condition for stability for Photodiode amplifier circuit

This is essentially trying to get the Aol curve to intersect the NG curve above the feedback pole frequency. A common rule of thumb for transimpedance design but actually misleading. 

I tried to explore that issue in this article on applying decomp VFA - which is what you would prefer to use in transimpedance to get the input voltage noise advantage. 

https://www.planetanalog.com/applying-high-speed-de-compensated-vfas-hitting-performance-targets-while-tuning-phase-margin-insight-10/#

And actually, that whole thing about 40dB closure rate being hazardous - I touched on that at the end of this article using a transimpedance design - common, but incorrect, rule of thumb. 

https://www.planetanalog.com/stability-issues-for-high-speed-amplifiers-introductory-background-and-improved-analysis-insight-5/

Normally I try to design the transimpedance stage for more BW than eventually required then control the final response in a 2nd stage or passive filter. The Zt stage will have some variability in response shape due to GBP variability - a topic covered recently in this thread - Having more Zt stage BW than needed also allows you to cutoff more of the noise peaking in a 2nd stage or passive filter. 

https://e2e.ti.com/support/amplifiers/f/14/t/917919

Hi Michael,

Thank you for your comments!

-Tim Claycomb

Hi Pankaj,

I would not rely too much on these formulas. Many of these formulas are highly idealized. For instance, they don't include the open loop output impedance of OPAmp. Only a thorough phase stability analysis can show what's exactly going on in the circuit.

I agree with Michael and do also try to design the TIA for having more bandwidth than required. I tend to choose a rather moderate phase lead capacitance. This can be very helpful, especially if the detector capacitance is very high (>300pF).

Can you show a schematic of your circuit?

Kai 

We have to rely on these somewhat simplified equations to get started - and yes, a full simulation of LG phase margin is prudent. the op amp open loop output impedance rarely gets into this unless the load is reactive. 

Not sure why all these later Zt design things are out there, pretty much all you need is in this document Xavier and I put together long ago - what is in here still applies. Once you have the 2nd order transfer function, which is a little messy, some easy simplifications will lead you to exactly what you want.

Normally, these designs start out with a photodiode C and then either a desired gain and/or BW - the required minimum GBP to deliver those is in this document. Then the feedback C sets the Q of the closed loop and having it peak is not necessarily oscillating. This says it is for high speed amplifiers, but it applies generally. 

2766.Transimpedance design flow using high speed op amps.pptx