[Laser] Re Photodiodes in series :To answer a common question in several direct mails

[F1AVYopto at aol.com]

Hi all
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