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

Circuit diagram

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.

For information regarding the node voltages and branch currents, see the article on the MATLAB amplifier in detail.

Component values

Part	On-chip label	Actual component
Resistors
R1	104	100kΩ
R2	103	10kΩ
R3	562	5.6kΩ
R4	202	2kΩ
R5	102	1kΩ
R6	510	51Ω
R7	241	240Ω
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
$VT_{2}$	W1S (13)	Philips BFT 92

MATLAB model

Main article: MATLAB amplifier 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, but some were changed to fit the model to actual data. 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\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.

The model itself can be found here.

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

We varied 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.

Power voltage

The amplifier's response to varying 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} ) from 0 to 10V is shown in the image below.

Note that the vertical axis can be read as either the output 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_{out}} ) in mV or as the transimpedance gain in 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 \Omega} .

Frequency

The amplifier's response to varying 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} ) is shown in the image below.

Note that the vertical axis can be read as either the output 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_{out}} ) in mV or as the transimpedance gain in 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 \Omega} .

Input current

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 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} ) and no DC bias.