4.6 Circuit Board Resonances

In passive circuit theory, an inductor and a capacitor in series or in parallel are resonant circuits. To illustrate the parallel resonance idea, consider a capacitor with stored energy. At time t = 0, the capacitor and inductor are connected parallel. Initially the current in the inductor is zero. Current will start building in the inductor. At some point all the energy stored in the capacitor is transferred to the inductor. At this time, the voltage across the capacitor is zero and the current in the inductor is at a maximum. The cycle continues with the charge building in the capacitor until the voltage is a negative maximum. If there are no losses, this back and forth movement of energy will continue indefinitely. The voltage across the circuit is a sine wave. At the peaks of voltage, all the energy is stored in the electric field of the capacitor. At the zeroes of voltage, all the energy is stored in the magnetic field of the inductor. The key factors in this resonance are the transfer of energy between the electric and magnetic fields and the time it takes for the energy to make the transfer.

A section of unterminated transmission line can be viewed as a type of resonant circuit. When a voltage V is switched on the line, a wave propagates down the line. At the open end of the line, a reflection takes place and a wave returns to the source. The reflection at the source returns this wave and the voltage source supplies no more energy to the line. Wave action continues indefinitely with the voltage at the open end alternating between 2 and 0 V. The total energy on the line is constant with the energy in constant motion. Just as before, the moving energy is stored in both the magnetic and the electric fields. The time of one cycle is twice the propagation time of the wave on the line. This is a step function resonance rather than a sinusoidal resonance. In parts of the transmission line where the voltage is zero, energy is stored in the inductance; and in other parts of the line where the current is zero, the energy is stored in the capacitance. The exchange of energy takes place at the leading edge of the wave.

When an unterminated stub is added to a terminated transmission line, the energy flow in the stub acts very much like a resonant circuit. If the stub is long enough, the energy moving back and forth in the stub can delay the settling time on the main line.