To Build A Folded Flexure Resonator

March 13, 1998
Copyright (c) 1998, Carnegie Mellon University
All Rights Reserved.

This tutorial provides basic steps about how to build a folded flexure resonator using the symbols and templates in the tarfile, "NODASv1.4.tar.gz". The resonator is a mechanical mass-spring-damper system consisting of a central shuttle mass that is suspended by two folded-beam flexures (one on each side of the shuttle mass). The resonator is driven in the preferred (vertical) direction by two electrostatic comb actuators (also called combdrives, one on the top and another at the bottom of the shuttle mass. The layout of the resonator is shown in Figure 1.

Fig. 1 Layout

Fig. 2 Schematic (Click to see detail)
The schematic of the resonator is shown in Figure 2. It consists of 5 plate- masses (representing 1 central shuttle mass, 2 shuttle yoke masses, and 2 combdrive masses), 2 combdrive_y, and 2 folded flexures. Each folded flexure contains 7 beams, and 2 anchors.
I. Prestep
    Untar the tar file "NODASv1.4.tar.gz" and save the untared files in your run directory. 
    Invoke SABER from the directory where these files are at - This is very important. 
    Otherwise, SaberSketch won't be able to locate the symbols and templates in 
    NODASv1.4, unless you specify the new saber path in login file.

