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→Limitations of the Model
The silicon photomultipliers (SiPM) we are using in our experiment were purchased from [http://www.photonique.ch/ Photonique]. Photonique also supplies analog electronics boards to amplify the signals from the SiPMs. This page discusses the analysis and modeling of the amplifier circuit.
The silicon photomultipliers (SiPM) we are using in our experiment were purchased from [http://www.photonique.ch/ Photonique]. Photonique also supplies analog electronics boards to amplify the signals from the SiPMs. This page discusses the analysis and modeling of the amplifier circuit as well as design of the amplifier suitable for the readout of the tagger microscope.
== The circuit diagram ==
== The circuit diagram ==
The amplifier circuit diagram shown below was developed through combining the diagram supplied by Photonique (lacking component values, and having several extra components) and the physical circuit (having most components labeled).
The amplifier circuit diagram shown to the right was developed through combining the diagram supplied by Photonique (lacking component values, and having several extra components) and the physical circuit (having most components labeled).
The component values are shown below. The capacitors are unlabeled on any diagram, so values are not known for those components.
The component values are shown below. The capacitors are unlabeled on any diagram, so values are not known for those components.
For information regarding the node voltages and branch currents, see the article on the [[MATLAB amplifier in detail]].
For information regarding the node voltages and branch currents, see the article on the [[MATLAB amplifier in detail]].
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; font-family:times"
{|
|[[Image:SSPM Amplifier Circuit Diagram.jpg|thumb|480px|Circuit diagram]]
||
{| align="center" border="1" cellpadding="1" cellspacing="0" style="text-align:center; font-family:times"
|+ '''Component values'''
|+ '''Component values'''
|-
|-
|-
|-
| VT<sub>2</sub> || W1S <small>(13)</small> || Philips BFT 92
| VT<sub>2</sub> || W1S <small>(13)</small> || Philips BFT 92
|}
|}
|}
== MATLAB model ==
== MATLAB model ==
Varying the input current from 0 to 2A results in a clean straight line that intersects the origin. Thus we can say that the amplifier has a transimpedance gain (programmable based on input parameters; in particular V<sub>c</sub>) and no DC bias.
Varying the input current from 0 to 2A results in a clean straight line that intersects the origin. Thus we can say that the amplifier has a transimpedance gain (programmable based on input parameters; in particular V<sub>c</sub>) and no DC bias.
== Limitations of the Model ==
One of the principal limitations of this model turned out to be its inability to predict high-frequency behavior. Though the bandwidth inherent in the transistors themselves (4-5 GHz) was not explicitly in the model, the low-pass behavior due to source capacitance and amplifier input impedance should appear in the solutions naturally. It turned out that the more accurate modeling of the SiPM discharge as parallel injection of I<sub>in</sub> ''in parallel'' with the intrinsic SiPM capacitor recovers this behavior. Including this capacitance (labeled ''CS'') and a parallel current injection loop restored the sensitivity to input impedance. This input impedance turned out to be a challenge for achieving faster signals desired in the tagger microscope electronics. This issue is further discussed in a dedicated page:[[SiPM Amplifier Optimization]]