**5. Electrostatically actuated RF-MEMS switch configurations for reconfigurable uniplanar circuits**

This section presents electrostatically actuated switch configurations which can easily be integrated in reconfigurable uniplanar circuits. All the considered devices were fabricated using the eight-mask surface micromachining process from FBK explained in Section 3. The structures are composed of a 1.8-μm-thick gold layer and reinforced with a 3.5-μm-thick superimposed gold frame to increase the rigidity of the cantilever or the bridge. The switches were designed taking into account the mechanical analysis described in Section 4.

To reduce the initial deformation of the switch membrane, different authors have reported on the effective stiffness of common suspensions types [26–28]. A coupled-field 3D finite element analysis (FEA) with ANSYS® Workbench™ can be used to model the mechanical structure and tune the measured initial deformation according to the residual stress produced by the fabrication process. The robustness of the design to manufacturing stresses can also be studied with this software.

The switch designs presented use either a clamped-clamped suspension or alternative suspension techniques such as straight-beam, curved-beam, or folded-beam which reduce the initial stress and the actuation voltage. Some FEA results are shown to assess the ability of the proposed suspensions to absorb the initial stress. Hysteresis measurements are also presented to show the featured pull-in and pull-out voltages. At the end of the section, **Table 1** summarizes the switch dimensions and the main mechanical parameters for the different switches.

The RF behavior of the switches, including equivalent circuits in ON and OFF states, is discussed in detail in Section 6.

#### **5.1. Cantilever-type switches for switchable asymmetric shunt impedances**

**Figure 10** shows a cantilever-type ohmic-contact switch, able to synthesize asymmetric shunt impedances in a CPW to control the CPW even mode as explained in Section 2.2.3. The cantilever is placed above a rectangular notch in the upper lateral ground plane to which is anchored using a suspension composed of two 16-μm-wide beams, providing a low spring constant value and a low pull-in voltage. The beams may be either straight-shaped (**Figure 10(a)**) or semi-circular-shaped (**Figure 10(b)**). The latter is used to reduce the initial deformation of the switch due to the residual stress [27] produced by the fabrication process [20, 52]. To compute the initial deflection, a 3D FEA using ANSYS® was performed. The initial stress values used for the simulation were *σ*<sup>2</sup> = 58 MPa (gold layer with a thickness *t*<sup>2</sup> = 1.8 μm) and *σ*<sup>1</sup> = 62 MPa (gold layer with a thickness *t*<sup>1</sup> = 3.5 μm). As shown in **Figure 10(c)**, the simulated initial deformation was −0.19 μm. The devices were fabricated on a quartz substrate (*ε<sup>r</sup>* = 3.8) with a thickness *h* = 300 μm and an air gap *gi* = 1.6 μm. An isolated, high-resistivity polysilicon lower electrode is placed in the notch underneath the cantilever. Three ohmic contacts are defined on the bottom edge, and small dimples (12 × 10 μm<sup>2</sup> ) of polysilicon are placed underneath, creating contact bumps to reduce the contact resistance and enhance the RF behavior.

capacitance (in case of the ohmic-contact parallel switch discussed in Section 5.2.3) occur but

**Figure 11** shows two fabricated capacitive-contact parallel switches. The change between ON and OFF states is performed by moving the suspended membrane, which can be actuated through bias pads connected to two symmetrical polysilicon electrodes placed under the membrane. A floating metal (FLOMET) strip is placed on top of the dielectric under the membrane. The overlapping area between FLOMET and a multi-metal layer under the bridge (CPW center conductor) defines a MIM capacitor, as described in Section 3. When the actuation voltage is equal or higher than the pull-in voltage *Vpull\_in*, the bridge collapses on the FLOMET, producing a reproducible, constant-value down-state capacitance. The resistance of the ohmic contact between the membrane and the FLOMET strip fixes the amount of switch

with a very limited impact on the circuit behavior.

