Errors in output due to low frequency
1] Offset
The output offset voltage is the dc voltage between the output terminal and ground for the circuit when the input terminal(s) are grounded.
Output offset is gain times input offset or 55mV, worst-case
Offset is caused by manufacturing variation or uncertainty
Can be reduced by using large devices. However, this increases chip area and therefore production cost
If we already know the offset voltage, then 2 ways to compensate it:

• Applying the input offset voltage
• Changing the negative level

2] 1/f Noise
caused by the defects in the interface between the gate oxide and the silicon substrate
e typical 1/f noise corner frequency of CMOS technology is in the order of several kHz to tens of kHz

3] Drift
Drift is caused by the cross-sensitivity of some error sources to temperature or time

To reduce offset, 3 types of offset cancellation techniques can be applied:

• trimming
• auto-zeroing
• chopping

Trimming:  reducing the offset during production, does not eliminate low-frequency noise
Auto-zeroing: sampling the offset of the amplifier in one clock phase, and then subtracting it from the input signal in the other clock phase.

• output offset storage
• input offset storage
• closed-loop offset cancellation - auxiliary amplifier

output offset storage

When CLK is 1, the inputs and X, Y of opamp shorted, and the output offset voltage is stored is Capacitor.
When CLK is 0, the input voltage is provided to the opamp and the offset voltage is compensated by capacitor voltage.
It limits the maximum gain of the amplifier


input offset storage


When CK is high, the output and input of the amplifier are shorted together by switches S1 and S2, placing the amplifier in a unity-gain configuration
The circuit reproduces the amplifier’s offset at nodes X and Y, storing the result on C1 and C2
stability issue

closed-loop offset cancellation - auxiliary amplifier


Used to isolate the offset storage capacitors from the signal path
The charge injection due to the mismatch of S3 and S4 contributes to the offset of Gm2
Gm2 is usually chosen to be at least 50 times smaller than Gm1.
cause noise folding


Chopping: continuous-time modulation technique


the input voltage Vin -> chopper (fch) -> square wave voltage -> amplication with input offset
-> demodulate chopper | modulates the offset to the odd harmonics of fch -> low pass filter
 
To completely remove the 1/f noise, the chopping frequency should be higher than the 1/f noise corner frequency