Help me to understand gainstage of pipeline ADC

[snoop835]

Hi all,

Anyone can help me to understand the switch capacitor circuit as shown in FIGURE 1 attachment. This circuit is used in a gainstage of pipeline ADC. I am looking for a mathematics behind the circuit operation. How does the circuit subtract the DAC output (Vdac +-) from the original input to create a residue voltage?

Anyone can derive the equations for me and explain how the circuit operates>

thanks

 

[tuza2000]

in phi_1 the cs an cf were incharge to vin,and phi_1p was used to cancel charge injection by the switches-bottom sampling.in phi_2 the charge in the cs is vref,and the cf is 2vin-vref,so it's function is substraction and 2 gain.