THE IMPACT OF THE PHOTODIODE ONTHE NONLINEARITY OF MICROWAVEPHOTONIC LINKS

Jun Hong, Chun Yang, Xiang-Hua Li, Yu-Hua Chong, andHong-Da XuSchool of Electronic Science and Engineering, SoutheastUniversity, Nanjing, Jiangsu province, China; Correspondingauthor: yangchun_seu@163.com

Received 31 January 2011

ABSTRACT: A new theory model for the nonlinearity of thecommercial PIN photodiodes (PDs) is presented and verified by

experiments in this article. The gain and the third-order spurious-freedynamic range (SFDR3) of a basic microwave photonic link have also

been studied including the nonlinearity of the PD. Numerical studiesindicate that the nonlinearity of PD decreases the practical microwavephotonic links’ performance. Compared with ideal PD links, the

maximum values of signal gain and SFDR3 in practical links deteriorateby 1.7 and 3 dB, respectively, at various biased points for modulator.VC 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:2325–

2327, 2011; View this article online at wileyonlinelibrary.com.

DOI 10.1002/mop.26268

Key words: microwave photonic link; spurious-free dynamic range;

nonlinearity; photodiode

1. INTRODUCTION

Microwave photonic links offer many advantages such as large

bandwidth, low-frequency-dependent loss, and immunity to elec-

tromagnetic interference. These characteristics make them prom-

ising alternatives for functions traditionally fulfilled by all-elec-

tronic components in both commercial and military application,

including cable-television, remote antenna, radio frequency (RF)

system, and so on [1–4].

The important performance criteria of microwave photonic

links include: (1) microwave gain, (2) noise figure, and (3) spu-

rious-free dynamic range (SFDR), which are dependent on the

nonlinearity of each component in the link. Previous researches

on the nonlinearity of the microwave photonic links include a

lot of literatures [5–9], where a lot of performances for micro-

wave photonic links have been studied systematically, but most

of them focused on the nonlinearity of Mach–Zehnder modulator

(MZM) and regarded photodiode (PD) as a linear device. This

would result in inconsistence between theory and practical links.

In fact, PIN PD is not an ideal linear device, especially working

near saturation. Lots of researches on the nonlinear model of the

PIN PD have been reported recently, but most of them are very

complex and not easy to be used in link analysis and design. An

accurate and simple nonlinear model of PD still needs to be

developed.

In this article, we propose a novel empirical model for the

nonlinearity of PD which agrees well with experimental results.

Considering the nonlinearities of both MZM and PD, we derived

the expressions of the gain (G) and the third-order spurious-free

dynamic range (SFDR3) of the microwave photonic link. The

results show that the nonlinearity of the link can be described

accurately based on this new PD model.

2. THEORY

The microwave photonic link studied in this article is shown in

Figure 1, which is a basic microwave photonic link and con-

structed mainly by a laser source, a MZM and a PIN PD.

2.1. Modeling for the PDBecause PIN PD is a nonlinear device, it is necessary to build a

PD nonlinear model that can accurately describe the nonlinear

characteristics. In previous articles, theory derivation for model-

ing the nonlinearity of PD mainly based on the rate equation

and the equivalent circuit is usually complex and difficult for

practical applications. Here, we propose a simple empirical for-

mula for characterizing the photocurrent with input optical

power as follows

IL ¼ Prqss

1þ PrqssIs

þ b� �c (1)

where IL and Is are the output current and saturation current,

respectively, Pr is the received average optical power, qss is the

small-signal input responsivity, and b and c are the parameters

that characterize the PD nonlinearity. The small-signal input

responsivity qss is about 0.4 for the commercial PIN PD detector

(EM4 169-03) used in this experiment. (Note that the parameter

S21 of this PD is greater than 20 GHz, therefore the responsivity

at DC and that at 5 GHz is nearly similar, which has been veri-

fied by experiments.) As shown in Figure 2, we found that Eq.

(1) agrees well with the experimental data in the condition of b¼ �2/3 and c ¼ 2. The other dotted lines are the polynomial

fitting curves that will be introduced below.

