Understanding Memristors: Breaking the Symmetry of Circuit Elements

[hikarusteinitz]

I'm confused about the need for a fourth fundamental circuit element. I learned that the idea of the memristor was conceived by observing the symmetry of the equations for charge, flux, current and voltage. We have, i=dq/dt , v=dphi/dt. Rrom the three elements: dV=Rdi, dphi=Ldi, and dq=Cdi. There is a missing relationship between dphi and dq, so the memristance was postulated as dphi=Mdq.

I don't think a new device had to be invented just to relate dphi with dq. A resistor follows the equation dv=Rdi, or V=IR for an ideal resistor. Since V=dphi/dt and and I=dq/dt then, dphi/dt=R(dq/dt). Then dphi=Rdq. Why is memristance still needed when resistance can relate flux and charge?

The equations for delta to wye transform and parallel and series arrangements for capacitors resembles that for conductances, while that for inductors resemble that of a resistor. creating another component breaks that symmetry. In AC analysis the impedance of a resistor is R, that of a capacitor is -jXc and that of an inductor is jXl for symmetry that of a memristor should be -M? a negative resistance?

 

[mfb]

M depends on q, while R does not depend on q. It is not a perfect symmetry, and you could call a resistor a special case of a memristor with constant M.