Is there an established way to model this PIR + JFET circuit?

Question

Pictured is a PIR (passive infra-red) sensor hooked up to a JFET.

The diagram is from these design notes, which describes the workings of the PIR sensor as:

The PIR motion sensor consists of two or more elements that output a voltage proportional to the amount of
incident infrared radiation. Each pair of pyroelectric elements are connected in series such that if the
voltage generated by each element is equal, as in the case of IR due to ambient room temperature or no
motion, then the overall voltage of the sensor elements is 0 V.

The circuit looks like a self-biasing JFET, which helps to understand what the mathematical relationship between the resistors, Vcc, and current might be. However, the self-biasing configuration doesn't have a voltage source at the gate, whereas this one does (the PIR).

Is there an established way to model circuits such as this? What I mean by that is, is there an equation which relates Vcc, the value of the resistors, and the voltage at the output of the pyro-electric element to the current flowing out of the JFET?

Answer 1

It's just a source follower if you are just considering the voltage at the pyroelectric element. So the output will more-or-less follow the input (gain of about 1) with an offset voltage (positive, of course, since all JFETs are depletion mode) that depends on the resistor and JFET characteristics.

^{simulate this circuit – Schematic created using CircuitLab}

However the pyroelectric element is going to behave more like a voltage source in series with a capacitor. The time constant will give you the behavior shown in Vir. And the light is going to be modulated by a Fresnel lens in most real motion detector applications.