The document discusses calculating the sensitivity of an optically unamplified receiver using either a PIN photodiode or APD photodiode with a TIA amplifier. It compares the two systems for NRZ and RZ signals with either an adapted filter or single-pole filter. It then calculates the maximum achievable distance. The key results are that an APD photodiode provides a sensitivity gain of 18-20 dB for NRZ signals and 45-100 dB for RZ signals compared to a PIN photodiode. The maximum transmission distance is also significantly higher for an APD-based system, ranging from 4-56 km depending on the configuration.

1. ESERCITAZIONE N° 2
Calcolare la Sensitivity di un Ricevitore Non Amplificato Otticamente
(fissando 12
10)( −
=ep 7=Q ) quando si utilizza fotodiodo PIN e un
amplificatore TIA oppure un fotodiodo APD e un amplificatore TIA, e
paragonando i due sistemi diversi nei seguenti casi:
1. Impulso NRZ con filtro adattato;
2. Impulso RZ con filtro adattato;
3. Impulso NRZ con filtro a singolo polo.
Infine, calcolare la massima distanza raggiungibile.
HzpAIRND /11,1500R:TIA
0.7x15,G0.8,R:APD
1=x1,=G0.85,=R:PIN
t =Ω=
===
Inoltre ricorda che:
LL htthhth
IRND
R
N
ξσξσ
22
2
02
==>=
hfRNP BRR = .
Un ricevitore realistico ha il seguente schema a blocchi:
RF
amplifier
PIN o
APDfiber
Low-pass filter
PR(t)
i(t)
t=topt
v(t) v(topt)

2. 1) NRZ + filtro adattato => Bh RrA L
=== ξ,1,1 00
a) PIN + TIA
6794.0== R
q
hf
Sη
Bt
Bt
Bt
th
S
x
S
R
RR
RR
RqrRG
Q
AG
Q
N
⋅⋅⋅⋅
⋅
⋅
⋅
+⋅⋅
⋅
=+= −
−
1106.1
2
)1011(
6794.01
7
11
6794.02
7
2 19
212
2
0
0
2
σ
ηη
B
R
R
e
N
8
009.5
06.36 +=
sGbitRB /5.2= => bitphNR /10054=
=> dBmPWP RR 93.24;21.3 −== µ
sGbitRB /10= => bitphNR /5045= => dBmPWP RR 90.21;45.6 −== µ
b) APD + TIA
6394.0== R
q
hf
Sη
Bt
Bt
Bt
th
S
x
S
R
RR
RR
RqrRG
Q
AG
Q
N
⋅⋅⋅⋅
⋅
⋅
⋅
+⋅⋅
⋅
=+= −
−
1106.1
2
)1011(
6394.015
7
115
6394.02
7
2 19
212
7.0
2
0
0
2
σ
ηη
B
R
R
e
N
7
548.3
06.255 +=
sGbitRB /5.2= => bitphNR /6687.964= => dBmPWP RR 11.35;308.0 −== µ
sGbitRB /10= => bitphNR /86.609= => dBmPWP RR 08.31;779.0 −== µ
Guadagno di Sensitivity dell’APD rispetto al PIN:
sGbitRB /5.2= dBGuadagno 18.10=
sGbitRB /10= dBGuadagno 18.9=

3. 2) RZ + filtro adattato => Bh nRnrA L
=== ξ,,1 00
a) PIN + TIA
6794.0== R
q
hf
Sη
Bt
Bt
Bt
th
S
x
S
R
nRR
nRR
RqrRG
Q
AG
Q
N
⋅⋅⋅⋅
⋅
⋅
⋅
+⋅⋅
⋅
=+= −
−
1106.1
2
)1011(
6794.01
7
11
6794.02
7
2 19
212
2
0
0
2
σ
ηη
B
R
nR
e
N
8
009.5
06.36 +=
sGbitRB /5.2=





=
=
=
10
5
2
n
n
n





=
=
=
bitphN
bitphN
bitphN
R
R
R
/3204
/4516
/7120





−==
−==
−==
dBmPWP
dBmPWP
dBmPWP
RR
RR
RR
89.29;02.1
40.28;44.1
42.26;27.2
µ
µ
µ
sGbitRB /10=





=
=
=
10
5
2
n
n
n





=
=
=
bitphN
bitphN
bitphN
R
R
R
/1620
/2276
/3578





−==
−==
−==
dBmPWP
dBmPWP
dBmPWP
RR
RR
RR
89.26;07.2
36.25;91.2
40.23;58.4
µ
µ
µ
Guadagno di Sensitivity rispetto al PIN:
sGbitRB /5.2=





=
=
=
10
5
2
n
n
n





=
=
=
dBGuadagno
dBGuadagno
dBGuadagno
95.4
47.3
49.1
sGbitRB /10=





=
=
=
10
5
2
n
n
n





=
=
=
dBGuadagno
dBGuadagno
dBGuadagno
93.4
46.3
5.1

4. b) APD + TIA
6394.0== R
q
hf
Sη
Bt
Bt
Bt
th
S
x
S
R
nRR
nRR
RqrRG
Q
AG
Q
N
⋅⋅⋅⋅
⋅
⋅
⋅
+⋅⋅
⋅
=+= −
−
1106.1
2
)1011(
6394.015
7
115
6394.02
7
2 19
212
7.0
2
0
0
2
σ
ηη
B
R
nR
e
N
7
548.3
06.255 +=
sGbitRB /5.2=