2.2. Modeling for the Microwave Photonic LinkThe modulated optical signal after the MZM can be expressed as

Pr ¼ 1

2aPo 1þ f cos

pVp

Vm

� �� �(2)

where a is the insertion loss factor of the modulator, Vp is the

half-wave voltage, Vm is the microwave signal plus dc biasing

voltage, Po is the average input optical power, and fFigure 1 Architecture of the photonic microwave link

Figure 2 Experimental (circle spots) and fitting data (lines) of output

current as a function of input average optical power

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 53, No. 10, October 2011 2325

determines the extinction ratio of the modulator by 1þf1�f. In the

following analysis, we assume f ¼ 1. The microwave signal

applied to the modulator is assumed as a sinusoidal wave with

angular frequency x, V(t) ¼ VMW sin(xt). The dc phase-shift

amplitude is defined by /b ¼ pVb

Vpand the microwave phase-shift

amplitude is /MW ¼ pVMW

Vp. We expand Eq. (2) with the Bessel

function of the first kind, and the modulated optical signal can

be expressed as

Pr ¼ 1

2apo½1þ J0ð/MWÞ cosð/bÞ� � apo sinð/bÞ

�Xþ1

0

J2nþ1ð/MWÞ sinðð2nþ 1ÞxtÞ

þ apo cosð/bÞXþ1

1

J2nð/MWÞ cosð2nxtÞ

(3)

To simplify Eq. (3) above, Jnð/MWÞ � ð/MWÞn=ð2nn!Þ can be

used in the case of small-signal approximation for VMW � Vp.

The theory formula for PD given by Eq. (1) is expanded

with Taylor polynomial as

IL ¼X1i¼1

biðPrÞi (4)

where bi is the constant coefficient of the i th harmonic modulated

optical signal. In Figure 2, the measured response curve of PD is

fitted by Eq. (4), where dashed, dotted, and dash-dotted lines rep-

resent the third, fourth, and fifth order fitting, respectively. It is

indicated that the accurate is higher for higher fitting order. It is

also easy to see that when the average input power is below 6

mW, the fifth expanding of Eq. (4) has sufficient accuracy. If the

operating characteristics of saturated zone are wanted to be under-

stood, the higher order expanding of Eq. (4) is needed. From Eqs.

(3) and (4), the fundamental and the harmonic signals in the prac-

tical link can be calculated and written as

Pnx � 1

2aPo cos /b þ

np2

� �Jnð/MWÞ

� �2�

P1i¼1

bi12aPoð1þ J0ð/MWÞ cosð/bÞÞ

� �i�1

� �2

ZL ð5Þ

The corresponding fundamental and harmonic signals in the

ideal link without PD linearity can also be calculated

P0nx � 1

2qaPo cos /b þ

np2

� �Jnð/MWÞ

� �2ZL (6)

Based on Eqs. (5) and (6), we can get the expressions of the

signal gain in the practical and ideal links, respectively, as follow

G ¼ aPo sinð/bÞp

2Vp

� �2

�

P1i¼1

bi12aPoð1þ J0ð/MWÞ cosð/bÞÞ

� �i�1

� �2

ZLZin ð7ÞG0 ¼ aqPo sinð/bÞ

p2Vp

� �2

ZLZin (8)

where ZL is the output impedance and Zin is the input imped-

ance. As for a typical intensity modulation–direct detection link,

the expressions of the SFDR3 can be derived as [10]

SFDR3 ¼ OIP3

Nout

� �23

(9)

where OIP3 ¼ ðpxÞ32=ðp3xÞ

12 and Nout ¼ Nth þ Nshot þ NRIN. Nth

is the thermal noise, Nth ¼ (1þG)kBT; Nshot is the shot noise of

the PD, Nshot ¼ 2qIdcZL; NRIN is the relative intensity noise of

the laser diode (LD), NRIN ¼ RinI2dcZL. The SFDR3 and SFDR03

can be written as

SFDR3 � J1ð/MWÞ2J3ð/MWÞ�13N

�23

outffiffiffi2

p

2aPo

ffiffiffiffiffiZL

psin/b �

X1i¼1

bi1

2aPoð1þJ0ð/MWÞ cosð/bÞÞ

� � !i�124

35

43

ð10Þ

SFDR03� J1ð/MWÞ2J3ð/MWÞ�1

3N�2

3out

ffiffiffi2

p

2aqPo

ffiffiffiffiffiZL

psin/b

� �43

(11)

3. EXPERIMENTS AND ANALYSIS

Experiments based on the schematic shown in Figure 1 are

performed. The LD used in experiments is a distributed feed-

back semiconductor laser (Ortel 1772) and the Rin equals to

�165 dBc/Hz at the operating frequency of 5 GHz and power

of 18 mW. The electro-optic modulator is a MZM (Agere

2623), and its Vp is about 3.2V at 5 GHz and its insertion

loss is about �3.5 dB. Modulator low-biasing technology was

usually employed for enlarging the SFDR3, and therefore

we will verify the impact of the PD’s nonlinearity on the

SFDR3 of the microwave photonic link by experiments in this

section.

Maintaining the output power of the LD as a constant (18

mW), the relationship between the normalized phase-shift

Figure 3 Gain as a function of the normalized dc phase-shift

amplitude

Figure 4 SFDR3 as a function of the normalized dc phase-shift

amplitude

2326 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 53, No. 10, October 2011 DOI 10.1002/mop

amplitude Ødc/p and the link gain is shown in Figure 3. The

circle dots and black solid line are the experimental and theory

data in the practical link, respectively, while the dotted line

designates the gain in the ideal link without PD nonlinearity.

