1 Introduction

Radio-frequency (RF) micro-electro-mechanical system (MEMS) switches operating at RF to millimetre-wave frequencies have many advantages over p-i-n diode or field-effect transistor (FET) switches, such as low or near-zero power consumption, high isolation, low insertion loss, and high linearity (Lee et al. 2006). These RF-MEMS switches use mechanical movements to short or open a transmission line; and normally can be integrated with a planar or coplanar waveguide (CPW).

There are many varieties of RF-MEMS switches. The switch can be in series or in shunt connected with the signal path; coupling method can be either capacitive or metal-to-metal (Chan et al. 2003); and actuation mechanism can be electrostatic (Kim et al. 2010), electromagnetic (Glickman et al. 2011), thermal (Daneshmand et al. 2009), piezoelectric (Park et al. 2006) or combined actuations (Cho and Yoon 2010). Electrostatic actuated RF-MEMS switches are the most prevalent technique in use today; due to their virtually zero power consumption, high switching speed (Kim et al. 2010), small electrode size, thin layers used, 50–200 µN of achievable contact forces, the possibility of biasing the switch using high-resistance bias lines (Rebeiz 2003), and the high compatibility with a standard Integrated Circuitry (IC) process (Chu et al. 2007). However, the largest challenge for electrostatic switches is their relative high actuation (or pull-in) voltage, which is around 20–80 V (Lee et al. 2006; Kim et al. 2010; Park et al. 2006; Mafinejad et al. 2013).

Usage of standard complementary metal-oxide semiconductor (CMOS) technologies have always been of great interest for the implementation of RF-MEMS devices due to their mature fabrication process, higher levels of integration, and also lower manufacturing cost (Fouladi and Mansour 2010). Nevertheless, generally standard 0.35 µm CMOS process fabricated devices require compatible operating voltage supply of 3.3 V or less than 3.3 V (Yusoff et al. 2004; Wey et al. 2002), which is insufficient to actuate the most developed electrostatically-actuated RF-MEMS switches. In order to monolithically integrate these RF-MEMS switches with active CMOS circuitry, an additional voltage-upconverter or an external off-chip circuit is needed (Lee et al. 2006), which will make the whole chip larger, more complex, and consume more power. Chan et al. and Goldsmith et al. indicated that a high actuation voltage also may lead to a shorter lifetime for capacitive RF-MEMS switches which use dielectric layers for isolation (Shalaby et al. 2009). Diverse RF-MEMS switch designs have been proposed by various researchers to reduce the actuation voltages. A dedicated RF-MEMS switch fabricated in 0.35 µm CMOS process has been reported to require a pull-in voltage of 7 V (Dai and Chen 2006). A bi-stable RF-MEMS switch was designed with a low actuation voltage of 5 V, but was not compatible with CMOS process (Lakamraju and Phillips 2005). Afrang et al. (Afrang and Abbaspour-Sani 2006) have introduced a CMOS fabricated membrane-based switch with actuation voltage of 12.5 V. Authors’ previous design on CMOS RF-MEMS switch managed to achieve a low pull-in voltage of 3 V (Ya et al. 2013), however, the relatively wide beams cannot be easily released with membrane in one step; an additional mask wet etch is needed. Moreover the long membrane design is hard to keep it in-plane during fabrication and operation which deteriorates a lot in its RF performance.

In this paper, an advanced low-voltage electrostatically-actuated shunt capacitive RF-MEMS switch is proposed by using MIMOS (Malaysia Institute of Microelectronic Systems) standard 0.35 µm (double poly triple metal) CMOS technology. The actuation voltage of 3.04 V was achieved by reduction of the beams’ spring constant while maintaining the structure’s robust using multi-response optimization method, which comprises Taguchi method and weighted principal component analysis (WPCA). The rest of the paper is divided into the following sections: Sect. 2 presents the detail designs of RF-MEMS switch. Section 3 displays the beams’ geometric optimization by Taguchi method and WPCA. Section 4 illustrates the simulation results of applied voltage with the membrane displacement, stress distributions, switching time, switch-on and switch-off capacitances, insertion loss and isolation, as well as a comparison of the designed switch with other related work.

