1 Introduction

The RF MEMS have been shown as one of the most important innovations in the design of modern pioneering communication applications, due to their low power usage, less insertion loss, and excessive isolation, and high linearity. MEMS switches have an exceptional RF efficiency contrasted with p-i-n diodes and field-effect transistors (FET) [1,2,3]. MEMS switches are classified as shunt and series capacitive switches depending upon their electrical setup. The switch created in this document is a shunt fixed-fixed switch that is effective at 35 GHz and can be utilized in ka band applications such as satellite and military applications and automobile speed detection. The restriction of the RF MEMS switch is its lifetime reliability. It can’t endure temperature level modifications and humidity effects [4]. It can’t hold up against to vibration and shocks. The polysilicon product utilized in the building procedure is a Brittle material.

RF MEMS shunt switches with serpentine spring structures have been utilized to accomplish low actuation voltage keeping adequate low isolation [5]. RF MEMS switches could not certify business requirements since of their bad reliability [6]. Several procedures have been conveyed. Amid these dielectric charging has been a significant issue. Issues based upon self-actuation because of excessive RF power and switches that do not self-actuate have been demonstrated [7]. Low loss fixed-fixed RF MEMS capacitive switches at greater frequencies and modeling of devices for design and optimization and gadget reliability [8]. Research studies and simulations mention that rectangle-shaped perforations offer much better outcomes compared to round and square type perforations [9]. A comparable switch is examined over a frequency variety of 0.6–40 GHz. they have accomplished an actuation voltage of 4.2 V at 0.9 μm and the insertion and return losses are − 0.44 and − 16 dB by utilizing dielectric material as aluminium nitride (AlN) and the material utilized for the beam is gold.

In this paper, an RF MEMS fixed-fixed switch is designed and simulate as spring constant, pull-in voltage switching time, and quality factor are computed. We validate the outcomes utilizing COMSOL software application and HFSS software application. The insertion losses and isolation losses are determined utilizing the HFSS software application. The graphs between voltage and displacement, switching time, losses, and the downstate capacitance and upstate capacitance are calculated.

The paper is arranged as follows, in Sect. 2 the design of the planned RF MEMS switch is debated, and the materials utilized in the building and construction of the switch are discussed. In Sect. 3 numerous outcomes such as pull-in voltage, spring constant, switching time, and Cd and Cu ratio examination of the switch and the RF performance features such as insertion and return losses in ON state and isolation losses in OFF state have been discussed. Section 4 concludes the entire paper.

2 Proposed Device and Its Specifications

The proposed RF MEMS switch is a shunt fixed-fixed switch. Through optimization, we acquire the height of substrate as 650 µm or below it, and above the substrate, the CPW layer is formed. The CPW space and the width of the signal line is selected to attain a specific impedance of 50 Ω. The space in between CPW lines is 45/75/45 is attained through conformal mapping which is nothing but a coordinate transformation technique and can be suitable for planar and non-planar transmission lines. The beam is of thickness 2 µm is holding at a height of 3 µm overhead the CPW line. The beam is integrated with square holes of 8 µm and meanders are placed at the same height as the beam and the layer of the switch is placed above the signal line utilizing anchors which are placed at the corner of each meander. The meanders are of the same thickness as the switch and positioned at the same height (Figs. 1, 2, 3, 4, 5, 6).

Fig. 1
figure 1

Schematic of RF MEMS Shunt switch

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Fig. 2
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Top view of proposed RF MEMS switch

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Fig. 3
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Switch Simulation at pull—in voltage 3.72 V

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Fig. 4
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Voltage vs displacement

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Fig. 5
figure 5

Up state capacitance of the switch

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Fig. 6
figure 6

Down state capacitance of the switch

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The proposed switch dimensions are given in Table 1.

Table 1 Specifications of the proposed design
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3 Results and Discussions

3.1 Pull-in Voltage

The pull-in voltage of the proposed switch is associated with the membrane attached to the fixed–fixed beam and Ohmic contact can be obtained from Eq. (1) [10],

$$ {V_p} = \sqrt {\frac{8kg_0^3}{{27{\varepsilon_0}A}}} $$
(1)

where ‘K’ is the obtained spring constant, ‘\({\varepsilon _0}\)’ = 8.85 × 10–12 F/m is the free space permittivity and ‘A’ is the covering area of CPW and beam.

The pull in voltage mainly depends on the spring constant (K), the gap between CPW and beam, A is the overlapping area. As spring constant increases pull-in voltage increases. Reducing the value of ‘K’ is the best way to reduce the pull in voltage. Pull in voltage can also be decreased by Increasing the Area. The spring constant or spring stiffness of the beam is obtained by [11],

$$ K = \frac{{Ew{t^3}}}{{4{l^3}}}$$
(2)

where ‘w’ is the width of the beam, ‘l’ are the length of the beam, ‘t’ is the thickness, ‘E’ is the young’s modulus. From the Eq. (2) the spring stiffness of the beam is obtained as 0.44989 N/m.

