CN105489978B - The method of adjustment of distributed MEMS phase shifter operating voltage based on phase-shift phase mechanical-electric coupling - Google Patents

Abstract

The invention discloses a method for adjusting the operating voltage of a distributed MEMS phase shifter based on the electromechanical coupling of the phase shift, including determining the structural parameters, material properties and electromagnetic working parameters of the distributed MEMS phase shifter; determining the standard value of the operating voltage V ₀ and the standard value of phase shift Δφ ₀ ; apply a working voltage of 2V ₀ to measure the phase shift Δφ _i in M MEMS bridges; compare the measured value of phase shift Δφ _i with the standard value Δφ ₀ ; when the measured value of phase shift Δφ _i > standard value Δφ ₀ , the MEMS bridge has an upward height error, calculate the equivalent circuit parameters and operating voltage adjustment; when the phase shift measurement value Δφ _i ≤ standard value Δφ ₀ , the MEMS bridge has a downward height error or no Error, calculate the equivalent circuit parameters and height error value, calculate the adjustment of the operating voltage; judge whether the adjustment of the operating voltage has been calculated for all; reapply to the corresponding MEMS bridge, and measure the overall phase shift of the distributed MEMS phase shifter Quantity; judge whether the electrical performance of the distributed MEMS phase shifter after adjusting the working voltage meets the index requirements. This method provides theoretical guidance for the reliability of practical work.

Description

Adjustment of Working Voltage of Distributed MEMS Phase Shifter Based on Electromechanical Coupling of Phase Shift method

technical field

The invention belongs to the technical field of microwave devices, in particular to a method for adjusting the working voltage of a distributed MEMS phase shifter based on electromechanical coupling of phase shift. The invention relates to a method for adjusting the operating voltage of a distributed MEMS phase shifter, which can be used to guide the adjustment amount of the operating voltage of the distributed MEMS phase shifter during the working process, so as to ensure that the phase shift amount meets the performance requirements.

Background technique

With the development of RF MEMS (Micro-electromechanical Systems) technology, MEMS phase shifters have been widely used in various radar and satellite navigation fields due to their advantages of miniaturization, low loss, low cost, and good performance. Among them, the distributed MEMS phase shifter is easier to manufacture, smaller in size and better in performance than other forms of MEMS phase shifters, and is known as "one of the most attractive devices", so it has become a research topic for domestic and foreign scholars. hotspots.

The distributed MEMS phase shifter utilizes the "R-L-C" network to realize the phase shifting function. The "R-L-C" network is composed of several "R-L-C" (phase-shifting) units according to certain rules, and each "R-L-C" unit can only complete limited phase-shifting. The "R-L-C" phase shifting unit appears in the form of a mechanical physical structure. To complete the phase-shifting function of the entire phase shifter, a large number of mechanical structural units are required. As the number of mechanical structural units increases stepwise, various side effects will also occur. Therefore, under the increasingly severe military requirements, it is particularly important to develop a distributed MEMS phase shifter with high performance and high anti-interference performance. Distributed MEMS phase shifter is a multidisciplinary system combining electromagnetics and precision mechanical structures. Its electrical performance depends not only on the design level of electromagnetic disciplines, but also on the design level of mechanical structures. Mechanical structure is not only the carrier and guarantee of electrical performance, but also often restricts the realization of electrical performance. At the same time, the realization of electrical performance also puts forward higher requirements for mechanical structure. The distributed MEMS phase shifter is a structure composed of multiple MEMS bridges repeatedly arranged. Due to the limitation of machining equipment precision and installation precision, and the influence of external loads such as vibration and thermal power consumption during the working process, the height of the MEMS bridge changes. , so that the phase shift amount of the phase shifter is deviated, and the performance is degraded. Therefore, in order to reduce the influence of the MEMS bridge height error on the phase shift and ensure the normal operation of the distributed MEMS phase shifter, the working voltage for controlling the MEMS bridge height must be adjusted.

Therefore, it is necessary to use the electromechanical coupling model between the structural parameters of the MEMS bridge and the phase shift of the distributed MEMS phase shifter, calculate the error of the height of the MEMS bridge according to the measured phase shift, and use the relationship between the control voltage and the height of the MEMS bridge The formula quickly gives the adjustment amount of the working voltage to ensure that the distributed MEMS phase shifter can still work normally under the influence of the external environment.

Contents of the invention

Based on the above-mentioned problems, in order to ensure the performance of the phase shift amount of the distributed MEMS phase shifter in the actual working environment, the present invention utilizes the electromechanical coupling model between the structural parameters of the distributed MEMS phase shifter MEMS bridge height and the phase shift amount to realize The coupling analysis of structural parameters and electrical parameters of the distributed MEMS phase shifter effectively solves the problem that the height of the MEMS bridge cannot be determined during the working process of the distributed MEMS phase shifter. Combined with the control relationship between the operating voltage and the MEMS bridge, the operating voltage can be directly obtained The adjustment amount provides a theoretical guidance for the reliability of the distributed MEMS phase shifter in actual work.

The technical solution that realizes the object of the present invention is, a kind of method for adjusting the operating voltage of the distributed MEMS phase shifter based on phase shift amount electromechanical coupling, the method comprises the following steps:

(1) According to the basic structure of the distributed MEMS phase shifter, determine the structural parameters, material properties and electromagnetic working parameters of the distributed MEMS phase shifter;

(2) According to the design requirements of the distributed MEMS phase shifter, determine the working voltage standard value V of the distributed MEMS phase shifter ₀ and the phase shift amount standard value Δφ ₀ ;

(3) Apply a working voltage of 2V ₀ to the distributed MEMS phase shifter, and measure the phase shift generated by the i-th (1≤i≤M) MEMS bridge among the M MEMS bridges under the working state of the distributed MEMS phase shifter Quantity Δφ _i ;

(4) Compare the measured value of phase shift Δφ _i with the standard value Δφ ₀ , if the measured value is greater than the standard value, continue to step 5, otherwise go to step 8;