2 RF-MEMS switch design

The structure of the RF-MEMS switch is illustrated in Fig. 1a. The RF-MEMS switch consists of a membrane, four folded beams, four straight beams, anchors and coplanar waveguide (CPW) lines. The four folded beams mainly provide support to the large membrane and the four straight beams are used to supply the DC bias. Figure 1b displays the geometric parameters of the membrane and beams, where the holes are used to release the membrane during the post-CMOS process. And Fig. 1c shows the cross-section view of the switch, where the four folded beams are connected to the ground lines of the CPW by via; and a very thin dielectric layer covers the CPW lines to consist the coupling capacitor during actuated state.

Fig. 1
figure 1

RF-MEMS switch design. a Overall view, b top view and c cross-section view (A–A′)

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When a DC bias voltage is applied between the membrane and signal line, there is a positive feedback between the electrostatic forces and the deformation of the membrane. The applied voltage creates electrostatic forces that bend down the beam and thereby reducing the gap to the ground substrate. The reduced gap between the membrane and signal line, in turn, increases the electrostatic forces. At a certain voltage, the electrostatic force overcomes the mechanical stress limit of the beam causing the system to be unstable, and the gap collapses. This critical voltage is called pull-in voltage or actuation voltage (V p ) and can be described as shown in (1) (Rebeiz 2003; Gupta 1997). Once the switch is actuated, a coupling capacitor induced between the membrane and signal line prevents the signal to be passed the signal line.

$$V_{p} = \sqrt {\frac{{8kg_{0}^{3} }}{{27\varepsilon_{0} A}}}$$
(1)

where, k is the spring constant of the membrane and beams; g 0 is the initial gap between the membrane and the signal line; ε 0 is the permittivity of air, 8.854 × 10−12 F/m; and A is the area of the membrane, namely the product of the membrane’s width and length (W m  × L m ).

The materials and thickness of each layer are determined by the CMOS fabrication process and is listed in Table 1. The membrane and CPW lines are made from aluminum (Al) and built by Metal3 and Metal1 layers of the standard process. The permittivity of the dielectric material between two metal layers is 4.99.

Table 1 Each layer thickness
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From (1) it can be seen that to achieve a low V p , the capacitive switch should have a small spring constant (k), large membrane area (A) and big initial gap (g 0 ). In this design, the initial gap is determined by the CMOS process (g 0  = g air  + t d ); the membrane area is generally decided by the coupling capacitance which is in pF range and does not have much space and flexibility to be modified here. Therefore, the main parameter that can be designed and controlled by the researchers is the spring constant (Dai and Chen 2006; Peroulis et al. 2003; Balaraman et al. 2002; Kuwabara et al. 2006; Jaafar et al. 2009). The relationship of V p and k can be observed in Fig. 2. Basically, in order to own a lower spring constant, the beam should have a less beam width or thinner beam thickness; but this will make the structure to become fragile and short-lived (Bao 2000). Optimization of beam lengths L1, L2 and L3, as well as beam width w to obtain a low spring constant while maintain a robust structure becomes an important problem for this low V p RF-MEMS switch design.

Fig. 2
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Relationship of V p and k

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3 Multi-response optimization method

There are four geometric parameters in the RF-MEMS switch as shown in Fig. 1b and the possible dimensions are listed in Table 2. These parameters need to be modified to obtain a low k and small maximum von Mises stress (σ v(max)) simultaneously, where the low k can led to a low V p as shown in Fig. 2 and the small σ v(max) can guarantee a robust structure (Chen and Harichandran 1998). Since every geometric parameter could be set with three different values, it will be tedious to simulate all their possible combinations (34 = 91 times). Therefore, a proper optimization technique is necessary here; it is also a general problem to be encountered by most RF-MEMS switches’ design (Shalaby et al. 2009; Philippine et al. 2013). The only difference from each work could be the optimized responses (such as switching speed, power handling capability or RF performance) (Shalaby et al. 2009; Badia et al. 2012) or geometric design (shapes or dimensions) (Peroulis et al. 2003; Gong et al. 2009).

Table 2 Geometric parameters with their possible values
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In this work, a multi-response optimization method which comprises Taguchi method and WPCA was employed to optimize the responses of the spring constant and maximum von Mises stress. This method could be simply implemented into other optimization problems which have single or multiple responses with diverse parameters. Figure 3 shows the multi-response optimization methodology. The optimized values are based on a 3-D structural-Electro-mechanics Finite Element Modeling (FEM) simulation results.

