Differential capacitance torque sensor

A differential capacitance torque sensor, comprising:

• a housing;
• upper and lower fixed substrates being spaced apart and oriented parallel with respect to one another, said upper and lower fixed substrates being secured in said housing;
• first and second longitudinally opposed upper electrodes respectively secured to first and second longitudinally opposed ends of said upper fixed substrate;
• first and second longitudinally opposed lower electrodes respectively secured to first and second longitudinally opposed ends of said lower fixed substrate;
• a longitudinally-extending, conductive proof mass centrally positioned between said upper and lower fixed substrates, said longitudinally-extending, conductive proof mass being pivotal about a central axis thereof, wherein a first end of said longitudinally-extending, conductive proof mass is positioned between said first upper electrode and said first lower electrode defining a first upper capacitor having a first upper capacitance C1 and a first lower capacitor having a first lower capacitance C2, a second end of said longitudinally-extending, conductive proof mass being positioned between said second upper electrode and said second lower electrode defining a second upper capacitor having a second upper capacitance C3 and a second lower capacitor having a second lower capacitance C4;
• a first voltage source having a constant first voltage V1 electrically connected across said longitudinally-extending, conductive proof mass, said first upper capacitor and said second lower capacitor;
• a second voltage source having a constant second voltage V2 connected in series with said first voltage source, said second upper capacitor and said first lower capacitor;
• and
• a third voltage source having a constant third voltage V3 connected in series with said second voltage source, wherein the first, second and third voltages satisfy
• V
• 2
• =
• γ
• γ
• +
• 1
• ⁢
• V
• 1
• +
• 1
• 1
• +
• γ
• ⁢
• V
• 3
• ,
• wherein γ is a parameter defined as
• γ
• =
• C
• 2
• +
• C
• 3
• C
• 2
• +
• C
• 4
• -
• 1.