**6. RF-MEMS switch electrical modeling and characterization**

#### **6.1. Parallel and series switch models**

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

The configuration of a capacitive-contact parallel switch is shown in **Figure 11**. It is able to control the propagation of the CPW even mode and simultaneously suppress the CPW odd mode because the lateral metal planes are permanently connected through the switch membrane. When the switch is in its "up" (OFF) state, the capacitance between the elevated membrane and the RF line underneath (*COFF*) is very 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 gets in contact with the floating metal deposited on top of the RF line, implementing the switch "down" (ON) state. In this case, the switch capacitance (*CON*) is that of the parallel-plate capacitor defined between the floating metal pad and the underneath RF line section, across a thin oxide layer. The thinner the oxide layer and the larger the overlapping area between the floating metal and the RF line, the larger is the ON capacitance *CON*. Thus, the device acts as a switched capacitance. For a highly efficient switch, it is desired to have a high capacitance ratio *CON*/*COFF*.

**Figure 16** shows an equivalent circuit of the switch, which applies to both states. Capacitance *C* accounts for the switched capacitance and adopts two possible values, *CON* and *COFF*. The resistance *RC* and inductance *LC* are membrane resistance and inductance, respectively, at either side of the capacitive contact. The RF frequency at which the switch presents a maximum insertion loss in its ON state is given by the approximate expression *f* <sup>0</sup> <sup>=</sup> (1/*π*)· √ \_\_\_\_\_\_\_\_ \_ <sup>2</sup> · *LC* · *CON*.

**Figure 16.** Capacitive-contact parallel-switch equivalent circuit.

A proper combination of the switch ON capacitance *CON* and inductance *LC* is selected to yield the desired operating frequency *f* 0 and membrane dimensions for a given fabrication technology. 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 slot dimensions. The inductance *Lp* and capacitance *Cp* are modeling the small parasitic effects 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 with a CPW even mode.

#### *6.1.2. Parallel and series ohmic-contact switches*

**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

The configuration of a capacitive-contact parallel switch is shown in **Figure 11**. It is able to control the propagation of the CPW even mode and simultaneously suppress the CPW odd mode because the lateral metal planes are permanently connected through the switch membrane. When the switch is in its "up" (OFF) state, the capacitance between the elevated membrane and the RF line underneath (*COFF*) is very 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 gets in contact with the floating metal deposited on top of the RF line, implementing the switch "down" (ON) state. In this case, the switch capacitance (*CON*) is that of the parallel-plate capacitor defined between the floating metal pad and the underneath RF line section, across a thin oxide layer. The thinner the oxide layer and the larger the overlapping area between the floating metal and the RF line, the larger is the ON capacitance *CON*. Thus, the device acts as a switched capacitance. For a highly efficient switch, it is desired to have a

**Figure 16** shows an equivalent circuit of the switch, which applies to both states. Capacitance *C* accounts for the switched capacitance and adopts two possible values, *CON* and *COFF*. The resistance *RC* and inductance *LC* are membrane resistance and inductance, respectively, at either side of the capacitive contact. The RF frequency at which the switch presents a maxi-

> <sup>0</sup> <sup>=</sup> (1/*π*)· √

\_\_\_\_\_\_\_\_ \_ <sup>2</sup> · *LC* · *CON*.

mum insertion loss in its ON state is given by the approximate expression *f*

**6. RF-MEMS switch electrical modeling and characterization**

in [56].

**6.1. Parallel and series switch models**

134 MEMS Sensors - Design and Application

*6.1.1. Capacitive-contact parallel switch*

high capacitance ratio *CON*/*COFF*.

**Figure 16.** Capacitive-contact parallel-switch equivalent circuit.

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. This capacitance, obtained from measurement, is 47 fF.

**Figure 17** shows an equivalent circuit of the switch for the OFF state (**Figure 17(a)**) and ON state (**Figure 17(b)**). The same parasitic inductance *Lp* and capacitance *Cp* as in the circuit of **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

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

the switch is in its ON state. This structure is favorably used in reconfigurable multimodal

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

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The CPW even mode can be controlled without suppressing the odd mode by using the bridge-type ohmic-contact series switch configuration shown in **Figure 13**. In this case, the equivalent circuit for the even mode is shown in **Figure 18**. In the OFF state, the switch behaves as a small series capacitance (*C* = *COFF* ≈ 6 fF), and it can be described as a series *R-L*