**Table 1.** Dimensions and mechanical parameters of the switches.

8‡

Calculated using the mechanical analysis of Section 4.

*5.2.1. Capacitive-contact parallel switch*

**Parameter Ohmic-cantilever** 

Supporting beam radius

Supporting beam width

Supporting beam length,

Supporting beam length,

Bottom electrodes area

Contact area (μm2

Spring constant, *keff*

Pull-in voltage, *Vpull\_in*

Resonant frequency

Floating metal area.

(μm)

(μm)

*b* (μm)

*e* (μm)

(μm2 )

(N/m)‡

(V)†

(KHz)

† Measured.

‡

\*

**straight/semicircle**

**Capacitive, clamped/**

RF-MEMS Switches Designed for High-Performance Uniplanar Microwave and mm-Wave Circuits

−/16 — — —

16 −/10 — 10

40 −/75 — 75

— −/45 — 77.5

13,500 2 × 22,800/2 × 7650 2 × 22,800 2 × 7650

2.3/1.6 104.5/32.5 104.5 15.4

10.6/8.8 60/14 49 14

/50 × 90\* 2 × 10 × 90 2 × 10 × 12

/25.3‡ 16.25†,‡ 17.1‡

**Ohmic-series Ohmic-**

http://dx.doi.org/10.5772/intechopen.76445

**parallel (SAB)**

129

**folded**

Figure 10(a)/10(b) 11(a)/11(b) 13(a) 14(a)

Meander length, *a* (μm) — −/30 — 30

Membrane width, *c* (μm) 90 90 100 90 Window width, *d* (μm) — — — 60 Membrane length, *f* (μm) 170 580/230 580 165

) 3 × 10 × 30 100 × 90\*

/6.6‡ 16.25 ‡

#### **5.2. Bridge-type switches**

Bridge-type switches can be used to perform both ohmic contacts and capacitive contacts in uniplanar circuits for multiple applications. In contrast to the cantilever-type switches, the bridge-types are symmetric structures and therefore (as discussed in Section 2.2), when actuated, they are able to control one of the fundamental CPW modes (either even or odd), leaving the other mode ideally unaffected. Some minor effects such as a small even-mode parasitic RF-MEMS Switches Designed for High-Performance Uniplanar Microwave and mm-Wave Circuits http://dx.doi.org/10.5772/intechopen.76445 129


\* Floating metal area.

superimposed gold frame to increase the rigidity of the cantilever or the bridge. The switches

To reduce the initial deformation of the switch membrane, different authors have reported on the effective stiffness of common suspensions types [26–28]. A coupled-field 3D finite element analysis (FEA) with ANSYS® Workbench™ can be used to model the mechanical structure and tune the measured initial deformation according to the residual stress produced by the fabrication process. The robustness of the design to manufacturing stresses can also be stud-

The switch designs presented use either a clamped-clamped suspension or alternative suspension techniques such as straight-beam, curved-beam, or folded-beam which reduce the initial stress and the actuation voltage. Some FEA results are shown to assess the ability of the proposed suspensions to absorb the initial stress. Hysteresis measurements are also presented to show the featured pull-in and pull-out voltages. At the end of the section, **Table 1** summarizes the switch dimensions and the main mechanical parameters for the different

The RF behavior of the switches, including equivalent circuits in ON and OFF states, is dis-

**Figure 10** shows a cantilever-type ohmic-contact switch, able to synthesize asymmetric shunt impedances in a CPW to control the CPW even mode as explained in Section 2.2.3. The cantilever is placed above a rectangular notch in the upper lateral ground plane to which is anchored using a suspension composed of two 16-μm-wide beams, providing a low spring constant value and a low pull-in voltage. The beams may be either straight-shaped (**Figure 10(a)**) or semi-circular-shaped (**Figure 10(b)**). The latter is used to reduce the initial deformation of the switch due to the residual stress [27] produced by the fabrication process [20, 52]. To compute the initial deflection, a 3D FEA using ANSYS® was performed. The initial stress values used for the simulation were *σ*<sup>2</sup> = 58 MPa (gold layer with a thickness *t*<sup>2</sup> = 1.8 μm) and *σ*<sup>1</sup> = 62 MPa (gold layer with a thickness *t*<sup>1</sup> = 3.5 μm). As shown in **Figure 10(c)**, the simulated initial deformation was −0.19 μm. The devices were fabricated on a quartz substrate (*ε<sup>r</sup>* = 3.8) with a thickness *h* = 300 μm and an air gap *gi* = 1.6 μm. An isolated, high-resistivity polysilicon lower electrode is placed in the notch underneath the cantilever. Three ohmic contacts

