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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.  
 
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.  
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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.
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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. The bounds of overall-amplifier β variation were taken conservatively: the worst scenario was one in which
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''all'' transistors are at the minimum β value.
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== Design Implementation ==
 
== Design Implementation ==
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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 the high gain setting, some simulations were done to assess the amplifier performance. The following problems were found in this approach:
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* 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.)
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* Power consumption is of order 200 mW at high gain setting
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* Component values necessary for high gain are not suitable for stable, <math>\beta</math>-independent design
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* Input impedance of the amplifier increase significantly in the high gain design. (This along with the SiPM capacitance sets the integration RC-time.) On the other hand, the effective impedance and therefore pulse shape varies with supply voltage.
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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 supply voltage remains constant but the summing stage offers additional amplification. Gain selection is accomplished with a FET switch, effectively altering the resistance in a transistor stage similar to the common emitter amplifier.
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The low impedance input stage was retained from the earlier design and applied the the summing circuit, since it pools currents from the individual amplifiers. In Photonique's design, the input signal sees the transistor base, base-biasing resistor, and a feedback resistor in parallel. The new input stages take the signal on the emitter (base held at a set DC value), in which case the signal sees the emitter resistor and the impedance looking into the emitter in parallel with each other. The latter dominates with an effective resistance of order 25&nbsp;&Omega;. The input stages are biased with generous amount of current to keep this value low.
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However, care must be taken to avoid creating integrators (low-pass filters) in the amplifiers that may stretch the pulse significantly.
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To maximize the possible running rate of the microscope, signals leaving the ampifier should be as fast as possible
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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.
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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
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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.
 
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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&nbsp;V taken as high gain setting, some simulations done to assess the amplifier performance.
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The amplifier provided by Photonique with a gain of roughly 3&nbsp;k&Omega; 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&nbsp;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&nbsp;mW at high gain setting
  −
* Component values necessary for high gain are not suitable for stable, <math>\beta</math>-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
 
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