I have thought for some time that by adding shunt/shunt  feedback to a bipolar transistor or mosfet (a JFET also but only AC coupled), that it would emulate a Triode tube with respect to the output I/V curve. So I decided to simulate it and check.  These devices, when biased for normal operation, have a output response that becomes independent of the supply used. This is the same for a Pentode tube like a 6L6, EL84, etc, where the screen grid has a constant bias allowing the plate voltage to vary significantly without changing the current flow through the tube.  By adding shunt/shunt feedback, which in this case is a feedback resistor from the collector to base of a Darlington device, the output I/V behavior becomes constrained by the biasing of the base and therefore affected by the changing voltage seen at the collector.

Shown below is a simple amplifier circuit, simulated in SPICE, using a Darlington  but without the feedback. You can see from the I/V(current  is the Y axis and voltage the X axis) curve that at a couple volts or so, the device is in the active region and as the voltage increases the current stay mostly the same.  The current through the device becomes independent of the voltage across it – like a Pentode or saturated mosfet.

Now lets add the shunt/shunt feedback as shown below. You can see with the new circuit, that as the device is turning on, there is a small but highly non-linear region. This is because the supply voltage is below the point of actually biasing the device all the way on. As the supply voltage is increased, the device is biased on but the current through the device now is dependent on the supply voltage because as the supply voltage changes so does the base bias and therefore the current flow through the collector circuit. The alters the I/V behavior the device to act like a Triode where the output I/V behavior is much like a simple linear resistor.

I used the Darlington in the manner in my Battery Amp with excellent results.