In this article, we will examine the fundamental components of any electric circuit – inductors (coils), capacitors (condensers), and resistors.
The property of a circuit to resist change in current by inducing a voltage in the opposite direction, or the magnitude of thereof, is called Inductance. It is the electromagnetic analogue of inertia.
Inductance is symbolized by the letter L, and a component (be it a semiconductor or a piece of wire) that exhibits inductance is called an inductor. A coil is a common example of an inductor.
Figure 1. The direction of a current and the resultant magnetic field
As in Figure 1, a current through a wire sets up a magnetic field in its vicinity (still remember those Physics 101 lectures?). Now, imagine what would happen if the current switched direction (as in audio). The direction of the magnetic field would also have to change – and the magnitude of the change in the magnetic field is proportional to the magnitude of change in current (including directions). That is, the magnetic field varies due to the change in current.
Now, a changing magnetic field always creates voltage in a direction that opposes the change in the current (Lenz’s Law) – this causes the net voltage to lag behind the current (because the magnetic field).
Figure 2. The phase difference between the voltage and current through an inductor
An AC circuit with an inductor will have the current ‘lead’ the voltage in phase (90 degrees for a pure inductor circuit).
(For a more detailed discussion on inductors, check http://en.wikipedia.org/wiki/Inductance)
Capacitance is the property of holding electric charges at a given voltage and allowing current to pass through only when there is a change in potential, or the magnitude thereof.
Capacitance is symbolized by the letter C, and a component that exhibits capacitance is called a capacitor. Two parallel metal plates is a common example of a capacitor.
Figure 3. Charges on a parallel plate capacitor
Image Source: http://www.electronics-tutorials.ws/capacitor/cap_1.html
Whenever there is a potential across two parallel metal plates (two sides of a capacitor), each plate obtains a positive or a negative charge. When the potential switches directions (as in audio), the plates change polarity, and a current flows, whose magnitude changes according to the change in the voltage. That is, the difference in potential is necessary for a current to flow.
Figure 4. The phase difference between the voltage and current through a capacitor
An AC circuit with a capacitor will have the current ‘lag’ the voltage in phase (-90 degrees for a pure capacitor circuit)
(For a more detailed discussion on inductors, check http://en.wikipedia.org/wiki/Capacitance)
While inductance and capacitance relay or impede signals depending on voltage and current, resistance is the property of impeding current regardless of changes in voltage and current, or the magnitude thereof.
Resistance is symbolized by the letter R, and a component that exhibits resistance is called a resistor.
Figure 5. Phases of voltage and current through a resistor
No mutual dependence exists between voltage and current in a resistor, so there is no phase difference.
Crossover networks in Loudspeakers
A typical loudspeaker could be roughly divided into three parts: the speaker unit, which creates the sound, the crossover network, which separates the signals by frequency, and the enclosure, which protects the speaker unit and the crossover network.
Figure 6. Structure of a loudspeaker
Image Source: http://en.wikipedia.org/wiki/Loudspeakers
Figure 7. Structure of a speaker unit
Image Source: http://en.wikipedia.org/wiki/Loudspeakers
The reason why a crossover network is necessary in speakers is because of the physical limitations of the speaker unit – normally speaking, a larger speaker unit will be able to play lower frequencies well, but will fail to produce high pitches, and vice versa. For instance, a large unit may be able to play a noise at 40Hz, which means that the core is vibrating 40 times per second – however, due to its large size and heavy weight, as well as the increased air resistance, it would be incapable of playing a high pitched 20kHz tone, lying on the other precipice of human hearing. Thus, Hi-fi speakers tend to use separate, dedicated units for the bass (called a woofer) and the treble (called a tweeter).
Multiple speaker units with dedicated frequency ranges require the signal to be separated frequency-wise and sent to the appropriate units, and the crossover network does just this. The raw input is filtered at the crossover network so that the lower frequencies are sent to the woofer and the upper frequencies to the tweeter.
Crossover networks are built using the properties of inductors and capacitors that we looked at earlier. For a brief review, the inductor resists rapid changes in current (higher frequencies), and on the other hand, the capacitor favors rapid changes in current. In other words, the inductor prevents higher frequencies from passing, and the capacitor prevents lower frequencies from passing. If these characteristics are used in tandem, the crossover network could be built from nothing but inductors, capacitors, and resistors. Easy, right?
Figure 8. An RC Low Pass Filter
Image Source: http://en.wikipedia.org/wiki/Low-pass_filter
Figure 9. An RC High Pass Filter
Image Source: http://en.wikipedia.org/wiki/High_pass_filter
Figures 8 and 9 depict a very simple Low Pass Filter and a very simple High Pass Filter made from a resistor and a capacitor.