Fig. 3
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Multi-response optimization methodology

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3.1 Taguchi method

Taguchi’s parameter optimization is an important method for robust design. Taguchi defines robustness as the “insensitivity of the system performance to parameters that are uncontrollable by the designer” (Taguchi et al. 1987). A robust design incorporates this concept of robustness into design optimization and aims at achieving designs that optimize given performance measures while minimizing sensitivities against uncontrollable parameters using different approaches, such as signal to noise ratio (Shalaby et al. 2009). The Taguchi approach itself can be utilized to determine the best parameters for the optimum design configuration with the least number of analytical investigations. Comparing with other optimization methods, such as Genetic Algorithm (GA) (Li et al. 2003) or Neural Network (Meng and Butler 1997), the proposed multi-response optimization does not need much statistical or technical background in that specific field, which can be easily implemented by engineering researchers (Roy 2010; Liao 2006). This method has not been widely employed for the optimization of RF-MEMS switch geometry but is more commonly used for process or product optimization. There are two major tools to be used in this method, which are orthogonal array (OA) and signal-to-noise ratio (S/N).

The folded and straight beams of the RF-MEMS switch will be analysed in terms of whole system’s k and σ v(max). In order to develop a RF-MEMS switch which could be implemented together with normal active CMOS circuitry as mentioned in part 1, a V p of 3 V is proposed. From Fig. 2, it can be seen that for our model, a V p  = 3 V RF-MEMS switch should have a k of 1.2827 N/m. Therefore, in Taguchi method, the S/N of k is calculated according to the characteristics of the nominal the best; such a ratio is selected when a specific target value is desired. The optimum of σ v(max) on the other hand employed the smaller the better characteristic. This is because in order to avoid the structure failure, with the applied voltage load, the beams and membrane’s total σ v(max) should be less than their material’s yield strength (Chen and Harichandran 1998). With smaller σ v(max), the structure experiences less stretch. The equations of both characteristics are shown in (2) and (3), respectively (Roy 2010).

Nominal the best:

$$S/N = - 10\log_{10} \left[ {\frac{{\left( {y_{1} - y_{0} } \right)^{2} + \left( {y_{2} - y_{0} } \right)^{2} + \cdots + \left( {y_{n} - y_{0} } \right)^{2} }}{n}} \right]$$
(2)

Smaller the better:

$$S/N = - 10\log_{10} \left[ {\frac{{y_{1}^{2} + y_{2}^{2} + \cdots + y_{n}^{2} }}{n}} \right]$$
(3)

where y 1 , y 2 , etc., are the simulation results, y 0  = 1.2827 N/m is the target value of results; and n is the number of observations with the same values of factors (here n = 1).

According to OA selector (Fraley et al. 2006), with four parameters and three levels of each parameter, OA of L9 is selected as shown in Table 3, where the level of “1”, “2” and “3” under parameter columns represent the corresponding parameter’s least, middle and largest values. The OA of Taguchi method has the capability to reduce the full factorial designs into highly fractionated factorial designs and to make the design of experiments very easy and consistent. In Table 3, each row signifies random single simulation run that has been carried out. The simulation results for both responses of spring constant and maximum von Mises stress were obtained by FEM simulations using software of Comsol Multiphysics 4.3®, where Electro-mechanics model was employed with the boundary condition of eight beams’ end fixed. By applying (2) and (3) for simulated k and σ v(max), the S/N for each simulation run can be calculated as listed in Calculated S/N columns. In order to get the parameters’ optimum condition for each response, the average S/N at each level for k and σ v(max) are calculated separately in Table 4 and plotted in Fig. 4. For all of these characteristics, the largest value of S/N represents a more desirable condition (Roy 2010); and the bigger Max–Min value means that corresponding parameter has more effect on the response, vice versa.

Table 3 Simulated results of spring constant (k) and maximum von Mises stress (σv(max)) with their corresponding S/N
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Table 4 Average values of S/N ratio for each response
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Fig. 4
figure 4

Mean S/N plots. a Mean S/N of spring constant and b Mean S/N of maximum von Mises stress

