An RF Modulation Based on k-th Order PWM Harmonic

A Sub-Nyquist Radio Frequency Pulse Width Modulation (RFPWM) technique, which extends the concept of Sub-Nyquist DACs to RFPWM, is introduced in this paper. The carrier frequency is selected as the
${k}$
-th order harmonic of the PWM switching frequency. This choice enables operation within an extended frequency range for a particular switching transistor in contrast to the conventional RFPWM approach, where the carrier and switching frequencies are identical. The feasibility of this methodology is verified by both extensive simulations and experimental measurements. While there is a reduction in output power proportional to the harmonic number, this approach has the potential to set the transmitted power to these fixed steps in an all-digital format without compromising spectral performance, as evidenced by comprehensive simulations. Furthermore, the method exhibits strong spectral performance within and outside the desired frequency bands across different quantization scenarios, covering carrier frequencies up to four times the switching frequency. The proof of concept for Sub-Nyquist RFPWM transmitter is a fully digital field-programmable gate array (FPGA) implementation, enabling adaptability to multistandard signals. The pulse position/pulse-width modulation is based on an outphasing approach, using the FPGA transceivers to generate the high-speed binary waveform. Measurements were carried out using a 1.4-MHz LTE 64-QAM signal with a PWM switching frequency of 311 MHz, achieving ACPR values below −39 dBc when the second and third harmonics were used as carrier frequencies (622 MHz and 933 MHz, respectively).