# Electrical Components of Printed Circuit Board Design

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## Resonance

Before we leave our hydraulic analogies, let's look at one more special case. Suppose we have the storage tank (capacitor) and paddle wheel (inductor) in parallel as shown in Figure 3-13. Suppose we turn on the pump long enough to have the paddle wheel turning freely (no resistance to the flow). Then, let's turn off the pump.

Figure 3-13. Hydraulic analogs for inductance and capacitance connected in parallel.

If the conditions are just right, inertia from the paddle wheel will cause water to continue flowing up into the lower storage tank. This will continue until the pressure in the tank gets strong enough to slow, and then stop, the paddle wheel. But when the paddle wheel finally stops, there will be considerable pressure in the tank. This will cause the paddle wheel to start turning in the opposite direction, moving water from the lower storage tank to the upper storage tank. This will continue until the pressure in the upper storage tank becomes strong enough to slow, and then stop, the paddle wheel. By that time, the pressure in the upper tank will be strong enough to start the paddle wheel turning in the opposite direction again, moving water from the upper storage tank to the lower one.

In the absence of friction (resistance), and if the tanks and paddle wheel are sized correctly, this can go on indefinitely! It requires no outside force or power to keep it going once it starts. (Of course, in the real world there is always friction, or resistance, but electronic circuits can be designed where these oscillations can be very large and strong.) If one component is very much larger or very much smaller than the other, then this oscillation will die out very quickly. But if the components happen to be sized just right, oscillations can continue for a very long time. This very special set of conditions is called resonance, and as we will see, it is a very important concept.