(5) When the phase shift measurement value Δφ _i is greater than the standard value Δφ ₀ , it can be obtained that the MEMS bridge has an upward height error, and the equivalent circuit parameters of the i-th MEMS bridge are calculated;

(6) Utilize the electromechanical coupling model of a single MEMS bridge, reversely calculate the height error value of the i-th MEMS bridge upward;

(7) Utilize the control relational expression of operating voltage to the height of MEMS bridge, according to the height error value of MEMS bridge upward, calculate the adjustment amount of operating voltage under two operating states of "up" and "down" of the i-th MEMS bridge respectively, and then Go to step (11);

(8) When the phase shift measurement value Δφ _i is less than or equal to the standard value Δφ ₀ , it can be obtained that the MEMS bridge has a downward height error, and the equivalent circuit parameters of the i-th MEMS bridge are calculated;

(9) Utilize the electromechanical coupling model of a single MEMS bridge, reversely calculate the downward height error value of the ith MEMS bridge;

(10) Utilize the control relationship expression of the working voltage to the height of the MEMS bridge, and calculate the adjustment amount of the working voltage under the "up" working state of the i-th MEMS bridge according to the downward height error value of the MEMS bridge;

(11) judge whether the adjustment amount of working voltage has been calculated to all MEMS bridges, if so, then obtain the adjustment amount of M MEMS bridge operating voltages, otherwise, measure the phase shift amount of next MEMS bridge, and repeat step ( 3) to step (11);

(12) Utilize the calculated operating voltage adjustment amount to reapply to the corresponding MEMS bridge to measure the overall phase shift amount of the distributed MEMS phase shifter;

(13) Determine whether the electrical performance of the distributed MEMS phase shifter after adjusting the voltage meets the index requirements. If it is satisfied, it means that the optimal adjustment amount of the operating voltage of the distributed MEMS phase shifter has been obtained, which can make the distributed MEMS phase shifter Reach the optimal performance in the working environment; otherwise, modify the structural parameters of the distributed MEMS phase shifter, and repeat steps (1) to (13) until the requirements are met.

The structural parameters of the step (1) distributed MEMS phase shifter include the length, width and thickness of the coplanar waveguide transmission line, the MEMS bridge and the dielectric layer, the distance between two adjacent bridges, and the height of the MEMS bridge from the dielectric layer ; The material properties of the distributed MEMS phase shifter include the relative permittivity of the dielectric layer; the electromagnetic operating parameters of the distributed MEMS phase shifter include the electromagnetic operating frequency ω of the distributed MEMS phase shifter.

Described step (5) calculates the equivalent circuit parameter of the i-th MEMS bridge when the phase shift measurement value Δφ _i is greater than the standard value Δφ ₀ :

(5a) compare the phase shift measured value in step (3) with the standard value of step (2), when the phase shift measured value Δφ _i is greater than the standard value Δφ ₀ , the MEMS bridge has an upward height error;

(5b) Calculate the equivalent circuit parameters of the i-th MEMS bridge. When the MEMS bridge is not loaded, the equivalent capacitance value C _t per unit length on the transmission line is:

In the formula, ε _r is the relative permittivity of the dielectric layer, c is the speed of light, Z ₀ is the characteristic impedance of the transmission line;

When the MEMS bridge is not loaded, the formula of the equivalent inductance L _t per unit length on the transmission line is:

In the formula, C _t is the equivalent capacitance value per unit length on the transmission line, and Z ₀ is the characteristic impedance of the transmission line.

Described step (6) utilizes the electromechanical coupling model of single MEMS bridge, back-calculates the upward height error value of i-th MEMS bridge:

(6a) Using the electromechanical coupling model of a single MEMS bridge and the measured value of the phase shift of the i-th MEMS bridge in step (3), the variable capacitance value C _ui (Δh) in the "up" working state can be calculated inversely. The coupling model is as follows:

In the formula, s is the distance between adjacent MEMS bridges, ω is the operating frequency, C _t is the equivalent capacitance value per unit length on the transmission line, L _t is the equivalent inductance value per unit length on the transmission line, and C _d is the "down" working The variable capacitance value in the state, C _ui (Δh) is the variable capacitance value in the "up" working state; Δφ _i is the measured value of the i-th MEMS bridge phase shift;

(6b) According to the variable capacitance value C _ui (Δh) in the "up" working state calculated in step (6a), using the relationship between the variable capacitance value and the MEMS bridge height error in the "up" working state, it can be inversely obtained The upward height error Δh of the i-th MEMS bridge, the relationship is as follows:

In the formula, w _c is the width of the central conductor, w _b is the width of the bridge, h is the ideal height of the MEMS bridge from the dielectric layer, t _d is the thickness of the dielectric layer, ε ₀ is the relative permittivity of air, ε _r is the dielectric layer Relative permittivity, L is the length of the MEMS bridge, and Δh is the height error of the MEMS bridge upward.

The step (7) utilizes the control relational expression of the working voltage to the height of the MEMS bridge, and according to the upward height error value of the MEMS bridge, calculates the adjustment of the working voltage under the two working states of the i-th MEMS bridge "up" and "down" respectively quantity:

(7a) The control relationship between the working voltage and the height of the MEMS bridge is as follows:

where k is the elastic stiffness of the MEMS bridge, h is the ideal height of the MEMS bridge, _ε0 is the relative permittivity of air, _wc is the center conductor width, and _wb is the bridge width;

(7b) According to the upward height error value of the MEMS bridge in step (6b), because the ideal working voltage under the MEMS bridge "up" working state is zero, so calculate the adjustment of the working voltage under the i-th MEMS bridge "up" working state The amount is as follows:

where k is the elastic stiffness of the MEMS bridge, _Δh is the upward height error of the MEMS bridge, _ε0 is the relative permittivity of air, wc is the width of the central conductor, and _wb is the width of the bridge;

(7c) According to the upward height error value of the MEMS bridge in step (6b), because the ideal working voltage of the MEMS bridge in the "down" working state is V _d ⁰ , the working voltage of the i-th MEMS bridge in the "down" working state is The adjustments are as follows:

where k is the elastic stiffness of the MEMS bridge, h is the ideal height of the MEMS bridge, Δh is the upward height error of the MEMS bridge, _ε0 is the relative permittivity of air, _wc is the center conductor width, and _wb is the bridge width .

