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Description
The classical pulse processing chain for a radiation detector consists of a charge sensitive amplifier followed by a shaping filter that optimizes the signal to noise ratio. Hybrid pixel detector readout circuits usually omit the band-pass filter stage because of area and power consumption constraints. Moreover, when digitizing the energy information using the Time-Over-Threshold principle, a charge sensitive amplifier whose feedback capacitor is reset at constant current provides superior linearity and dynamic range than the circuit including the shaper.
In this paper we analyze the behavior of a classical charge sensitive amplifier with constant current discharge of the feedback capacitor with the input transistor current from circuit basic principles and compare the results with measured results in the Timepix3 chip. The expression for the Equivalent Noise Charge due to the preamplifier input transistor thermal noise is:
$$ ENC^2_s = \frac{K_BTN_{\gamma}\frac{C_F(C_F+C_I)^2}{(C_FC_I+C_FC_O+C_IC_O)}}{q^2\alpha^2}$$
Where $K_B$ is the Boltzmann constant, T is the temperature in degrees Kelvin, N is the excess noise factor, $\gamma$ is a parameter measuring the degree of inversion of the transistor, $C_I$, $C_F$ and $C_O$ are the input, feedback and output capacitances respectively q is the electron charge and
$$ \alpha = ma x( e^{\frac{1}{\tau_{fall}}} -e^{\frac{1}{\tau_{rise}}} ), t>0$$
$\alpha$ is a parameter accounting for the separation of the time constants defining the preamplifier output rise and fall times. An important conclusion is that, provided the rise time and the fall time constants are far apart, the noise due to the input transistor is independent of its transconductance and as a consequence, independent of the input transistor power consumption. The reason is that when increasing the current in the input transistor, its noise decreases but the bandwidth over which the noise is integrated increases by the same amount, the two effects cancelling each other. If the device operates in a low count rate environment substantial reductions in power consumption can be obtained with little or no noise penalty.
The measurements below show 241Am source spectra measured with Timepix3 [1] at preamplifier bias currents of $2.4\mu A$ (left) and 150nA (right). In the paper we will report on full circuit simulations helping to identify optimized power consumption depending on the count rate environment including any trade-offs between power consumption, maximum count rate, noise and minimum operating threshold.
[1] T. Poikela et al. 2014 JINST 9 C05013
