## Amplitude independent RF instantaneous frequency measurement system using photonic Hilbert transform

Optics Express, Vol. 16, Issue 18, pp. 13707-13712 (2008)

http://dx.doi.org/10.1364/OE.16.013707

Acrobat PDF (208 KB)

### Abstract

A photonic instantaneous frequency measurement system capable of measuring both RF frequency and power simultaneously, is conceived and practically demonstrated. This system employs an RF photonic Hilbert transformer together with low-cost, low-frequency photo-detectors to obtain two orthogonal DC measurements. This system exhibits a frequency range of 1–10 GHz. Wider frequency range can be achieved through integration.

© 2008 Optical Society of America

## 1. Introduction

5. L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. **18**, 1188–1190 (2006). [CrossRef]

5. L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. **18**, 1188–1190 (2006). [CrossRef]

9. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Wideband RF photonic in-phase and quadrature-phase generation,” Opt. Lett. **33**, 98–100 (2008). [CrossRef] [PubMed]

5. L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. **18**, 1188–1190 (2006). [CrossRef]

## 2. Orthogonal measurement IFM concept

*V*

_{∘}

*cos*Ω

*t*, the DC voltages, present at the output of the Low-pass filters, are:

*cot*Ω

*τ*, which is a function of RF frequency but is independent of the RF tone amplitude (

*V*

_{∘}). This establishes an amplitude (

*V*

_{∘}) independent relation between the IFM output signal and the input RF frequency. Once we have established the measured frequency, the amplitude can also be measured using the output of either Module 1 or Module 2 using

*V*

_{DC1}or

*V*

_{DC2}equation, respectively. As the output signals are DC terms, this system can be implemented low-cost while still enabling broad band frequency measurement; however, practical implementation of such system, requires broad band delays and mixers which can be challenging in the microwave domain. Microwave photonics may thus be an attractive solution.

## 3. Orthogonal measurement IFM system proposal

9. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Wideband RF photonic in-phase and quadrature-phase generation,” Opt. Lett. **33**, 98–100 (2008). [CrossRef] [PubMed]

_{1}, and λ

_{2}) transversal filter with a reference tap (λ

_{∘}) in between. Carriers λ

_{∘}and λ

_{2}are combined using a 3dB optical coupler. This combined signal together with λ1 are modulated oppositely to make the desired combination as shown in Fig. 2 inset a) [9

9. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Wideband RF photonic in-phase and quadrature-phase generation,” Opt. Lett. **33**, 98–100 (2008). [CrossRef] [PubMed]

_{1}and λ

_{2}are again combined using a 3dB coupler to make the two-tap transversal filter (Fig.2 inset c)) while λ

_{°}remains separated and is used as the reference (Fig. 2 inset b)). Both signals are then detected, DC-filtered and measured by digital voltmeters.

## 4. Orthogonal measurement IFM model

_{∘}is present. Assuming the same

*V*

_{π}and loss for MZMs, the DC component of the output signal present at the output of PD1 can be described as [10]:

*P*∘ is optical power corresponding to λ

_{∘},

*V*

_{π}is the MZM half-wave voltage,

*P*

_{RF}is the RF power present at the input of each path, and

*Z*

_{PD}and

*Z*

_{in}are photo-detector output impedance and MZMs input impedance respectively. Note that MZM1 and MZM2 are assumed to have the same characteristics. The factor G can be defined as

*G*=

*r*

*G*

_{LPF}

*L*

^{2}

_{MZM}

*L*

_{W}

_{DM}

*G*

_{EDFA}where

*r*is the responsivity of the photo-detector,

*G*

_{LPF},

*L*

_{MZM},

*L*

_{WDM}, and

*G*

_{EDFA}are the gain of the low-pass filter, the MZMs optical insertion loss, WDM loss, and EDFA gain, respectively. The absolute magnitude response of the RF Path is

*M*(

*Ω*) (Fig. 2) and the phase difference of the RF Path relative to the Optical Path is

*ϕ*(Ω) (Fig. 2) [10]. For brevity, we will use

*M*and

*ϕ*instead of

*M*(Ω) and

*ϕ*(Ω). Also we defined the factors α

_{∘}, β

_{∘}, γ

*∘*as:

_{1}, and λ

_{2}), generates its own DC component assuming a linear characteristic for PD2. Therefore, the DC component produced by each wavelength, present at the output of PD2 can be described as:

_{1}, and λ

_{2}respectively. The delay between λ

_{1}and λ

_{2}caused inside the cascaded grating is τ′, and factors

*α*

_{90},

*β*

_{90},

*γ*

_{90}are defined as in Eq. (3) but with

*P*

_{∘}replaced by

*P*

_{90}where

*P*

_{90}is the optical power level of both carriers λ

_{1}and λ

_{2}. The total DC component present at the output of PD2, can then be calculated by adding Eq. (5) and Eq. (6) and simplifying the result:

## 5. Orthogonal IFM demonstration

*M*and

*ϕ*, the RF Path must first be characterized before IFM demonstration.

### 5.1. RF Path characterization

*M*) and phase response of the RF Path relative to the Optical Path (

*ϕ*). Due to dispersive nature of the co-axial cable, the frequency dependence of

*M*, and

*ϕ*will be non-trivial, and therefore must be measured empirically.

_{1}and λ

_{2}were off. The laser λ

_{∘}wavelength and power were set to λ

_{0}=1550

*nm*and

*P*

_{∘}=10.7

*d*

*Bm*≈11.7

*m*

*W*respectively. A Vector Network Analyzer (VNA) was used to characterize the RF Path. To measure the phase difference

*ϕ*of the RF Path relative to the Optical Path, Port 1 of the VNA was connected instead of RF signal generator and Port 2 of the VNA was connected to the output of the photo-detector. The VNA was then calibrated while the two ends of the co-axial cable were disconnected and replaced by two matched loads. The co-axial cable was returned while the input of MZM1 was disconnected and the Wilkinson power divider terminated with a matched load. The VNA then measured phase response of the RF Path with respect to the Optical Path. The absolute response of the RF Path (

*M*) was also measured by the VNA with no calibration needed. Figure 3 shows the measured absolute magnitude of the RF Path (

*M*) and phase of the RF Path relative to the Optical Path (

*ϕ*). The magnitude response decreased with increasing frequency. A resonance point at 5.5 GHz is evident which can be attributed to the onset higher order modes. To use this measurements in our experiments, it had been ensured that the cable was completely fixed as the resonance frequency can vary due to vibrations. The phase response is almost linear over the whole band although there are some deviations for frequencies higher than 5.5 GHz. The results of Fig. 3(a) and Fig. 3(b) show that the amplitude and phase of the RF link is well-behaved below 5 GHz, importantly, that the relative phase of the path has an almost linear dependance on frequency in that range. The system will thus be suitable for frequency measurement in this frequency range.

### 5.2. Orthogonal Measurements IFM characterization

_{∘}, λ

_{1}and λ

_{2}were set to 1550, 1551.5, and 1548.5nm respectively. The optical powers corresponding to these three wavelengths were set to 11.7, 17, and 11.7mW respectively. The factor

*G*was calculated to be 0.95, and the delay τ′ was 80ps corresponding to nulls in the transversal response at 0 and 12.5 GHz. Both MZMs input impedance (

*Z*

_{in}) and photo-detector output impedance (

*Z*

_{PD}) were 50Ω.

*V*

_{π}of the both MZMs was 5V. Four different RF power levels (PRF=3,6,9,12 dBm) were used to gain four sets of measurements. Figure 4 shows the measurements taken from digital voltmeters along with the predicted voltage obtained from Eq. (4) and (7). Excellent agreement between predicted and measured results is evident. As the nulls of the transversal filter response (0 and 12.5 GHz) are outside of the frequency measurement range (1–10GHz), they do not severely impact IFM function; however, some fading is evident at the band-edges. These measurements were then used to predict the RF frequency using Eq. (8), and the results are shown in Fig. 5(a). The RF power level was also predicted using Eq. (4) and shown in Fig. 5(b). Good agreement between measurement and prediction results is evident. Due to oscillatory nature of of Eq. (4), and Eq. (7), unambiguous frequency measurement is only possible in each half a period of Fig. 5(a) therefore, there are nine distinct bands within which frequency measurement is unambiguous. Due to zero gradient at peaks and nulls of the sine curve, sensitivity is less at edges of each band. Due to co-axial cable loss at higher frequencies (>9 GHz), some inconsistencies limit the system functionality. Equation (4) and Eq. (7), indicate a sinusoidal frequency response. By reducing the differential delay τ, the system bandwidth can be increased. Approximating