**Figures 19** and **20** compare the measured to simulated results of the switches presented in Section 5 and modeled in Section 6.1. The switch insertion loss (ON state) and isolation (OFF

**Figure 20.** (a) Measured isolation (OFF) and insertion loss (ON) of the fabricated ohmic-contact parallel switch (SAB) shown in **Figure 14(a)** compared to simulations using the circuit model shown in **Figure 17**. (b) Measured isolation (OFF)

**Parameter Capacitive: direct clamp/folded Ohmic: parallel Ohmic: cantilever Ohmic: series**

(nH) 0 0 0 0 0.02 0.02 0 0

 (fF) 8.5 8.5 3 3 0 0 6 6 *LC(*pH) 28 / 7 28 / 7 180 180 100 100 0 230 *C* (fF) 1 / 30.5 3800 / 1530 0.9 − 5.1 − 3.35 − *RC* (Ω) 0.27 / 0.1 0.27 / 0.1 0.3 3.2 0 1 0 2.4

(Ω)\* 76.1 / 78.6 76.1 / 78.6 100 100 45.3 45.3 97 97

(Ω)\* 118.7 / 148.5 118.7 / 148.5 195 195 63.5 63.5 152 152

**Table 2.** Equivalent circuit elements of **Figures 16**–**18** (switches **Figures 10**, **11**, **13**, and **14**).

**OFF ON OFF ON OFF ON OFF ON**

and insertion loss (ON) of the fabricated bridge-type ohmic-contact series-switch shown in **Figure 13(a)**.

filters, as explained in Section 7.2.

**6.2. Experimental characterization**

state) are plotted as a function of frequency.

circuit in the ON state.

*Lp*

*Cp*

*Z*0*x*

*Z*0*x*<sup>2</sup>

x = e (even) or o (odd) according to **Figures 16**–**18**.

\*

**Figure 18.** Ohmic-contact series-switch equivalent circuit. (a) OFF. (b) ON.

**Figure 19.** Measured isolation (OFF) and insertion loss (ON) of the fabricated switches compared to simulations of circuit models. (a) Capacitive-contact parallel switch shown in **Figure 11(b)** (model in **Figure 16**). (b) Cantilever-type ohmic-contact parallel switch shown in **Figure 10(a)** (model in **Figure 17**).

characteristic impedances *Z*0s and *Z*0s2 which depend on the CPW line and slot dimensions. For both states, we consider the same membrane resistance *RC* and inductance *LC*. In OFF state, the capacitance *COFF* between the elevated membrane and the two RF ohmic contacts is taken into account, although its effect is almost negligible.

To control the CPW even-mode propagation using ohmic-contact switches, the cantilevertype switch configuration shown in **Figure 10** can be used. It is observed that the odd mode is suppressed using air bridges. Therefore, the equivalent circuit for this kind of switches is the same as the one shown in **Figure 17**, but changing the CPW line characteristic impedances *Z*0s and *Z*0s2 with *Z*0e and *Z*0e2, respectively. If the two air bridges were removed, the CPW line is able to propagate the CPW odd mode simultaneously to the even mode. In this case, the cantilever-type switch configuration can be used to generate the CPW odd mode whenever the switch is in its ON state. This structure is favorably used in reconfigurable multimodal filters, as explained in Section 7.2.

The CPW even mode can be controlled without suppressing the odd mode by using the bridge-type ohmic-contact series switch configuration shown in **Figure 13**. In this case, the equivalent circuit for the even mode is shown in **Figure 18**. In the OFF state, the switch behaves as a small series capacitance (*C* = *COFF* ≈ 6 fF), and it can be described as a series *R-L* circuit in the ON state.

#### **6.2. Experimental characterization**

characteristic impedances *Z*0s and *Z*0s2 which depend on the CPW line and slot dimensions. For both states, we consider the same membrane resistance *RC* and inductance *LC*. In OFF state, the capacitance *COFF* between the elevated membrane and the two RF ohmic contacts is

**Figure 19.** Measured isolation (OFF) and insertion loss (ON) of the fabricated switches compared to simulations of circuit models. (a) Capacitive-contact parallel switch shown in **Figure 11(b)** (model in **Figure 16**). (b) Cantilever-type

To control the CPW even-mode propagation using ohmic-contact switches, the cantilevertype switch configuration shown in **Figure 10** can be used. It is observed that the odd mode is suppressed using air bridges. Therefore, the equivalent circuit for this kind of switches is the same as the one shown in **Figure 17**, but changing the CPW line characteristic impedances *Z*0s and *Z*0s2 with *Z*0e and *Z*0e2, respectively. If the two air bridges were removed, the CPW line is able to propagate the CPW odd mode simultaneously to the even mode. In this case, the cantilever-type switch configuration can be used to generate the CPW odd mode whenever

taken into account, although its effect is almost negligible.

ohmic-contact parallel switch shown in **Figure 10(a)** (model in **Figure 17**).

