Preamp for very small signal

[Terry Bites]

I get the impression that you need a floating input.
Ground is generally pretty filthy in todays switchmode environments.
Assume its crappy unless proven otherwise. Just design that problem out.
EMI can easily burry a small signal. Low noise opamp amps won't cure that.
You'll need some RFI filtering at the input.
And you'd be wanting some decent CMRR @50/ 60Hz for 30uV signals unless you're living in a Faraday cage.
Inst amps tend to be pretty low bandwidth at high gain. GBPs of 1MHz are typical. So 10kHz @ 60dB.
 
My suggested mic amp has a 192 KHz BW@ 60dB, 10x the max frequency of interest, that's not bad. And no, I dont work for or flog THAT products

Then there are fully differential amps with spectacular specs. Sub nV noise, insane bandwidths. They make for great front ends, ideal for low Z sources.
See attched sketch of a possible configuration.

[AndyC_772]

My concern would be common mode noise pickup; as others have said, the signal level itself isn't particularly low, but you'll need excellent CMRR otherwise all you'll do is pick up mains hum. It doesn't help that your signal is 48 Hz and so, more or less, is the mains.

I'd be using a transformer to give the necessary CMRR. As a bonus, you can pick one with, say, a 10:1 turns ratio to increase the signal level at the same time.

[gnuarm]

Apologies, V1 is a 30uV peak to peak, 0v being the low value, 50Hz, 50% duty cycle square wave.

Still confused.  If V1 is a square wave, what is this circuit intended to do? 

BTW, the RC is not 100 ohms * 100 uF.  It's 100,100 ohms * 100 uF, or around 10 seconds.  The waveform at VA should still be a square wave of 20 Vpp.  That's an output.  It is not impacted by any of the circuit connected to it.  It's the voltage on IN- that will be an odd waveform that could likely look what you are showing as VA. 

Until you fix the issues with the simulation you've provided, I certainly can't help you.  If this is LTspice, post your schematic file as text and I can run the simulation myself.

[magic]

If possible one should go for an DC coupled first amplifier stage. This avoids the rather large coupling capacitor that would be needed to get AC coupling of suppressing DC gain with the low resistance needed to keep the noise down.

The slight slope visible in the simulation would be less of an issue for the low on ratio pulses that are described (100 µs pulse with some 20 ms period). So the 100 ohm and 100 µF should be OK in this respect. More like that one would want less than 100 ohm to keep the noise low. 100 ohm have already more noise than an OPA1612.

I suggested the large capacitor for 50Hz signals, but it's 50Hz repetition rate of a 5kHz signal apparently, so I was overly pessimistic and the capacitance could be greatly reduced.

Definitely feedback resistance should be decreased if one is nuts about noise. For 60dB gain, 10/10k is typically good enough and only slightly affects even the lowest noise IC opamps.

THAT1510/SSM2019/INA103 for ultimate low noise with balanced differential input. These chips beat DIY instrumentation amps made of opamp ICs by using only one transistor per input pin.

[moffy]

If possible one should go for an DC coupled first amplifier stage. This avoids the rather large coupling capacitor that would be needed to get AC coupling of suppressing DC gain with the low resistance needed to keep the noise down.

The slight slope visible in the simulation would be less of an issue for the low on ratio pulses that are described (100 µs pulse with some 20 ms period). So the 100 ohm and 100 µF should be OK in this respect. More like that one would want less than 100 ohm to keep the noise low. 100 ohm have already more noise than an OPA1612.

Thanks for the clarification about the low duty cycle, Magic and you are right 100uF in such a case would be more than sufficient.