Described step (8) when phase shift amount measurement value Δφ _i is less than or equal to standard value Δφ ₀ , calculate the equivalent circuit parameter of the i-th MEMS bridge:

(8a) Compare the measured value of phase shift in step (3) with the standard value of step (2), when the measured value of phase shift Δφ _i is less than the standard value Δφ ₀ , it can be concluded that the MEMS bridge has a downward height error , when the phase shift measurement value Δφ _i is equal to the standard value Δφ ₀ , the MEMS bridge has no error, and the working voltage does not need to be adjusted;

(8b) Calculate the equivalent circuit parameters of the i-th MEMS bridge. When the MEMS bridge is not loaded, the equivalent capacitance value C _t per unit length on the transmission line is:

In the formula, ε _r is the relative permittivity of the dielectric layer, c is the speed of light, Z ₀ is the characteristic impedance of the transmission line;

When the MEMS bridge is not loaded, the formula of the equivalent inductance L _t per unit length on the transmission line is:

In the formula, C _t is the equivalent capacitance value per unit length on the transmission line, and Z ₀ is the characteristic impedance of the transmission line.

Described step (9) utilizes the electromechanical coupling model of single MEMS bridge, reversely calculates the downward height error value of the ith MEMS bridge:

(9a) Using the electromechanical coupling model of a single MEMS bridge, and the measured value of the phase shift of the i-th MEMS bridge in step (3), the variable capacitance value C _ui (Δh) in the "up" working state can be calculated inversely. The coupling model is as follows:

In the formula, s is the distance between adjacent MEMS bridges, ω is the operating frequency, C _t is the equivalent capacitance value per unit length on the transmission line, L _t is the equivalent inductance value per unit length on the transmission line, and C _d is the "down" working The variable capacitance value in the state, C _ui (Δh) is the variable capacitance value in the "up" working state"; Δφ _i is the measured value of the i-th MEMS bridge phase shift;

(9b) According to the variable capacitance value C _ui (Δh) in the "up" working state calculated in step (9a), using the relationship between the variable capacitance value and the MEMS bridge height error in the "up" working state, it can be inversely obtained The downward height error Δh of the i-th MEMS bridge, the relationship is as follows:

In the formula, w _c is the width of the central conductor, w _b is the width of the bridge, h is the ideal height of the MEMS bridge from the dielectric layer, t _d is the thickness of the dielectric layer, ε ₀ is the relative permittivity of air, ε _r is the dielectric layer Relative permittivity, L is the length of the MEMS bridge, Δh is the height error of the MEMS bridge downward.

The step (10) utilizes the control relational expression of the working voltage to the height of the MEMS bridge, and calculates the adjustment amount of the working voltage under the "up" working state of the i-th MEMS bridge according to the downward height error value of the MEMS bridge. According to step (7a) In the middle working voltage to the control relational expression of MEMS bridge height, utilize step (9b) the height error value of MEMS bridge downward, because the ideal working voltage under the MEMS bridge " up " work state is zero, so calculate the ith MEMS bridge " The adjustment value of the working voltage in the working state is as follows:

where k is the elastic stiffness of the MEMS bridge, _Δh is the downward height error of the MEMS bridge, _ε0 is the relative permittivity of air, wc is the width of the central conductor, and _wb is the width of the bridge.

Compared with the prior art, the present invention has the following characteristics:

1. The present invention utilizes the coupling model of the coupling relationship between the key structural parameter MEMS bridge height and the electric parameter phase shift amount in the distributed MEMS phase shifter, and can directly analyze that the distributed MEMS phase shifter is affected by the internal load environment and The influence of the external load environment leads to the influence of the height offset of the MEMS bridge on the phase shift, which solves the problem that the structural parameters and electrical parameters cannot be obtained directly at present.

2. Using the electromechanical coupling model of the distributed MEMS phase shifter, when the phase shift of the distributed MEMS phase shifter is measured, the error of the height of the MEMS bridge can be quantitatively obtained, and the control relationship between the working voltage and the height of the MEMS bridge can be quickly A reasonable working voltage adjustment is given, which effectively reduces the influence of the environmental load on the electrical performance of the distributed MEMS phase shifter under actual working conditions.

Description of drawings

Fig. 1 is a kind of flow chart of the adjustment method of the distributed MEMS phase shifter operating voltage based on phase shift electromechanical coupling of the present invention;

Figure 2 is a schematic diagram of the partial structure of the distributed MEMS phase shifter in the "up" working state;

Figure 3 is a schematic diagram of the partial structure of the distributed MEMS phase shifter in the "down" working state;

Fig. 4 is a schematic cross-sectional view of a distributed MEMS phase shifter.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Referring to Fig. 1, the present invention is a method for adjusting the working voltage of a distributed MEMS phase shifter based on electromechanical coupling of phase shift, and the specific steps are as follows:

Step 1, determine the structural parameters and electromagnetic working parameters of the distributed MEMS phase shifter.

The structural parameters of the distributed MEMS phase shifter are shown in Figure 2, including the length, width and thickness of the coplanar waveguide transmission line, MEMS bridge and dielectric layer, the distance between two adjacent bridges, and the height of the MEMS bridge from the dielectric layer. Material properties of distributed MEMS phase shifters, including relative permittivity of dielectric layers. The electromagnetic working parameters of the distributed MEMS phase shifter include the electromagnetic working frequency ω of the distributed MEMS phase shifter.

Step 2, determining the standard value V ₀ of the working voltage and the standard value Δφ ₀ of the phase shift amount of the distributed MEMS phase shifter.

Step 3, measure the phase shift Δφ _i generated by the i-th (1≤i≤M) MEMS bridge of the distributed MEMS phase shifter.

Apply a working voltage of 2V ₀ to the distributed MEMS phase shifter, and measure the phase shift Δφ _i of the i-th (1≤i≤M) MEMS bridge among the M MEMS bridges under the working state of the distributed MEMS phase shifter .

