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CACD Group updated 2000.03.30 Author Janez Puhan |
Windingless Inductor1Inductors are an important part of passive circuit design. Depending on the frequency, inductors can be composed of a few turns of wire wound around a small ferrite core or of thousands of windings surrounded by a weighty iron core. In some applications, they may be replaced with smaller and less expensive synthetic inductors synthesised with operational amplifiers. For inductors, a 90 degree phase lag of sinusoidal current compared to voltage is characteristic. However, ohmic losses in the windings and cores cause a deviation of phase lag from theoretical 90 degree value. In the following simulation, this displacement may be used as a criterion of quality in an extended frequency range. The circuitThe input file (windingless_inductor_1.cir)electronic capacitor I * C series = c1 r2 / r1 * R series = r1 .control set units = degrees ac dec 40 0.01Hz 1kHz plot db(i(v1)) ph(i(v1)) xlabel f[Hz] + ylabel 'current magnitude [dB] / phase[degree]' title 'AC analysis' plot mag(i(v1)) real(i(v1)) imag(i(v1)) xlabel f[Hz] ylabel current[A] + title 'AC analysis' .endc v1 0 1 dc 0 ac 1 r1 4 1 1k r2 2 3 100k c1 3 0 10nF e1 2 0 1 2 1meg e2 4 0 3 4 1meg .end The resultsWindingless Inductor 2A less expensive alternative is shown in the next circuit. It needs only one amplifier but has higher ohmic losses caused by resistors r1 + r2 lying in series with the inductance c1 * r1 * r2. In the graph, this is indicated by a phase lag in the current. The circuitThe input file (windingless_inductor_2.cir)windingless inductor II * L series = r1 r2 c1 * R series = r1 + r2 .control set units = degrees ac dec 40 10Hz 1megHz plot db(i(v1))+200 ph(i(v1)) xlabel f[Hz] + ylabel 'current magnitude [dB] / phase[degree]' title 'AC analysis' plot mag(i(v1)) real(i(v1)) imag(i(v1)) xlabel f[Hz] ylabel current[A] + title 'AC analysis' .endc v1 0 1 dc 0 ac 1 r1 1 3 1k r2 0 2 100k c1 1 2 10nF e1 3 0 2 3 1meg .end The results |
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