Design techniques for switched-capacitor broad-band phase-splitting networks

A phase-splitting network is another type of circuit that is suitable to be integrated using the switched-capacitor (SC) technique. However, using existing all-pass SC configurations to realize such networks results in excessive capacitance spread because phase-splitting networks have very low real poles under a wide signal frequency band. Simple analytical expressions derived in this paper show that combining first-order sections of such networks into low-
Q
biquads does not reduce the capacitance spread unless the dynamic range of the filter can be sacrificed. A new biquad configuration is proposed for capacitor area efficient realization of low pole all-pass filters. The biquad combines a
T
-cell with a conventional integrator. The
T
-cell integrator realizes the low pole with a product of two capacitance ratios instead of a single capacitance ratio to reduce the capacitance spread. A simple and systematic design procedure is presented for the determination of capacitance values as a function of the poles to be realized. The design procedure achieves minimum total capacitance and equal dynamic range for all amplifiers simultaneously. Commonly performed rescaling of capacitance values after computer simulation is not necessary. The new biquad attenuates offset and flicker noise. However, finite amplifier dc gain and white noise have greater influence on the filter performance. Analytical expressions for transfer function deviations are derived which indicate the amplifier dc gain necessary for a given
\omega_0
tolerance. Computer simulations show that the total integrated noise of the
T
-cell biquad only slightly increases compared to that of the conventional biquad realizing the same function. A design example is given which illustrates the design procedure. Compared to the realization of the same transfer function with conventional biquads,
T
-cell realization reduces the total capacitor area by almost a factor of 20.