Step 4, comparing the phase shift measured value Δφ _i with the standard value Δφ ₀ .

If the measured value is greater than the standard value, continue to step 5, otherwise go to step 8.

Step 5, when the phase shift measured value Δφ _i is greater than the standard value Δφ ₀ , calculate the equivalent circuit parameters of the i-th MEMS bridge.

(5a) compare the phase shift measurement value in step 3 with the standard value of step 2, when the phase shift measurement value Δφ _i is greater than the standard value Δφ ₀ , the MEMS bridge has an upward height error;

(5b) Calculate the equivalent circuit parameters of the i-th MEMS bridge. When the MEMS bridge is not loaded, the equivalent capacitance value C _t per unit length on the transmission line is:

In the formula, ε _r is the relative permittivity of the dielectric layer, c is the speed of light, Z ₀ is the characteristic impedance of the transmission line;

When the MEMS bridge is not loaded, the formula of the equivalent inductance L _t per unit length on the transmission line is:

In the formula, C _t is the equivalent capacitance value per unit length on the transmission line, and Z ₀ is the characteristic impedance of the transmission line.

Step 6: Using the electromechanical coupling model of a single MEMS bridge, back-calculate the upward height error value of the i-th MEMS bridge.

(6a) Using the electromechanical coupling model of a single MEMS bridge and the measured value of the phase shift of the i-th MEMS bridge in step 3, the variable capacitance value C _ui (Δh) in the "up" working state can be reversely calculated. The coupling model as follows:

In the formula, s is the distance between adjacent MEMS bridges, ω is the operating frequency, C _t is the equivalent capacitance value per unit length on the transmission line, L _t is the equivalent inductance value per unit length on the transmission line, and C _d is the "down" working The variable capacitance value in the state, C _ui (Δh) is the variable capacitance value in the "up" working state; Δφ _i is the measured value of the i-th MEMS bridge phase shift;

(6b) According to the variable capacitance value C _ui (Δh) in the "up" working state calculated in step (6a), using the relationship between the variable capacitance value and the MEMS bridge height error in the "up" working state, it can be inversely obtained The upward height error Δh of the i-th MEMS bridge, the relationship is as follows:

In the formula, w _c is the width of the central conductor, w _b is the width of the bridge, h is the ideal height of the MEMS bridge from the dielectric layer, t _d is the thickness of the dielectric layer, ε ₀ is the relative permittivity of air, ε _r is the dielectric layer Relative permittivity, L is the length of the MEMS bridge, and Δh is the height error of the MEMS bridge upward.

Step 7, according to the upward height error value of the MEMS bridge, calculate the adjustment amount of the working voltage of the i-th MEMS bridge under the two working states of "up" and "down".

(7a) The control relationship between the working voltage and the height of the MEMS bridge is as follows:

where k is the elastic stiffness of the MEMS bridge, h is the ideal height of the MEMS bridge, _ε0 is the relative permittivity of air, _wc is the center conductor width, and _wb is the bridge width;

(7b) According to the upward height error value of the MEMS bridge in step (6b), because the ideal working voltage under the MEMS bridge "up" working state is zero, so calculate the adjustment of the working voltage under the i-th MEMS bridge "up" working state The amount is as follows

where k is the elastic stiffness of the MEMS bridge, _Δh is the upward height error of the MEMS bridge, _ε0 is the relative permittivity of air, wc is the width of the central conductor, and _wb is the width of the bridge;

(7c) According to the upward height error value of the MEMS bridge in step (6b), because the ideal working voltage of the MEMS bridge in the "down" working state is V _d ⁰ , the working voltage of the i-th MEMS bridge in the "down" working state is The adjustments are as follows:

where k is the elastic stiffness of the MEMS bridge, h is the ideal height of the MEMS bridge, Δh is the upward height error of the MEMS bridge, _ε0 is the relative permittivity of air, _wc is the center conductor width, and _wb is the bridge width .

Step 8, when the phase shift measured value Δφ _i is less than or equal to the standard value Δφ ₀ , calculate the equivalent circuit parameters of the i-th MEMS bridge.

(8a) Compare the measured value of phase shift in step 3 with the standard value in step 2. When the measured value of phase shift Δφ _i is less than the standard value Δφ ₀ , it can be obtained that the MEMS bridge has a downward height error. When the phase shift When the measured value Δφ _i is equal to the standard value Δφ ₀ , the MEMS bridge has no error and the working voltage does not need to be adjusted;

(8b) Calculate the equivalent circuit parameters of the i-th MEMS bridge. When the MEMS bridge is not loaded, the equivalent capacitance value C _t per unit length on the transmission line is:

In the formula, ε _r is the relative permittivity of the dielectric layer, c is the speed of light, Z ₀ is the characteristic impedance of the transmission line;

When the MEMS bridge is not loaded, the formula of the equivalent inductance L _t per unit length on the transmission line is:

In the formula, C _t is the equivalent capacitance value per unit length on the transmission line, and Z ₀ is the characteristic impedance of the transmission line.

Step 9: Using the electromechanical coupling model of a single MEMS bridge, back-calculate the downward height error value of the i-th MEMS bridge.

(9a) Using the electromechanical coupling model of a single MEMS bridge and the measured value of the phase shift of the i-th MEMS bridge in step 3, the variable capacitance value C _ui (Δh) in the "up" working state can be reversely calculated. The coupling model as follows:

In the formula, s is the distance between adjacent MEMS bridges, ω is the operating frequency, C _t is the equivalent capacitance value per unit length on the transmission line, L _t is the equivalent inductance value per unit length on the transmission line, and C _d is the "down" working The variable capacitance value in the state, C _ui (Δh) is the variable capacitance value in the "up" working state"; Δφ _i is the measured value of the i-th MEMS bridge phase shift;

(9b) According to the variable capacitance value C _ui (Δh) in the "up" working state calculated in step (9a), using the relationship between the variable capacitance value and the MEMS bridge height error in the "up" working state, it can be inversely obtained The downward height error Δh of the i-th MEMS bridge, the relationship is as follows:

In the formula, w _c is the width of the central conductor, w _b is the width of the bridge, h is the ideal height of the MEMS bridge from the dielectric layer, t _d is the thickness of the dielectric layer, ε ₀ is the relative permittivity of air, ε _r is the dielectric layer Relative permittivity, L is the length of the MEMS bridge, Δh is the height error of the MEMS bridge downward.

