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These photodiode modules are often integrated into 
more complete receiver packages similar to the flange-
mount and plug-in varieties of the transmitters. In these 
receivers, circuitry reverse biases the diodes to 
increase the response speed. Receivers also contain 
monitor and alarm outputs. Some receivers may 
include a post amplifier, broadband current transformers, 
and/or impedance matching networks to improve 
the link gain. Due to such circuitry, the efficiency of a 
receiver generally will differ from the responsivity of the 
photodiode chip alone. 

Fiber-Optic Cable 

A fiber-optic cable is the third primary component in a 
linear optical link. Single-mode fiber, as opposed to 
multimode fiber, is always used with Agere Systems’ 
links because of its low dispersion and low loss. At a 
wavelength of 1310 nm, the fiber attenuates the optical 
signal by less than 0.4 dB/km; at 1550 nm, less than 

0.25 dB/km. Typically, the fiber is cabled in rugged yet 
flexible 3 mm diameter tubing and connected to the 
transmitter and receiver with reusable optical connectors. 
The modular nature of the cable simplifies the 
design of the physical architecture of the system and 
enables a wide range of configuration possibilities. 
Although Agere Systems does not supply optical fiber, 
several important considerations should be followed in 
selecting these components. The section entitled 
Selection of Optical Fiber Components, page 19, 
describes these issues in detail. 
Link Design Calculations 

When selecting the proper components for a fiber-optic 
link, there are several critical quantities that must be 
defined and calculated prior to its implementation, just 
as would be done with any RF or microwave communication 
link. Topics of discussion in this section include 
link gain, bandwidth, noise, dynamic range, and distortion, 
and the use of that information as an example for 
a typical link. The detailed equations in this section 
also have been incorporated into various design programs, 
which a Agere Systems’ applications engineer 
can use to provide the predicted performance of a link 
in a specific application. 

Agere Systems Inc. 


Application Note 
RF and Microwave Fiber-Optic Design Guide April 2001 

Link Design Calculations (continued) 

Gain 

The RF loss (or gain) of an optical link is a function of 
four variables, including transmitter efficiency, fiber 
loss, receiver efficiency, and the ratio of the output to 
input impedances. In its most basic form, the power 
gain of the link can be written in terms of the input and 
output currents as 

equation 1, 

.IOUT. 2.ROUT.

GLINK = --------------------------

. IIN .. RIN . 

where ROUT is the load resistance at the receiver output 
and RIN is the input resistance of the laser transmitter. 
The (IOUT/IIN) term can be expanded in terms of the 
link characteristics as: 

equation 2 

IOUT (ηTX RF, (ηRX R

, ))

------------= ----------------------------------------------


IIN LOPT 

where ηTx, RF is the efficiency of the total transmitter, 
including any amplifiers and matching networks, in 
converting input RF currents into optical power modulations. 
ηRx, RF is the efficiency of the total receiver in 
converting optical power modulations into RF output 
current. (This RF value is not the same as the dc photodiode 
responsivity, as described in the section on 
Bandwidth, page 8.) The units for ηTx, RF and ηRx, RF 
are W/A and A/W, respectively. LO is the optical loss of 
the fiber portion of the link measured as: 

equation 3 

Optical Power at Transmitter 

, ---------------------LORATIO 
= -----------------------------------------------------


Optical Power at Receiver 

Lo = 10 log LO, RATIO 

–20 

–30 

–40 

–50 

–60 

–70 

–80 

1 3 5 7 911 

LINK GAIN (dB) 


Substituting equation 2 into equation 1 then gives the 
total gain of a link: 

equation 4, 

(ηRX RF. 2 ROUT

,)C 

, ------------------------GLINK 
RATIO, = (ηTX R).---------------.------. 

. LORATIO. RIN .

,. 