From Figure 3, it is easy to see that the value of the gain is

relatively smaller than that in the ideal link due to the nonli-

nearity of the PD in the practical link, especially in the low-

biasing points. In ideal links, the maximum gain, which is 1.7

dB more than that in the practical link, appears at the quadra-

ture point of the MZM because of the highest electronic–optic

conversion efficiency, but in practical links the bias point corre-

sponding the maximum gain deviates from the quadrature point

and equals to 0.45p.Figure 4 gives the SFDR3 as a function of the normalized dc

phase-shift amplitude. The circle dots and black solid line are

the experimental and theory data in the practical link, respec-

tively, while the dotted line designates the gain in the ideal

link. The inset picture represents the relationship of the normal-

ized phase-shift amplitude Ødc/p and the SFDR3 difference

between the ideal and practical links. The nonlinearity of the

PD also degrading the SFDR3, as shown in Figure 4, the maxi-

mum SFDR3 equals to 106.8 dBHz2/3 at /b/p ¼ 0.85 in the

ideal link, while the maximum SFDR3 equals to 103.8 dBHz2/3

at /b/p ¼ 0.80 in the practical link, which suggests that the

maximum value of the SFDR3 is decreased by 3 dB due to the

nonlinearity of the PD. The inset picture includes that the

SFDR3 difference increase from 0 to 4.8 dB with the increase

of the Ødc/p.

4. CONCLUSION

A novel empirical formula has been presented to model the non-

linearity of the PIN PD, which was proved correct by experi-

ments. Based on the simple model of the nonlinearity of PD, the

nonlinearities of a basic microwave photonic link have also

been analyzed systematically. Our analysis included not only the

MZM’s but also the PD’s nonlinearity, so this model can pro-

vide enough accuracy for system designers and analysts. Results

show that the nonlinearity of the PD could decrease the SFDR3

in practical links, and the maximum value of the SFDR3 was

decreased by 3 dB.

In conclusion, because of its ease of applicability and simple

conceptual basis for this model proposed in this article, we

anticipate that the method will be accurate for modeling the

nonlinearity of PD and of value in understanding and evaluating

the nonlinearity of microwave photonic links.

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VC 2011 Wiley Periodicals, Inc.

PERFORMANCES OF A MID-INFRAREDCH4 DETECTION DEVICE USING ANOPTIMIZED ASYMMETRICELLIPSE GAS-CELL

Wei-Lin Ye, Chuan-Tao Zheng, Xin Yu,Zhan-Wei Song, and Yi-Ding WangState Key Laboratory on Optoelectronics, College of ElectronicScience and Engineering, Jilin University, Changchun, 130012,People’s Republic of China; Corresponding author:zhengchuantao578@163.com or wangyiding47@yahoo.com.cn

Received 6 January 2011

ABSTRACT: We demonstrate a mid-infrared CH4 detection device usinga novel fabricated asymmetric ellipse light-collecting gas-cell. Structural

optimizations are performed for fast gas-diffusion speed and high detectionsensitivity. Detection experiments on standard CH4 samples show that thedetection sensitivity is about 9 ppm within the concentration range 8~1000

ppm, the minimum detection limit is about 8 ppm, and the 10~90% responsetime is as fast as 6.0 s. This fabricated device with asymmetric gas-cell

reveals superior performances to the previous reported device withsymmetric gas-cell in our laboratory. VC 2011 Wiley Periodicals, Inc.

Microwave Opt Technol Lett 53:2327–2330, 2011; View this article online

at wileyonlinelibrary.com. DOI 10.1002/mop.26282

Key words: mid-infrared detection; asymmetric ellipse gas-cell;detection sensitivity; minimum detection limit; response time

1. INTRODUCTION

The detection on CH4 is essential especially in mine environ-

ment for avoiding disasters and human death. Therefore, some

researches contributed to this field have been drawn much atten-

tion during the past several decades [1–4]. Within the available

detection principle, spectrum absorption possesses the advan-

tages including wide measuring range, high sensitivity, good se-

lectivity, longevity, and fast response [5, 6]. During the design

of the detection device based on spectral absorption principle,

the optimization on gas-cell is a key step determining the detec-

tion performances, and many gas-cells with various structures

are reported in several works [7–10].

However, it is worth to note that most of the existing experimen-

tal devices with rather high sensitivity are not suitable for wide-

spreading field measurements, as they are rather expensive due to

the complex reflective mirrors and expensive infrared lasers [11–

13]. A compromise selection between cost and performance should

be considered. In view of these concerns, in our laboratory, a

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 53, No. 10, October 2011 2327