MATLAB amplifier in detail

The model of the SiPM amplifier is a system of 24 equations in 24 variables that has been linearized so that it can be solved by MATLAB.

Parameters and variables

The MATLAB model has a number of parameters and variables to describe the amplifier circuit, including the 24 unknowns, 4 inputs, and numerous constants.

Input parameters

There are four input parameters:

• Input current: $I_{in}$ (A)
• Bias voltage: $V_{b}$ (V)
• Power voltage: $V_{c}$ (V)
• Frequency: $f$ (Hz)

Unknown variables

There are twenty-four unknown variables. The locations (and directions in the case of currents) are labeled on the circuit diagram.

• Node voltages: $V_{1}$, $V_{2}$, $V_{3}$, $V_{4}$, $V_{5}$, $V_{7}$, $V_{out}$
  • Note: there is no $V_{6}$ on this circuit; it was a redundant variable with $V_{c}$.
• Resistor currents: $I_{1}$, $I_{2}$, $I_{3}$, $I_{4}$, $I_{5}$, $I_{6}$, $I_{7}$, $I_{t}$
• Transistor currents: $j_{b}$, $j_{c}$, $j_{e}$, $k_{b}$, $k_{c}$, $k_{e}$
• Capacitor currents: $h_{1}$, $h_{2}$, $h_{3}$

Constants

• Resistors
  • $R_{1}=100{\mbox{k}}\Omega$
  • $R_{2}=10{\mbox{k}}\Omega$
  • $R_{3}=5.6{\mbox{k}}\Omega$
  • $R_{4}=1.2{\mbox{k}}\Omega$
  • $R_{5}=1{\mbox{k}}\Omega$
  • $R_{6}=53\Omega$
  • $R_{7}=240\Omega$
  • $R_{t}=50\Omega$
• Capacitors
  • $C_{1}=100{\mbox{nF}}$
  • $C_{2}=0.1{\mbox{nF}}$
  • $C_{3}=100{\mbox{nF}}$
  • $C_{5}=10{\mbox{nF}}$
• Transistors

$R_{1}$	104	$100{\mbox{k}}\Omega$
$R_{2}$	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	$240\Omega$
$VT_{1}$	E2P (1717)	Philips BFS 17A
$VT_{2}$	W1S (13)	Philips BFT 92