Why would this circuit have a "maximum" output power?

Question

For the circuit above, in addition to what's labeled, the Zener voltage is given as Vz = 4.7V, and we have that 11.5V < Vin < 13.5V. Now, as long as the op amp is not saturated, and the Zener diode is ideal, then V+ = V- = Vz, so that Vout = Vz(R3 + R4)/R4 = Vz(1 + R3/R4).

But then they ask, what is the maximum output power once a load RL is added? Okay, but Vout apparently has no dependence whatsoever on RL; it has already been fixed by the Zener voltage in conjunction with the voltage divider. Then the output power is just Vout^2 / RL, so the output power is unbounded as RL approaches zero.

Am I missing something? Especially because I don't see how to incorporate the transistor here -- I believe it's a safety device that siphons current away from the output to prevent overload, but how does it enter the mathematical analysis? And later they ask for the variation of the collector current, so surely it enters somehow.

Answer 1

A shunt regulator works by drawing current through a series resistance (R1) to create a voltage drop that maintains a particular output voltage. If the load draws no current, all of it flows through the transistor. As the load draws more current, less current flows through the transistor. At some amount of load current, the transistor current drops to zero, and the circuit goes out of regulation. This is the "maximum power" point.

Note that regardless of the load current (at Vout), the input current (at Vin) to this circuit is a constant value!

Answer 2

The shunt regulator attempts to regulate the output to 9.4V. Now if the output voltage falls to less than 9.4V the shunt regulator is inactive.

The maximum power the circuit can deliver to the load if the regulator is inactive is when the impedance is matched to the source (22Ω), and the power will be 0.5*Vin^2/44Ω. I'm ignoring the 20k loading, but to be really precise you'd include it.

For the range of voltages given (11.5V < Vin < 13.5V) that's 1.5W to 2.1W when the output voltage will be Vin/2.

The maximum power the circuit can deliver and stay in regulation is lower, the current through the 22 ohm resistor could be as low as 95mA so the maximum power (with minimum input voltage) would be 0.9W (again ignoring the 20k of the two resistors).

Answer 3

Illustrating @Spehro Pefhany, here is the "behavior" of this "regulator" ...

3 cases of charge are considered (60, 80, 100 Ohm).