Thus, the pull-in voltage of the switch is attained by replacing the value of k and the value of the ‘go’ in Eq. (1) and it is obtained theoretically as 3.72 V.

The behavioral features of the switch are simulated by using the COMSOL 5.2 tool. Potential difference is applied across the lower and upper actuation electrodes which cause the actuation of the switch.

3.2 Capacitance Analysis

Variation of capacitance with voltage applied between electrodes is plotted by electrostatic analysis. Good dielectric materials generally have a relative permittivity between 3.4 and 13. In the switch discussed, a dielectric material is taken as silicon nitride which has a dielectric constant of 9.5. The up capacitance of the switch can be assessed by the equation [12].

$$ {C_u} = \frac{{{\varepsilon_0}A}}{{g + \frac{{t_d}}{{\varepsilon_r}}}} $$
(3)

The down state capacitance is given by

$$ {C_d} = \frac{{{\varepsilon_0}{\varepsilon_r}A}}{{t_d}}$$
(4)

where ‘ε0’ is the free space permittivity, ‘εr’ dielectric layer permittivity, ‘A’ is the overlapping area, g is the gap between the electrodes and td is the thickness of dielectric layer.

The up and down state capacitance are calculated methodically from the above equations are 110 fF and 1.58 pF. The capacitance ratio of 113.50 is attained from the switch proposed.

3.3 Resonance Frequency

The maximum displacement of the switch takes place at the resonant frequency. The space among the electrodes in the switch is taken as 3 µm. The frequency of the switch is obtained by the equation [13].

$$ {F_r} = \frac{1}{2\pi }\sqrt{\frac{K}{m}} $$
(5)

where ‘m’ is the effective mass of the beam and ‘K’ is the spring constant of the beam. The resonant frequency is calculated as 7.1 kHz.

3.4 Quality Factor

The quality factor is the function of spring constant, resonant frequency and the damping coefficient. The structure of the membrane defines the damping coefficient and there are many methods for reducing the damping ratio. The damping coefficient is obtained from the equation,

$$ b = \frac{3}{2\pi }\frac{{\mu {A^2}}}{{g^3}} $$
(6)

where ‘µ’ = 1.885 × 10–5 is air viscosity, g is the gap and ‘A’ is the overlapping area. Thus, the quality factor is obtained from,

$$ Q = \frac{K}{{2\pi {f_0}b}}$$
(7)

The damping ratio and quality factor are 2.8 × 10–4 and the quality factor is 7.1 × 10–9.

3.5 Switching Time Analysis

The applied voltage is responsible for the changes in the switching time. Greater the applied voltage stronger the electrostatic forces acting on the beam to displace it. Switching speed defines the device performance. The switching time is given by the equation [14,15,16,17]

$$ {T_s} = \frac{{3.67{V_p}}}{{{V_s}{\omega_0}}} $$
(8)

where Vs is the actuation voltage and the pull-in voltage is Vp, (Vs = 1.4Vp) and ω0 is the angular resonant frequency.

The switching period of the proposed switch is calculated by using the above equation and a graph is drawn for different voltages as shown in Fig. 7.

Fig. 7
figure 7

Switching time graph of the switch

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3.6 RF-Performance Analysis

The RF performance is analyzed in the ON and OFF state of the switch. The return and insertion are measured in the ON state, and the isolation is in the OFF state. By reducing the number of connectors or selecting low insertion loss devices we can achieve low insertion loss. As power is expensive at greater frequencies, electromechanical switches provide the lowest possible loss along the transmission line [18,19,20]. The S-parameters of return, insertion, and isolations are shown in Figs. 8, 9, and 10.

Fig. 8
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Measured Return loss (S11) at 31 GHz

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Fig.9
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Insertion (S12) of the switch at 31 GHz

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Fig. 10
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Isolation of proposed switch at 35 GHz

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The return and insertion losses are obtained as − 26.6, − 0.22 dB at 31 GHz, and the isolation measured as − 36.4 dB at 35 GHz frequency.

4 Conclusion

This work displays the design and simulation of a capacitive shunt RF MEMS fixed–fixed switch analyzed at a frequency of 35 GHz. The actuation structure used in this paper is anchored with the help of meanders having holes on the membrane which helps to reduce the pull-in voltage of the switch. By implementing the electromechanical analysis, the spring constant of the switch is observed as 0.44 N/m and a pull-in voltage of 3.72 V is obtained from the simulations. The switch is simulated in HFSS software. It exhibits insertion and return loss of − 0.22 and − 26.6 dB, and the isolation of − 36.4 dB at 35 GHz. Based on the performance of the switch it can be used for Ka-band Radar applications.