Noise Minimization of MOSFET Input Charge Amplifiers Based on $\Delta\mu$ and $\Delta{\rm N}$$1/f$ Models

Low-Power Amplifier for Readout Interface of Semiconductor Scintillator

“…The flicker noise of MOS transistors may have two different origins [14], [16]. The model assumes that the flicker noise in the drain current results from the fluctuation in the number of charge carriers.…”

“…The derivation of the optimal sizing of the input transistor that operates in the strong-inversion region is presented in [14]. The total ENC is expressed in terms of three design variables: the Fig.…”

“…Fig. 2 shows the minimum achievable ENC for the case of a fixed biasing current [14] with no constraints on and , assuming that the input transistor operates in strong inversion. When the biasing current limit is higher than the optimal current obtained in the unconstrained optimization, the suboptimum capacitive ratio tends toward as the noise becomes dominant; when the biasing current is lower than , the suboptimum capacitive ratio moves to as the thermal noise becomes dominant.…”

“…If and are fixed, the minimum thermal noise is achieved at the lowest ; the minimum for the flicker noise is achieved for . 1) Unconstrained Optimization: In order to have the input transistor biased in the weak-inversion regime, the following condition has to be satisfied [14]: (13) where (14) This leads to an upper limit on the biasing current (15) Therefore, the optimum is chosen as the largest current that keeps the input transistor in the weak-inversion regime: (16) where (17) The optimum and can be found by equating partial derivatives of (12) with zero, which gives the unconstrained weak-inversion optima in the form: (18) When the above optima are feasible, the absolute minimum ENC in the weak-inversion regime is: (19) For our specific sensor, the unconstrained optimization leads to a minimum ENC of 348 at the biasing current of 44 . The input transistor width is 33 mm and the shaping time constant is 124 .…”

“…To reduce the thermal noise from has to be small, which leads to a higher voltage drop for the fixed biasing current. To reduce the flicker noise from , the length of the transistor is increased [14]. Noise from can be neglected due to the large resistance .…”