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lesson27 - Lesson 27 Capacitors and Inductors II (Sections...

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Lesson 27 – Capacitors and Inductors II (Sections 5-5 and 5-7) (CLOs 6-2 and 6-3) This is the second of two lessons on Capacitors and Inductors. This lesson discusses combining multiple devices and introduces two new operational modules, the integrator and differentiator. A computer exercise on an Op-amp integrator and differentiator can be useful. This is an easy lesson. You might even find time to give a quiz – or catch up if you’re behind. There are three topics to discuss. The first is how to combine Inductors and Capacitors, the second involves two additional Op- Amp modules – integrators and differentiators, and the third is how to analyze L and C circuits at dc. You can derive the relationship for series and parallel L ’s and C ’s or you can simply tell your students that – L ’s behave like R ’s and C ’s behave like G ’s. (OK – just say the reverse of R ’s). Do a few examples, but students really do not have difficulty with this. In developing the integrator and differentiator, it is a GREAT opportunity to review node voltage analysis and the i-v relationships for inductors and capacitors. Some students want to write i = ( v 1 - v 2 ) /C . It may have not sunk in that the i-v characteristics of capacitors and inductors are differential/integral relationships. Use this effort to bring out this fact. After you derive the relationship, it would be useful to show the block diagram of both to include the inverting and weighting part of the derivation. Figure 6-17 in the text summaries all of the Op-Amp modules studied thus far. They need either to memorize these relationships or know how to derive them. Suggest doing an example of how an integrator or differentiator works. Example 6-10 is somewhat similar to the computer exercise (below). Old-timers (whoever they are) might tell students – especially Aerospace majors who define aircraft or satellite performance by a set of coupled differential equations (e.g. yaw, pitch and roll) – that differential equations were once solved exclusively using analog computers. Example 6-11 shows how a circuit could actually solve a first-order integral equation. Finally using the derivative equations show the behavior of capacitors and inductors at dc. Do an example with inductors and capacitors driven by a dc source. Actually, redraw the circuit with capacitors replaced with opens and inductors with shorts. This will be useful when we develop transfer functions for filters. Finally, you might upgrade the summary table to include the new stuff from this lesson. Device/Model Resistance – R Inductance – L Capacitance – C Units ohms, henrys, H farads, F Circuit Symbol + _ v R i R R + _ v L i L L + _ v C i C C Voltage Equation v R = i R R v L = L di L /dt v C = (1 /C ) 0 t i C dt + v C (0 + ) Current Equation i R = v R G = v R /R i L = (1 /L ) 0 t v L dt + i L (0 + ) i C = C dv C /dt Power Equation p R = i R × v R p L = i L × v L p C = i C × v C
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lesson27 - Lesson 27 Capacitors and Inductors II (Sections...

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