Fundamental design consideration of sampling circuit

This paper discusses a theoretical issue of a sampling circuit to maximize SNR while keeping its bandwidth constant, in order to realize a wideband large dynamic range sampling circuit for communication system and measuring instrument applications. We consider two time-constants τ
₁
, τ
₂
in the sampling circuit, where is a product of (signal source internal impedance + sampling switch on-resistance) and (hold capacitance), and τ
₂
is a sampling time window (aperture time). We have derived that τ
₂
= 1.50τ
₁
is the condition to maximize SNR keeping the bandwidth constant. We will call it as a strobe sampling circuit when τ
₂
= 1.50τ
₁
is realized.