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B. The signal input-to-output relationship for this circuit can be obtained as a particular case of Eq. 8 simply by putting e~= 0, R3 = 0, R$ -> •*>. Doing so, Eq. 8 gives: R i + R? = -~——~ . e+ R l v (Eq. 12) which shows that the noninverting configuration gives a gain which is always larger than 1 and becomes equal to 1 in the case of the buffer or voltage-follower circuit (R2 = 0) shown in Fig. 14. Fig. 14: Gain one noninverting configuration (output stage) A buffer realized with the connection of Fig.
Owing to the presence of series and RL-noise, filtering can improve the signal-to-noise ratio. Here we want to evaluate the signal-to-noise ratio at the output of the simple RC - CR filter shown in Fig. 18. FROM PREAMPLIFIER OUTPUT Fig. 18: RC INTEGRATOR AMPLIFIER RC-CR shaper RC DIFFERENTIATOR The transfer function of this filter for sinusoidal wave is: . —— L . 1 + jwRC 1 + joRC transfer function of the RC integrator transfer function of the RC differentiator To evaluate the noise at the filter output we must remember that the noise sources considered here are UNCORRELATED .
Active filters based on operational amplifiers usually employ only R,C components because real inductors differ too much from their ideal model. When inductors are required, they can be simulated with active networks employing only R,C elements. Here attention will be restricted to the filters that are of interest in nuclear electronics applications. Fig. 16: Operational configurations with nonresistive external elements The circuits of Fig. 16 can be analyzed by means of Laplace transform. According to this method the input time-dependent generators e(t), i(t) are replaced by their Laplace transform generators E(s), I(s), where s is the complex Laplace variable.