretical model to accurately predict the fre- quency dependence of the dc term of the photodetector output. B. Photonic IFM Model An optical carrier with angular frequency and power can be represented as , where . Similarly, the RF signal with angular frequency and power exerts an input voltage of , where across an input impedance of . For the system of Fig. 2, the RF signal is divided 50 : 50 using a broadband Wilkinson power divider; the input voltage to the modulator will thus be . The output of the modulator is (1) where and are the modulator insertion loss, dc bias voltage, and half-wave voltage, respectively. Substituting 1041-1135/$25.00 © 2008 IEEE e01109 Highlight e01109 Rectangle e01109 Rectangle e01109 Rectangle e01109 Rectangle e01109 Highlight e01109 Highlight e01109 Highlight 1522 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 20, NO. 18, SEPTEMBER 15, 2008 Fig. 2. Experimental setup of proposed photonic IFM. the expression for and expanding the right-hand side of (1) into a Fourier series using Bessel functions of the first kind, the dc, fundamental, and harmonic components of the modu- lated optical carrier can be separated. Ignoring the harmonic fre- quency components, can be approximated as (2) The output of MZM1 becomes the input to MZM2. This is modulated by the same input RF signal delayed by a differ- ential time with respect to the optically carried RF signal. Since the modulating signal is attenuated and delayed by the co-axial cable in a nontrivial way, it should be represented as , where is the frequency-depen- dent amplitude response of the co-axial cable and denotes the frequency-dependent phase response of the co-axial cable relative to the optical path. For brievity, we will use and instead of and . Using (2) with as input, the output of MZM2 is (3) Assuming similar modulators are used and both are biased at quadrature, we have and the sine and cosine of bias terms of (3) are all equal to . In addition, for V and small , the following inequalities also hold and . Bessel terms of (3) can be approximated (4) Therefore, (3) can be written as (5) where and are (6) where is detected by the photodetector. The photodetector voltage can be estimated as (7) where , and are the photodetector load impedance and re- sponsivity, respectively, and is voltage gain of the low-pass filter. Substituting (5) into (7), and simplifying by dropping the terms and , the dc component of can be approximated as (8) where the factor is defined as . It is evi- dent from (8) that the photodetector dc voltage includes fre- quency-dependent functions and . Therefore, it can be used to measure the input RF frequency . IV. PHOTONIC IFM DEMONSTRATION Having established a relationship between the dc output of the photodetector and RF input frequency, it should now be pos- sible to demonstrate frequency measurement. However, as each parameter in (8) is known, except and , the RF path must first be empirically characterized. A. RF Path Characterization To predict the dc voltage of the photodetector by (8), it is nec- essary to have the absolute magnitude response of the RF path and phase response of the RF path relative to the optical path as a function of frequency . Due to dispersive nature of the co-axial cable, the frequency dependence of , and will be nontrivial, and must be measured empirically. The system was configured as shown in Fig. 2. The laser wavelength and power were set to nm and mW. The factor was calculated to be 1.2 and the RF signal generator output power was set to 20 mW which resulted in mW as there was 4-dB loss in the Wilkinson power divider and RF cables. The input impedance of both MZMs SARKHOSH et al.: REDUCED COST PHOTONIC IFM SYSTEM 1523 Fig. 3. (a) Absolute magnitude response ���, and (b) phase response of the RF path relative to the optical path ���. Fig. 4. (a) Measured and predicted photodetector dc voltage. (b) Measured fre- quency versus input frequency. and the output impedance of the photodetector were 50 . The of the both MZMs was 5 V. A vector network analyzer (VNA) was used to characterize the RF path. To measure the phase response of the RF path rel- ative to the optical path , Port 1 of the VNA was connected instead of the RF signal generator and Port 2 was connected to the output of the photodetector. The VNA was then calibrated with the two ends of the co-axial cable replaced by matched loads. The cable was returned while the input of MZM1 was ter- minated in a matched load. The VNA then measured the phase response of the RF path with respect to the optical path. The for- ward transmission amplitude response of the RF path was also measured using the VNA. Fig. 3 shows the measured magnitude of the forward trans- mission of the RF path and phase of the RF path relative to the optical path. The magnitude response decreases with increasing frequency as expected. A resonance at 5.5 GHz is evident which can be attributed to the onset higher order modes. The cable was stabilized as the resonance frequency could vary due to vibra- tions. The phase response is almost linear over the whole band neglecting minor deviations for frequencies higher than 5.5 GHz due to the impedance loading of higher order modes. Fig. 4(a) and (b) shows that the amplitude and phase of the RF path are well-behaved below 5 GHz, where the relative phase is almost linear with frequency. The system will thus be suitable for fre- quency measurement in this frequency range. B. IFM Characterization Having established all of the parameters in (8), the operation of the IFM system can now be demonstrated. The system was configured as depicted in Fig. 2 with the parameters defined in Section IV-A. The dc voltage was measured as a function of RF input frequency as presented in Fig. 4(a). Clear oscillatory behavior is evident as predicted. The response predicted using (8) is also presented in Fig. 4; excellent agreement is evident. To perform frequency measurement, a look-up table was gen- erated using (8) and the empirically measured RF cable magni- tude and phase response ( and ) relating measured dc voltage to input RF frequency as depicted in Fig. 3(a). This look-up table was then used to find the input frequencies that correspond to measured dc outputs. Due to the oscillatory nature of (8), un- ambiguous frequency measurement is only possible within each half period of Fig. 4(a). Restricting the frequency mapping to one half period (2.2–3 GHz), unambiguous frequency measure- ment can be demonstrated. The measured frequencies in the 2.2- to 3-GHz band are presented in Fig. 4(b). Fig. 4(a) shows that oscillations in (8) can be detected up to about 10 GHz. Beyond this frequency, losses