Methods and apparatus for source and load power transfer control

A power transfer electrical system comprising:

• a) an electrical source circuit comprising an impedance, Zsource, that generates an electrical signal comprising a first electrical signal comprising a voltage, VRx1, and a second electrical signal comprising a voltage, VRx2, at an output;
• b) an electrical sink circuit comprising an impedance, ZLoad, having an input that is electrically connected to the output of the electrical source circuit;
• c) at least one of the electrical source circuit and the electrical sink circuit comprising a controllable electrical element;
• d) a differencing circuit having a first input that is electrically connected to the output of the electrical source circuit and a second input that is electrically connected to the input of the electrical sink circuit, the differencing circuit generating a difference signal at an output;
• and
• e) a controller having an input connected to the output of the differencing circuit, and an output connected to the controllable electrical element, the controller generating a control signal that controls the controllable electrical element so that a power, PLoad (Total), transferred from the electrical source circuit to the electrical sink circuit is given by an equation:
• P
• Load
• ⁡
• (
• Total
• )
• =
• P
• Load
• ⁡
• (
• V
• R
• ×
• 1
• )
• +
• P
• Load
• ⁡
• (
• V
• R
• ×
• 2
• )
• =
• Re
• ⁢
• {
• V
• R
• ×
• 1
• 2
• ⁡
• (
• 1
• -
• A
• )
• 2
• +
• V
• R
• ×
• 2
• 2
• (
• Z
• Antenna
• +
• Z
• Load
• )
• 2
• ⁢
• Z
• Load
• }
• ,
• wherein the controller determines a value for the controllable electrical element in response to the difference signal that results in a value of variable A that provides a particular portion of the first electrical signal being reflected and simultaneously provides another portion of the second electrical signal being extracted.