## Inductor-Capacitor (LC) Oscillator, Hydraulic Analogy

Easy-to-Understand LC Oscillator Models
for Physics & Engineering Students

Connecting a capacitor to an inductor creates an oscillator. Once started, charge flows back and forth between the two sides of the capacitor at a fixed frequency, even after peak charge, voltage, and current decrease due to energy loss.

A hydraulic capacitor is a cylinder divided by a flexible rubber sheet. Here's an oblique view and a cross-section side view.  A hydraulic inductor is a water wheel connected through a rigid axle to a heavy stone flywheel, with a housing that forces the water in a clockwise direction when the water flows from left to right.  Here's a conceptual view and a cross-section side view.  The following diagram shows an inductor-capacitor (L-C) circuit, capacitor and inductor connected end-to-end. You start by pumping water into the left side of the capacitor, pressurizing the water. The potential energy is stored in the stretched rubber sheet separating the two sides of the capacitor. You remove the pump and allow the circuit to run freely. The rubber sheet forces the water through the inductor, causing the inductor's flywheel to spin faster and faster. When the rubber sheet reaches the neutral position, the pressure is zero but the flywheel momentum and current are at their maximum. As the flywheel continues to turn, it pressurizes the water and forces it into the opposite side of the capacitor, stretching the rubber sheet in the opposite direction. When the flywheel runs out of energy and stops, the capacitor is fully pressurized in the opposite direction. The same process runs in reverse, returning the circuit to the original starting position if there is no friction. With loss of energy to friction, the rubber membrane comes back into a less-stretched maximum position, but it still oscillates with the same period.

#### Electronic Oscillator

For the electronic inductor-capacitor (L-C) circuit, you start by charging the capacitor, raising the charge to the same voltage as a battery. The potential energy is stored in the electric field that holds the charge on the two sides of the capacitor. You disconnect the battery, connect the capacitor to the inductor, and allow the circuit to run freely. The voltage of the capacitor forces the accumulated charge through the inductor, causing the inductor's magnetic flux to build up. The flux is like the momentum of the flywheel in the hydraulic circuit. When the capacitor runs out of charge, the voltage is zero but the flux and current are at their maximum. The magnetic flux forces the current to continue flowing into the opposite side of the capacitor, raising the voltage and building up the charge across the capacitor in the opposite direction. When the magnetic flux runs out of energy and the current stops flowing, the capacitor is fully charged in the opposite direction. The same process runs in reverse, returning the circuit to the original starting point if there is no loss to wire resistance. With loss of energy to resistance, the capacitor carries less charge at the maximum point, but it still oscillates with the same period.

If you take a charged capacitor as the starting point (time=0), the voltage across the two devices is the cosine function and the current through the circuit is the sine function. • Period = 2π SQRT(Inductance x Capacitance)

• Frequency = 1/(Period)

The frequency of the oscillator does not depend on the amount of charge. Charging the capacitor to a higher voltage increases the amplitude of the voltage and current but does not affect the frequency. This is just like a guitar string, which vibrates at the same frequency whether plucked gently or strongly, producing the same note in either case. Only the volume is affected. Like a guitar string, the amplitude dies away due to friction/resistance.

An L-C oscillator can be used as a tuner in a Crystal Radio.

Capacitor Hydraulic Analogy

Inductor Hydraulic Analogy

LC Oscillator in Crystal Radio

Back to Main Hydraulic Analogy Page

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