Fibre Bandwidth Estimates
Tony Weidberg 19/7/06
Fujikura Fibre
This is a radiation hard pure silica core SIMM fibre. Some very simple measurements
of the speed of this fibre have been made and used to estimate the bandwidth of this
fibre. A Truelight VCSEL was used as the light source. Using a very short reflector
ribbon the measured fall time (20%-80%) using a TEK probe/scope was 0.819 ps. The
same measurement was repeated using a reflector ribbon at the end of one of the SCT
cables in the ATLAS pit. The fall time was measured to be 1.335 ns. The fibre length
was estimated by measuring the “time of flight” and assuming a propagation speed of
5ns/m the length is 184 m. To make a conservative estimate of the fibre bandwidth we
will ignore the finite speed of the VCSEL, optical probe and ‘scope. Assuming an
exponential shape, the time constant is given by
  t 2080 / ln( 4)
Which gives = 0.96 ns. The frequency response for an exponential time decay is
given by
1
H( f ) 
1  i 2f 
Therefore the frequency range over which |H(f)| exceeds half its maximum value is
given by
f 
0.276

 0.29 GHz
So, using the measured length of the long fibre we obtain a lower bound on the
bandwidth of the Fujikura fibre of 53 MHz km. If the rise time with the short fibre
length were to be subtracted in quadrature from the measured rise time, the resulting
estimate for the bandwidth would be 80 MHz km.
POF Fibre
This is a radiation tolerant GRIN fibre which has no P dopant in the core. This fibre is
currently being used by the ATLAS Pixel detector; 10 metre lengths of the Fujikura
fibre are used for the highest radiation zone and then spliced to ~ 100m of this GRIN
fibre. The manufacturer’s specification for the bandwidth of this fibre is
1121 MHz km.
Conclusions
If 10 metre lengths of SIMM fibre were spliced to 80 metres of the GRIN fibre (the
longest length of fibre required for ATLAS), the speed of the SIMM (GRIN) fibre
would be 5.3 (14.0) GHz. The speed would therefore be limited by the bandwidth of
the SIMM fibre. For a wide variety of pulse shapes the bit rate B should not exceed
1/4, which for rectangular pulses implies that the maximum bit rate should not
exceed
BMAX  f
 7.6 GBits / s
0.7
The simulated pulse shapes for a clock frequency of 2, 3 and 4 GHz (corresponding to
data rates of 4, 6, 8 GBits/s) are shown in Figure 1, Figure 2 and Figure 3.
f=2 GHz
1
0.8
0.6
Output (a.u.)
0.4
0.2
0
-0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
-0.4
-0.6
-0.8
-1
t (ns)
Figure 1 Simulated eye diagram for f= 2 GHz. Only effect of SIMM fibre dispersion is allowed
for in this plot. Input is unit step function.
f=3 GHz
1
0.8
0.6
Output (a.u.)
0.4
0.2
0
-0.2
0
0.05
0.1
0.15
0.2
0.25
0.3
-0.4
-0.6
-0.8
-1
t (ns)
Figure 2 Same as Figure 1 for f=3 GHz.
1
J. Wilson and J. Hawkes, Optoelectronics am introduction, 3 rd edition, Prentice Hall.
0.35
f=4 GHz
1
0.8
0.6
Output (a.u.)
0.4
0.2
0
-0.2
0
0.05
0.1
0.15
0.2
0.25
-0.4
-0.6
-0.8
-1
t (ns)
Figure 3 Same as Figure 1 for f=4 GHz.
These results suggest that the mixed SIMM/GRIN fibre should be fast enough for data
transmission up to ~ 4 GBits/s but would not be fast enough for 10 Gbits/s. These
simple estimates should be verified with the correct lengths of SIMM and GRIN fibre
spliced together.