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Figure 4a suggests that in order to obtain the desired spring constant of 1.2827 N/m, the four parameters should be set as: w = w 2  = 2.5 µm, L1 = (L1) 3  = 30 µm, L2 = (L2) 1  = 30 µm and L3 = (L3) 2  = 65 µm. Figure 4b illustrates that to obtain a structure with smallest von Mises stress and longer lifetime, the parameters should be set as: w = w 3  = 3 µm, L1 = (L1) 1  = 20 µm, L2 = (L2) 2  = 35 µm and L3 = (L3) 1  = 60 µm. The contribution of each parameter to the spring constant and von Mises stress was calculated using Pareto analysis of variance (ANOVA) technique (Park and Antony 2008) and is shown in Fig. 5. These optimization results illustrate that the geometric parameters’ settings for achieving both low spring constant and small von Mises stress simultaneously do not coincide. Generally, Taguchi method is better to be used for optimizing a single response or one design objective with many controllable parameters or factors, as in (Fahsyar and Soin 2012; Su and Yeh 2011). For this multi-response optimization, if all the responses have same parameters’ setting, then the optimized result is obtained; if the responses have conflict parameters’ setting, then a trade-off technique among them is needed. Here, in order to obtain the trade-off parameters for low spring constant and small von Mises stress designs, a further calculation of multi-response optimization, namely WPCA was conducted, as mentioned in Fig. 3.

Fig. 5
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Percentage contribution of each factor to the both responses. a Spring constant, and b Maximum von Mises stress

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3.2 Weighted principal component analysis

Principal component analysis (PCA) is a multivariate statistical method used for data reduction purpose. The basic idea is to represent a set of variables by a smaller number of variables known as principal components. It involves a mathematical procedure that reduces the dimensions of a set of variables by reconstructing them into uncorrelated combinations (Wu and Chyu 2004). However, there are still some obvious shortcomings in the PCA method. First, only the principal components with eigenvalues ≥1 are chosen to be analysed in PCA. Second, when more than one principal component (eigenvalue ≥1) is selected, the required trade-off for a feasible solution is unknown; and third, the multi-response performance index cannot replace the multi-response solution when the chosen principal component can only be explained by total variation (Liao 2006). WPCA is a method bases on PCA while all principal components and their weights are taken into consideration. In order to completely explain variation for all responses, WPCA uses the explained variation as the weight to combine all principal components into a multi-response performance index (MPI) for the further optimization results produced (Liao 2006). Experimental results using WPCA have been reported by some researchers to provide higher accuracy than the conventional PCA (Fan et al. 2011; Pinto da Costa et al. 2011).

3.2.1 WPCA procedure

In order to compute WPCA and obtain the MPI, a simple procedure needs to be carried out as follows. First, using (4) (Jaafar et al. 2009) normalizes the S/N values for all the responses. The normalized value can get rid of the difference between different units and it should be located in the range of 0 to 1. Second, PCA is performed by using the normalized S/N values to obtain the values of explained variation of all the responses, the eigenvalues and eigenvectors of each principal component. Last step is to calculate MPI by (5), where all the principal components and their explained variations or weights are considered (Liao 2006).

$$x_{i}^{*} \left( j \right) = \frac{{x_{i} \left( j \right) - x_{i} \left( j \right)^{ - } }}{{x_{i} \left( j \right)^{ + } - x_{i} \left( j \right)^{ - } }}$$
(4)

where, x i (j) means the S/N value of jth response at ith experiment number, x * i (j) is the normalized response, x i (j)+ is the maximum value of x i (j) at jth response, and x i (j)− is the minimum value of x i (j) at jth response.

$$MPI = \sum\limits_{j = 1}^{r} {W_{j} Z_{j} }$$
(5)

where, Z j is the jth principal component which can be obtained by (6); W j is the weight (or explained variation) of jth principal component; and r refers to the total of response number.

$$Z_{j} = \sum\limits_{i = 1}^{p} {a_{ji} x_{i}^{*} \left( j \right)}$$
(6)

where, a ji is the eigenvector which satisfies the relation of ∑  p i=1 a 2 ji  = 1.

3.2.2 Multi-response optimization by WPCA

Following the WPCA procedures introduced in last part, the S/N normalized values for both spring constant and maximum von Mises stress were calculated by (4), as shown in Table 5. Add-Ins tool of XLSTAT in Microsoft Excel® has been used to compute PCA, where the normalized S/N values of k and σ v(max) were set as the Observations or variables; and the simulation run numbers were set as the Observation labels. After the calculation, a complete PCA datasheet was displayed in Microsoft Excel®. Table 6 summarized some important PCA data.

