SiPM Amplifier Optimization

The SiPM amplifier currently in use for SiPM characterization (Photonique item "AMP_0604") must be adapted for tagger microscope use. The following is a brief outline of the design requirements. They are discussed in detail in the following sections

1. adjustable gain, ranging from readout of hundreds of pixels to calibration with single-photon counting
2. less than 15% gain variability on transistor $\beta$ ($h_{FE}$) parameter
3. summing circuit to pool SiPM signals in groups of 5 (readout of individual channels must not affect readout of the some regardless of termination used)
4. minimized pulse duration for higher running rates
5. minimized power consumption

Design Requirements

One of the most important considerations in the amplifier design is the target data acquisition system. Currently, the microscope is slated to be read out by a 12-bit flash ADC with a 250 MHz sampling rate and range settings of -2V, -1V and -0.5V.

Gain

The amplifier provided by Photonique with a gain of roughly 3 kΩ was well suited for single photon counting. However, for typical signals ranging in the hundreds of SiPM pixels, this gain excessive. However, the option of switching back to single photon detection for the purposes of calibration would be a nice feature.

From the perspective of expected signal amplitudes (taking into account optical and SiPM's quantum efficiencies) signals around 300 pixels (px) are expected. With a SiPM gain of about 2 × 10⁵ ~ 9.6 pC are expected to be deposited. Design uncertainties that go into the full calculation summarized here can easily allow variation in this result by a factor of two or more. Roughly estimating this charge to be contained in a triangular pulse with 5 ns FWHM (after all the broadening inherent in the amplifier) yields a total signal peak of 0.5 mA. With this figure and the full range of the ADC (2V) it seems that 3 kΩ is still appropriate. However this does not leave room for variation discussed above. Instead, a goal of sub-1 kΩ gain was adopted.

For the high gain setting, the issue is mainly the vertical resolution of the ADC. For most of the duration of this project, the 8-bit version of the ADC was planned to be allocated for microscope readout, imposing a stringent requirement on gain in order to avoid the digitization noise inherent in signals only a few adc voltage steps. The 12-bit ADC makes clean readout of single pixel wavefunctions more realistic: at the most sensitive scale of 0.5 V, the resolution is 0.12 mV. However, we must also take into account noise and a possible factor of two loss in the split of the signal between the ADC and the CFD (constant fraction discriminator to prepare for time pick-off.) This time, it is appropriate to take a pessimistic scenario of the pulse shape: taking a triangular pulse with 30 ns FWHM, leading to a single pixel current peak of 0.27 μA. Under these conditions, gain of 7 kΩ is enough, giving 15 adc steps per pixel.

Minimal Dependence on $\beta$

Dependence of a design on a value β of a transistor is never a good idea, given its variability as a function of temperature. The value also varies between one transistor and the next. The high speed transistors necessary in this design are already at a disadvantage with respect to this design goal, due to their low beta with the result of greater significance of the parameter's variation. This issue will be discussed at length below.

While it is true that this variation can be compensated by adjusting the bias voltage on the SiPM to alter the gain, this sort of tweaking is not desirable. The detection efficiency changes right along with the gain. (Detection of the maximimum number of photons is critical for good time resolution.) With these concerns in mind, a design requirement of gain variation no greater than 15% variation was set.

Summing Circuit

While the microscope contains 500 optical channels resulting from the two-dimensional segmentation of the focal plane, only the energy bin information is important. The vertical column of 5 scintillating fibers in the focal plane can then have its signals summed, reducing the count of channels requiring readout to 100. However, the design of the microscope calls for individual readout in 5 columns spread around the focal plane in order to retain the knowledge of the two-dimensional orientation of the electron stripe.

Thus a summing circuit is necessary to tie together 5 amplifiers. Drivers for single channel readout must still be available on the board and their output must be available on the board's interface pins. (The choice of which group of channels can be accessed is up to the layout of the backplane board.) The individual channel and summing circuit outputs must remain independent regardless of termination. This means that the input to the summing circuit must have its own current source so that the load on the individual channel is not relevant. Additionally, as has been discussed above under gain requirements, the summing circuit must offer additional gain when system is set to high gain mode.

Short Pulses

The duration of the amplified signals is, in essence, the dead time of the channel. (Pulses with significant overlap are difficult to distinguish.) The lower bound of the pulse width is set by the scintillator. The BCF-20 intended for use in the microscope has a decay time of 2.7 ns. A somewhat stricter restriction is set by the sampling rate of the ADC - 250 MHz. A rough (and vague) guideline of 15  total signal duration has been observed during the design.

Power Consumption

Operation of over 500 such amplifiers (spares are available on each board) in a sealed box presents an issue of heat management. High temperatures inside the microscope should be avoided especially due to the sensitivity of SiPM parameters on temperature. Note also that the amplifiers will be packed very tightly (~5 mm strips) in the final layout. 30 mW has been set as the power budget per amplifier. The restriction on the summing circuit is not as critical, because there are 5 times fewer such circuits in the microscope. Contribution from the actual AC signals and various voltage regulators are negligible and are not taken into account.

Design Implementation

However, care must be taken to avoid creating integrators (low-pass filters) in the amplifiers that may stretch the pulse significantly.

To maximize the possible running rate of the microscope, signals leaving the ampifier should be as fast as possible

Going from this integrated charge figure to actual signal heights requires knowledge of the pulse duration due to pulse shaping in the amplifier. However, gain and pulse shape are coupled in the amplifier design - one resetting the goals for the other.

The initial approach to this problem of gain switching was just that suggested by Photonique documentation: turning up the amplifier supply voltage. With the transistors' maximal voltage rating of 15 V taken as high gain setting, some simulations done to assess the amplifier performance.

The amplifier provided by Photonique with a gain of roughly 3 kΩ was well suited for single photon counting. However, for typical signals ranging in the hundreds of SiPM pixels, this gain excessive. However, the option of switching back to single photon detection for the purposes of calibration would be a nice feature. The initial approach to this problem of gain switching was just that suggested by Photonique documentation: turning up the amplifier supply voltage. With the transistors' maximal voltage rating of 15 V taken as high gain setting, some simulations done to assess the amplifier performance. The following problems were found in this approach:

• Gain saturates with increasing supply voltage leading to poor gain separation between the two modes (recall that the low gain setting needs to be much lower for real signals.)
• Power consumption is of order 200 mW at high gain setting
• Component values necessary for high gain are not suitable for stable, $\beta$-independent design
• Input impedance of the amplifier increase significantly in the high gain design. On the other hand, the effective impedance and therefore pulse shape varies with supply voltage.

A low-impedance input stage was designed to alleviate the last issue, but the rest remained serious concerns and challenges. An alternate design was adapted in which the summing stage further amplifies the signal. Now, however, instead of doing this with supply