APD (Avalanche Photodiode) Active Quenching Circuit (AQC) Waveforms & Circuit Behavior

Question

I am reading a paper tiled Avalanche photodiodes and quenching circuits for single-photon detection

The paper presents an Active Quenching Circuit schematic, briefly describes its operation, and shows the voltage waveforms for nodes of interest. I understand how the circuit operates for the most part:

• APD is reverse biased above the breakdown level (Geiger mode) initially
• photon absorbed in active area of APD triggers avalanche current
• a comparator senses the avalanche pulse and outputs a pulse that controls the output of a driver
• This driver outputs a signal that controls a switch or MOSFET to connect the circuit to a voltage supply below the breakdown level
• APD avalanche current is quenched
• The driver outputs a signal that reconnects the circuit to the operating (above breakdown) voltage

The circuit schematic and voltage waveforms are shown below:

I am trying to understand the electrical behavior of the circuit (beyond the description that I gave above). I am mainly confused about the high pulse, and exponential voltage transition sections of waveform b, and the corresponding sections on waveform c.

Any explanation would be appreciated

Answer 1

The comparator has infinite input impedance. No currents flow into its inputs, approximately speaking.

The photodiode current must flow into RS1 - it has nowhere else to go. From Ohms law, RS1 voltage (b) is a proportional measure of photodiode current. So you can interpret (b) as photodiode current.

As the photodiode turns off and the current goes below the avalanche current, its capacitance acts as a differentiator for the voltage (a), thus the exponential decay you observe.

(c) is the output of the CC+RS2 differentiator. It differentiates the voltage at (a).

That's all that's needed to explain the waveforms.

Recall that real differentiators don't have infinite bandwidth. If you model one mathematically, either using numerical methods or analytically, you'll see that the exponential decay is an inherent characteristic.