Linear frequency tuning in an LC-resonant system using a C–V response controllable MEMS varactor
© The Author(s) 2017
Received: 19 March 2017
Accepted: 30 August 2017
Published: 4 September 2017
This paper proposes a device level solution to achieve linear frequency tuning with respect to a tuning voltage (V tune ) sweep in an inductor (L)–capacitor (C) resonant system. Since the linearity of the resonant frequency vs. tuning voltage (f–V) relationship in an LC-resonant system is closely related to the C–V response characteristic of the varactor, we propose a C–V response tunable varactor to realize the linear frequency tuning. The proposed varactor was fabricated using microelectromechanical system (MEMS) surface micromachining. The fabricated MEMS varactor has the ability to dynamically change the C–V response characteristic according to a curve control voltage (V curve-control ). When V curve-control was increased from zero to 9 V, the C–V response curve was changed from a linear to a concave form (i.e., the capacitance decreased quickly in the low tuning voltage region and slowly in the high tuning voltage region). This change in the C–V response characteristic resulted in a change in the f–V relationship, and we successfully demonstrated almost perfectly linear frequency tuning in the LC-resonant system, with a linearity factor of 99.95%.
KeywordsC–V response Linearity LC-resonant system Microelectromechanical systems (MEMS) varactor Resonant frequency Voltage-controlled oscillator (VCO)
Today’s multi-band wireless communication devices and systems use various frequencies, and therefore require frequency tunable modules, which have been the subject of continuous study. Among them, the voltage-controlled oscillator (VCO) is one of the key components for changing the output frequency in wireless communication systems. Among its various characteristics, the linearity of the VCO’s output frequency tuning is a critical figure-of-merit in most applications. For example, the linearity of the output frequency sweep is directly connected to the range accuracy of the frequency modulation continuous wave (FMCW) radar system . In phase-locked loop circuits, it is known that the nonlinear frequency tuning characteristic in a VCO is one of the main sources affecting phase noise degradation .
In the common VCO, which uses inductor (L)–capacitor (C) resonant systems (LC–VCO), a varactor is the main device for changing the output frequency . Solid-state varactors based on semiconductors, however, produce a fixed C–V response curve that is not suitable for a linear f–V response, and it is not changeable once it is fabricated. As a result, it is difficult to linearize the output frequency response with conventional varactors. Accordingly, there have been notable efforts to linearize the f–V response by employing specifically designed circuits [4–6]. However, these complicated circuits tend to increase the cost of the system design and consume more electrical power, which are undesirable features.
To address these problems, this study focused on the C–V response of the varactor itself, to achieve linear frequency tuning in the LC resonant system without any circuit based support. First, we sought the kind of C–V response characteristic necessary to achieve the linear frequency tuning. Then a MEMS varactor satisfying the required C–V response characteristic was designed and fabricated using surface micromachining. At this step, the core concept for this kind of varactor was adopted from the previous paper . However, since the capacitor needs to be connected with an inductor to demonstrate linear f–V tuning in this paper, the design and fabrication process were fully modified to achieve the goal. The fabricated MEMS varactor was then integrated with a monolithically fabricated spiral inductor to verify its effect on frequency linearization.
Proposed concept and design
Required C–V response
Next, a reasonable boundary condition is set to determine α and β. The minimum and maximum tuning voltages (V tune ) are set as 0 and 15 V, respectively, and the capacitances for each voltage are set to be 900 fF (V = 0 V) and 400 fF (V = 15 V), respectively, for operation at frequency ranges of several GHz. According to (3), the L value does not affect the C–V response shape, and in this work it is set to 2 nH to obtain several GHz output oscillation frequencies.
Figure 1c represents the required C tune –V tune response in (3) in order to achieve the linear output frequency tuning characteristic shown in Fig. 1b for several parasitic capacitances (C p ). As can be seen in Fig. 1c, we need a concave shape in the C–V response of the varactor, and more importantly, the C–V response characteristic should be changeable (tunable), since the C p might be unknown or vary from system to system.
Proposed MEMS varactor
There have been a lot of works on RF MEMS capacitors to acquire a unique property that is not easily achieved by the conventional semiconductor-based technology [7–11]. These works tell that the MEMS capacitors have much more flexibility in the design that determines the C–V response. Therefore, we made use of the MEMS technology to satisfy the specific C–V response. Although, it has integration issues, the MEMS variable capacitor provides two main benefits: a possibly high Q-factor from its high conductive metal signal path, and variable tuning characteristic even adaptive to unknown parasitic components.
The proposed MEMS varactor shown in Fig. 2a has an another electrode, which is a curve-control electrode, to control the C–V response curve shape. The initial position of the top plate in the capacitor section is closer to the bottom plate as we apply V curve-control . This results in an increase in the initial capacitance (at V tune = 0 V) in the C tune –V tune curve, as shown in Fig. 2b (solid line), while the final capacitance (at the maximum tuning voltage) is preserved, since the V curve-control loses its attractive effect as the control plate moves up. Therefore, as we increase V curve-control , the shape of the C–V tune curve becomes a more concave form . In this way, we can control the C–V response characteristic of the varactor to accommodate the parasitic capacitance, to eventually achieve the linear output frequency tuning discussed in Fig. 1.
