Electric Circuits, Global Edition
Electric Circuits, Global Edition
10th Edition
ISBN: 9781292060545
Author: James W. Nilsson, Susan Riedel
Publisher: Pearson Education Limited
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Chapter 12, Problem 5P
To determine

State the reason for why the function f(t)=/π2+t2 generates an impulse function for 0.

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Vs(t) + v(t) + vi(t) ZR ZL Figure 1: Second order RLC circuit Zc + ve(t) You are requested to design the circuit shown in Figure 1. The circuit is assumed to be operating at its resonant frequency when it is fed by a sinusoidal voltage source Vs (t) = 2sin(le6t). To help design your circuit you have been given the value of inductive reactance ZL = j1000. Assume that the amplitude of the current at resonance is Is (t) = 2 mA. Based on this information, answer the following to help design your circuit. Use cartesian notation for your answers, where required.
For a band-rejection filter, the response drops below this half power point at two locations as visualised in Figure 7, we need to find these frequencies. Let's call the lower frequency-3dB point as fr and the higher frequency -3dB point fH. We can then find out the bandwidth as f=fHfL, as illustrated in Figure 7. 0dB Af -3 dB Figure 7. Band reject filter response diagram Considering your AC simulation frequency response and referring to Figure 7, measure the following from your AC simulation. 1% accuracy: (a) Upper-3db Frequency (fH) = Hz (b) Lower-3db Frequency (fL) = Hz (c) Bandwidth (Aƒ) = Hz (d) Quality Factor (Q) =
V₁(t) ww ZRI ZLI Z12 Zci Zcz Figure 4. Notch filter circuit topology ши Consider the second order resonant circuit shown in Figure 4. Impedances ZLIZ C1. ZL2. Z c2 combine together forming a two-stage "band- reject" filter, so called because it rejects a "band" (aka range) of frequencies. This circuit topology is also commonly referred to as a "band-stop" filter or "notch" filter. The output of the DAB receiver block has been approximated via Thevenin's theorem for you as a voltage source Vs (t) and associated series impedance Z RI To succeed in our goal, we are going to use an iterative design approach. First we will design the interference rejector, and then repeat the process, using the output of the interference rejector to check the provided waveform converter works as intended.
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