Step 10, according to the downward height error value of the MEMS bridge, calculate the adjustment amount of the working voltage of the i-th MEMS bridge in the "up" working state.

According to the control relationship between the working voltage and the height of the MEMS bridge in step (7a), using the downward height error value of the MEMS bridge in step (9b), because the ideal working voltage under the "up" working state of the MEMS bridge is zero, the first calculated The adjustment amount of the working voltage of the i MEMS bridge "up" working state is as follows:

where k is the elastic stiffness of the MEMS bridge, _Δh is the downward height error of the MEMS bridge, _ε0 is the relative permittivity of air, wc is the width of the central conductor, and _wb is the width of the bridge.

Step 11, judging whether the adjustment amount of the working voltage has been calculated for all MEMS bridges.

If yes, then the adjustments of the M MEMS bridge operating voltages have been obtained, otherwise, measure the phase shift of the next MEMS bridge, and repeat step 3 to step 11;

Step 12, measuring the overall phase shift of the distributed MEMS phase shifter.

Using the calculated operating voltage adjustment, re-apply to the corresponding MEMS bridge to measure the overall phase shift of the distributed MEMS phase shifter.

Step 13, judging whether the electrical performance of the distributed MEMS phase shifter after the voltage adjustment meets the index requirement.

If it is satisfied, it means that the optimal adjustment amount of the operating voltage of the distributed MEMS phase shifter has been obtained, which can make the distributed MEMS phase shifter achieve optimal performance in the working environment; otherwise, modify the structural parameters of the distributed MEMS phase shifter , and repeat steps 1 to 13 until the requirements are met.

Advantages of the present invention can be further illustrated by following simulation experiments:

1. Determine the parameters of the distributed MEMS phase shifter

In this example, a 4-bit distributed MEMS phase shifter with a working frequency of 1GHZ (the standard phase shift amount of each MEMS bridge is 22.5°) is taken as an example. Figure 2 is a schematic diagram of four MEMS bridges. Figure 2 and Figure 3 are partial structural schematic diagrams of MEMS phase shifters in "up" and "down" working states. In Figure 2, A is the dielectric layer, B is the MEMS bridge, and C is the coplanar waveguide transmission line, and D is the distance between the MEMS bridges. Figure 4 shows a schematic cross-sectional view of a distributed MEMS phase shifter. The geometric model parameters of the distributed MEMS phase shifter are shown in Table 1, and the material properties are shown in Table 2.

Table 1 Geometric model parameters of distributed MEMS phase shifter

Table 2 Material properties of distributed MEMS phase shifters

2. Reverse calculation of the error of the height of the MEMS bridge of the distributed MEMS phase shifter

1. Measure the phase shift generated by each MEMS bridge in the 4 MEMS bridges under the 2V ₀ working state of the distributed MEMS phase shifter

According to the measured value of the phase shift of the first MEMS bridge in actual work is 21.92°, since the measured value is less than the standard value of 22.5°, the MEMS bridge has a downward height error.

2. Calculate the parameter value of the equivalent circuit of the distributed MEMS phase shifter

2.1 Calculate the equivalent capacitance C _t per unit length on the transmission line as shown in formula (1):

In the formula, ε _r is the relative permittivity of the dielectric layer, the relative permittivity of silicon nitride is 7, c=3×10 ⁸ m/s is the speed of light Z ₀ is the characteristic impedance of the transmission line is 50;

2.2 Calculate the equivalent inductance value L _t per unit length on the transmission line through the equivalent capacitance value per unit length, such as formula (2):

In the formula, C _t is the equivalent capacitance value per unit length on the transmission line, Z ₀ is the characteristic impedance of the transmission line is 50.

3. According to the measured value of the first MEMS bridge above, calculate the error of the height of the first MEMS bridge based on the electromechanical coupling model

3.1 The relationship between the phase shift and the height of the MEMS bridge electromechanical coupling model is as follows:

Bring the measured value distribution of the phase shift of the four MEMS bridges in Table 3 into Formula 3 to obtain the capacitance value in the "up" working state during the working process;

3.2 Using the relationship between the variable capacitance value and the height error of the MEMS bridge in the "up" working state, that is, formula 4 can be reversed to obtain the upward height error Δh of the MEMS bridge.

The height error value of the first MEMS bridge is 0.54um.

3. Calculate the adjustment amount of the first MEMS bridge working voltage

Bring the above-mentioned upward height error value of the first MEMS bridge into Equation 5. Since the MEMS bridge has a downward height error, it is only necessary to adjust the working voltage in the "up" working state. The working voltage adjustment amount is shown in the following formula:

In the formula, the value of the elastic coefficient k of the MEMS bridge is 69.4×10 ¹⁵ N/m, and the calculated working voltage adjustment of the first MEMS bridge is 1.14V.

4. Calculate the working voltage adjustment of the remaining three MEMS bridges

According to the above process, measure the measured values of the phase shifts of the remaining three MEMS bridges in turn, calculate the height error values of the three MEMS bridges, and finally calculate the working voltage adjustments of the three MEMS bridges. Summarize the data of the four MEMS bridges, as shown in Table 3, Table 4, and Table 5:

Table 3 Measured value of phase shift of four MEMS bridges

Table 4 The error values of 4 MEMS bridge heights

Table 5 Adjustment of working voltage of 4 MEMS bridges

Since the measured values of the phase shifts of the MEMS bridges are all smaller than the standard values, it can be known that the MEMS bridges all generate downward errors. Corresponding to the adjustment of the working voltage of the MEMS bridge, an upward electrostatic force should be generated to make the MEMS bridge return to the standard position. To ensure that the MEMS bridge is at the standard value in the "up" working state can ensure that the phase shift of the MEMS bridge is at the standard value. It can be seen from the examples that the adjustment amount of the working voltage can be quickly calculated by using the electromechanical coupling model, which can ensure the normal operation of the distributed MEMS phase shifter and effectively reduce the influence of the environmental load of the distributed MEMS phase shifter on its electrical performance under actual working conditions .