**Figure 18.** Ohmic-contact series-switch equivalent circuit. (a) OFF. (b) ON.

136 MEMS Sensors - Design and Application

**Figures 19** and **20** compare the measured to simulated results of the switches presented in Section 5 and modeled in Section 6.1. The switch insertion loss (ON state) and isolation (OFF state) are plotted as a function of frequency.

**Figure 20.** (a) Measured isolation (OFF) and insertion loss (ON) of the fabricated ohmic-contact parallel switch (SAB) shown in **Figure 14(a)** compared to simulations using the circuit model shown in **Figure 17**. (b) Measured isolation (OFF) and insertion loss (ON) of the fabricated bridge-type ohmic-contact series-switch shown in **Figure 13(a)**.


**Table 2.** Equivalent circuit elements of **Figures 16**–**18** (switches **Figures 10**, **11**, **13**, and **14**).

In **Table 2**, the values of the equivalent circuit elements obtained to fit measurement are listed. The capacitive switch features a high capacitance ratio (*CON*/*COFF* = 50.2). The ohmic switches feature low insertion loss (<1 dB) and high isolation (>20 dB) for f < 10 GHz (parallel switch) and for f < 25 GHz (series switch).

(described in Section 5.2.2) and a power divider. **Figure 21(b)** shows the measured performance of the circuit, featuring a 180° ± 5° phase shift between both states in a bandwidth of

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

**Figure 22(a)** shows the photograph of a second compact, uniplanar 180° phase switch fabricated on a quartz substrate [10]. In this case, it is based on an air-bridged CPW cross [57]. The two CPW arms of the cross are loaded with capacitive-contact MEMS switches (described in Section 5.2.1). The two phase-switch states (0°/180°) are obtained by actuating the MEMS switches in opposite states (ON/OFF and OFF/ON), resulting in a multimodal interaction between the two CPW modes (even and odd) at the air-bridged cross. The CPW-to-slotline transition [39] at the input port and the CPW taper at the output port are included in order to enable the measurement of the circuit with a probe station. **Figure 22(b)** shows the measured results of phase shift between both states and insertion loss, featuring 180° +1.8°/−1° and ± 0.1 dB insertion-loss unbalance, respectively, in a very wide bandwidth (5–25 GHz). The

**Figure 23(a)** shows a second-order bandwidth-reconfigurable bandpass filter, which was fab-

slotline short-circuit (*K*12). The filter features multimodal immittance inverters (MIIs) based on CPW-to-slotline transitions [37, 58] which are embedded in the input and output slotline resonators. As shown in **Figure 23(b)**, two cantilever-type ohmic-contact MEMS switches (described in Section 5.1) are used to enable reconfigurable MIIs. When actuated, the switches modify the input and output coupling of the filter (*K*01 and *K*23), resulting in a change in the filter's fractional bandwidth (FBW). To keep the central frequency constant, another cantilever MEMS switch (also shown in **Figure 23(b)**) is integrated in *K*12 and actuated simultaneously. **Figure 23(c)** shows the filter measured results. It features two FBW states of 0.082 (when the inner switches are actuated) and 0.043 (when the outer switches and the impedance inverter

**Figure 24(a)** shows a second-order bandpass filter fabricated on a 5-KΩ-cm high-resistivity silicon substrate (ε<sup>r</sup> = 11.9, *h* = 200 μm), which uses switchable air bridges or SABs [6] (shown in **Figure 24(b)**) similar to the SAB of **Figure 14(a)**. The SABs are described in Section 5.2.3. Like

**Figure 22.** (a) Manufactured 180° phase switch. (b) Measured insertion loss for the two states and phase shift between

*/2* slotline resonators are coupled by a

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35% (14–20 GHz), with an insertion loss smaller than 2 dB in both paths.

measured insertion loss is better than 2 dB in 10–20-GHz frequency band.

switch are actuated), while maintaining a constant center frequency (18.9 GHz).

ricated on a quartz substrate (*h* = 500 μm) [11]. The *λ<sup>o</sup>*

**7.2. Uniplanar bandpass filters**

the two states.
