# Extending OTDR Distance Span by External Front-End Optical Preamplifier

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## Abstract

**:**

## 1. Introduction

## 2. Analysis

#### 2.1. Basic OTDR Model

_{0}into the fiber, then the power P

_{T}(z) of the pulse propagating downstream the fiber, is the exponential function of distance z of the observation point from the fiber near-end (OTDR):

_{T}(z) = P

_{0}× 10

^{−α·z/10}

_{s}+ α

_{a}is the sum of the scattering and absorption losses expressed in dB/km.

_{s}(z) = α′

_{s}× ΔzP

_{T}(z)

_{s}= 0.23·α

_{s}and Δz denote the fiber loss and the light pulse length, respectively.

_{gr}= w × c/n

_{gr}≈ w × c/n

_{gr}, n

_{gr}, and c denote the pulse duration, the group velocity in the fiber, the group refractive index (justifiably approximated by the ordinary index n), and the speed of light in vacuum, respectively.

_{BS}(z) = T

_{s}× S × α′

_{s}× Δz × P

_{0}× 10

^{−2α·z/10}

_{s}is the transmission coefficient of the OTDR directional coupler.

_{BS}(0) = T

_{s}× S × α′

_{s}× Δz × P

_{0}

_{BS}(L) = T

_{s}× S × α′

_{s}× Δz × P

_{0}× 10

^{−2α·L/10}

_{BS}(0) being about 50 dB below the incidence power level P

_{0}, is close to the noise floor of the receiver, and is therefore commonly referred to as Noise Equivalent Power (NEP) [10], so that the SNR must be increased by averaging, which effectively reduces NEP to:

_{eff}= NEP/n

^{1/2}

_{eff}, Figure 3.

#### 2.2. OTDR Performance Parameters–Dynamic Range and Distance Span

_{BS}(0) − NEP

_{eff}]

_{eff}. A way to do it is averaging, as it is already elaborated above and illustrated in Figure 3, where significant improvements are achieved within the first three minutes of averaging, implying no need for a longer average time.

#### 2.3. OTDR Receiver Noise Floor Model

#### 2.3.1. Noise Floor vs. Noise Figure

_{no}at the receiver output than the input noise power spectral density P

_{ni}multiplied by the transmission gain G of the device, assuming shot noise at the input [11]:

_{no}/G × P

_{ni}= 1 + NEP

_{eff}/G × P

_{ni}

_{eff}is linear with the noise figure F:

_{eff}= (F − 1) × G × P

_{ni}

_{eff}and consequent extension of its dynamic range and, finally, distance span [1].

#### 2.3.2. APD Noise Figure

^{−15}W/Hz

^{½}[12,13] determined mostly by shot noise due to stochastic behavior of photons and signal multiplication therefore the name: Poisson noise, which is sometimes also referred to as “gain noise” [11], and described by the excess noise factor ENF [12]. Moreover, a number of other affecters determine the APD noise floor, among them the reverse bias voltage and load. As related to the latter, Johnson noise is caused by the thermal motion of charged particles in a resistive element, and is typically much stronger than the intrinsic shot noise for low bandwidth applications, when the effective noise floor is therefore to the large extent determined by the load resistance.

#### 2.3.3. ODC Noise Figure

#### 2.3.4. Noise Figure of Cascaded ODC and APD

_{1,2}of the cascaded two blocks is to the large extent determined by the noise figure F

_{1}of the first block (with large gain G

_{1}>> 1) in the series:

_{1,2}=F

_{1}+ (F

_{2}− 1)/G

_{1}≈ F

_{1}

_{DC}(equal to its NF), deteriorates the noise figure of the cascade Equation (11) even further to:

_{OTDR}=A

_{DC}+ (F

_{APD}− 1) × A

_{DC}= A

_{DC}× F

_{APD}

#### 2.3.5. Noise Figure of OA with Small-Loss Coupling

## 3. OTDR Dynamic Range and Distance Span Extension by Inserting Front-End OA

#### 3.1. Dynamic Range and Distance Span Extension Prediction Model

_{OC+OA}=A

_{OC}× F

_{OA}

_{OC}<< A

_{DC}, and 1 < F

_{OA}<< F

_{APD}, from Equation (12) and Equation (13), it implies that:

_{OC+OA}<< F

_{OTDR}

_{OC+OA+OTDR}=F

_{OC+OA}+ (F

_{OTDR}– 1)/G

_{OC+OA}≈ F

_{OC+OA}= A

_{OC}× F

_{OA}

_{OC+OA}≈ G

_{OA}>> A

_{OC}(quite justifiably as G

_{OA}is of the order of 10

^{3}and thereby much larger than the OC insertion loss A

_{OC}).

