I honestly have no idea what is the best way to find RL for maximum power transfer in this circuit. enter image description here

What I do know, first and foremost, is that the RL resistor can be found as the Thevenin-equivalent resistance, R_th. I believe superposition is usually a good way to solve circuits like this, but even if I try to remove the current source and short-circuit the voltage source, I still have the dependent sources that complicate things further.

I tried removing the RL resistor first, so that perhaps I can find V_th as the open circuit, but the placement of the resistor really sets it at an awkward position, because there's also a dependent source at the bottom half that I can simplify with the mesh-current method. I tried using mesh-current method to set up a supermesh at the bottom half of the circuit, but even with that, both dependent sources are based off of i_A and v_A. A similar problem happens the same when I attempt to use node-voltage method, in that while I can setup a supernode along the voltage-controlled dependent source, there still remains the other current sources.

I really don't want to give up on this problem, but the more I try to make sense of this circuit, the more confused and frustrated I get. Can someone please help here? What am I doing wrong?


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