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Challenge_28

# Challenge_28 - What ODE does this transfer function model 1...

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EEL 3135: Dr. Fred J. Taylor, Professor Lesson Title: Laplace Transforms Lesson Number: 28 (Supplemental) Challenge Problem The device under study is shown in Figure 1. The antenna coils turn the RFID reader’s time varying magnetic field into current (therefore power). The capacitor “tunes” the circuit to 134kHz. Figure 4: RFID system At a high-level the RFID can be modeled as shown in Figure 1. The input is assumed to be a voltage source v(t) and the output a voltage v 0 (t), and the input-output transfer function is given by: H(s)=(s-a)/((s-a) 2 + ϖ 0 2 ) for real parameters “a” and “ ϖ 0 ”. Assume the system is initially at-rest.

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Unformatted text preview: What ODE does this transfer function model? 1 EEL 3135: Dr. Fred J. Taylor, Professor Response From (s 2-2as +(a 2 + ϖ o 2 ))V (s) = (s-a)V(s) it must follow that: d 2 v (t)/dt 2-2a dv (t)/dt + (a 2 + ϖ o 2 )v (t) = dv(t)/dt – av(t) Suppose, for illustrative purposes, a=0.02, ϖ =10, H(s) = (s-.01)/(s 2 – 0.02s + (.01 2 +10 2 ) = (s-.01)/(s 2 – 0.02s + (100.0001)) » [H,w] = freqs([1,-.01],[1, 0.02, 100.002]); » plot(w,abs(H)) » plot(w,360*angle(H)/(2*pi)) Magnitude frequency response. Phase response. 2 90 °-90 °...
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Challenge_28 - What ODE does this transfer function model 1...

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