Peter Kurahashi
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My problem is this: Simulations of the S&H circuit from “Simulating SC Filters in SpectreRF” for sampling frequencies above the Nyquist rate don’t match theory.
Using Ken’s work as a guide my reasoning goes like this. When sampling above the Nyquist rate only the zero sideband is of interest because there is no aliasing. The sampled spectral density therefore becomes:
Ss = Src*fc^2 for abs(f) <or= fc/2
Implementing the hold operation:
Sh = [(1-m)*Tc*sinc(f*(1-m)*Tc)]^2 * Ss Sh(0) ~ [(1-m)*Tc]^2 * Ss(0) because sinc goes to 1 Sh(0) ~ [(1-m)*Tc]^2 * Src(0)*fc^2 Sh(0) ~ (1-m)^2 * Src(0)
Taking m=0.4, Sh(0) ~ 0.36 Src(0)
Sc = St + Sh where St = m*Src, therefore Sc(0) = 0.4 Src(0) + 0.36 Src(0) = 0.76 Src(0)
This result was confirmed using C. –A. Gobet’s method in “Spectral distribution of a sampled first order lowpass filtered white noise,” Inst. Elec. Eng. Electron. Lett., no. 19, vol. 17, pp. 720-721, Sept. 1981.
Both solutions show that for a resistance of 2.3kohms which gives a continuous time DC spectral density of 38 aV^2/Hz, the composite DC spectral density should be 0.76 times this or 29aV^2/Hz.
When the S&H circuit is simulated in SpectreS the results match well for sampling frequencies well under the noise cutoff frequency. But when the sampling rate is increased above the Nyquist rate Sc(0) reaches a limit to just under 100aV^2/Hz, 2.5 times Src(0).
For my simulations I tried both an ideal switch with a noisy resistor and a pair of mosfet switches. Both showed the same behavior. I used a maxsideband of 50 and as I increased the clock frequency I adjusted the required maxacfreq. Sampling above the Nyquist rate and selecting zero sideband only showed the same results.
Any ideas?
Thanks, Peter
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