Foundations of VHF, UHF and Microwave NEMS Resonators
2.2 Experimental Foundation
2.2.4 Resonance Detection and Electronic Readout
Two-port network analysis is probably the most canonical and also convenient approach to perform RF detection and measurements of a NEMS resonance. Fig. 2.13 demonstrates the most important three schemes of two-port network analyses for NEMS resonators. All these schemes have hitherto been implemented in real measurements.
The efficiency of each is limited by interplay between the resonance’s electromechanical impedance and the response due to the impedance mismatch and parasitic effects.
The transmission scheme in Fig. 2.13(a) has been directly used for HF and up to
~200MHz resonators with close to 50Ω impedance, and used with shunt 50Ω resistance to decrease the impedance mismatch for devices having large DC resistances (from
>100Ω to well in the kΩ range) such as nanowires [30]. The reflection scheme shown in Fig. 2.13(b) has been more often applied to HF/VHF resonators [23,28,29], mostly by employing a directional coupler in lieu of the circulator shown.
Fig. 2.13 Electronic readout schemes and measurements diagrams. (a) Two-port transmission measurement scheme with single device. (b) Two-port reflection measurement with single device.
(c) Two-port balanced-bridge measurement with a pair of devices.
Both the transmission and reflection schemes quickly lose their efficiency when the device frequency approaches the UHF range and the device electromechanical impedance
becomes even smaller, as compared to the effect of any commonly existing parasitics.
As shown in Fig. 2.13(c), a prototype of the balanced-bridge scheme [31] was developed to evade this issue to some extent. This scheme involves a pair of devices with very close DC resistances, and has been proven to have better efficiency than both the transmission and reflection schemes in detecting UHF NEMS resonances. However, this scheme and its underlying theory only take care of the effects of the DC resistance mismatch and its better efficiency has only been manifested with VHF devices. It still suffers from only obtaining very small resonance signals when implemented in the UHF range. Later we made improvements, or the second generation of the bridge scheme [25], but this progress was unsubstantial and did not completely solve the problem. Our latest but significant improvements for large signal readout from a typical UHF NEMS resonance was catalyzed and squeezed out in our desperate development of the NEMS oscillator technology. The analyses and implementation of this third generation bridge scheme is presented in Chapter 3.
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