That value's far too high. John, how'd you measure it,
exactly?
5 x 10Meg in series, at 20KHz ;-)
50M and 0.16pF gives -3dB at 20kHz, but if 0.05pF is
assumed for a single part, that's a 60kHz bandwidth
you may enjoy. If you use five resistors in series,
you'd like to say that's 0.05pF/5 = 0.01pF for the
50M, and therefore -3dB at 330kHz.
,- -||- +- -||- +- -||- +- -||- +- -||- ,
---+-/\/\--+-/\/\--+-/\/\--+-/\/\--+-/\/\--+---
But watch out, you'll need to construct that five-
resistor stack carefully, because stray capacitance
from the wiring and resistor bodies, etc., forming a
T network, will damage the TIA's frequency response.
,- -||- +- -||- +- -||- +- -||- +- -||- ,
---+-/\/\--+-/\/\--+-/\/\--+-/\/\--+-/\/\--+---
_|_ _|_ _|_ _|_
--- Cs --- --- ---
| | | |
--+-------+-------+-------+-- gnd
We might be talking about Cs in the 0.01pF territory.
That's why I usually use a single resistor, and fix
it for bandwidth using the R-C-R trick I've mentioned
several times before here on s.e.d.
Cf ,-- adjust so R1 = Rf Cf/C1,
,- -||- , R1 / the new apparent Cf is
---+-/\/\--+---+--/\/\----- given by Cf' = C1 R2/Rf
Rf | C1 R2
'--||--/\/\-- gnd
(In production it's possible Cf may be sufficiently
predictable to use a fix value for R1.) In practice
it's easy to get an effective Cf = 0.0025pF or better.
But one has to realize that in doing so he's depending
on the use of just one small Rf resistor and is relying
on its single-capacitance model. Frankly, that would
be difficult to do with multiple resistors in strings.
One more non-trivial issue, how to test these beasts.
If a signal-generator test is desired, one shouldn't
depend on simply using a high-value resistor to create
the TIA's test current, because that resistor also has
self capacitance, which could make the amplifier look
better than it really is, etc. Instead, you can make
a corrected resistor this way,
R1 Rs, high-value
---/\/\---+---/\/\/-----
_|_
--- C <-- I like to use adjustable capacitors
|
gnd
Now, how to calibrate the "corrected resistor"? For that
I use a perfect "calibrated" amplifier, which in turn has
been adjusted with a lower value corrected Rs, which ...
This scene is pretty trivial in the 50M region, but it
can get rather tricky for Rf = 1G-ohm and up. For such
values and high frequencies, one soon realizes they're
really using capacitors rather than resistors, as the
feedback and gain-determining elements.