ABSTRACT
We have seen that a step input of voltage e5 causes a ramp current i =est/ L. A step input of current(, gives rise to a voltage impulse function of size (area) Lis. The frequency response of the inductance element is obtained from the sinusoidal transfer function as follows:
di e = L-= LDi
dt i 1 -(D)=- e LD
Note that at very low frequencies (w-+ 0) a small voltage amplitude can produce a very large (approaching oo as w-+ 0) current. Thus an inductance is sometimes said to approach a short circuit for low frequencies, and under such conditions could be replaced in a circuit diagram with just a piece of "connecting wire." [Recall that in circuit diagrams one shows R's, C's, and L's connected by pieces of perfectly conducting (no voltage drop) "wire."] At high frequencies (w-+ oo) note that the current produced by any finite voltage approaches zero. Thus we often say that an inductor approaches an open circuit at high frequencies, and could thus just be "cut out" of a circuit diagram under such conditions. For a capacitance, just the reverse frequency behavior was observed; the capacitance approaches a short circuit at high frequencies and an open circuit at low frequencies. One can often use these
simple rules to quickly estimate the behavior of complex circuits at low and high frequency. Just replace the L's and C's by open or short circuits, depending on which frequency range you are interested in. Remember for real circuits, however, that real L's always become R's for low frequency.
