Displacement of Comb Drive Actuator Calculator

Calculator

Drive mode

Single drive voltage V

Left voltage V

Right voltage V

Finger pairs N

Finger thickness µm

Finger gap µm

Relative permittivity

Initial overlap µm

Allowed overlap travel %

Stiffness method

Known stiffness N/m

Beam count

Young modulus GPa

Beam length µm

Beam width µm

Layer thickness µm

Stiffness correction factor

Moving mass µg

Formula Used

The lateral comb drive capacitance gradient is:

dC/dx = 2Nε₀εᵣt / g

The single sided electrostatic force is:

F = 1/2 V² dC/dx = Nε₀εᵣtV² / g

The differential force is:

Fnet = Nε₀εᵣt(Vright² - Vleft²) / g

The actuator displacement is:

x = F / k

For the folded beam estimate, this tool uses:

k ≈ beam count × correction factor × Ehw³ / L³

How to Use This Calculator

Select single sided or differential drive mode.
Enter the voltage values used by your actuator.
Add finger pair count, finger thickness, gap, and overlap.
Select known stiffness or estimate stiffness from folded beams.
Enter mass if you also want an estimated natural frequency.
Press the calculate button and review the result above the form.
Use the CSV or PDF button to save the output.

Example Data Table

Case	Voltage V	Finger Pairs	Thickness µm	Gap µm	Stiffness N/m	Expected Use
Low travel sensor trim	20	80	20	3	3.5	Small position tuning
General MEMS shuttle	30	120	25	2	2	Balanced travel and stiffness
High force layout	45	180	30	2	5	Stronger restoring spring

Understanding Comb Drive Motion

A comb drive actuator is a common microelectromechanical device. It uses interleaved fingers to turn voltage into sideways motion. When voltage rises, an electric field forms between fixed and moving fingers. The field creates an attractive force. That force pulls the shuttle along its travel axis. The motion is small, but it can be very precise.

Why Displacement Matters

Displacement tells you how far the shuttle moves. It helps decide mirror tilt, switch position, valve opening, or sensor tuning range. A good estimate also protects the device. Too much travel can crash fingers, bend springs, or reduce repeatability. This calculator links geometry, voltage, dielectric setting, and stiffness in one workflow.

Main Design Inputs

The strongest inputs are finger pair count, finger thickness, gap, and voltage. More finger pairs increase capacitance gradient. A thicker device layer also increases force. A smaller gap increases force, but it also raises fabrication risk. Stiffness controls how much the shuttle moves for a given force. A soft spring gives more travel. A stiff spring gives better stability and higher resonance.

Known Or Estimated Stiffness

Many designs already have a simulated spring constant. In that case, enter the known stiffness. For early sizing, use the folded beam option. It estimates stiffness from Young's modulus, beam count, beam length, beam width, and layer thickness. This is a simplified model. Final designs should still be checked with finite element simulation and measured test data.

Reading The Results

The result gives capacitance gradient, electrostatic force, effective stiffness, displacement, approximate capacitance, stored energy, stroke ratio, and optional resonance. A positive differential result moves toward the right side. A negative result moves toward the left side. The travel check compares absolute displacement with the selected overlap limit.

Practical Use

Use the calculator to compare design choices quickly. Try a voltage sweep. Change the gap carefully. Increase finger count when more force is needed without raising voltage. Increase spring width when the device needs stronger restoring force. Keep enough overlap margin. Treat fringing fields, residual stress, air damping, and end stops as separate design checks.

Exported reports help document assumptions. They make review easier during layout discussions, lab planning, and client signoff before prototype masks are finally ordered.

FAQs

What is a comb drive actuator?

It is a micro actuator with interleaved fixed and moving fingers. Voltage creates an electrostatic force between the fingers. The force moves a shuttle sideways against spring stiffness.

Which displacement formula is used?

The calculator uses x = F / k. Force comes from the comb drive capacitance gradient. Stiffness comes from your known value or the folded beam estimate.

Why does gap strongly affect displacement?

A smaller gap increases electric field strength and capacitance gradient. That raises force for the same voltage. Very small gaps can increase fabrication difficulty and risk finger contact.

What does finger pair count mean?

It is the number of active overlapping finger pairs. More pairs increase capacitance gradient. That increases electrostatic force and displacement when stiffness and voltage stay unchanged.

Can this handle differential drive?

Yes. Select differential mode and enter left and right voltages. The tool uses the difference between squared voltage terms to estimate net force direction and travel.

Is the folded beam stiffness exact?

No. It is an early design estimate. Real stiffness can change due to anchors, residual stress, process variation, and folded flexure details. Use simulation for final layout.

Why enter moving mass?

Mass is optional. When entered, the calculator estimates natural frequency from stiffness and mass. This helps compare response speed and dynamic behavior.

Does the formula include fringing fields?

No. The main calculation uses a parallel plate sidewall approximation. Fringing fields, end effects, damping, and contact stops should be reviewed separately for accurate final design.