MIT10_626S11_lec05

MIT10_626S11_lec05 - Lecture 5. Impedance spectroscopy MIT...

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Unformatted text preview: Lecture 5. Impedance spectroscopy MIT Student Last time we talked about the non-linear response to DC voltage, and today we will discuss about the AC linear response at frequency . A simplified model of voltage response of galvanic cell can be written as V(I,Q)=V (Q)- (I,Q) If we consider small perturbations around a reference state (constant current), voltage, current and charge can be expressed as V=V-V ref I=I-I ref Q=Q-Q ref Since we are assuming small changes (perturbation), we can use taylor expansion to express V voltage, ! ! !"# where + R !"# I (1) ! ! !"# = ! ! ! ! ! !"# , ! !"# = ! ! ! ! ! ! !"# , ! !"# ! ! ! ! ! !"# , ! !"# , C !"# = differencial capacitance R !"# = ! ! ! ! ! !"# , ! !"# = ! ! ! ! ! !"# , ! !"# , R !"# = differencial resistance I = Q t Consider alternating-current (AC) sinusoidal perturbations at frequency and introduce complex amplitudes for the perturbations (to induce phase lag): V=Re( V e i t )= V cos( t) ; chose t to fit real number for V, V :real number) i I= Re( I e t )= I cos( t+ ) i t Q= Re( Q e ) , where I =i Q since I = ! ! !...
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MIT10_626S11_lec05 - Lecture 5. Impedance spectroscopy MIT...

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