Noise adds in a RMS fashion unless it is correlated. So a differential
amplifier can cancel common mode noise, but that is about it. The diode,
being a single ended device, seems to me to be impossible to bias in a
manner where the noise from the bias circuitry will cancel out.
Note it may not be the case you need the full 7GHz if it is only the
mixer product you are feeding the photodiode. That is, the diode will
see the difference prouct.
You can get gain and bandwidth in multiple stages. The first stage will
determine the noise if you do it correctly. It has been my experience
that anything high gain I try to build oscillates. [And of course
intentional oscillators just sit there.] You will need to insure there
is no feedback through the supply rails. In this respect, going fully
differential will be better.
I can't speak for JFET at high frequencies, but there is a lumped model
for the BF862. You need to create a subcircuit for it. I had spent quite
a bit of time designing a high speed photodiode front end, but junked
the design when a different part of the system couldn't be made in a
cost effect manner. Anyway, you need to check the limits of the
manufacturers lumped circuit.
The JFET bootstrap really has two functions. That of a low capacitance
high impedance input and a low impedance output. If you read the
literature, there are multiple transistor circuits used to get the
output impedance lower. There isn't much that can be done regarding
input impedance.
Trolling the net, RF transformers seem to have an upper limit of 5GHz.
Just thinking out loud here, you can get a little gain with a
transformer, get rid of DC, bias the diode, and generate a fully
differential signal. It is a route worth looking into.
<snip>
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