Described herein are systems and methods that allow for correcting a residual frequency offset in the GHz frequency range by using low-complexity analog circuit implementations of a broad-band frequency detector that comprises two analog polyphase filters in a dual configuration. Each filter comprises an RC network of cross-coupled capacitors that facilitate filters with opposite passbands and opposite stop-bands. In various embodiments, the outputs of the two filters are combined to obtain power metrics that when subtracted from each other, deliver a measure of the imbalance between the positive and negative halves of a frequency spectrum. Since the measure is substantially proportional to a frequency offset within a linear range spanning 5 GHz or more, the polyphase filters may be used in a broad-band frequency detector that, based on the measure, adjusts the frequency offset.

A first input terminal is connected to a point of connection of a drain terminal of a first transistor and a gate terminal of a fourth transistor. A second input terminal is connected to a point of connection of a drain terminal of a third transistor and a gate terminal of a second transistor. One of first through fourth output terminals to is connected to a source terminal of each of the first through fourth transistors to. A gate terminal of the first transistor and a drain terminal of the second transistor are connected, and a gate terminal of the third transistor and a drain terminal of the fourth transistor are connected.

A polyphase filter operates to provide capacitive compensation to drive a multiphase network for generating quadrature signals. The polyphase filter can include a capacitive compensation mechanism at internal nodes. The capacitive compensation mechanism includes a first phase lag circuit between a first internal node and a second internal node and a second phase lag circuit coupled between a third internal node and a fourth internal node. The first internal node is coupled to the second internal node via a first inductor coupled to a first resistor, the second internal node is coupled to the third internal node via a second inductor coupled to a second resistor, the third internal node is coupled to the fourth internal node via a third inductor coupled to a third resistor, and the fourth internal node is coupled to the first internal node via a fourth inductor coupled to a fourth resistor.

A polyphase filter operates to provide capacitive compensation to drive a multiphase network for generating quadrature signals. The polyphase filter can include a capacitive compensation mechanism at internal nodes. The capacitive compensation mechanism includes a first phase lag circuit between a first internal node and a second internal node and a second phase lag circuit coupled between a third internal node and a fourth internal node. The first internal node is coupled to the second internal node via a first inductor coupled to a first resistor, the second internal node is coupled to the third internal node via a second inductor coupled to a second resistor, the third internal node is coupled to the fourth internal node via a third inductor coupled to a third resistor, and the fourth internal node is coupled to the first internal node via a fourth inductor coupled to a fourth resistor.

Transmission-line filtering with enhanced frequency response is disclosed. In an example aspect, an apparatus includes a transmission-line filter to enhance a frequency response of a filtering operation. The transmission-line filter includes an input port, an output port, and multiple transmission-line base units. The multiple transmission-line base units are disposed between the input port and the output port and are coupled to the input port and the output port. Each of the multiple transmission-line base units includes a respective transmission line of multiple transmission lines. At least one transmission-line base unit of the multiple transmission-line base units includes a multi-resonant circuit.

A method for in-phase (I) and quadrature (Q) signal generation is disclosed. The method may include a first stage receiving a differential input signal. The first stage may also generate first differential in-phase and quadrature output signals, which may be sent by the first stage to a second stage. The second stage may generate second differential in-phase and quadrature output signals, which may have amplitude and phase mismatches less than an amplitude and phase mismatches of the first differential output signals. The second stage may then output the second differential I/Q output signals.

Provided is a polyphase filter, which is capable of achieving amplitude matching and phase matching while achieving a low insertion loss with a single-stage configuration. A first variable resistor and a second variable resistor have resistance values that are equal to each other, and the resistance values are set so as to correct an amplitude error between orthogonal signals of outputs of a first output terminal to a fourth output terminal. A first variable capacitor, a second variable capacitor, a third variable capacitor, and a fourth variable capacitor have capacitance values that are equal to one another, and the capacitance values are set so as to correct a phase error between the orthogonal signals of the outputs of the first output terminal to the fourth output terminal.

A first and second input tone are applied to a continuous-time complex filter within an integrated circuit. The magnitude of the output of the filter at the frequency of each of the first and second input tones are measured and compared to determine the value of a filter tuning control signal. A tuning control signal is applied to the filter with the determined value to tune the filter.

Provided is a polyphase filter, which is capable of achieving amplitude matching and phase matching while achieving a low insertion loss with a single-stage configuration. A first variable resistor and a second variable resistor have resistance values that are equal to each other, and the resistance values are set so as to correct an amplitude error between orthogonal signals of outputs of a first output terminal to a fourth output terminal. A first variable capacitor, a second variable capacitor, a third variable capacitor, and a fourth variable capacitor have capacitance values that are equal to one another, and the capacitance values are set so as to correct a phase error between the orthogonal signals of the outputs of the first output terminal to the fourth output terminal.