II. Placing a component to a schematic
   1. Open a new window in SABER with the name of "Schematic new_sch1" on the top
   2. Press the right mouse button and choose "Get Part/By Symbol Name" 
      from the pop-up manual. A little panel with a title "Get and Place
      Symbol By Name" will pop up.
   3. Select "Yes" within the box "Add to Parts Gallery?" and use Browse to
      get a list of the symbols (components) in the NODASv1.4
   4. Highlight the symbol you want to place to your new schematic and
      click on "Ok" and then "Place" button. The symbol will show in the middle
      of the screen. Every part you have selected and placed to the screen
      will end up in the "User Parts Library" on the pop-up manual when 
      you click your right mouse button. From now on, you can select them
      directly from the "User Parts Library" instead of "By Symbol Name". 
III. Some basic skills in manipulating the symbols
   1. Move a symbol around
        - point to the symbol with the cursor, click on the left button 
      and hold it, drag the symbol to any location, and release the button. 
      This skill is useful when you want to connect two components together.
   2. Remove a misplaced symbol or connection
        - point to the symbol or connection, click left button, and press 
      the delete key from the keyboard
   3. Connect components
        - drag component A close to component B; move A around until
      all the nodes on both ports overlap with each other exactly(i.e., x to x, phi to phi) 
        - release the mouse button. Once the correct connection is
      established, all nodes boxes should disappear. Instead, straight lines
      can be seen between two ports
        - adjust the distance between A and B by dragging a part around. 
      * Hint: if the space between two components is limited, you may have to 
      reduce the grid and snap spacing using Edit from the main manual
      and select "Schematic preferences" from the pull-down manual. 
   4. Change the size of a component 
        - The size parameters of a component can be changed by clicking on the
      right mouse button and selecting "Symbol Properties" from the pop-up
      manual. But the view size of a component can not be changed. They 
      can only be adjusted by zoom in and out icons from the manual bar on the
      top of the screen. Therefore, in order to fit all the components into to
      your circuit, you need to adjust the distance among the components.
   5. Rotate and flip a component 
        - A vertical beam can be obtained by rotating the beam component
      by 90 degrees. Rotation can be done by pointing to the component and
      clicking on the right mouse button. 
      * Remember after you rotate a component, you have to change the value of 
      parameter "angle" by clicking on the right mouse button and selecting
      "Symbol Properties". At present, only rotation of beam within range -180o
      to 180o by keeping node b as rotation origin is suggested. Please do not 
      rotate other type of components.
IV. Steps to build a folded flexure resonator
   1. Place a plate_mass_ns (ns stands for north and south ports. The reason
      for choosing it is that there are only two connections for the center
      mass) from the Browse manual to the schematic (refer to II) as the
      central shuttle mass. Then place 2 plate_mass_faces as the 2 shuttle 
      yoke masses and connect one to the top and another to the bottom of the 
      center mass (refer to III-3). Finally, place and connect 2 more
      plate_mass_ns as the combdrive masses to the 2 yoke masses.
   2. Select a combdrive_y from the Browse list and place it to the screen.
      Connect the combdrive_y to the plate_mass_ns properly (refer to III-3). 
      Place another combdrive_y, and  connect it to another plate_mass_ns. 
      Place and connect anchors to the top end of upper combdrive_y and to the
      bottom end of lower combdrive_y.
   3. Select a beam and place it horizontally to the top right of the 
      plate_mass_face and copy one to the bottom right, top left, and top right
      of the plate_mass_faces.
   4. In order to connect 2 beams perpendicularly to one another, click on 
      one of them, rotate it to +90o, then specify the value of its 
      "angle" parameter to be 90, and specify the "angle" of the horizontal beam
      to be 0, then connect them properly. 
      * Two important points here are: 1) make sure to change the angle parameter
      for each of the 6 vertical beams to be 90 degree (III-5); 2) Because 3 vertical
      beams have to be placed between the 2 horizontal beams, the total length of 
      the 3 vertical beams must be equal to the total length of the masses between
      the connection points to beams on the mass of the shuttle yoke. In our case, 
      the length of 3 beams is 102u. Therefore, the length of the masses between 
      the 2 beam connection points including the center mass and a half of the each 
      yoke mass has to adjust to 102u also. So, the length of center mass is adjusted 
      to 66u. Plus 18u for half of the length of each yoke, the total length of masses 
      sums up 102u. 
   5. Place 2 more horizontal beams and 2 anchors to each side.
   6. Place standard mechanical/electrical parts from "Parts Gallery" which are
      provided by the manufacturer. In the example, a dc voltage, which can
      be found from "Pats Gallery/electrical/electrical source/voltage source",
      is placed on a horizontal beam.
   7. Specify the size and angle parameter values for each of the components by 
      editing "symbol properties".
   8. A mechanical reference point is always needed for layout position calculation. 
      The reference point can be any mechanical point on the schematic. Get the component 
      "layout-origin" by symbol name (or from part gallery if you already put it in your
      part gallery) and place it to the screen. Connect the node x0, y0 and
      phi0 to the mechanical nodes for x, y and phi at the point you want it to
      be the reference point. This point is now the layout origin (0,0) on your chip. 
      In Fig2, layout-origin is connected to the bottom end of the lower combdrive_y 
      where an anchor is also connected to the same point, meaning that this point 
      is a fixed point on the chip as well as the layout origin on chip for layout
      position calculation.
   9. Place a resistor from "Parts Gallery"/electrical/passive elements/resistors
      to the vs node on the top combdrive, and then place an op-amp to from a 
      transresistor sensing circuit as shown in Fig2. 
   10. Electrical ground can be found from "Parts Gallery / electrical". Put it where you 
      need a ground for electrical connection.
   11. Mark the important nets - normally each net has a net name on it 
      by default. You can give a specific name for those important point.
      For example, the input point is at the vr port on the bottom combdrive.
      Its number was n2543. Now it can be changed to vin by highlighting the part,
      clicking the right mouse button, and selecting "Attributes".
      The output point is at the top combdrive and can be renamed as vout.
A complete folded flexure resonator has been completed. Save your file
and begin simulation.
V. Simulation and Analysis
   1. After you saved your file, click on "design" from the main menu on the top
      of the screen. Select "Use" then "your design (file) name" from the
      the pull-down manual.
   2. Go to "design/netlist ff" to generate a netlist from the schematic.
   3. Come out of sketch window to the unix command window, type in 
      "perl convert.pl ff" to run a perl script. It will go through totally seven 
      steps, and give out a series of calculation results of the layout position.
   4. Go back to sketch window, close the original schematic, and click on 
      "file/open/design". You can see there is a new schematic created called 
      "ff_disp". Open it. This new schematic is basicly the same as the original 
      one, except the component "layout_origin" is removed. It's not useful for 
      the analysis of displacement. Instead, parameter "Xc" and "Yc" for the 
      components are now assigned to new values obtained in the previous step 
      to represent the layout position at the center of the component.
   5. Click on the ">cmd" icon on the upper right corner of the screen. A little
      window (SABER TRANSCRIPT WINDOW) will pop up. You can monitor your simulation. 
   6. Go to "Analysis" on the top main menu and select any type of analysis you
      want such as dc, ac, or transient.

Good luck!