GLINK, dB = 20 log(ηTx, RF)(ηRx, RF) – 2 LO 

+ 10 log(ROUT/RIN) 
The factors of ηTx, RF and ηRx, RF are sometimes converted 
to a form more similar to traditional RF gains by 
taking 20log, so that equation 4 can be simplified to: 

equation 5, 

GLINK, dB = TG + RG – 2Lo + 10 log(ROUT/RIN) 

where TG is the transmitter gain in dB2W/A and RG is 
the receiver gain in dB2A/W. TG and RG are related to 
the unit’s total RF efficiency expressed in W/A or A/W 
as follows: 

equation 6, 

TG = 20log (Tx, RF) 

equation 7, 

RG = 20log (Rx, RF) 

For example, combining a 75 Ω transmitter with a TG 
of –1 dB2W/A, a 75 Ω receiver with an RF of +20 dB2A/ 
W and a 12 dB optical loss, would give an RF gain for 
the link of: 

G = –1 dB2W/A + 20 dB2A/W – 2 (12 dB) +10log(75/75) 
= –5 dB. 

Figure 6 shows the effects of optical loss and transmitter 
RF efficiency for a receiver with an efficiency of 

0.375 mA/mW (RG of –8.51dB2A/W), as calculated 
with equation 4. The Appendix, page 28, contains additional 
sets of curves for other typical transmitter and 
receiver efficiencies. 
N TX RF = 0.1 
N TX RF = 0.075 
N TX RF = 0.06 
N TX RF = 0.02 

13 15 17 19 21 

OPTICAL LOSS (dB) 1-1218F 

Figure 6. Effects of Optical Loss and Transmitter RF Efficiency 

Agere Systems Inc. 


Application NoteApril 2001 RF and Microwave Fiber-Optic Design Guide 

Link Design Calculation (continued) 

Doubling the Optical Loss Term 

An interesting and often overlooked aspect of 
equation 4 is the 2 LO term. As this indicates, for each 
additional dB of optical loss, there is an additional 2 dB 
of RF loss. This oddity occurs as a result of converting 
optical power to RF energy. Here, the RF current is 
directly proportional to the optical power, but the RF 
power equals the square of the RF current. When taking 
the log, this squared term turns into a factor of 2 in 
front of the optical loss. 

For example, a transmitter and receiver pair that have a 
–35 dB RF gain when they are directly connected with 
0 dB of optical loss, would have a –39 dB RF gain when 
connected with a 2 dB loss fiber. 

Resistively Matched Components 

To calculate the total insertion loss for a specific link, 
consider the broadband resistively matched link shown 
in Figure 7. In this case, the laser transmitter includes 
the laser diode, with a typical impedance of 5 Ω, and a 
resistor to raise the total input impedance, RIN, up to 
the impedance of the external signal source. The photodiode 
module includes the photodiode, with a typical 
impedance of several kΩ, and a resistor RPD to match 
to the output impedance RL. Such matching resistors 
substantially improve the VSWR of the link over that of 
an unmatched link. 

Due to this extra photodiode resistor, the current output 
from the receiver, IOUT, will be less than the total current 
produced by the photodiode chip, IPD. The RF efficiency 
of the receiver, ηRx, RF, is therefore 
correspondingly smaller than the responsivity of the 
photodiode chip alone, RPD: 

GLINK = –35 dB 

RS RIN 


IIN 
VS 


equation 8, 
RPD

ηRx RF=

, 

. RPD
RPD + ROUT 

For a 50 Ω matched system, RPD and ROUT each 
would be approximately 50 Ω, therefore, the receiver 
RF efficiency would be half that of the photodiode chip 
on its own. This decreases the overall link gain by 6 
dB. 

For a resistively-matched photodiode receiver: 

equation 9, 

ηRx, RF = RPD/2 

The transmitter RF efficiency, on the other hand, does 
not experience such a drop of 6 dB due to the fact that 
the matching resistor is placed in series rather than in 
parallel. Therefore, within the bandwidth of a transmitter, 
its RF efficiency is approximately equal to the dc 
modulation gain of the laser diode. 

