Investigation of a resonant sample and hold circuit

A resonant sample and hold circuit is analyzed which consists of a periodically operated switch, an inductor L and a capacitor C in series. Dissipative elements associated with these are represented by Rs, which also includes any source impedance, RL and Rc, respectively, and are taken into account. The switch is closed for an interval equal to one half the natural period of oscillation T2 of the circuit. This is assumed to be much smaller than the sampling interval T_S. The impedance of the open switch is taken as infinite. The circuit has the following advantages. It produces a peak near one half the sampling frequency which can be controlled by changing the resistances Rs, RL, Rc singly or in any combination. This can be used in pulse amplitude or pulse code modulation systems to equalize the cutoff of the reconstruction low-pass filters. The circuit also exhibits maximum attenuation at the carrier frequency ws. The current through the switch is sinusoidal with a peak amplitude several times smaller than what it would be if no resonant inductor were used. The voltage across the capacitor during charging is sinusoidal of frequency ω₂2. This makes possible the reduction of the bandwidth requirements of the high input impedance amplifier through which, for example, the capacitor voltage is coupled to an analog-to-digital (A/D) converter.