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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 circuit diagram ==
{| align="right" border="1" cellpadding="8" cellspacing="0" style="background:#f9f9f9; text-align:center"
|+ '''Component values'''
|-
! style="font-weight:bold" | Part || On-chip label || Actual component
|-
! colspan="3" style="background:#ffdead; text-align:left" | Resistors
|-
| <math>R_1</math> || 104 || <math>100k\Omega</math>
|-
| <math>R_2</math> || 103 || <math>10k\Omega</math>
|-
| <math>R_3</math> || 562 || <math>5.6k\Omega</math>
|-
| <math>R_4</math> || 202 || <math>2k\Omega</math>
|-
| <math>R_5</math> || 102 || <math>1k\Omega</math>
|-
| <math>R_6</math> || 510 || <math>51\Omega</math>
|-
| <math>R_7</math> || 241 || <math>240\Omega</math>
|-
! colspan="3" style="background:#ffdead; text-align:left" | Transistors
|-
| <math>VT_1</math> || E2P <small>(1717)</small> || Philips BFS 17A
|-
| <math>VT_2</math> || W1S <small>(13)</small> || Philips BFT 92
|}
The amplifier circuit diagram shown here 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 to the right. The capacitors are unlabeled on any diagram, so values are not known for those components.
== MATLAB model ==
''Main article: [[MATLAB amplifer in detail]]''
We developed a model for this circuit in MATLAB to simulate its behavior and study various parameters, especially gain as a function of power voltage. The Photonique documentation claims that the power voltage can be varied between four and nine volts in order to tune the gain of the amplifier. The MATLAB model is a linearized system of twenty-four equations, with the voltages and currents on the circuit being the twenty-four unknowns. There are four input parameters: input current (<math>I_{in}</math>, in amps), the bias voltage (<math>V_b</math>, in volts), the power voltage (<math>V_c</math>, in volts), and the frequency (<math>f</math>, in hertz). The resistor values are mostly the same as the ones given for the above diagram, except for <math>R_4</math> (now <math>1.2k\Omega</math>) and <math>R_6</math> (now <math>53\Omega</math>). We also add a load resistor from <math>V_{out}</math> to GND, with a value of <math>50k\Omega</math>. The transistors are described by a series of parameters from the [http://en.wikipedia.org/wiki/Gummel-Poon_Model Gummel-Poon SPICE model], and we included our best guesses of the capacitor values.
== Responses of the model ==
We ran simulations of the MATLAB model while varying the input parameters to generate data on how the amplifier responds to each input. We used as a baseline test the inputs <math>V_b = 20V</math>, <math>V_c = 5V</math>, <math>f = 100MHz</math>, and <math>I_{in} = 1mA</math>, then varied one parameter at a time to generate responses.
=== Bias voltage ===
=== Power voltage ===
=== Frequency ===
=== Input current ===
== The circuit diagram ==
{| align="right" border="1" cellpadding="8" cellspacing="0" style="background:#f9f9f9; text-align:center"
|+ '''Component values'''
|-
! style="font-weight:bold" | Part || On-chip label || Actual component
|-
! colspan="3" style="background:#ffdead; text-align:left" | Resistors
|-
| <math>R_1</math> || 104 || <math>100k\Omega</math>
|-
| <math>R_2</math> || 103 || <math>10k\Omega</math>
|-
| <math>R_3</math> || 562 || <math>5.6k\Omega</math>
|-
| <math>R_4</math> || 202 || <math>2k\Omega</math>
|-
| <math>R_5</math> || 102 || <math>1k\Omega</math>
|-
| <math>R_6</math> || 510 || <math>51\Omega</math>
|-
| <math>R_7</math> || 241 || <math>240\Omega</math>
|-
! colspan="3" style="background:#ffdead; text-align:left" | Transistors
|-
| <math>VT_1</math> || E2P <small>(1717)</small> || Philips BFS 17A
|-
| <math>VT_2</math> || W1S <small>(13)</small> || Philips BFT 92
|}
The amplifier circuit diagram shown here 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 to the right. The capacitors are unlabeled on any diagram, so values are not known for those components.
== MATLAB model ==
''Main article: [[MATLAB amplifer in detail]]''
We developed a model for this circuit in MATLAB to simulate its behavior and study various parameters, especially gain as a function of power voltage. The Photonique documentation claims that the power voltage can be varied between four and nine volts in order to tune the gain of the amplifier. The MATLAB model is a linearized system of twenty-four equations, with the voltages and currents on the circuit being the twenty-four unknowns. There are four input parameters: input current (<math>I_{in}</math>, in amps), the bias voltage (<math>V_b</math>, in volts), the power voltage (<math>V_c</math>, in volts), and the frequency (<math>f</math>, in hertz). The resistor values are mostly the same as the ones given for the above diagram, except for <math>R_4</math> (now <math>1.2k\Omega</math>) and <math>R_6</math> (now <math>53\Omega</math>). We also add a load resistor from <math>V_{out}</math> to GND, with a value of <math>50k\Omega</math>. The transistors are described by a series of parameters from the [http://en.wikipedia.org/wiki/Gummel-Poon_Model Gummel-Poon SPICE model], and we included our best guesses of the capacitor values.
== Responses of the model ==
We ran simulations of the MATLAB model while varying the input parameters to generate data on how the amplifier responds to each input. We used as a baseline test the inputs <math>V_b = 20V</math>, <math>V_c = 5V</math>, <math>f = 100MHz</math>, and <math>I_{in} = 1mA</math>, then varied one parameter at a time to generate responses.
=== Bias voltage ===
=== Power voltage ===
=== Frequency ===
=== Input current ===