Wideband phase-locked loop circuit with real-time phase correction for frequency modulation atomic force microscopy

Abstract

We have developed a wideband phase-locked loop (PLL) circuit with real-time phase correction for high-speed and accurate force measurements by frequency modulation atomic force microscopy (FM-AFM) in liquid. A high-speed operation of FM-AFM requires the use of a high frequency cantilever which, however, increases frequency-dependent phase delay caused by the signal delay within the cantilever excitation loop. Such phase delay leads to an error in the force measurements by FM-AFM especially with a low Q factor. Here, we present a method to compensate this phase delay in real time. Combined with a wideband PLL using a subtraction-based phase comparator, the method allows to perform an accurate and high-speed force measurement by FM-AFM. We demonstrate the improved performance by applying the developed PLL to three-dimensional force measurements at a mica/water interface.

High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions

“…The ideal resonator-PLL system should track the corresponding resonant frequency as closely and quickly as possible. While direct feedback loops respond to perturbations much faster than the resonator's characteristic amplitude timescale (typically τ =2 Q / ω 0 , where Q and ω 0 are the quality factor and the angular resonant frequency of the resonator) the case of PLL-mediated feedback 29 30 31 32 33 and its dynamics 34 35 36 have been less studied. Therefore, we first developed a Laplace domain model for the resonator-PLL system to understand and then tailor the closed-loop system dynamics.…”

Steady-state and transient behavior in dynamic atomic force microscopy

“…( 68) is then merely an integral of frequency, and a first-order PLL defined by its proportional gain alone would suffice for good performance. Although in ultra-high vacuum this assumption holds very well [39], with lower quality factors as typical in ambient or liquid environments there can be significant deviations which can cause experimental artifacts [45,46]. Note that most textbooks [43,47,48] deal with PLLs in the context of signals and communications systems, where the detected phase is indeed the integrated change of the reference frequency.…”

A novel amplitude and frequency demodulation algorithm for frequency-modulation atomic force microscope

“…In general, the frequency demodulation techniques could be classified as: (a) feed forward demodulation, (b) pulse conversion demodulation based on zero crossing detection, (c) feedback demodulation involving frequency or phase lock loop (PLL) [14]. In the PLL-based feedback demodulation, the incoming FM signal is compared with the locally generated reference signal to calculate the phase error [15][16][17]. Although PLL-based demodulation technique is applied for FM-AFM widely, the response time of the control loops is limited by the low pass filters which are used within the PLL [18].…”