underneath, creating contact bumps to reduce the contact resistance and enhance the RF

Bridge-type switches can be used to perform both ohmic contacts and capacitive contacts in uniplanar circuits for multiple applications. In contrast to the cantilever-type switches, the bridge-types are symmetric structures and therefore (as discussed in Section 2.2), when actuated, they are able to control one of the fundamental CPW modes (either even or odd), leaving the other mode ideally unaffected. Some minor effects such as a small even-mode parasitic

) of polysilicon are placed

**5.1. Cantilever-type switches for switchable asymmetric shunt impedances**

are defined on the bottom edge, and small dimples (12 × 10 μm<sup>2</sup>

were designed taking into account the mechanical analysis described in Section 4.

ied with this software.

128 MEMS Sensors - Design and Application

cussed in detail in Section 6.

switches.

behavior.

**5.2. Bridge-type switches**

**Table 1.** Dimensions and mechanical parameters of the switches.

capacitance (in case of the ohmic-contact parallel switch discussed in Section 5.2.3) occur but with a very limited impact on the circuit behavior.

#### *5.2.1. Capacitive-contact parallel switch*

**Figure 11** shows two fabricated capacitive-contact parallel switches. The change between ON and OFF states is performed by moving the suspended membrane, which can be actuated through bias pads connected to two symmetrical polysilicon electrodes placed under the membrane. A floating metal (FLOMET) strip is placed on top of the dielectric under the membrane. The overlapping area between FLOMET and a multi-metal layer under the bridge (CPW center conductor) defines a MIM capacitor, as described in Section 3. When the actuation voltage is equal or higher than the pull-in voltage *Vpull\_in*, the bridge collapses on the FLOMET, producing a reproducible, constant-value down-state capacitance. The resistance of the ohmic contact between the membrane and the FLOMET strip fixes the amount of switch

and an air gap *gi* = 1.6 μm. Each actuation electrode has an area of 90 × 85 μm<sup>2</sup>

fringing fields) calculated, as with the previous switch, using 2.5-D planar-simulation software. As with the cantilever switch shown in **Figure 10(b)**, the deformation of the bridge due to stress gradients was simulated using ANSYS® 3D FEA. As shown in **Figure 11(c)**, the maximum initial deflection is 0.11 μm. The simulated stiffness constant is *keff* = 32.5 N/m, and the calculated pull-in voltage is *Vpull\_in* = 15.6 V. **Figure 12** shows the measured hysteresis of the switch. The measured pull-in voltage when the isolation is higher than 12 dB at 10 GHz is *Vpull\_in* = 14 V.

A photograph of an ohmic-contact series switch is shown in **Figure 13(a)**. It was fabricated on a quartz substrate with a thickness *h* = 500 μm and an air gap *gi* = 2.7 μm The CPW line does not have continuity under the membrane. When the membrane is in its up state, the switch is OFF, while when the membrane is in a down state, the switch is ON, since the metallic membrane puts into contact the two sides of the CPW line. Two electrodes are placed under the membrane at both sides to generate the actuation force. The area of each actuation electrode is