Table 5 Normalized S/N values and computed MPI
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Table 6 Explained variation and eigenvector
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By using (5), MPI can be calculated as below (7) and the values were displayed in the form of the standard OA of L9, as shown in Table 5. Calculation of the mean values of MPI at each level for each factor allows us to obtain the final optimized combinations for the multiple responses. Specific to this case, the values are w 2 (L1) 3 (L2) 1 (L3) 2 , as displayed in Table 7 and Fig. 6, where w = w 2  = 2.5 μm, L1 = (L1) 3  = 30 µm, L2 = (L2) 1  = 30 µm, and L3 = (L3) 2  = 65 μm.

Table 7 Average MPI for each factor at each level
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Fig. 6
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Mean value of MPI

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$$\begin{aligned} MPI = W_{1} Z_{1} + W_{2} Z_{2} \hfill \\ = 0.61913 \times \left[ {Z1_{(k)} \times x_{i}^{*} \left( 1 \right) + Z1_{{(\sigma_{v(\hbox{max} )} )}} \times x_{i}^{*} \left( 2 \right)} \right] + 0.38087 \times \left[ {Z2_{(k)} \times x_{i}^{*} \left( 1 \right) + Z2_{{(\sigma_{v(\hbox{max} )} )}} \times x_{i}^{*} \left( 2 \right)} \right] \hfill \\ \end{aligned}$$
(7)

3.3 Summary of the optimized results

The RF-MEMS switch’s beams geometric optimization with the objectives of (1) low spring constant, (2) small maximum von Mises stress, (3) multiple responses has been done separately in the aforementioned sections. The geometric parameters were set differently according to the different objectives, as shown the summary in Table 8. The same optimized result for multi-response design (Model c) and low spring constant design (Model a) is mainly due to the selection of the parameters’ value range (in Table 2). This reasonable values range was estimated and selected by the limitations of whole chip design dimension, fabrication, as well as the design specifications. A trade-off Model c is supposed to be different from both Model a and Model b; Model b stands for the optimum condition for small von Mises stress (σ v(max)) design. But after the calculation, Model c is more inclined to Model a, this is because: (1) the beam lengths of L1, L2 and L3 have much less effect on the σ v(max) (Fig. 5b, totally around 5 %) comparing k (Fig. 5a, totally around 68 %); (2) the optimized beam width for both σ v(max) (w = 3 µm) and k (w = 2.5 µm) are very close. Moreover, both Model a and Model b’s contribution has been considered and calculated by (7). After validation, Model c has spring constant of V p  = 3.04 V and maximum von Mises stress of σ v(max) = 20.255 MPa, as shown in Figs. 7 and 8, which meets with our design objective, further different parameters’ value range has not been tried (as shown the work flow in Fig. 3). However, WPCA is a necessary step when there is different optimized parameters’ setting for different responses.

Table 8 Geometric parameters’ setting with different motivated optimization
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Fig. 7
figure 7

Spring constant simulations for the optimized models

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Fig. 8
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Von Mises stress simulations for the optimized models. a Model a and Model c and b Model b

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4 Simulations of the optimized RF-MEMS switch

The optimized geometric dimensions have been obtained by Taguchi method and WPCA. In this part, its static property, dynamic property, and RF performance is investigated by FEM simulations.

4.1 Electro-mechanical analysis

The simulation model is established in accordance with the dimensions in Table 1 and the multi-response optimized values in part 3. The materials’ properties of each layer can be found in Table 9, which directly follows the setting from the IntelliSuite v8.7® software’s material library, except the thin silicon dioxide layer’s dielectric constant of 4.99. The boundary conditions are set as: (1) the bottom plate of silicon (Si) substrate is fixed; (2) all the beams’ ends are set as fixed face; and (3) potential of the signal line is set to zero to simplify the simulation; and the membrane is assigned with varying voltage load, in order to find V p . The model is then meshed using rectangular elements of less than 10 µm.

Table 9 Materials’ properties
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The simulation result of membrane’s vertical displacement with the varying applied voltage is displayed in Fig. 9. It can be seen that the membrane totally collapses on the bottom plate at the voltage of 3.04 V which is the optimized switch’s V p . Figure 10 shows 3D results of the membrane’s vertical displacement and stress distribution during actuated state, respectively, where the obtained σ v(max) of 20.255 MPa is much less than the yield strength of Al, 90 MPa (Dai et al. 2005).