*ϕ*(Ω)=Ωτ, it can easily be seen that the sinusoidal period is

## 6. Conclusion

## References and links

1. | H. Gruchala and M. Czyzewski, “The instantaneous frequency measurement receiver in the complex electromagnetic environment,” in |

2. | J. B. Y. Tsui and D. L. Sharpin, “Frequency measurement receiver with bandwidth improvement through synchronized phase shifted sampling,” United States Patent 5198746, 30 Mar. 1993. |

3. | L. Fan, C-H. Ho, S. Lanamaluru, and K. Chang, “Wide-band reduced-size uniplanar magic-T, hybrid-ring, and de Ronde’s CPW-slot couplers,” IEEE Trans. Microwave Theory Tech. |

4. | S. Kumar, A. Mohammadi, and D. Klymyshyn, “A direct 64QAM modulator suitable for MMIC applications,” Microwave J. |

5. | L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. |

6. | A. J. Seeds and K. J. Williams, “Microwave photonics,” IEEE J. Lightwave Technol. |

7. | R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microwave Theory Technol. |

8. | J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. |

9. | H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Wideband RF photonic in-phase and quadrature-phase generation,” Opt. Lett. |

10. | N. Sarkhosh, H. Emami, L. A. Bui, and A. Mitchell, “Reduced cost microwave photonic instantaneous frequency measurement system,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

(350.4010) Other areas of optics : Microwaves

(060.5625) Fiber optics and optical communications : Radio frequency photonics

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: May 15, 2008

Revised Manuscript: August 14, 2008

Manuscript Accepted: August 19, 2008

Published: August 21, 2008

**Citation**

H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, "Amplitude independent RF
instantaneous frequency measurement
system using photonic Hilbert transform," Opt. Express **16**, 13707-13712 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-13707

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### References

- H. Gruchala and M. Czyzewski, "The instantaneous frequency measurement receiver in the complex electromagnetic environment," in Proceedings of International Conference on Microwave, RADAR, and Wireless Communications (MIKON2004) 1, 155-158 (2004).
- J. B.Y. Tsui and D. L. Sharpin, "Frequency measurement receiver with bandwidth improvement through synchronized phase shifted sampling," United States Patent 5198746, 30 Mar. 1993.
- L. Fan, C-H. Ho, S. Lanamaluru, and K. Chang, "Wide-band reduced-size uniplanar magic-T, hybrid-ring, and de Ronde�??s CPW-slot couplers," IEEE Trans. Microwave Theory Tech. 43, 2749-2758 (1995). [CrossRef]
- S. Kumar, A. Mohammadi, and D. Klymyshyn, "A direct 64QAM modulator suitable for MMIC applications," Microwave J. 40, 116-122 (1997).
- L. V. T. Nguyen and D. B. Hunter, "A photonic technique for microwave frequency measurement," IEEE Photon. Technol. Lett. 18, 1188-1190 (2006). [CrossRef]
- A. J. Seeds and K. J. Williams, "Microwave photonics," J. Lightwave Technol. 24, 4628-4641 (2006). [CrossRef]
- R. A. Minasian, "Photonic signal processing of microwave signals," IEEE Trans. Microwave Theory Tech. 54, 832-846 (2006). [CrossRef]
- J. Capmany, B. Ortega, and D. Pastor, "A tutorial on microwave photonic filters," J. Lightwave Technol. 24, 201-229 (2006). [CrossRef]
- H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, "Wideband RF photonic in-phase and quadrature-phase generation," Opt. Lett. 33, 98-100 (2008). [CrossRef] [PubMed]
- N. Sarkhosh, H. Emami, L. A. Bui, and A. Mitchell, "Reduced cost microwave photonic instantaneous frequency measurement system," IEEE Photon. Technol. Lett. (In Press).

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