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RF Amplifier Required Power Derivation

Davis Borders

Published Sep 23, 2026• 0 citations
Publisher

Abstract

Analytical derivation of the required RF power amplifier gain and output power for pulsed NMR qubit excitation. Derives the complete physical pipeline connecting digital DDS signals, DAC output voltage, resonant coil parameters, Ampère's Law B1 field generation, and rotating frame coordinate transformations under the Rotating Wave Approximation (RWA) to determine peak RF magnetic field, required voltage gain (G in dB), and average power (P in dBm) for target flip angles (pi/2, pi).

DOI
10.5281/zenodo.22910213

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Analytical derivation of the required RF power amplifier gain and output power for pulsed NMR qubit excitation. Derives the complete physical pipeline connecting digital DDS signals, DAC output voltage, resonant coil parameters, Ampère's Law B1 field generation, and rotating frame coordinate transformations under the Rotating Wave Approximation (RWA) to determine peak RF magnetic field, required voltage gain (G in dB), and average power (P in dBm) for target flip angles (pi/2, pi).
Precise manipulation of a quantum bit (qubit) magnetic dipole moment requires exact control over the radiofrequency (RF) excitation field amplitude, pulse envelope, and duration. This paper presents a complete analytical derivation linking target quantum logic gate flip angles (α = π/2, π) to the necessary physical RF power amplifier (PA) parameters—specifically voltage gain (G) and peak output power (P ). Starting from a digital direct synthesis (DDS) driving model, we map unitless digital baseband signals through a digital-to-analog converter (DAC) and an impedance-matched resonant LC tank into the physical transverse magnetic field (B1). Applying a coordinate transformation to the rotating frame under the Rotating Wave Approximation (RWA) and modeling Gaussian pulse truncation (τ = nσ), closed-form expressions are derivedfor G and P . This analytical framework provides a direct link between physical hardware specifications and target quantum state rotations.
Arbitrary Waveform Generators (AWGs) have widespread applications in telecommunications, quantum computing, and biomedical engineering, among others, due to their ability to generate a wide range of waveforms precisely and instantaneously. This work focuses on developing a scalable and energy-efficient AWG for qubit control. A simple methodology for bringing up a Radio-Frequency System-on-Chip (RFSoC) board and using it to generate various arbitrary waveforms has been discussed. A software-hardware codesign paradigm has been used in this work to dynamically control the output frequency, voltage and shape of the arbitrary waveforms. Similarly, the on-the-fly programmability of four Digital to Analog convertor (DAC) channels and four Analog to Digital Converter (ADC) channels have been tested. The voltage and frequency response of the DAC output has also been characterised to better understand the limitations of the RFSoC. The DAC-ADC loopback characterisation was also performed to prepare the RFSoC for qubit state readout measurements. Over the last few decades, the Direct Digital Synthesiser (DDS) has been a popular choice for generating specific waveforms, such as sinusoidal and ramp waveforms, due to its low cost, simple design, and high precision. Several prior-art works were surveyed, and the trade-offs and strengths of each architecture were summarised. A benchmarking table is prepared based on the Power, Performance and Area (PPA) analysis to make design selection easier for DDS designers. Two Figure of Merit definitions and scaling equations have also been used to normalise the specifications to a target process node (28 nm CMOS), to provide a more accurate comparison among state-of-the-art DDS designs on Application Specific Integrated Circuits (ASICs), and to set expectations for future architectural advancements in DDS design. Finally, a viable DDS-based AWG architecture for ASIC implementation has also been proposed based on the benchmarking.
Radio-frequency (RF) amplifiers based on direct current (DC) superconducting quantum interference device (SQUID) have low-noise performance for precision physics experiments. Gain curves of SQUID RF amplifiers depend on several parameters of the SQUID and operation conditions. We are developing SQUID RF amplifiers for application to measure very weak RF signals from ultra-low-temperature high-magnetic-field microwave cavity in axion search experiments. In this study, we designed, fabricated and characterized SQUID RF amplifiers with different SQUID parameters, such as number of input coil turn, shunt resistance value of the junction and coupling capacitance in the input coil, and compared the results.
We report an rf parametric amplifier that exploits the gate-tunable quantum capacitance of a semiconductor two-dimensional electron gas at cryogenic temperatures. The prototype amplifier exhibits a gain approximately 30 dB up to an input power of − 66 dBm and a noise temperature T N ∼ 2 K at approximately 370 MHz while dissipating approximately a microwatt of power. Operable at tesla-scale magnetic fields and temperatures ranging from millikelvin to a few kelvin, the quantum capacitance parametric amplifier may find utility in the readout circuit of spin qubits. Here, a quantum dot system is used to verify amplifier performance, improving the signal-to-noise ratio of the readout by approximately 9 dB.
At present, it is one of various effective approaches for quantum algorithm to using the nuclear magnetic resonance (NMR) experiment technology. NMR uses radio frequency (RF) electromagnetic pulses to rotate the spins. By tuning the frequency of the RF-field to the precession frequency of a particular spin, the power of the applied pulse controls how much the spin will rotate. The axis of the rotation is determined by the direction of the applied RF-field. By selecting the appropriate RF pulses, arbitrary single-spin rotation can be carried out. In other words, using RF pulses we can perform any single-qubit operation. Communication between the qubits is accomplished through the spin-spin interaction in model. A simulation approach in this paper is described to realize quantum Fourier transform algorithm (QFT).
Superconducting qubits are the promising candidate to realize large-scale quantum computing systems. Well-known quantum algorithms, such as Shor's algorithm, require at least10510^{5}105to10610^{6}106qubits to execute. Accordingly, classical systems for controlling superconducting qubits must also be scalable. One critical scalability challenge lies in the circuit cost of an RF pulse generator used to implement quantum gate operations. This poster proposes a cost-effective architecture for an RF pulse generator tailored to superconducting qubits. Most existing works use arbitrary waveform generators (AWGs) that require both a high-bandwidth memory (HBM) and a high-performance digital-analog converter (DAC) to achieve the highest gate fidelity with an optimized RF pulse waveform. The proposed pulse generator architecture significantly simplifies both the generator circuit and the waveform of the RF pulse to cost-aware square pulses. This architecture eliminates the requirement for power- and cost-intensive AWG, which is a major obstacle in realizing scalable quantum computers. Additionally, this poster demonstrates that our architecture can mitigate the error source associated with simplified RF pulses. Quantum dynamics simulation of transmon qubits, wherein the state of the system evolves with time, demonstrates that our pulse generator can achieve practically the same fidelity of gate operations for single and multiple qubits as ideal RF pulses while substantially reducing the sampling rate of DACs and the bandwidth of memories.