Thank you for your reply.
From the paper: "An 8-bit 200-MSample/s pipelined ADC with mixed-mode front-end S/H circuit", it mentioned that if the sampling rate is Fs, N-bit resolution, and the feedback factor is beta, then the unit gain bandwidth of the S/H amplifier should be larger than 2(N+1)*Fs*ln2/beta.
Comparing it with your equation "signal BW/error". Assume N=7( error 0.01), beta=0.5, and Fs=2*signal BW=20K, then the result 2(N+1)*Fs*ln2/beta=3MHz, which is quite close to your result. So the equation of "signal BW/error" is very handy.
I just don't know how they get the equation 2(N+1)*Fs*ln2/beta.