Polar envelope correction mechanism for enhancing linearity of RF/microwave power amplifier

Claim 2

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said gain and phase adjustment circuit comprises a variable attenuator coupled in cascade with a phase shifter, said phase shifter comprising a quadrature hybrid circuit terminated in a varactor diode circuit, said varactor diode circuit comprising a first pair of varactor diodes coupled between a first voltage reference node and a first port of said quadrature hybrid circuit, and a second pair of varactor diodes coupled between said first voltage reference node and a second port of said quadrature hybrid circuit, each of said first and second pairs of varactor diodes having first electrodes thereof connected in common and being coupled to receive a control voltage generated by said phase/amplitude controller.

Claim 3

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said gain and phase adjustment circuit comprises a vector modulator containing a quadrature hybrid connected to first and second controlled phase shifters having vector outputs combined in an in-phase power combiner, to produce a resultant signal vector having a variable amplitude and phase in accordance with control signals generated by said phase/amplitude controller, and wherein each of said phase shifters comprises a quadrature hybrid circuit terminated in a varactor diode circuit, said varactor diode circuit comprising a first pair of varactor diodes coupled between a first voltage reference node and a first port of said quadrature hybrid circuit, and a second pair of varactor diodes coupled between said first voltage reference node and a second port of said quadrature hybrid circuit, each of said first and second pairs of varactor diodes having first electrodes thereof connected in common and being coupled to receive a respective control signal generated by said phase/amplitude controller.

Claim 4

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said gain and phase adjustment circuit comprises a vector modulator containing a quadrature hybrid connected to first and second controlled phase shifters having vector outputs combined in an in-phase power combiner, to produce a resultant signal vector having a variable amplitude and phase in accordance with control signals generated by said phase/amplitude controller, and wherein each of said phase shifters comprises a quadrature hybrid circuit terminated in a varactor diode circuit, said varactor diode circuit comprising a first pair of varactor diodes coupled between a first voltage reference node and a first port of said quadrature hybrid circuit, and a second pair of varactor diodes coupled between said first voltage reference node and a second port of said quadrature hybrid circuit, each of said first and second pairs of varactor diodes having first electrodes thereof connected in common and being coupled to receive a respective control signal generated by said phase/amplitude controller.

Claim 5

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a differential peak detector, which is operative to control gain adjustment imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between amplitudes of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain through said power amplifier between said input port and said output port, and wherein said phase/amplitude controller further comprises a phase detector bridge circuit, which is operative to control phase adjustment of said input signal imparted by said gain and phase adjustment circuit, in accordance with a relationship between phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant phase through said amplifier between said input port and said output port, and wherein said phase detector bridge circuit is coupled through respective transmission line sections of a transmission line bridge to said first and second signal paths, and includes peak detectors which are operative to detect peaks of signals coupled through said respective transmission line sections, said peaks of signals being coupled to a differential amplifier, which provides, to said gain and phase adjustment circuit, a difference control signal V.sub.Φ proportional to the difference of the phase of the envelopes of signals coupled through said respective transmission line sections.

Claim 6

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a differential peak detector, which is operative to control gain adjustment imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between amplitudes of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain through said power amplifier between said input port and said output port, and wherein said phase/amplitude controller further comprises a phase detector bridge circuit, which is operative to control phase adjustment of said input signal imparted by said gain and phase adjustment circuit, in accordance with a relationship between phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant phase through said amplifier between said input port and said output port, and wherein said phase detector bridge circuit is coupled through respective transmission line sections of a transmission line bridge to said first and second signal paths, and includes peak detectors which are operative to detect peaks of signals coupled through said respective transmission line sections, said peaks of signals being coupled to a differential amplifier, which provides, to said gain and phase adjustment circuit, a difference control signal V.sub.Φ proportional to the difference of the phase of the envelopes of signals coupled through said respective transmission line sections.

Claim 7

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a first power divider coupled to said feedback signal path and being operative to split said feedback signal path into third and fourth signal paths, and a second power divider coupled to said second signal path and being operative to split said second signal path into fifth and sixth signal paths, said third and fifth signal paths being coupled to peak detectors, which supply peaks of signals on said third and fifth signal paths to a first differential amplifier, the output of which is a control voltage V A for controlling the adjustment of gain of said input signal by said gain and phase adjustment circuit.

Claim 8

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a first power divider coupled to said feedback signal path and being operative to split said feedback signal path into third and fourth signal paths, and a second power divider coupled to said second signal path and being operative to split said second signal path into fifth and sixth signal paths, said third and fifth signal paths being coupled to peak detectors, which supply peaks of signals on said third and fifth signal paths to a first differential amplifier, the output of which is a control voltage V A for controlling the adjustment of gain of said input signal by said gain and phase adjustment circuit.

Claim 9

A power amplifier circuit according to claim 4, wherein said fourth and sixth signal paths are coupled through phase-matched limiters to a wideband Gilbert cell multiplier, an output of which is filtered by means of a low pass filter and applied to a first input of a second differential amplifier, said differential amplifier having a second input coupled to receive an adjustable DC offset voltage, said second differential amplifier having an output which generates a control voltage V.sub.Φ for controlling the adjustment of phase of said input signal by said gain and phase adjustment circuit.