=
=
=
10
5
2
n
n
n





=
=
=
bitphN
bitphN
bitphN
R
R
R
/4.479
/4.572
/8.756





−==
−==
−==
dBmPWP
dBmPWP
dBmPWP
RR
RR
RR
14.38;153.0
37.37;183.0
16.36;241.0
µ
µ
µ
sGbitRB /10=





=
=
=
10
5
2
n
n
n





=
=
=
bitphN
bitphN
bitphN
R
R
R
/2.367
/7.413
/9.505





−==
−==
−==
dBmPWP
dBmPWP
dBmPWP
RR
RR
RR
28.33;469.0
76.32;529.0
89.31;647.0
µ
µ
µ
Guadagno rispetto a NRZ +
APD:
sGbitRB /5.2=





=
=
=
10
5
2
n
n
n





=
=
=
dBGuadagno
dBGuadagno
dBGuadagno
03.3
26.2
05.1
sGbitRB /10=





=
=
=
10
5
2
n
n
n





=
=
=
dBGuadagno
dBGuadagno
dBGuadagno
20.2
68.1
81.0
Guadagno rispetto a RZ + APD:
sGbitRB /5.2=





=
=
=
10
5
2
n
n
n





=
=
=
dBGuadagno
dBGuadagno
dBGuadagno
25.8
97.8
74.9
sGbitRB /10=





=
=
=
10
5
2
n
n
n





=
=
=
dBGuadagno
dBGuadagno
dBGuadagno
45.6
40.7
49.8

5. 3) NRZ + filtro a singolo polo =>
BPh
Tf
B
P
BP
Rf
er
R
f
A
Rf
L
P
513.2
,9934.01
,513.28.0
,8.0
2
0
0
==
=−=
==≅
=
−
πξ
π
π
π
a) PIN + TIA
6794.0== R
q
hf
Sη
Bt
Bt
Bt
th
S
x
S
R
RR
RR
RqrRG
Q
AG
Q
N
⋅⋅⋅⋅
⋅
⋅
⋅
+⋅⋅
⋅
=+= −
−
9934.0106.1
513.2
2
)1011(
6794.01
7
513.21
6794.02
7
2 19
212
2
0
0
2
σ
ηη
B
R
R
e
N
8
9932.7
62.90 +=
sGbitRB /5.2= => bitphNR /16077= => dBmPWP RR 89.22;14.5 −== µ
sGbitRB /10= => bitphNR /8084= => dBmPWP RR 86.19;33.10 −== µ
Sensitivity Penalty dovuto al filtro realistico:
sGbitRB /5.2= dBGuadagno 04.2=
sGbitRB /10= dBGuadagno 04.2=
b) APD + TIA
6394.0== R
q
hf
Sη
Bt
Bt
Bt
th
S
x
S
R
RR
RR
RqrRG
Q
AG
Q
N
⋅⋅⋅⋅
⋅⋅
⋅
⋅
⋅
+⋅⋅
⋅
=+= −
−
9934.0106.1
513.2
2
)1011(
6394.015
7
513.215
6394.02
7
2 19
212
7.0
2
0
0
2
σ
ηη

6. B
R
R
e
N
7
662.5
9789.640 +=
sGbitRB /5.2= => bitphNR /1773= => dBmPWP RR 46.32;566.0 −== µ
sGbitRB /10= => bitphNR /1207= => dBmPWP RR 11.28;54.1 −== µ
Guadagno di Sensitivity dell’APD rispetto al PIN:
sGbitRB /5.2= dBGuadagno 65.2=
sGbitRB /10= dBGuadagno 97.2=
Calcolo della Massima Distanza Ottenibile maxL :
α
α RTX
TXRX
PP
LLPP
−
=⇒⋅−= max
Supponiamo di avere: GHzRbKmdBdBmPRX 10;/2.0;10 ==−= α
-10
P(z)
[dBm]
z
[Km]
Slop is α
Impulso NRZ
PIN+TIA e
SPF -19 86
Impulso NRZ
PIN+TIA
-24 93
Impulso RZ
50%
PIN+TIA
Impulso NRZ
PIN+TIA e SPF
-28 11
Impulso NRZ
APD+TIA
-31 08
49.3 59.5 67 90.55 105.4

7. Nel caso di filtro adattato:
⋅ NRZ con TIAPIN + => KmL 5.59max =
⋅ %50RZ con TIAPIN + => KmL 0.67max =
⋅ NRZ con TIAAPD + => KmL 4.105max =
Nel caso di filtro a singolo polo:
⋅ NRZ con TIAPIN + => KmL 3.49max =
⋅ NRZ con TIAAPD + => KmL 55.90max =