Claims (7)

1. A method for adjusting the operating voltage of a distributed MEMS phase shifter based on phase shift electromechanical coupling, characterized in that it may further comprise the steps: (1) According to the basic structure of the distributed MEMS phase shifter, determine the structural parameters, material properties and electromagnetic working parameters of the distributed MEMS phase shifter; The structural parameters of the distributed MEMS phase shifter include coplanar waveguide transmission lines, the length, width and thickness of the MEMS bridge and the dielectric layer, the distance between two adjacent bridges, and the height of the MEMS bridge from the dielectric layer; the distributed The material properties of the MEMS phase shifter include the relative permittivity of the dielectric layer; the electromagnetic operating parameters of the distributed MEMS phase shifter include the electromagnetic operating frequency ω of the distributed MEMS phase shifter; (2) According to the design requirements of the distributed MEMS phase shifter, determine the working voltage standard value V of the distributed MEMS phase shifter ₀ and the phase shift amount standard value Δφ ₀ ; (3) Apply a working voltage of 2V ₀ to the distributed MEMS phase shifter, and measure the phase shift Δφ _i produced by the i-th MEMS bridge in the M MEMS bridges under the working state of the distributed MEMS phase shifter; where, 1 ≤i≤M; (4) Compare the phase shift measured value Δφ _i with the standard value Δφ ₀ , if the measured value is greater than the standard value, then continue to step (5), otherwise go to step (8); (5) When the phase shift measurement value Δφ _i is greater than the standard value Δφ ₀ , it can be obtained that the MEMS bridge has an upward height error, and the equivalent circuit parameters of the i-th MEMS bridge are calculated; (6) Utilize the electromechanical coupling model of a single MEMS bridge, reversely calculate the height error value of the i-th MEMS bridge upward; (7) Utilize the control relational expression of operating voltage to the height of MEMS bridge, according to the height error value of MEMS bridge upward, calculate the adjustment amount of operating voltage under two operating states of "up" and "down" of the i-th MEMS bridge respectively, and then Go to step (11); (8) When the phase shift measurement value Δφ _i is less than the standard value Δφ ₀ , it can be obtained that the MEMS bridge has a downward height error, and the equivalent circuit parameters of the i-th MEMS bridge are calculated; (9) Utilize the electromechanical coupling model of a single MEMS bridge, reversely calculate the downward height error value of the ith MEMS bridge; (10) Utilize the control relationship expression of the working voltage to the height of the MEMS bridge, and calculate the adjustment amount of the working voltage under the "up" working state of the i-th MEMS bridge according to the downward height error value of the MEMS bridge; (11) judge whether the adjustment amount of working voltage has been calculated to all MEMS bridges, if so, then obtain the adjustment amount of M MEMS bridge operating voltages, otherwise, measure the phase shift amount of next MEMS bridge, and repeat step ( 3) to step (11); (12) Utilize the calculated operating voltage adjustment amount to reapply to the corresponding MEMS bridge to measure the overall phase shift amount of the distributed MEMS phase shifter; (13) Determine whether the electrical performance of the distributed MEMS phase shifter after adjusting the voltage meets the index requirements. If it is satisfied, it means that the optimal adjustment amount of the operating voltage of the distributed MEMS phase shifter has been obtained, which can make the distributed MEMS phase shifter Reach the optimal performance in the working environment; otherwise, modify the structural parameters of the distributed MEMS phase shifter, and repeat steps (1) to (13) until the requirements are met. 2. the adjustment method of the distributed MEMS phase shifter operating voltage based on phase shift amount electromechanical coupling according to claim 1, it is characterized in that, step (5) is carried out as follows: (5a) compare the phase shift measured value in step (3) with the standard value of step (2), when the phase shift measured value Δφ _i is greater than the standard value Δφ ₀ , the MEMS bridge has an upward height error; (5b) Calculate the equivalent circuit parameters of the i-th MEMS bridge. When the MEMS bridge is not loaded, the equivalent capacitance value C _t per unit length on the transmission line is: <mrow><msub><mi>C</mi><mi>t</mi></msub><mo>=</mo><msqrt><mfrac><mrow><msub><mi>&amp;epsiv;</mi><mi>r</mi></msub><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msqrt><mo>/</mo><msub><mi>cZ</mi><mn>0</mn></msub></mrow> In the formula, ε _r is the relative permittivity of the dielectric layer, c is the speed of light, Z ₀ is the characteristic impedance of the transmission line; When the MEMS bridge is not loaded, the formula of the equivalent inductance L _t per unit length on the transmission line is: <mrow><msub><mi>L</mi><mi>t</mi></msub><mo>=</mo><msub><mi>C</mi><mi>t</mi></msub><msubsup><mi>Z</mi><mn>0</mn><mn>2</mn></msubsup></mrow> In the formula, C _t is the equivalent capacitance value per unit length on the transmission line, and Z ₀ is the characteristic impedance of the transmission line. 3. the adjusting method of a kind of distributed MEMS phase shifter operating voltage based on phase shift electromechanical coupling according to claim 1, it is characterized in that, step (6) is carried out as follows: (6a) Using the electromechanical coupling model of a single MEMS bridge and the measured value of the phase shift of the i-th MEMS bridge in step (3), the