As an example, consider a transmitter with a dc modulation 
gain of 0.1 W/A, a resistively matched receiver 
with a dc responsivity of 0.75 and a fiber with an optical 
loss of 3 dB. To the first order, RF efficiency of the 
transmitter will be 0.1 W/A and the RF efficiency of the 
receiver will be 0.375 A/W. If both the transmitter and 
receiver are matched to 50 Ω, then the impedance 
matching term of equation 4 drops out, leaving an RF 
link gain of approximately: 

equation 10, 

GLINK, dB = 20 log(ηTx, RF(ηRx, RF)) – 2 LOPT, dB 
.ROUT.

+10 log . ---------------.

RIN 
GLINK (20 log [(0.1 mW/mA) (0.375 mA/mW)] 

– 2 x 3 dB + 0 
IPd 


IIN 

RS 
ROUT 


SIGNAL LASER OPTICAL PHOTODIODE LOAD 1-1219F 
SOURCE MODULE FIBER MODULE 

Figure 7. Resistively Matched Link 

Agere Systems Inc. 


Application Note 
RF and Microwave Fiber-Optic Design Guide April 2001 

Link Design Calculation (continued) 

Reactively Matched Link 

To overcome such a loss, many links incorporate additional 
amplifiers, which are described more fully in the 
sections on Receiver Noise, page 10; Placement of 
Amplifiers, page 15; and in the section entitled Example, 
page 15. As an alternative for narrowband systems, 
the link gain can be improved by impedance 
matching so that the laser diode and photodiode see 
an effective ROUT/RIN > 1. The matching electronics 
used in such links are carefully designed to produce 
this extra gain without creating reflections or poor 
VSWR. 

Bandwidth 

The range of frequencies over which a fiber-optic link 
can transmit is limited by the bandwidth of the transmitter 
and receiver and by the dispersion of the optical 
fiber. The bandwidth limit of a link generally is defined 
as the frequency at which the microwave modulation 
response decreases by 3 dB. 

In most cases, the bandwidth of the laser transmitter 
limits a link’s frequency response, therefore, the 

0 

–5 

–10 

–15 

–20 

–25 

–30 

–35 

–40 

AMPLITUDE (dB) 

response of the basic laser diode chip shown in 
Figure 8 is of prime interest. 

As can be seen, the frequency response of the chip 
varies with the bias current, thus an optimum point is 
chosen to balance this frequency response and other 
current-sensitive parameters such as noise, linearity, 
and life of the device. When integrating the laser chip 
into a complete transmitter, other components such as 
amplifiers or matching networks also can limit the 
response. 

The bandwidth of receivers is limited by the capacitance 
and carrier transient times of the photodiode chip 
or by additional electrical components such as amplifiers 
and matching networks. In most cases, the speeds 
of these receivers are faster than that of the other components 
in the link. 

In certain situations, the fiber itself may smear out rapidly 
varying signals due to the fact that different wavelengths 
travel at different speeds along a fiber. To avoid 
this chromatic dispersion, lasers with narrow optical 
bandwidths, such as Lucent’s DFB lasers, are used 
with fiber that has low dispersion. Using a DFB at 
1310 nm, where fibers have a natural minimum in their 
dispersion, bandwidths in excess of 15 GHz can be 
achieved over fibers as long as tens of kilometers. The 
section on Dispersion, page 20, describes these fiber 
effects more fully. 

10 3020 
40 
50 
60 mA 
II = IO – ITH 
0 2 4 6 8 10 12 14 16 18 20 
FREQUENCY (GHz) 
1-1118F 

Figure 8. Laser Frequency Response as a Function of Increasing Bias Current 

Agere Systems Inc. 


Application NoteApril 2001 RF and Microwave Fiber-Optic Design Guide 

Link Design Calculation (continued)