## New Programmable CMOS Fuzzifier and C2V Circuits  
**Applicable in FLC Chip for Signal Processing of MEMS**  
**[PERSON] 1,\({}^{\dagger}\), [PERSON] 2,\({}^{\star}\) and [PERSON] 3,\({}^{\dagger}\)**  
\({}^{1}\) Department of Electrical Electronics Engineering, Science and Research Branch,  
Islamic Azad University, Tehran 14778-93855, Iran; E-Mail: [EMAIL_ADDRESS]  
\({}^{2}\) Department of Electrical Electronics Engineering, Iran University of Science and Technology,  
Tehran 16846, Iran  
\({}^{3}\) Department of Electrical Electronics Engineering, Khaje Nasir Toosi University of Technology,  
Tehran 19991-43344, Iran; E-Mail: [EMAIL_ADDRESS]  
\({}^{\dagger}\) These authors contributed equally to this work. \({}^{\star}\) Author to whom correspondence should be addressed; E-Mail: [PERSON]EMAIL_ADDRESS]r;  
Tel. : +98-912-340-5024; Fax: +98-21-7724-0487. Academic Editor: [PERSON]  
_Received: 15 June 2015 / Accepted: 11 August 2015 / Published: 18 August 2015_  
This paper presents the design and simulation of improved circuits of Fuzzifier and capacitance to voltage (C2V) converter. The Fuzzifier circuit is designed based on analog advantages such as low die area, high accuracy, and simplicity which are added to the fuzzy system advantages. For implementing this idea, a programmable Membership Function Generator (MFG) including differential pair circuit as a Fuzzifier is proposed. The MFG generates arbitrary forms of Gaussian, Trapezoidal, and Triangular shapes. The shape types are achieved using control switches and different reference voltages. This structure is also general purpose in tuning the slope of Membership Functions (MFs) using scaled transistors with different _W/L_ ratios. With a specific purpose in mind, we used it here to generate fuzzy language terms from sensed classic data of a blood glucose microsensor. Thus we proposed a C2V circuit to convert capacitance variations (from MEMS glucose microsensor) to voltage values as classic data. The proposed mentioned circuits can be applicable in design of Fuzzy Logic Controller (FLC) chips to detect blood glucose, process its data in Fuzzy environment, and control insulin injection of diabetic patients by MEMS micropumps. The simulation results are achieved by MATLAB and  
where  
\[\alpha_{i}=\frac{V_{in}-V_{REFi}}{V_{TH}}\]  
\[\beta_{i}=\mu C_{\alpha}\,\frac{W_{i}V_{TH}}{2I_{o}L_{i}}\]  
\(V_{in}\) is the input voltage, \(V_{REFi}\)'s are the reference voltages, \(V_{TH}\) is the MOS transistor threshold voltage, \(\mu C_{\alpha\alpha}\), \(W_{i}/L_{i}\) are the parameter and size of transistors, and \(I_{o}\) is the constant current source. On the ends of the input range [9], this relation can be simplified without \(V_{TH}\) as Equation (3):  
\[I_{i}=\frac{1}{2}I_{o}\times\left[1+(V_{in}-V_{REFi})\sqrt{\frac{\kappa}{I_{o}} -\left(\frac{\kappa}{2I_{o}}\right)^{2}(V_{in}-V_{REFi})^{2}}\right] \tag{3}\]  
where  
\[\kappa=\mu\,C_{\alpha}\,\frac{W_{i}}{L_{i}}\]  
When \(V_{in}\) increases, two currents \(I_{l}\) and \(I_{2}\) start to descend and ascend for obtaining membership functions. According to Equation (3) and at the point where \(V_{in}=V_{REFi}\), each current becomes as Equation (4):  
\[I_{i}=I_{i+1}=\frac{1}{2}I_{o} \tag{4}\]  
If \(V_{in}\) continues to increase then transistors M\({}_{1}\) and M\({}_{2}\) enter the cutoff and linear regions respectively. Choosing different reference voltages using control switches cause a change on currents \(I_{l}\) and \(I_{2}\). Also, using different \(W/L\) ratios results in changing shape and slope of membership functions. According to the [9] and first differential pair of Figure 1 and then using Equation (3), we can calculate the maximum of \((V_{in}-V_{REFi})\) as Equation (5):  
Figure 1: Differential pair circuit. \[ \begin{split}&\frac{\partial\left(V_{in}-V_{REFi}\right)}{\partial I_{i }}=\ 0\\ &\Rightarrow\ \left(V_{in}-V_{REFi}\right)_{\max}\ =\ 2\sqrt{\frac{Io}{\kappa}}=\ 2\sqrt{\frac{\mu\ C_{ox}W_{,i}\left(\Delta\ V_{0}\ \right)^{2}}{2\ \kappa\ L_{i}}}=\ \sqrt{2\ V_{0}}\end{split}