variable capacitance value C _ui (Δh) in the "up" working state can be calculated inversely. The coupling model is as follows: <mrow><msub><mi>&amp;Delta;&amp;phi;</mi><mi>i</mi></msub><mo>=</mo><mi>&amp;omega;</mi>mi><msqrt><mrow><msub><mi>L</mi><mi>t</mi></msub><msub><mi>C</mi><mi>t</mi></msub></mrow></msqrt><mrow><mo>(</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mfrac><msub><mi>C</mi><mi>d</mi></msub><mrow><mi>s</mi><mo>&amp;times;</mo><msub><mi>C</mi><mi>t</mi></msub></mrow></mfrac></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><msub><mi>C</mi><mrow><mi>u</mi><mi>i</mi></mn>mrow></msub><mrow><mo>(</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi><mo>&amp;times;</mo><msub><mi>C</mi><mi>t</mi></msub></mrow></mfrac></mrow></msqrt><mo>)</mo></mrow></mrow> In the formula, s is the distance between adjacent MEMS bridges, ω is the operating frequency, C _t is the equivalent capacitance value per unit length on the transmission line, L _t is the equivalent inductance value per unit length on the transmission line, and C _d is the "down" working The variable capacitance value in the state, C _ui (Δh) is the variable capacitance value in the "up" working state; Δφ _i is the measured value of the i-th MEMS bridge phase shift; (6b) According to the variable capacitance value C _ui (Δh) in the "up" working state calculated in step (6a), using the relationship between the variable capacitance value and the MEMS bridge height error in the "up" working state, it can be inversely obtained The upward height error Δh of the i-th MEMS bridge, the relationship is as follows: <mrow><msub><mi>C</mi><mrow><mi>u</mi><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mrow><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><mfrac><msub><mi>w</mi><mi>c</mi></msub><mi>n</mi></mfrac><msub><mi>w</mi><mi>b</mi></msub></mrow><mrow><mi>h</mi><mo>+</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>-</mo><mfrac><mrow><mo>(</mo><mi>j</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mi>n</mi></mfrac><mfrac><mrow><msub><mi>w</mi><mi>c</mi></msub><mi>&amp;Delta;</mi><mi>h</mi></mrow><mi>L</mi></mfrac><mo>+</mo><mfrac><msub><mi>t</mi><mi>d</mi></msub><msub><mi>&amp;epsiv;</mi><mi>r</mi></msub></mfrac></mrow></mfrac></mrow> In the formula, w _c is the width of the central conductor, w _b is the width of the bridge, h is the ideal height of the MEMS bridge from the dielectric layer, t _d is the thickness of the dielectric layer, ε ₀ is the relative permittivity of air, ε _r is the dielectric layer Relative permittivity, L is the length of the MEMS bridge, and Δh is the height error of the MEMS bridge upward. 4. the adjusting method of a kind of distributed MEMS phase shifter operating voltage based on phase shift amount electromechanical coupling according to claim 1, it is characterized in that, step (7) is carried out as follows: (7a) The control relationship between the working voltage and the height of the MEMS bridge is as follows: <mrow><mi>V</mi><mo>=</mo><msqrt><mfrac><mrow><mn>8</mn><msup><mi>kh</mi><mn>3</mn></msup></mrow><mrow><mn>27</mn><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><msub><mi>w</mi><mi>c</mi></msub><msub><mi>w</mi><mi>b</mi></msub></mrow></mfrac></msqrt></mrow> where k is the elastic stiffness of the MEMS bridge, h is the ideal height of the MEMS bridge, _ε0 is the relative permittivity of air, _wc is the center conductor width, and _wb is the bridge width; (7b) According to the upward height error value of the MEMS bridge in step (6b), calculate the adjustment amount of the working voltage under the "up" working state of the i-th MEMS bridge as follows: <mrow><msub><mi>&amp;Delta;V</mi><mrow><mi>u</mi><mi>i</mi></mrow></msub><mo>=</mo><msqrt><mfrac><mrow><mn>8</mn><msup><mi>k&amp;Delta;h</mi><mn>3</mn></msup></mrow><mrow><mn>27</mn><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><msub><mi>w</mi><mi>c</mi></msub><msub><mi>w</mi><mi>b</mi></msub></mrow></mfrac></msqrt></mrow> where k is the elastic stiffness of the MEMS bridge, _Δh is the upward height error of the MEMS bridge, _ε0 is the relative permittivity of air, wc is the width of the central conductor, and _wb is the width of the bridge; (7c) According to the upward height error value of the MEMS bridge in step (6b), the adjustment amount of the operating voltage of the i-th MEMS bridge in the "down" working state is as follows: <mrow><msub><mi>&amp;Delta;V</mi><mrow><mi>d</mi><mi>i</mi></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow><mi>d</mi><mi>i</mi></mrow></msub><mo>-</mo><msubsup><mi>V</mi><mi>d</mi><mn>0</mn></msubsup><mo>=</mo><msqrt><mfrac><mrow><mn>8</mn><mi>k</mi><msup><mrow><mo>(</mo><mi>h</mi><mo>+</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>)</mo></mrow><mn>3</mn></msup></mrow><mrow><mn>27</mn><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><msub><mi>w</mi><mi>c</mi></msub><msub><mi>w</mi><mi>b</mi></msub></mrow></mfrac></msqrt><mo>-</mo><msqrt><mfrac><mrow><mn>8</mn><msup><mi>kh</mi><mn>3</mn></msup></mrow><mrow><mn>27</mn><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><msub><mi>w</mi><mi>c</mi></msub><msub><mi>w</mi><mi>b</mi></msub></mrow></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mrow><mn>8</mn><mi>k</mi></mrow><mrow><mn>27</mn><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><msub><mi>w</mi><mi>c</mi></msub><msub><mi>w</mi><mi>b</mi></msub></mrow></mfrac></msqrt><mo>&amp;lsqb;</mo><msqrt><msup><mrow><mo>(</mo><mi>h</mi><mo>+</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>)</mo></mrow><mn>3</mn></msup></msqrt><mo>-</mo><msqrt><msup><mi>h</mi><mn>3</mn></msup></msqrt><mo>&amp;rsqb;</mo></mrow> where k is the elastic stiffness of the MEMS bridge, h is the ideal height of the MEMS bridge, Δh is the upward height error of the MEMS bridge, _ε0 is the relative permittivity of air, _wc is the center conductor width, and _wb is the bridge width . 