SiPM Amplifier

The silicon photomultipliers (SiPM) we are using in our experiment were purchased from 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

Component values

Part	On-chip label	Actual component
Resistors
$R_{1}$	104	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 100\mbox{k}\Omega}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_2}	103	$10{\mbox{k}}\Omega$
$R_{3}$	562	$5.6{\mbox{k}}\Omega$
$R_{4}$	202	$2{\mbox{k}}\Omega$
$R_{5}$	102	$1{\mbox{k}}\Omega$
$R_{6}$	510	$51\Omega$
$R_{7}$	241	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 240\Omega}
Transistors
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle VT_1}	E2P (1717)	Philips BFS 17A
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle VT_2}	W1S (13)	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 (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_{in}} , in amps), the bias voltage (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_b} , in volts), the power voltage (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_c} , in volts), and the frequency (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} , in hertz). The resistor values are mostly the same as the ones given for the above diagram, except for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_4} (now Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.2\mbox{k}\Omega} ) and $R_{6}$ (now Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 53\Omega} ). We also add a load resistor from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{out}} to GND, with a value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 50\mbox{k}\Omega} . The transistors are described by a series of parameters from the 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_b = 20\mbox{V}} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_c = 5\mbox{V}} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f = 100\mbox{MHz}} , and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_{in} = 1\mbox{mA}} , then varied one parameter at a time to generate responses.

Bias voltage

Varying the bias voltage from 0 to 50V. Within this range the output (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{out}} ) does not vary at all.

Input current

Varying the input current from 0 to 2A results in a clean straight line. Performing a linear regression results in the equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{out} = 3.2534/mbox{k}\Omega * I_{in}} .