Metamaterial phase shifters

A method of operating a phase shifter, comprising:

• receiving a phase shift input value;
• determining a set of voltage control signals based on the phase shift input value;
• and
• transmitting the set of voltage control signals to a network of tunable impedance elements to shift a phase of an input signal to the phase shifter such that a magnitude of an output signal of the phase shifter and a magnitude of the input signal to the phase shifter are substantially similar;
• wherein the network of tunable impedance elements comprises a spatially-periodic arrangement of tunable impedance elements, with spatial periodicity in at least one spatial dimension being less than one-half of free-space wavelength.

A phase shifter, comprising:

• a network of tunable impedance elements;
• and
• a controller coupled to the network of tunable impedance elements and configured to:
• receive a phase shift input value;
• and
• determine a corresponding tuning voltage to be supplied to each tunable impedance element of the network of tunable impedance elements based on the phase shift input value, the network of tunable impedance elements being configured to shift a phase of an input signal based on tuning voltages supplied to the network of tunable impedance elements by the controller;
• wherein the input signal is a continuous-wave signal and wherein the controller is further configured to determine the corresponding tuning voltage to be supplied to each tunable impedance element of the network of tunable impedance elements based a dependency of impedances of the tunable impedance elements and impedances of non-tunable branches of the network of tunable impedance elements on one of:
• a frequency of the continuous-wave signal;
• at least one local magnitude of radio frequency voltage or current of the continuous-wave signal;
• and
• a frequency and at least one local magnitude of radio frequency voltage or current of the continuous-wave signal.

A phase shifter, comprising:

• a network of tunable impedance elements;
• and
• a controller coupled to the network of tunable impedance elements and configured to:
• receive a phase shift input value;
• and
• determine a corresponding tuning voltage to be supplied to each tunable impedance element of the network of tunable impedance elements based on the phase shift input value, the network of tunable impedance elements being configured to shift a phase of an input signal based on tuning voltages supplied to the network of tunable impedance elements by the controller;
• wherein the controller is configured to determine the corresponding tuning voltage for each tunable impedance element based on an approximation of the network of tunable impedance elements as a network of lumped ports with characteristic impedances representing impedance values of tunable impedance elements of the network.

A phase shifter, comprising:

• a network of tunable impedance elements;
• and
• a controller coupled to the network of tunable impedance elements and configured to:
• receive a phase shift input value;
• and
• determine a corresponding tuning voltage to be supplied to each tunable impedance element of the network of tunable impedance elements based on the phase shift input value, the network of tunable impedance elements being configured to shift a phase of an input signal based on tuning voltages supplied to the network of tunable impedance elements by the controller;
• wherein the controller is configured to determine the corresponding tuning voltage for each tunable impedance element of the network of tunable impedance elements such that a magnitude of an output signal of the network of tunable impedance elements and a magnitude of an input signal to the network of tunable impedance elements are substantially equal.

A phase shifter, comprising:

• a network of tunable impedance elements;
• and
• a controller coupled to the network of tunable impedance elements and configured to:
• receive a phase shift input value;
• and
• determine a corresponding tuning voltage to be supplied to each tunable impedance element of the network of tunable impedance elements based on the phase shift input value, the network of tunable impedance elements being configured to shift a phase of an input signal based on tuning voltages supplied to the network of tunable impedance elements by the controller;
• wherein the controller is configured to determine the corresponding tuning voltage for each tunable impedance element of the network of tunable impedance elements such that a ratio of a magnitude of an output signal of the network of tunable impedance elements to a magnitude of an input signal to the network of tunable impedance elements is approximately constant for all possible phase shift input values.