you can find a yageo (phicom) document that gives impedance values versus frequency (up to GHz range) for several resistance values and SMT shapes. It is not just capacitance that counts.
I hope this will help you to extract a spice model.
Assuming the resistor stack is in the feedback you might have to compensate at the PD node. Sounds silly but a varicap diode there plus a nifty 20+ kilohertz carrier or pulse scheme might be needed so you can automatically compensate for the feedback capacitance. Factory adjustments are usually poo-pooed upon these days (at least I never use them). Sure you need all this gain right away?
Recipe for disaster :-) You could add capacitive compensation (like an oscilloscope probe). But this would require some post-manufacturing adjustments / calibration depending on the required frequency linearity. If the frequency range is limited, you might get away with a capacitive divider (if it is a divider you're trying to make) that is dominated by its capacitors rather than its resistors at the frequency range of interest.
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That value's far too high. John, how'd you measure it, exactly?
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.
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
It's probably much higher for 0603 parts. I made a bunch of measurements for caps on a PCB a year ago, but I seem to have misplaced the folder. The problem with my fancy impedance-measuring instruments and their special fixtures is the ZERO cal step, which can cancel out legitimate portions of the measurement.
A better way to take accurate measurements is in-situ, on a PCB, rather than with the test fixture. Toward that end my PCB engineer has created a test board for all types of components and I plan to order soon and take measurements with it next month. We need them for a section in AoE 3rd edition, on component properties.
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