For this switch, the switching and release times were key parameters in radiometric applications, as discussed in Section 7. The measured switching and release times are 100 μs and 15 μs*,* respectively. To more accurately assess the switch behavior after the membrane release (evolving from ON state to OFF state), the energy model discussed in Section 4 was applied

tion) at a given RF frequency (*f* = 3 GHz) was measured after removing the applied actuation voltage. Then, from the energy equation (Eq. (2)), which can be solved numerically, the evolu-

lar switch design (**Figure 18(a)**), the switch transmission coefficient magnitude as a function

**Figure 12.** Measurement of hysteresis of the switch with a folded suspension (**Figure 11(b)**) showing pull-in and

as follows. The evolution in time of the switch transmission coefficient magnitude |*S*21(*t*)

. As with the previous switches, the bias pads are isolated from the membrane

)was calculated. Next, using the equivalent circuit for this particu-

, which gives a capacitance of 1.5 pF (without taking into account the

RF-MEMS Switches Designed for High-Performance Uniplanar Microwave and mm-Wave Circuits

tor area is 90 × 50 μm<sup>2</sup>

*5.2.2. Ohmic-contact series switch*

using thin high-resistivity silicon bias lines.

120 × 190 μm<sup>2</sup>

pull-out traces.

tion of the capacitance *C*(*yr*

. The MIM capaci-

131

http://dx.doi.org/10.5772/intechopen.76445


**Figure 10.** Cantilever-type ohmic-contact switch. (a) Straight-shaped suspension. (b) Semi-circular-shaped suspension. (c) Simulation of initial deformation due to residual stress on the semi-circular suspension device.

**Figure 11.** Capacitive-contact parallel switch. (a) Fabricated switch using a clamped-clamped membrane. (b) Fabricated switch using a folded-beam suspension. (c) for a device with a folded-beam suspension: Simulation of initial deformation due to residual stress.

RF insertion loss. The MIM capacitor combined with the membrane inductance defines an RLC circuit in the down state. The RF equivalent circuit details are given in Section 6.

The capacitive switch shown in **Figure 11(a)** uses a clamped-clamped membrane suspension. The device was fabricated on a quartz substrate with a thickness *h* = 500 μm and an air gap *gi* = 2.7 μm. The area of each actuation electrode is 120 × 190 μm<sup>2</sup> . The MIM capacitor area is 90 × 100 μm<sup>2</sup> , which gives a capacitance of 3.8 pF. The capacitive switch of **Figure 11(b)** uses a folded-beam suspension. It was fabricated on a quartz substrate with a thickness *h* = 300 μm and an air gap *gi* = 1.6 μm. Each actuation electrode has an area of 90 × 85 μm<sup>2</sup> . The MIM capacitor area is 90 × 50 μm<sup>2</sup> , which gives a capacitance of 1.5 pF (without taking into account the fringing fields) calculated, as with the previous switch, using 2.5-D planar-simulation software. As with the cantilever switch shown in **Figure 10(b)**, the deformation of the bridge due to stress gradients was simulated using ANSYS® 3D FEA. As shown in **Figure 11(c)**, the maximum initial deflection is 0.11 μm. The simulated stiffness constant is *keff* = 32.5 N/m, and the calculated pull-in voltage is *Vpull\_in* = 15.6 V. **Figure 12** shows the measured hysteresis of the switch. The measured pull-in voltage when the isolation is higher than 12 dB at 10 GHz is *Vpull\_in* = 14 V.

#### *5.2.2. Ohmic-contact series switch*

RF insertion loss. The MIM capacitor combined with the membrane inductance defines an

**Figure 11.** Capacitive-contact parallel switch. (a) Fabricated switch using a clamped-clamped membrane. (b) Fabricated switch using a folded-beam suspension. (c) for a device with a folded-beam suspension: Simulation of initial deformation

**Figure 10.** Cantilever-type ohmic-contact switch. (a) Straight-shaped suspension. (b) Semi-circular-shaped suspension.

(c) Simulation of initial deformation due to residual stress on the semi-circular suspension device.