Fig. 9
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Applied voltages vs. membrane’s vertical displacement

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Fig. 10
figure 10

3D view of the optimized RF-MEMS switch’s simulations with V p  = 3.04 V. a Z-displacement distribution and b Von Mises stress distribution

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4.2 Actuation time and capacitance

The RF-MEMS switch’s actuation time is limited by the mechanical structure and basically is inversely proportional to the membrane and beam’s total resonant frequency (Mafinejad et al. 2013). A time dependent simulation by Comsol Multiphysics 4.3® has been conducted to estimate this optimized RF-MEMS switch’s actuation time. The boundary conditions are set similar as the previous simulation, except a step-up voltage load is applied on the membrane, as shown in Fig. 11. The high level voltage of the step function of 3.5 V is a bit higher than the V p ; and its rising time is adjusted within 1 µs. Then the simulated results of membrane’s movement and switch’s capacitances are presented in Fig. 12. Figure 12a shows that, when applied voltage at low stage (near to 0 V), the membrane almost keeps at its original position (z-displacement = 0 µm). Once the applied voltage is increased to 3.5 V at t = 20 µs; the beams start to bend down until the membrane reaches the maximum displacement at t = 33.5 µs. Therefore, the actuation time of the optimized switch is 13.5 µs. Figure 12b illustrates the switch-on and switch-off capacitances are 0.14 and 7.31 pF, respectively. The capacitance ratio of the optimized switch is around 52.

Fig. 11
figure 11

Voltage load in time domain

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Fig. 12
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Simulation of the optimized RF-MEMS switch in time domain. a Membrane’s movement, and b capacitances of switch-on and switch-off

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4.3 RF performance

Electromagnetic (EM) simulator of AWR Design Environment 10® has been used to compute the RF responses (S-parameters) of the RF-MEMS switch. When the switch state is ON, no actuation occurs and the RF signal passes underneath the membrane with relatively little attenuation. Its return loss (S11) and insertion loss (S21) is presented in Fig. 13, where return loss is −1.51 dB and insertion loss is −5.65 dB at 42 GHz. This relatively high insertion loss is mainly due to the small fixed gap (g 0 ) between two meal layers and low-resistivity silicon substrate which is limited by the CMOS fabrication process. When the switch is actuated, the metal-dielectric-metal sandwich produces a low impedance path to the surrounding CPW grounds (Yao et al. 1999); this prevents the RF signal from traversing beyond the switch, and the switch state is OFF. During this state, the return loss (S11) of −0.60 dB and isolation (S21) of −24.38 dB at the frequency of 40 GHz is shown in Fig. 14.

Fig. 13
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S-parameters of switch-on state

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Fig. 14
figure 14

S-parameters of switch-off state

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Table 10 presents the comparison of our work with some typical developed capacitive RF-MEMS switches. It shows our proposed switch’s V p is low enough to be integrated with most CMOS circuitry while other properties are kept in a reasonable range.

Table 10 Comparison of developed capacitive RF-MEMS switches
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5 Conclusion

A novel shunt capacitive RF-MEMS switch using standard 0.35 µm CMOS process has been designed, optimized and simulated. The RF-MEMS switch employs four supporting folded beams and four straight beams as DC voltage supply paths. Both Taguchi method and WPCA have been used to optimize the switch’s geometric parameters. A complete optimization methodology for multiple responses has been developed in this work. By employing a L9 orthogonal array and calculation of the S/N from each simulation results, the best combination of the four parameters for the nominated spring constant design is w 2 (L1) 3 (L2) 1 (L3) 2 ; and the best combination for smallest von Mises stress design is w 3 (L1) 1 (L2) 2 (L3) 1 . By using WPCA and calculating the MPI as well as their mean values at each level for each parameter, the multi-response optimized design is w 2 (L1) 3 (L2) 1 (L3) 2 , where, w = w 2  = 2.5 µm, L1 = (L1) 3  = 30 µm, L2 = (L2) 1  = 30 µm and L3 = (L3) 2  = 65 µm.

For the multi-response optimized RF-MEMS switch, a very low pull-in voltage of 3.04 V can be achieved and compatible with the most CMOS power supply requirements. The simulated actuation time of the optimized switch is 13.5 µs and the capacitance ratio is 52. The insertion loss and isolation is −5.65 dB and −24.38 dB at the frequency of 40 GHz, respectively. The whole optimization methodology not only can be applied for RF-MEMS switch’s geometric parameters’ optimization, but also can be used for other RF-MEMS devices’ optimization process, especially with multiple responses or objectives.