Design of the structural parameters
This section details the process of designing dimensional parameters. Therefore, the author suggests that readers who are not interested in the designing process skip this section.
To achieve the linear f–V response, it is beneficial to set the initial C–V response curve to be linear when the curve control voltage is zero (V curve-control = 0 V). According to previous works, the linearity of the C–V response is mainly determined by the ratio of l 2 and l 3 [12, 13] shown in Fig. 2a. When l 3 increases leaving l 2 unchanged from the optimal length showing a linear C–V response, the C–V curve is changed to a concave form. On the other hand, as l 3 decreases without changing l 2 , the C–V response is turned into a convex shape. In addition, another variable exists in this work: The ratio of the gap height between the capacitor section and the actuator section. In other words, the length of l 3 (which determines the total length of the varactor) can be shortened by reducing the gap in the capacitor section so that it is smaller than that of the actuator section. Taking these points into account, the capacitance in the capacitor section can be described as follows:
By relating (7) to the rotational restoring force generated from the levering beam, the model for the actuation section is described as follows:
Now that the C–V response equation is developed, the relationship among the variables can be analyzed by plotting the coefficient of the second order term in C cap after expanding (10) in the Taylor series.
Results and analysis
A photoresist (PR) is patterned two times as a sacrificial layer. The first PR is patterned and additionally cured at high temperature for hardening (150 °C, step (4)) because the second PR is patterned on top of the first PR to form the capacitor section. The high temperature treatment changes the molecular structure of PR so that it is insensitive to UV light. In this way, a different thickness of PR sacrificial layer can be achieved, as shown in step (5). This difference realizes the desired gap ratio (g ratio ) between the capacitor section and actuator section discussed in Fig. 3. After thermally evaporated Cu is deposited as a seed layer, the levering beam is formed by electroplating in step (6). In step (7), the capacitor and inductor are formed, simultaneously. As the last step, the seed Cu layer and PR sacrificial layer are removed by respective wet etchants, followed by a critical point dryer (CPD) release process.
The difference in gap heights between the capacitor section and the actuator section was verified by scanning electron microscope (SEM) images, as shown in Fig. 5b. In the middle of the actuator beam, there is a specific point where the gap height is differently formed, so that it is 1 μm in the capacitor section (left direction) and 1.4 μm in the actuator section (right direction). The serially connected spiral inductor is suspended from the bottom with the same height as that of the actuator section (1.4 μm).
Measurements and analysis
These results are well matched to the relationship between the C–V response and f–V response that we discussed previously. As expected from Fig. 1c, the linear f–V response is achieved when the capacitor shows a concave C–V response. This is the first experimental demonstration that the concave C–V response results in a linear f–V response in an LC resonator module. In view of Q-factor, the proposed device did not show a high Q due to the fact that the RF signal should pass though the relatively narrow levering beam. This can be solved by changing the signal path by splitting the bottom electrode . Additionally, increasing the thickness of the bottom plate would be an effective solution for the high Q-factor .
In contrast, the proposed LC resonator has the capacity to control the shape of the C–V response within the module, so that the resonant frequency can be linearly tuned without any external circuital supports. Since the oscillation frequency of the VCOs is the resonant frequency of the inductor and varactor connected in parallel as discussed in the ‘proposed concept and design’ section, this high f–V linearity is obviously expected to be shown even in the form of VCOs.
In addition to managing the frequency linearity, the proposed device is able to cover much wider range of resonant frequencies. This results in a much higher figure of merit, as shown in Fig. 8b.
In this paper, a device level approach was conducted to achieve linear output frequency tuning in an LC resonant system. The proposed concept was successfully demonstrated using a developed C–V response tunable MEMS varactor and a monolithically-integrated spiral inductor. The fabricated LC module exhibited almost perfect linear frequency tuning characteristics, from 3.125 to 4.175 GHz with a linearity factor of 99.95%. Integration of the proposed MEMS capacitor with the VCO circuits could require an extra fabrication cost. However, since this device-level solution can reduce the complexity of RF circuits as well as relative power consumption, this development can be favorably considerable in multi-band RF system design.
CHH carried out overall design, fabrication, measurement and analysis of the results, and drafted the manuscript. YHY supported fabrication process and measurement. SDK analyzed failure issue of fabrication and made solutions especially sacrificial layer process. MHS suggested fabrication plan, method, and material selection. All authors participated in editing process of the final manuscript. All authors read and approved the final manuscript.
We also thanks to members of our laboratory (3D micro-nano structures lab.) for sincere comments on this research.
The authors declare that they have no competing interests.
Availability of data and materials
The datasets supporting the conclusions of this article are included within the article and its additional files.
This research was supported by the Center for Integrated Smart Sensors funded by the Ministry of Science, ICT & Future Planning as “Global Frontier Project” (No. CISS-2012054187), and by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-IT1402-06.
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