Real-Time Precompensation Option

The HDAWG-PC Real-Time Precompensation option ensures that the signal at the device under test matches the one designed on the HDAWG Arbitrary Waveform Generator. Through the principle of inverse filtering, this feature minimizes the effect of imperfections in the signal path. At its heart is a widely configurable digital filter applied in real time before the generated waveform is converted into an analog signal.

Typical use cases for the HDAWG-PC are experiments where the sample is in a cryogenic environment. For these setups, the wiring from the arbitrary waveform generator to the sample introduces several kinds of signal distortion even if meticulously designed. A well-configured precompensation filter ensures excellent performance even in the presence of:

• Signal droop caused by high-pass filters in bias tees and DC blocks.
• Overshoots caused by spurious capacitances in chip bonds and planar circuit designs.
• Undershoots due to spurious inductances.
• Reflections and standing waves due to impedance mismatches.
• Amplifier ringing.

Working in real time, the HDAWG-PC generates corrections even for long signals on the scale of seconds without consuming waveform memory. Real-time precompensation is the only method that tracks history effects over multiple pulses in a dynamically generated pattern, similarly to what happens for quantum error correction with fast feedback.

All filter parameters can be optimized based on a step response measurement of the distorted signal at the device under test. The LabOne Precompensation Simulator enables a direct comparison between the simulated AWG output, the theoretical signal shape that this filter would compensate, and the measured signal at the device as uploaded by the user. Users can treat the linear filters independently and eliminate signal imperfections sequentially, starting with the largest one and proceeding in a well-structured manner. For each filter, the Simulator is used to match the measured signal with the simulation; the filter parameters so deduced are then transferred to the hardware. If a subsequent measurement indicates that fine-tuning is necessary, this is rapidly accomplished by in-situ tuning while observing the measured signal evolve towards a clean, rectangular step response. This results in an optimized filter that is applicable to all signal shapes. Usery can work in the LabOne AWG Sequencer, confident that the signal at the device matches the designed waveform exactly.

High-pass compensation

High-pass compensation relies on an infinite impulse response (IIR) filter with a finely tunable time constant integrating the signal over time, thus inverting the effect of AC coupling. To avoid overflow when the input signal has a non-zero average, the high-pass compensation can be reset from the AWG Sequencer between pulse trains. As the precompensated signal grows linearly over time and is ultimately limited by the AWG output voltage, there is a trade-off between the achievable step height of a square pulse and the maximum pulse width.

Exponential compensation

Exponential compensation adds multiple exponentially decaying terms to a step in the signal. With up to 8 available stages, users can correct for multiple spurious inductances and capacitances in the circuit. Exponential compensation works best for overshoots and undershoots smaller than about 10% of the step height. In this case, a sum of exponential terms is an accurate generic model for such defects.

Bounce compensation

The bounce correction adds a delayed copy of the input signal to itself and effectively compensates back-and-forth reflections causing interference fringes in the frequency domain or delayed steps in the time domain. The available delay range covers standing-wave dimensions of up to about 10 m in an RG58 cable.

Finite impulse response (FIR) compensation

For the shortest time constants (down to 1 nanosecond), a fully configurable finite impulse response (FIR) filter allows users to tweak step edges in the signal to achieve minimum settling times to the sub-percent level. Amplifiers with bandwidths matching that of the HDAWG may show ringing on the nanosecond time scale and represent typical use cases. The FIR filter also serves as an extension of the bounce correction if multiple standing waves are present in the setup. The FIR filter offers great flexibility and performance at the cost of a more advanced optimization workflow compared to that of other filters. It is configured with the LabOne APIs; a tuning routine typically consists in applying FIR models available in Python, MATLAB^®, or LabVIEW^® to the measured step response, and running a numerical optimization to minimize the deviation from the rectangular target signal.