Noise gain in TIA opamp

I=92m a bit embarrassed to be asking this question, (I thought I understood this circuit.) But I=92ve gotten myself confused. I=92m looking at voltage noise gain in TIA amplifiers. I understand the cause of the gain increase as the frequency goes up, the capacitance to ground at the inverting input. But why do I get a huge peak right where the voltage gain crosses the open loop gain curve of the opamp? Do I need to write down the loop equations and solve them? Some term in the denominator is =91blowing up=92 (going to zero).

I had this =91silly=92 idea that the noise gain is rising at 10dB/dec and the opamp open loop gain is decreasing by the same amount so that once they meet the gain would then stay constant as a function of frequency. This obviously doesn=92t happen, and I did a quick LTspice.

George (feeling like an idiot) Herold

Spice file follows. (I tried adding the file as an attachement but couldn't do that via google groups.)

Version 4 SHEET 1 5945676 13421556 WIRE 1440 -96 1392 -96 WIRE 1536 -96 1504 -96 WIRE 1392 -32 1392 -96 WIRE 1424 -32 1392 -32 WIRE 1536 -32 1536 -96 WIRE 1536 -32 1504 -32 WIRE 1296 64 1264 64 WIRE 1392 64 1392 -32 WIRE 1392 64 1360 64 WIRE 1440 64 1392 64 WIRE 1536 80 1536 -32 WIRE 1536 80 1504 80 WIRE 1568 80 1536 80 WIRE 1440 96 1408 96 WIRE 1408 112 1408 96 WIRE 1408 224 1408 192 WIRE 1264 240 1264 64 FLAG 1264 240 0 FLAG 1408 224 0 SYMBOL voltage 1408 96 R0 WINDOW 0 44 47 Left 0 WINDOW 123 44 90 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V1 SYMATTR Value "" SYMATTR Value2 AC 1. SYMBOL cap 1360 48 R90 WINDOW 0 0 32 VBottom 0 WINDOW 3 32 32 VTop 0 SYMATTR InstName C1 SYMATTR Value 1.6n SYMBOL OPAMPS\\OPAMP 1472 16 R0 SYMATTR InstName U1 SYMATTR SpiceLine Aol=3D10K SYMBOL res 1520 -48 R90 WINDOW 0 56 92 VBottom 0 WINDOW 3 34 27 VTop 0 SYMATTR InstName R5 SYMATTR Value 100K SYMBOL cap 1504 -112 R90 WINDOW 0 -2 69 VBottom 0 WINDOW 3 -27 -19 VTop 0 SYMATTR InstName C2 SYMATTR Value 0p TEXT 1888 256 Left 0 !.ac oct 25 1k 10Meg TEXT 1888 296 Left 0 !.include opamp.sub

I=92m a bit embarrassed to be asking this question, (I thought I understood this circuit.) But I=92ve gotten myself confused. I=92m looking at voltage noise gain in TIA amplifiers. I understand the cause of the gain increase as the frequency goes up, the capacitance to ground at the inverting input. But why do I get a huge peak right where the voltage gain crosses the open loop gain curve of the opamp? Do I need to write down the loop equations and solve them? Some term in the denominator is =91blowing up=92 (going to zero).

I had this =91silly=92 idea that the noise gain is rising at 10dB/dec and the opamp open loop gain is decreasing by the same amount so that once they meet the gain would then stay constant as a function of frequency. This obviously doesn=92t happen, and I did a quick LTspice.

George (feeling like an idiot) Herold

Reply to
George Herold
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George Herold a écrit :

Think about how much phase rotation you have around the loop. And now, why is noise gain rising up?

--
Thanks,
Fred.
Reply to
Fred Bartoli

Hi Fred, Thanks for the response. Hmmm.... With a lot of gain the phase 'snaps', right across at the gain peak. But why the gain peak?

I've been writing down the loop equations. The second time through*, I got that the gain at resonance should be the ratio of two 'times'. the RC time/ GBW 'time'. or the GBW /RC 'freq'. 10Meg/1kHz in the example I posted ~80dB, close enough?

(The whole equation looks like Gain=3D a0*t(RC)/{(t(a0)+t(RC)} Where a0 is the DC open loop gain and t(a0)/a0 is the GBW time. t(a0) is the time where the open loop response starts to roll off.

George H.

  • the first time through I got the zero frequency open loop resopnse gain. (But I was sloppy and threw away some factors I should have kept.)
Reply to
George Herold

Attaching your schematic .asc as a test.

Reply to
ehsjr

At unity loop gain, you've got almost 90° phase shift from the opamp plus another almost 90° shift from the RC feedback network, which is almost 180° phase shift. You're not far from having build an oscillator. (in real life, additional parasitic poles will ensure you reliable oscillations)

This phase shift builds positive feedback and gives you heaps of gain enhancement (resonance) near the unity loop gain, hence your noise gain peaking...

I didn't get through your maths but just drop ao, which is just obscuring things, and think GBW product. In the region of interest the opamp is almost always already behaving asymptotically and you can (often) accurately model it as a single pole at DC.

So, the max will occur at sqrt(GBW/(2*pi*tau)) frequency and will be (2*pi*GBW*tau), and this amounts to the sqrt of product and ratio of the respective frequencies.

--
Thanks,
Fred.
Reply to
Fred Bartoli

=EF=BF=BDm

t 10dB/dec and

=EF=BF=BDm

t 10dB/dec and

OK did you do that via google groups? I mucked about, but couldn't get it to accept an attachment.

George H.

Reply to
George Herold

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Yeah sorry for the math weirdness.... Your '(2*pi*GBW*tau)' is the gain I get as long as 1/(2*pi*tau) isn't too close to the GBW.

I'm writing an appendix explaining how to choose the parallel cap to put across the feedback resistor, and ran into the limits of my own understanding. (As often happens when you try explaining something to someone else.)

Thanks for the help,

George H.

Reply to
George Herold

This is what ASC.EXE did for your schematic, George:

Sadly, C1 was bunched up against a wire so the 1.6n was truncated, but I would have just then edited that text by hand or else gone back to the LTspice schematic and moved C1 slightly. With slight adjustments, your schematic becomes:

That was also automatically generated, doesn't require an attachment or some series of ASCII commands that need to be copied, pasted, saved, and then loaded up to see. And it is produced directly from the schematic, so any changes made to it are automatically hauled in, rigorously.

Your schematic would have been easy to do by hand, I suppose. Winfield Hill routinely did a good job of it when posting, all by hand.

Anyway, there it is.

Jon

Reply to
Jon Kirwan

No, not Google Groups. And the test failed - the attachment does not open in LT spice when you double click it. It still can be saved to file and then opened with LT spice, I think, but I wanted to see if it would open directly.

The cause of the failure has nothing to do with your schematic - I just used yours to kill two birds with one stone: provide an attachment that others could use without the need for cut and paste, and test whether my attachment of the schematic could be launched directly.

Ed

Reply to
ehsjr

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