Hi, friends,

I'm designing Switched Capacitor 1bit DAC for Audio DAC. I can simulate the conventional SC filter with analog input(Spectre PSS & PAC). But in this case, the input is Sigma-Delta Modulator 1bit digital output and there is no sine input. Instead of analog sine input, Conventinal input port is tied to Vref and the digital outputs of sigma delta modulator are switching the signal path.

Please check the attached file. I can't understand how they remove the Vref from Equation(3). In the Equation (1),(2), there is Vref. Of course, this circuit is not the same structure as mine, but I think the calculating method will be same.

Could you let me know the paper or book title in which there is a detailed explanation about how to calculate the transfer function of Switched Capacitor 1bit DAC? Basic papaers about SC 1bit DAC will be a huge help to me.  

I found the following papers, but the structure is not the same.
Can this method be applied to the SC 1bit DAC of attached file?
   http://www.ieice.org/explorer/ITC-CSCC2008/pdf/p1513_P2-25.pdf

1 More question!
Could you let me know the Spectre AC (or PAC) simulation method of this kind of circuit ( Switched Capacitor 1bit DAC ) ?
I mean not tran simulation.