Claim 10

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a first in-phase, three-way power divider which divides said feedback signal path into third, fourth and fifth in-phase paths, and a second in-phase, three-way power divider which divides said second signal path into sixth, seventh and eighth in-phase paths, wherein said third and sixth paths are coupled to respective peak detectors, which are coupled to respective inputs of a first differential amplifier, said first differential amplifier providing an amplitude control voltage V A for controlling the adjustment of gain of said input signal by said gain and phase adjustment circuit.

Claim 11

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a first in-phase, three-way power divider which divides said feedback signal path into third, fourth and fifth in-phase paths, and a second in-phase, three-way power divider which divides said second signal path into sixth, seventh and eighth in-phase paths, wherein said third and sixth paths are coupled to respective peak detectors, which are coupled to respective inputs of a first differential amplifier, said first differential amplifier providing an amplitude control voltage V A for controlling the adjustment of gain of said input signal by said gain and phase adjustment circuit.

Claim 12

A power amplifier circuit according to claim 6, wherein said fourth and fifth paths are phase shifted by plus and minus 45° phase shifters, to yield a +90° differential phase between said fourth and fifth paths, and where said seventh and eighth paths are phase shifted by minus and plus 45° phase shifters, to yield a -90° differential phase between said seventh and eighth paths, said phase shifted fourth and seventh paths being summed and coupled by way of a first peak detector to a first input of a second differential amplifier, and wherein said phase shifted fifth and eighth are summed and coupled by way of a second peak detector to a second input of a second differential amplifier, said second differential amplifier generating a control voltage .sub.Φ for controlling the adjustment of phase of said input signal by said gain and phase adjustment circuit.

Claim 13

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a quadrature hybrid, which is coupled to translate said second signal path into quadrature signals that are respectively coupled to first inputs of first and second Gilbert multipliers, second inputs of which are derived from first and second in-phase outputs of an in-phase power divider to which said feedback signal path is coupled, said first and second Gilbert multipliers being coupled through respective low pass filters to amplifiers, which generate control voltages V A and V.sub.Φ for controlling adjustment of gain and phase, respectively, of said input signal by said gain and phase adjustment circuit.

Claim 14

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said phase/amplitude controller comprises a quadrature hybrid, which is coupled to translate said second signal path into quadrature signals that are respectively coupled to first inputs of first and second Gilbert multipliers, second inputs of which are derived from first and second in-phase outputs of an in-phase power divider to which said feedback signal path is coupled, said first and second Gilbert multipliers being coupled through respective low pass filters to amplifiers, which generate control voltages V A and V.sub.Φ for controlling adjustment of gain and phase, respectively, of said input signal by said gain and phase adjustment circuit.

Claim 15

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said gain and phase adjustment circuit comprises a slow gain/phase adjuster, connected in cascade with a fast gain/phase adjuster.

Claim 16

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and wherein said gain and phase adjustment circuit comprises a slow gain/phase adjuster, connected in cascade with a fast gain/phase adjuster.

Claim 17

A power amplifier circuit according to claim 9, wherein said phase/amplitude controller is coupled through respective slow and fast loop filters to said slow gain/phase adjuster and said fast gain/phase adjuster, respectively.

Claim 18

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and further including an alarm circuit containing window comparator circuits that monitor control signals applied to said gain and phase adjustment circuit and are operative to generate an alarm signal in response to excursions beyond the normal control voltage levels indicating a failure of said gain and phase adjustment circuit to properly adjust the gain and phase of said input signal to be amplified by said power amplifier.

Claim 19

A power amplifier circuit comprising: an input port to which an input signal to be amplified is applied; an output port from which an output signal is derived; a first signal path coupled to said input port; a power amplifier disposed in said first signal path and being operative to amplify said input signal applied to said input port and to provide an amplified output signal at said output port; a gain and phase adjustment circuit installed in said first signal path and coupled in circuit with said power amplifier; a second signal path coupled to said input port and being operative to delay a portion of said input signal conveyed thereover; and a phase/amplitude controller having a first input coupled via a feedback signal path to receive a portion of said amplified output signal and a second input port coupled to receive a delayed portion of said input signal conveyed over said second signal path, and controlling gain and phase adjustments imparted by said gain and phase adjustment circuit to said input signal to be amplified by said power amplifier, in accordance a relationship between the amplitudes and phases of the envelope of the delayed portion of said input signal conveyed over said second signal path and the envelope of said portion of said amplified output signal conveyed over said feedback signal path, so as to maintain constant gain and phase through said power amplifier between said input port and said output port; and further including an alarm circuit containing window comparator circuits that monitor control signals applied to said gain and phase adjustment circuit and are operative to generate an alarm signal in response to excursions beyond the normal control voltage levels indicating a failure of said gain and phase adjustment circuit to properly adjust the gain and phase of said input signal to be amplified by said power amplifier.

Claim 20

A power amplifier circuit according to claim 11, wherein outputs said window comparator circuit are integrated and coupled to respective threshold detectors that provide alarm signals indicating that adjustment of the gain and phase of said input signal to be amplified by said power amplifier is not valid, in response to a failure of an amplified signal at said output port to track the input signal applied to said input port.