Maximum Power Transfer

The circuit below is a Thevenin equivalent of an output device (V_O, R_O) and an input device. Let the input resistor R_I be the load for the output.

The power dissipated in R_I, P_I=I²R_I. The power dissipated in R_O, P_O=I²R_O. The power generated by V_O=IV_O. The current is I=V_O/(R_I+R_O). So,

PI=I2RI.
   =(VO2/(RI+RO)2)RI.

The maximum (dP_I/dR_I=0) is at R_I=R_O and this is the maximum power.

• Maximum power R_I: R_I=R_O
• Maximum voltage drop across R_I: R_I>>R_O
• Maximum current R_I: R_I<<R_O

References

Fischer-Cripps. A.C., The Electronics Companion. Institute of Physics, 2005.