[Laser] Photodiodes in series

[F1AVYopto at aol.com]

Hi all
To answer a common question in several direct mails:
The formula In=  (4KTf / Rshunt)^1/2 seems to show the Johnson noise 
deacreases with  Rshunt.
In fact we need Vnoise.
On infinite load : Vnoise = In x Rshunt =  (4KTf / Rshunt)^1/2 x Rshunt
Vnoise = (4KTf / Rshunt)^1/2 x (Rshunt^1/2 .  Rshunt^1/2)
If you reduce Rshunt you find Vnoise = (Rshunt.4KTf)^1/2
So  the Johnson noise increases like the square root of Rshunt.
At the same time  the Vsignal is Vs = Rshunt .IL   (IL is the useful 
photoelectric  current).
Vs increases directly with Rshunt.
So the Vs / Vn (the S/N !)  increases as the Rshunt square root on an 
infinite load.
It is why the higher  the photodiode Rshunt, the higher the sensitivity limit.
It is also why the  PN photodiodes are often more sensitive than the PIN 
photodiodes but the PN  photodiodes are slower because their big capacitance and 
their long  recombination time.
73 Yves F1AVY