Autozeroed amplifier aliased wideband noise

[ytass]

Hi there,

I am trying to design a low noise amplifier for biological evoked potentials. I am tossing up whether or not to use autozeroing technique, correlated double sampling, or chopper stablization. I have been given very tight power consumption requirements (about 30uW max) operating at a 3.3V supply. The amplifier will be 3 stages, with variable gain from 50-80dB in 10dB steps. I would like to use autozeroing because I am of the understanding that chopper stablisation requires more power? Is that correct? Given that I think I should use autozero technique, I am having trouble defining the input transistors noise performance.

V_thermal^2 = 4kT * 2/3 * 1/gm for a mos transistor in saturation. I want to bias my input differential pair in moderate inversion, but i think this thermal noise equation is still not a bad approximation for moderate inversion region.
Thus the two input tranistors contribute V_in^2 = 16/3 * kT * 1/gm.

Now, what I dont understand is, if I use autozero technique, how much will this thermal noise increase by? If my signal bandwidth is about 10 kHz (biological signals are low frequency!) and my autozeroing frequency is 30 kHz, then what will be my actual (i.e. normal + aliased) noise that I would see at the input of my op amp? So if I want my input referred noise to be less than xuV/rms, then I want to know what value of gm i should design for.

I hope that an experienced designer can lend a hand to a junior designer.

Thank you so much in advance.

 

[ytass]

Hi there again,

Is there an experienced analog designer who can point me in the right direction? It would be much appreciated.

 

[rfsystem]

If you using an autozero technique or correlated double sampling you have a sampled high pass function for the noise from the opamp. That reduce also the 1/f noise. What is not reduced is the noise from the switches. Because you typical add the noise voltage of two switches from two phases the noise voltage is uncorrelated and sampled. This sampled noise voltage could be calculated by integrating the voltage noise density up to infinity. Typical there is some bandwidth limit. Then you get the voltage noise rms. That is the noise voltage sampled. Because you take the difference between two phases (autozero) you have to add the sampled noise voltage of both phase by square.

I had a similar project more than a decade before. The charge injection should be careful compensated or minimized. The biological voltage sources have some 100pF but also high MOhm source impedance. So some fQ injection impact your accuracy!

 

[JT]

When you refer to signal bandwidth, is this the amplifier bandwidth ?

For autozeroing, what you basically do, is sampling of the offset on a cap. This causes a foldback of the noise equal to signal bandwidth/autozero frequency.

In your case, you have 10kHz signal bw and 30kHz autozeroing, so you should have no foldback of the thermal noise.

However, take into account that your amplifier needs to settle enough during autozeroing, that's why I'm a bit puzzled that your BW < autozero frequency. (otherwise you'll introduce an error which might even be worse than your 1/f noise) You should have an amplifier bandwidth that is several times (10 or so) higher than the auto zero frequency, to make sure your output settles during the autozeroing.

A realistic case is for example a bw = 1MHz, and autozero freq of 30kHz. This gives you about 30 times foldover (it could be that I'm missing a sqrt somewhere) of the noise in the 0 to 30kHz bandwidth.

If you combine this with the attenuation of the offset and the low frequency 1/f noise, you get a partial attenuation of the 1/f noise.

Personally I'm more in favour of chopping. If you choose your frequencies wisely you don't have to bother about folding back of noise, and you can get almost 100% attenuation of the 1/f noise and offset. You can then optimize your design for low thermal noise (high gm), and still keep the area reasonably small (1/f is less important).

A nice presentation about autozeroing can be found here :
h**p://www.ewh.ieee.org/tc/sensors/Tutorials/makinwa.pdf

 

[rfsystem]

JT,

you found an excellent paper! The difference between Autozero and Chopper is clearly shown. I only have to notice that the chopper mixing is not multiplying with a pure sinewave. It is typical a square waveform. So all harmonics of the square waveform lead to noise folding. The advantage is that the total sum of all folding components is limited and not defined by the trade of settling time versus noise bandwidth.