The capacitive switch shown in **Figure 11(a)** uses a clamped-clamped membrane suspension. The device was fabricated on a quartz substrate with a thickness *h* = 500 μm and an air gap

folded-beam suspension. It was fabricated on a quartz substrate with a thickness *h* = 300 μm

, which gives a capacitance of 3.8 pF. The capacitive switch of **Figure 11(b)** uses a

. The MIM capacitor area is

RLC circuit in the down state. The RF equivalent circuit details are given in Section 6.

*gi* = 2.7 μm. The area of each actuation electrode is 120 × 190 μm<sup>2</sup>

90 × 100 μm<sup>2</sup>

due to residual stress.

130 MEMS Sensors - Design and Application

A photograph of an ohmic-contact series switch is shown in **Figure 13(a)**. It was fabricated on a quartz substrate with a thickness *h* = 500 μm and an air gap *gi* = 2.7 μm The CPW line does not have continuity under the membrane. When the membrane is in its up state, the switch is OFF, while when the membrane is in a down state, the switch is ON, since the metallic membrane puts into contact the two sides of the CPW line. Two electrodes are placed under the membrane at both sides to generate the actuation force. The area of each actuation electrode is 120 × 190 μm<sup>2</sup> . As with the previous switches, the bias pads are isolated from the membrane using thin high-resistivity silicon bias lines.

For this switch, the switching and release times were key parameters in radiometric applications, as discussed in Section 7. The measured switching and release times are 100 μs and 15 μs*,* respectively. To more accurately assess the switch behavior after the membrane release (evolving from ON state to OFF state), the energy model discussed in Section 4 was applied as follows. The evolution in time of the switch transmission coefficient magnitude |*S*21(*t*) | (isolation) at a given RF frequency (*f* = 3 GHz) was measured after removing the applied actuation voltage. Then, from the energy equation (Eq. (2)), which can be solved numerically, the evolution of the capacitance *C*(*yr* )was calculated. Next, using the equivalent circuit for this particular switch design (**Figure 18(a)**), the switch transmission coefficient magnitude as a function

**Figure 12.** Measurement of hysteresis of the switch with a folded suspension (**Figure 11(b)**) showing pull-in and pull-out traces.

*5.2.3. Ohmic-contact parallel switch (switchable air bridge)*

ical resonant frequency *f*

tion is smaller than 0.16 μm.

curve shown in **Figure 9**.

(ANSYS®).

**Figure 14(a)** shows a switchable air bridge (SAB) that can be used in CPW reconfigurable multimodal circuits for a selective use of the CPW odd mode. The device was fabricated on a quartz substrate with a thickness *h* = 300 μm and an air gap *gi* = 1.6 μm. The structure features a reinforced gold membrane with two ohmic contacts at the edges. The bridge membrane is anchored to isolated islands by folded-beam suspensions, made of a 1.8-μm-thick, 10-μm-wide single gold layer. When an actuation voltage equal or higher than the pull-in voltage *Vpull\_in* is applied, the bridge collapses over an underpass metal layer connected to the ground planes of the CPW. The SAB has an air gap of 1.6 μm, and the distance between the membrane and the bottom ohmic contacts over the underpass metal layer is 1.3 μm. The measured hysteresis of the ohmic switch is shown in **Figure 14(b)**. The pull-in voltage was measured when the isolation is higher than 17 dB at 10 GHz. The measured pull-in voltage is *Vpull\_in* = 14 V, and the simulated stiffness constant is *keff* = 15.4 N/m. The first-mode mechan-

RF-MEMS Switches Designed for High-Performance Uniplanar Microwave and mm-Wave Circuits

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133

The air gap of ohmic contacts placed on the top and bottom electrodes could be affected by stress gradients during fabrication. As with the previous switches, the deformation of the bridge was simulated using ANSYS® 3D FEA. The structure can handle positive- and negative-stress gradients without compromising on the function of the switch. **Figure 15(a)** shows the deformation of the bilayer membrane. For this case, the simulated maximum initial deflec-

The measured topography of the device just after fabrication (**Figure 15(b)**) shows a very good agreement with the 3D FEA results, thus validating this analysis. This model can then be used to extract the nonlinear stiffness values that in turn can modify the potential energy

**Figure 15.** (a) Initial deformation due to residual stress. (b) Measured topography of the device just after fabrication.