_{OC+OA+OTDR}≈ A

_{OC}·F

_{OA}<< F

_{OTDR}= A

_{DC}× F

_{APD}

_{BS}(0) – NEP

_{OC+OA+OTDR}] – [P

_{BS}(0) – NEP

_{OTDR}] = NEP

_{OTDR}– NEP

_{OC+OA+OTDR}

_{ni}, the noise floor NEP

_{OTDR}for the OTDR alone is:

_{OTDR}= (F

_{OTDR}– 1) × G

_{OTDR}× P

_{ni}

_{OC+OA+OTDR}≈ NEP

_{OA}= (F

_{OA}– 1) × G

_{OA}× P

_{ni}

_{OTDR}(specifically its constituents A

_{DC}and F

_{APD}) and gain G

_{OTDR}are rarely given in technical specifications, whereas its noise floor NEP

_{OTDR}(in dB units) can be easily estimated by subtracting the specified dynamic range from the maximal output optical power level.

_{OA}and gain G

_{OA}is always specified, whereas it is not the case with the OA noise floor NEP

_{OA}.

_{sOTDR}/P

_{nOTDR}= G

_{OTDR}·S

_{inp}/NEP

_{OTDR}= 1

_{inp}is the input signal power, and introducing the optical pre-amplifier implies the following SNR at the OTDR receiver output:

_{sOA+OTDR}/P

_{nOA+OTDR}= G

_{OA}·× G

_{OTDR}·× S

_{inp}/(G

_{OTDR}·× NEP

_{OA}+ NEP

_{OTDR})

_{sOA+OTDR}/P

_{nOA+OTDR}= G

_{OA}·× NEP

_{OTDR}/(G

_{OTDR}·× NEP

_{OA}+ NEP

_{OTDR})

_{sOA+OTDR}/P

_{nOA+OTDR})/1 = G

_{OA}·× NEP

_{OTDR}/(G

_{OTDR}·× NEP

_{OA}+ NEP

_{OTDR})

_{OA}[dB] + NEP

_{OTDR}[dBm] – 10 log(G

_{OTDR}·NEP

_{OA}+ NEP

_{OTDR})

_{OA+OTDR}[km] = ΔDR[dB]/2 × α[dB/km]

#### 3.2. Dynamic Range and Distance Span Extension Prediction Values

_{OTDR}value to be close to −50 dBm, which corresponds to NEP

_{OTDR}= 10 nW on the linear scale.

_{OA}of 30 dB and the noise figure F

_{OA}of 6 dB [22]. The latter implies the OA noise floor spectral density value of 10

^{−5}nW/Hz

^{1/2}[11], so that the noise bandwidth of 0.2 MHz (in accordance with the pulse duration of 5 μs), results with:

_{OA}= 10

^{−5}nW/Hz

^{1/2}·× (2·10

^{5})

^{½}× Hz

^{1/2}= 447 × 10

^{−5}nW

_{OTDR}= 10 dB.

## 4. Preliminary Test Results

#### 4.1. Test System

#### 4.2. Results

#### 4.3. Discussion and Potential Model Enhancements

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**OTDR trace. (

**a**) with a short pulse for better event resolution; (

**b**) with a longer pulse for a longer span.

Wavelength | 1300 nm | 1550 nm |
---|---|---|

A = α_{s} + α_{a} | 0.4 dB/km = 1.092/km | 0.2 dB/km = 1.046/km |

α′_{s} | 0.074/km | 0.036/km |

W | 1 μs | 1 μs |

T_{s} | 1 | 1 |

S | 9.8 × 10^{−4} | 9.8 × 10^{−4} |

P_{BS}(0)/P_{0} | −48.4 dB | −51.5 dB |

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**MDPI and ACS Style**

Lipovac, A.; Lipovac, V.; Hamza, M.; Batoš, V.
Extending OTDR Distance Span by External Front-End Optical Preamplifier. *Electronics* **2021**, *10*, 2275.
https://doi.org/10.3390/electronics10182275

**AMA Style**

Lipovac A, Lipovac V, Hamza M, Batoš V.
Extending OTDR Distance Span by External Front-End Optical Preamplifier. *Electronics*. 2021; 10(18):2275.
https://doi.org/10.3390/electronics10182275

**Chicago/Turabian Style**

Lipovac, Adriana, Vlatko Lipovac, Mirza Hamza, and Vedran Batoš.
2021. "Extending OTDR Distance Span by External Front-End Optical Preamplifier" *Electronics* 10, no. 18: 2275.
https://doi.org/10.3390/electronics10182275