In order to read out the signal from a germanium detector, it is necessary to have a few basic components in place. Generically, the raw current signal from a detector must first be amplified by apreamplifier, then perhaps further amplified by anamplifier. Then this amplified signal may be read out by digitizing the signal, resulting in a waveform for later, offline analysis. When waveforms are to be digitized they often use only a preamplifier, as the amplifier usually provides some shaping which is useful for compressing the signal into a single recorded point value, such as amplitude.
3.4.1 Readout Electronics for theMAJORANA DEMONSTRATOR
The electronics readout chain for the MAJORANADEMONSTRATORconsists of a low-mass front end (LMFE), a two-stage preamplifier, and a digitizer. The exact implementation used is somewhat unusual, due to the specific low-radioactivity constraints in place. A schematic diagram of the principal components is shown in figure 3.12.
A current signal is formed inside the detector, which is directly injected onto the gate of a JFET on the LMFE. The LMFE is physically located inside the detector unit, approximately 1 cm from the detector itself;
Figure 3.10: Color indicates the maximum difference in time at the 50 percent timepoint between waveforms in a cloud, at each point over the detector cross section. Detector is an enriched ORTEC detector, so the bevel and point contact are visible.
Figure 3.11: Color indicates the maximum difference in time at the 50 percent timepoint between waveforms in a cloud, at each point over the detector cross section. Detector is a BEGe, so the ditch outline is visible, with some edge effects.
Figure 3.12: A high-level schematic overview of the MJD signal readout chain.
it is near the detector’s base temperature, slightly above liquid nitrogen temperature, and under vacuum. The LMFE is electrically connected to four coaxial signal cables, thesource,drain,feedback, andpulser. These all connect to the warm electronics outside through several meters of cable, a vacuum flange, and multiple connector pairs. Immediately on the warm, non-vacuum side of the flange, the signals are passed to the “preamplifier card”, mounted on a motherboard which provides power.
The LMFE is electronically a component of the feedback loop of the preamplifier, but is physically distinct from the rest of the preamplifier due to background constraints, so the components are often considered as separate features.
The preamplifier design was performed at LBL, and is based on a folded cascode arrangement. The folded cascode design is ideal for producing a good output voltage swing and common-mode range with high output impedance [74]. The primary challenges of the MJD design are that it must be low noise and low radioactive background. The low background aspect is achieved by reducing the potentially radioactive mass of components near the detector, giving rise to a feedback loop of several meters in length. As the signal frequency increases, the time required for a signal to be transmitted along the cable eventually exceeds the time for the signal to go out of phase. This long feedback then limits the maximum risetime and bandwidth of the signals which are amplified.
3.4.2 Modeling of installed electronics
In order to develop a realistic model of the electronics, we performed numerical simulations of the full amplifier circuit between the detector and the digitizer. Although as-built schematics of the electronics were not available, we were able to infer the full design from the physical circuits.
Perhaps the most common software for modeling analog and mixed-signal circuits is the open-source SPICE software. While SPICE refers to a particular package, there are many variants of the original frame- work, designed either for particular analyses or adopted by electronics manufacturers for their own standard tools. The version used in this work is the open-source C++ based Xyce software, developed by a group at Sandia National Laboratory for solving large and complex circuits in parallel [75, 76]. While technically not a SPICE derivative, Xyce is completely compatible with SPICE, and should be indistinguishable from SPICE to most users.
SPICE modelers take as an input a “netlist”. This is a file containing a list of components, their properties, and to what each component is electrically connected, as a complete description of the circuit.
Using the SPICE model we were able to reproduce the basic features of the signals and to design a filter model which can be applied to simulated waveforms.
3.4.3 Electronics Effects on Waveforms
When visually looking at a MAJORANAgermanium detector waveform, there are three primary features. The most obvious is therising edge; the detailed shape of this contains information about how the charges moved through the detector before reaching higher field areas. The full rising edge usually occurs within about1µs of the signal onset. The next obvious feature is thefalling edgeordecaying tailregion of the falling edge. This is from the capacitive coupling of the first and second stages of the preamp, a high-pass filter with a decay time of around 75µs. Finally, thebaselineahead of the rising edge contains no detector signal, and the higher frequency variation from the mean baseline value can be used as a measure of the noise. This baseline is usually at about 0V, but, due to a slow time-constant recovery of the signal, the entire baseline can also shift between subsequent events. The distinguishing point between the baseline and the rising edge ist0, the signal start time. Often, the readout is tuned such that the rising edge occurs near the
Figure 3.13: Regions of signals waveforms discussed in this chapter. The waveform is a voltage signal in the time domain.
The preamplifier also acts as a long-decay-time high-pass filter with a time constant around 3 ms. Within a single waveform, it is difficult to see the effect of this, however, multiple events in rapid succession will offset the total baseline due to this, so it is necessary to track.
Additionally, the preamplifier, like all real circuits, is incapable of reproducing arbitrarily high frequency signals, and acts as a low-pass filter. By comparing the response to real waveforms and those simulated using SPICE, the response is found to closely match that of a 2nd order filter.