*0m* = 17.1 kHz was obtained from the electromechanical analysis

**Figure 13.** Ohmic-contact series switch. (a) Fabricated switch. (b) Measured and simulated time evolution of the microwave isolation after release (switch going from ON state to OFF state).

**Figure 14.** Ohmic-contact parallel switch (switchable air bridge) using a folded-beam suspension. (a) Fabricated switch. (b) Measurement of hysteresis showing pull-in and pull-out traces.

of frequency |*<sup>S</sup>*21(*f*)| was computed which, assuming no parasitic effects (*Lp* = 0 and *Cp* = 0) and no inner line sections, is expressed as

no inner line sections, is expressed as 
$$\left| \mathcal{S}\_{\text{z}}(\boldsymbol{\hat{\beta}}) \right| = \frac{4\pi Z\_{\boldsymbol{\omega}} \mathcal{C}(\boldsymbol{y}\_{\boldsymbol{\cdot}})}{\sqrt{1 + \left(4\pi Z\_{\boldsymbol{\omega}} \mathcal{C}(\boldsymbol{y}\_{\boldsymbol{\cdot}})\right)^{2}}} \tag{4}$$

where *Z0* is the reference impedance and *f* is the RF frequency. **Figure 13(b)** compares the simulated evolution of |*S*21(*t* ) | calculated using Eq. (4) (particularized at *f* = 3 GHz) to the measured |*<sup>S</sup>*21(*t*) | for the series ohmic-contact switch shown in **Figure 13(a)**, showing a good agreement.

#### *5.2.3. Ohmic-contact parallel switch (switchable air bridge)*

**Figure 14(a)** shows a switchable air bridge (SAB) that can be used in CPW reconfigurable multimodal circuits for a selective use of the CPW odd mode. The device was fabricated on a quartz substrate with a thickness *h* = 300 μm and an air gap *gi* = 1.6 μm. The structure features a reinforced gold membrane with two ohmic contacts at the edges. The bridge membrane is anchored to isolated islands by folded-beam suspensions, made of a 1.8-μm-thick, 10-μm-wide single gold layer. When an actuation voltage equal or higher than the pull-in voltage *Vpull\_in* is applied, the bridge collapses over an underpass metal layer connected to the ground planes of the CPW. The SAB has an air gap of 1.6 μm, and the distance between the membrane and the bottom ohmic contacts over the underpass metal layer is 1.3 μm. The measured hysteresis of the ohmic switch is shown in **Figure 14(b)**. The pull-in voltage was measured when the isolation is higher than 17 dB at 10 GHz. The measured pull-in voltage is *Vpull\_in* = 14 V, and the simulated stiffness constant is *keff* = 15.4 N/m. The first-mode mechanical resonant frequency *f 0m* = 17.1 kHz was obtained from the electromechanical analysis (ANSYS®).

The air gap of ohmic contacts placed on the top and bottom electrodes could be affected by stress gradients during fabrication. As with the previous switches, the deformation of the bridge was simulated using ANSYS® 3D FEA. The structure can handle positive- and negative-stress gradients without compromising on the function of the switch. **Figure 15(a)** shows the deformation of the bilayer membrane. For this case, the simulated maximum initial deflection is smaller than 0.16 μm.

The measured topography of the device just after fabrication (**Figure 15(b)**) shows a very good agreement with the 3D FEA results, thus validating this analysis. This model can then be used to extract the nonlinear stiffness values that in turn can modify the potential energy curve shown in **Figure 9**.

of frequency |*<sup>S</sup>*21(*f*)| was computed which, assuming no parasitic effects (*Lp* = 0 and *Cp* = 0) and

**Figure 14.** Ohmic-contact parallel switch (switchable air bridge) using a folded-beam suspension. (a) Fabricated switch.

