Electrical Resonance

November 19, 2008 Educational Radio Net, PSRG 26th session, Lee Bond N7KC

The impedance series is now history. During the course of that 13 week series we looked at several of the most fundamental ideas in the physics of electrical phenomenon and, hopefully, gained some practical knowledge of how these ideas link together to form a basis for our understanding of all things electrical. Let's exercise some of this earlier impedance series material and see how it can be applied to solve practical problems which are routinely encountered on the bench. The first study examined the potentiometer or "pot" and its behavior when used as a voltage divider. The second study examined how energy is moved from a source to a load and also considered the effect of a transmission line in this process. This third study will look at the phenomenon of resonance in both the mechanical and electrical worlds and extend the idea to antennas.

Lets consider mechanical systems first to get an intuitive feel for resonance.

We have all experienced autos which produce nasty sounds at certain speeds or engines where certain parts tend to vibrate depending on engine rpm. Suppose that we have an engine with some sort of attached bracket and the engine is at idle. If we very slowly advance the engine throttle to increase rpm’s there may be a engine rotational speed where the bracket starts to vibrate very strongly. If we continue to advance the throttle, the bracket vibration diminishes and disappears altogether. The mechanical configuration of the bracket has a "natural" frequency which is the frequency of vibration which develops when excited by the engines complicated sounds.

Another demonstration example is a wine goblet shattering when excited by acoustic energy which matches the natural frequency of the goblet. Finally, lets consider the pendulum in a clock. If the clock is unwound and the pendulum is activated we know that it will oscillate back and forth with diminishing amplitude until it stops. The pendulum has a natural frequency primarily determined by its length. If the clock is wound, however, there is a bit of clock mechanism which "taps" the pendulum very slightly at the correct moment to keep the pendulum swinging at constant amplitude, at the natural frequency, and for as long as the energy to produce the tap is present.

All of these examples show that very small forcing energies at the natural frequency of a mechanical system may cause dramatic vibration amplitudes due to resonance. Resonance frequency is where the forcing frequency matches the natural frequency of a system.

The situation in the electrical world is much the same as in the mechanical. Small signals (forcing energy) can appear dramatically larger due to electrical circuit resonance. Such circuits are always structured with resistance, inductance, and capacitive elements. The resistance element stands alone in being immune to the effects of forcing frequencies since the resistance converts energy directly to heat and stores nothing. In contrast to the resistance element, inductance and capacitive elements do not dissipate energy rather they store energy in the form of electric or magnetic fields during one portion of the cycle and return it to the circuit during the next.

Inductance associated with a forcing frequency creates a reactance product which increases with frequency whereas capacitance associated with a forcing frequency creates a reactance product which decreases with frequency. Therefore, given an assembly of resistance, inductive reactance, and capacitive reactance, there is a possibility that at some specific frequency the reactive components value will be equal and opposite hence cancel since they carry opposite sign. Electrical resonance generally indicates that net reactance is zero at a particular frequency. At this resonant frequency the circuit impedance is purely resistive.

One good example of electrical resonance is given by the tuning circuit in a typical radio receiver. The broadcast band, for instance, contains various amounts of energy from 550 Khz to 1500 Khz. The radio needs to respond to a specific station located in this continuum of signals. Using a parallel resonant circuit which is tunable allows one to slide across the band in search of the desired signal. Very slight amounts of received energy from the antenna will excite the resonant circuit and produce signal levels much higher than the excitation level. It is important to note that incoming signal energy is not increased by resonance rather signal amplitude is increased which is then amplified by a suitable active circuit.

Trapping circuits can be constructed from resistive, capacitive, and inductive elements as well. To facilitate this function the elements should be wired in series. At the resonant frequency the net reactance will be zero leaving only resistance as the circuit element. At frequencies off resonance the circuit impedance will always be larger than at resonance due to the combination of series resistance and predominate reactance.

Another example of impedance changing with frequency is the antenna. Lets consider a simple dipole cut to the center of any band. If you were to connect an antenna analyzer to the dipole and sweep from the lower to the upper band edge you would see the antennas feed point impedance, or combination of resistance and reactance, dip at the cut frequency and show only a resistive component. This is the radiation resistance of the antenna at resonance. Resonance frequency is that frequency where net reactance is zero.

Given that the antenna inductance and capacitance values are fixed, at frequencies above the resonance point the antenna is too long, inductive reactance increases, and the antenna impedance increases. Conversely, at frequencies below the resonance point the antenna is too short, capacitive reactance increases and the antenna impedance increases. Since maximum power transfer occurs when transmission line characteristic impedance matches the radiation resistance of the antenna, the trick is to adjust antenna elements such that, at the desired operating frequency, the net reactance is zero and maximum radio frequency current flows in the antenna elements. Since the dipole has a feed point impedance of about 72 ohms at resonance, driving it directly with 50 ohm coaxial line and a 1:1 balun would yield a VSWR of 72/50 or 1.44:1 minimum. Various matching schemes are available to adjust the feed point impedance to match the transmission line.

In certain circumstances electrical resonance can be a nuisance. For example, consider the guy wires associated with a tower installation. Wires similar in length to the radiating elements can seriously detract from a desired radiation pattern. A careful look may reveal that many compressive egg shell insulators may be used to break up the total length of the guys such that any single guy length cannot produce harmonically related radiation in concert with the actual antenna.

In summary, resonance can be a help or hindrance. Electrical resonance is a fundamental concept of electrical theory and, in practical terms, makes our radio endeavors possible.

This concludes the set up for the discussion of resonance. Are there any questions or comments?

This is N7KC for the Educational Radio Net