5. the adjustment method of a kind of distributed MEMS phase shifter working voltage based on phase shift amount electromechanical coupling according to claim 1, it is characterized in that, step (8) is carried out as follows: (8a) Compare the measured value of phase shift in step (3) with the standard value of step (2), when the measured value of phase shift Δφ _i is less than the standard value Δφ ₀ , it can be concluded that the MEMS bridge has a downward height error , when the phase shift measurement value Δφ _i is equal to the standard value Δφ ₀ , the MEMS bridge has no error, and the working voltage does not need to be adjusted; (8b) Calculate the equivalent circuit parameters of the i-th MEMS bridge. When the MEMS bridge is not loaded, the equivalent capacitance value C _t per unit length on the transmission line is: <mrow><msub><mi>C</mi><mi>t</mi></msub><mo>=</mo><msqrt><mfrac><mrow><msub><mi>&amp;epsiv;</mi><mi>r</mi></msub><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msqrt><mo>/</mo><msub><mi>cZ</mi><mn>0</mn></msub></mrow> In the formula, ε _r is the relative permittivity of the dielectric layer, c is the speed of light, Z ₀ is the characteristic impedance of the transmission line; When the MEMS bridge is not loaded, the formula of the equivalent inductance L _t per unit length on the transmission line is: <mrow><msub><mi>L</mi><mi>t</mi></msub><mo>=</mo><msub><mi>C</mi><mi>t</mi></msub><msubsup><mi>Z</mi><mn>0</mn><mn>2</mn></msubsup></mrow> In the formula, C _t is the equivalent capacitance value per unit length on the transmission line, and Z ₀ is the characteristic impedance of the transmission line. 6. the adjusting method of a kind of distributed MEMS phase shifter operating voltage based on phase shift electromechanical coupling according to claim 1, it is characterized in that, step (9) is carried out as follows: (9a) Using the electromechanical coupling model of a single MEMS bridge and the measured value of the phase shift of the i-th MEMS bridge in step (3), the variable capacitance value C _ui (Δh) in the "up" working state can be calculated inversely. The coupling model is as follows: <mrow><msub><mi>&amp;Delta;&amp;phi;</mi><mi>i</mi></msub><mo>=</mo><mi>&amp;omega;</mi>mi><msqrt><mrow><msub><mi>L</mi><mi>t</mi></msub><msub><mi>C</mi><mi>t</mi></msub></mrow></msqrt><mrow><mo>(</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mfrac><msub><mi>C</mi><mi>d</mi></msub><mrow><mi>s</mi><mo>&amp;times;</mo><msub><mi>C</mi><mi>t</mi></msub></mrow></mfrac></mrow></msqrt><mo>-</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><msub><mi>C</mi><mrow><mi>u</mi><mi>i</mi></mn>mrow></msub><mrow><mo>(</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi><mo>&amp;times;</mo><msub><mi>C</mi><mi>t</mi></msub></mrow></mfrac></mrow></msqrt><mo>)</mo></mrow></mrow> In the formula, s is the distance between adjacent MEMS bridges, ω is the operating frequency, C _t is the equivalent capacitance value per unit length on the transmission line, L _t is the equivalent inductance value per unit length on the transmission line, and C _d is the "down" working The variable capacitance value in the state, C _ui (Δh) is the variable capacitance value in the "up" working state; Δφ _i is the measured value of the i-th MEMS bridge phase shift; (9b) According to the variable capacitance value C _ui (Δh) in the "up" working state calculated in step (9a), using the relationship between the variable capacitance value and the MEMS bridge height error in the "up" working state, it can be inversely obtained The downward height error Δh of the i-th MEMS bridge, the relationship is as follows: <mrow><msub><mi>C</mi><mrow><mi>u</mi><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mrow><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><mfrac><msub><mi>w</mi><mi>c</mi></msub><mi>n</mi></mfrac><msub><mi>w</mi><mi>b</mi></msub></mrow><mrow><mi>h</mi><mo>+</mo><mi>&amp;Delta;</mi><mi>h</mi><mo>-</mo><mfrac><mrow><mo>(</mo><mi>j</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mi>n</mi></mfrac><mfrac><mrow><msub><mi>w</mi><mi>c</mi></msub><mi>&amp;Delta;</mi><mi>h</mi></mrow><mi>L</mi></mfrac><mo>+</mo><mfrac><msub><mi>t</mi><mi>d</mi></msub><msub><mi>&amp;epsiv;</mi><mi>r</mi></msub></mfrac></mrow></mfrac></mrow> In the formula, w _c is the width of the central conductor, w _b is the width of the bridge, h is the ideal height of the MEMS bridge from the dielectric layer, t _d is the thickness of the dielectric layer, ε ₀ is the relative permittivity of air, ε _r is the dielectric layer Relative permittivity, L is the length of the MEMS bridge, Δh is the height error of the MEMS bridge downward. 7. the adjusting method of a kind of distributed MEMS phase shifter operating voltage based on phase shift amount electromechanical coupling according to claim 1, it is characterized in that, step (10) is to MEMS bridge height according to operating voltage in step (7a) Using the height error value of the MEMS bridge downwards in step (9b), the ideal working voltage under the "up" working state of the MEMS bridge is zero, so calculate the working voltage under the i-th MEMS bridge "up" working state The adjustments are as follows: <mrow><msub><mi>V</mi><mrow><mi>u</mi><mi>i</mi></mrow></msub><mo>=</mo><mo>-</mo><msqrt><mfrac><mrow><mn>8</mn><msup><mi>k&amp;Delta;h</mi><mn>3</mn></msup></mrow><mrow><mn>27</mn><msub><mi>&amp;epsiv;</mi><mn>0</mn></msub><msub><mi>w</mi><mi>c</mi></msub><msub><mi>w</mi><mi>b</mi></msub></mrow></mfrac></msqrt></mrow> where k is the elastic stiffness of the MEMS bridge, _Δh is the downward height error of the MEMS bridge, _ε0 is the relative permittivity of air, wc is the width of the central conductor, and _wb is the width of the bridge.