**Figure 13.** Ohmic-contact series switch. (a) Fabricated switch. (b) Measured and simulated time evolution of the

\_\_\_\_\_\_\_\_\_\_\_\_\_\_ <sup>1</sup> <sup>+</sup> (4*πZ*<sup>0</sup> *fC*(*yr*))

is the reference impedance and *f* is the RF frequency. **Figure 13(b)** compares the



<sup>2</sup> (4)

√

no inner line sections, is expressed as

simulated evolution of |*S*21(*t* )

where *Z0*

measured |*S*21(*t*)

agreement.

<sup>|</sup>*S*21(*f*)| <sup>=</sup> <sup>4</sup>*πZ*<sup>0</sup> *fC*(*<sup>y</sup>* \_\_\_\_\_\_\_\_\_\_\_\_ *<sup>r</sup>*)

(b) Measurement of hysteresis showing pull-in and pull-out traces.

microwave isolation after release (switch going from ON state to OFF state).

132 MEMS Sensors - Design and Application

**Figure 15.** (a) Initial deformation due to residual stress. (b) Measured topography of the device just after fabrication.

**Table 1** shows the dimensions and the main mechanical parameters of the switches presented in this section. The membrane/cantilever height is 1.6 μm in all cases except for the capacitive-contact parallel switch with the clamped-clamped membrane and the ohmiccontact series switch, both featuring a membrane height of 2.7 μm. While the pull-in voltages are measured, the spring constant and the mechanical resonant frequency are computed using the 3D FEA method presented in Section 4. For the ohmic-contact series switch, the mechanical resonant frequency was also measured using the method reported in [56].

A proper combination of the switch ON capacitance *CON* and inductance *LC* is selected to yield

RF-MEMS Switches Designed for High-Performance Uniplanar Microwave and mm-Wave Circuits

nology. Short even-mode CPW transmission line sections are considered at each side of the membrane, with characteristic impedances *Z*0e and *Z*0e2 which depend on the CPW line and

due to changes in the width of the CPW central strip and lateral ground planes and can be obtained by adjusting their values to fit a 2.5 D electromagnetic simulation of the CPW structure. The CPW propagation constant and characteristic impedance are also obtained from the electromagnetic simulation of a straight CPW line section of the same dimensions excited

The configuration of an ohmic-contact parallel switch (switchable air bridge or SAB) is shown in **Figure 14**. This switch is used to efficiently control the CPW odd-mode propagation. When the switch is in its "up" (OFF) state, the capacitance between the elevated membrane and the two RF ohmic contacts at either lateral metal plane is negligible (*C*=*COFF* < 1 fF) because the overlap area for contacts is extremely small. When a bias voltage greater than the pull-in voltage is applied between the membrane and the lower electrodes, the membrane moves down and the two edges get in contact with the lateral metal planes, implementing a "bridge" which performs a double ohmic contact (switch "down"—ON—state). The membrane has a window in the center part to reduce the capacitance between the membrane and the central CPW strip, in such a way to minimize the impact on the propagation of the CPW even mode.

**Figure 17** shows an equivalent circuit of the switch for the OFF state (**Figure 17(a)**) and ON

**Figure 16** can be observed, but will certainly have different values because they are now modeling the CPW odd mode. The CPW line sections now refer to the CPW odd mode with

and capacitance *Cp*

and membrane dimensions for a given fabrication tech-

and capacitance *Cp*

as in the circuit of

are modeling the small parasitic effects

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135

0

the desired operating frequency *f*

slot dimensions. The inductance *Lp*

*6.1.2. Parallel and series ohmic-contact switches*

This capacitance, obtained from measurement, is 47 fF.

state (**Figure 17(b)**). The same parasitic inductance *Lp*

**Figure 17.** Ohmic-contact parallel-switch equivalent circuit. (a) OFF. (b) ON.

with a CPW even mode.
