The history of electronics has been marked by the introduction of components that have opened the doors to new solutions and technologies. The real revolution took place with the transistor, preceded by the diode, which marked the definitive birth of digital electronics, leading to the introduction of microprocessors. Next we will take a look at the main electronic components and their characteristics.

Resistance is a component which opposes the passage of electric current, dissipating energy in the form of heat. It is labelled with the letter R and is measured in Ohm. As we'll later see, when we'll describe Ohm's law, resistance combines voltage V and current I in one single formula. In particular, if we apply a voltage V to a resistance R, the flow of a current I is generated and the three quantities in question are combined in the following formula:

Equation 4.1. Ohm's Law

This component is made up of two parallel metal plaques placed at a very short distance from one another. If we apply a voltage to the two plaques, the latter are capable of maintaining the accumulated charge, thus generating an electric field within the slit that separates the two, which can be likened to the passage of a current as shown in the figure:

The quantity of charge that a capacitor is able store is called Capacity (C) and it is measured in Farad.

The figure shows a capacitor with a capacity C, to which a voltage V is applied. The following is the formula combining capacity, voltage and stored charge:

Equation 4.2. Charge of a capacitor

When we apply a voltage to a capacitor which was initially uncharged, the latter will begin to store electrons until it reaches its maximum charge limit. Beyond this limit the capacitor is no longer capable of storing charge and, if voltage is removed, the capacitor shall remain charged. A charged capacitor has a constant voltage at its far ends and if it then gets connected to a resistance it discharges onto the latter thus generating a current. The two processes of charge and discharge of a capacitor are not instantaneous but require a certain amount of time to take place, depending on the capacitor's characteristics and the circuit it is inserted in. While the capacitor is charging, charges with opposite polarities accumulate on the two plaques, and this movement of charges generates a current. This behaviour is at the heart of high-pass filter circuits [Filters ] .

Now let's imagine that we apply a sinusoidal voltage to the capacitor. If the sinusoid's rate is such that the positive half wave is faster than the capacitor's charging time, the capacitor won't reach its maximum charge limit in time, and the negative half wave shall arrive and discharge it. This way the current flow within the capacitor is never interrupted. Vice versa if we have a low frequency applied voltage, the capacitor reaches its maximum charge before the positive half wave expires and in that precise instant blocks the current flow. So, a capacitor blocks the flow of low frequencies (which cause its complete charge which in turn interrupts the charge flow) and can be used as a high-pass filter.

When a conductor is immersed in a magnetic field, the latter attracts the electrons inside the conductor, making them move and therefore generating a current. Vice versa, close to a conductor which has a current flowing through it, a magnetic field whose force lines are distributed as follows is generated:

In circuits the inductor is labelled with the letter L and its *inductance*-value is measured in Henry. An inductor is basically a conductor rolled up in a spiral shape. When a current passes through it, a magnetic field is generated whose line forces are distributed as follows:

An inductor can be used effectively as a low-pass filter, by making the most of the magnetic field's inertia. By applying a current with a sinusoidal rate a magnetic field is generated which also has a sinusoidal rate. However, if the frequency is too high, the negative half wave generates a magnetic field with line-forces that are opposite to those generated by the positive half wave which haven't yet had time to run out: the current-flow therefore gets blocked. The following figure shows us an example of a low-pass filter circuit:

By combining inductors and capacitors we can make band-pass filter circuits:

When we apply a signal which contains a variety of different frequencies to a capacitor, like an audio signal for example, the capacitor will react differently to every separate frequency. Moreover, seeing that each component has been built with materials which have certain characteristics, to describe its behaviour we will adopt a quantity value which takes into account these characteristics. This quantity is called *impedance* and is labelled with the letter Z. In a capacitor it has the following value:

Equation 4.3. Impedance of a capacitor

This formula indicates that the impedance of a capacitor depends on frequency. Moreover, it has two components: the first is called *resistivity* and gives the value of the component's actual resistance. The second is called *reactance* and introduces dependency on frequency. Finally the symbol j indicates that reactance is an *imaginary number*. Don't worry! We won't be going any deeper than this. What we have said so far will suffice to understand the significance of these factors in relation to audio signals and their related circuits. Notice that in f=0 (as in direct current), the capacitor's current becomes infinite, simulating an open circuit, whilst in f=infinity the impedance coincides with resistance.

Similarly, in inductors we have an impedance value of:

Equation 4.4. Impedance of an inductor

Notice how in f=0 impedance coincides with resistance, whilst in f=infinity the inductor behaves like an open circuit. From this point of view, the capacitor and the inductor have opposite behaviours.

This component allows current to flow in one direction only. By applying a voltage with a certain polarity at its far ends, we obtain a current flow. If then we apply the opposite polarity, we have an absence of current flow. The following symbol is used in circuits to represent this component:

One particular kind of diode is the LED (Light Emitting Diode). This component has the faculty of emitting a beam of photons (in other words: it lights up!) when a current flows through it.

A transistor is obtained by setting up two diodes in a certain way. It has three terminals: *base*, *collector* and *emitter*.

This is its symbol:

It is used in a variety of modalities and setups. What is interesting from a sound engineering point of view is its amplification functions.

A transistor is capable of supplying power amplification as well as a voltage and current amplification. Let's take a look at a transistor in action.

If we apply a little variation in voltage between the emitter and the base, the current experiences a relatively high excursion on the emitter. A fraction of this variation in the current is gathered by the collector, thus increasing the difference in potential between the base and the collector. So, one little variation in the potential applied between the base and the emitter, produces a rather high change in the voltage between the base and the collector, resulting therefore in voltage amplification.

This kind of amplifier is capable of amplifying the difference between two signals. The following is the symbol used to identify it:

It is commonly used as an input stage for balanced connections [Balanced electric connections ] and in VCA faders [VCA controls ] .

This component makes the most of the *electromagnetic induction* phenomenon^{[6
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of conductors that are coiled up in a spiral. If in the proximity of a coil through which current is flowing, we place another coil, the magnetic field of the first one will take over the second, thus generating a current flowing through the latter. The number of spirals of each coil determines the difference between the two currents and consequently determines the relationship between the voltages at the two extremities of the two coils.

So, a transformer, as its name suggests, transforms one voltage into another. The following figure shows a transformer in which its primary coil has 20 spires and the secondary has 10 spires. If we apply a voltage of 10 V to the primary coil we obtain a voltage of 5 V on the secondary one:

Another important characteristic of transformers is their ability to act as impedance adapters. When connecting two components it is necessary, as we shall see when we go on to speak about the amplification chain, for the output impedance of the first component and the input of the second one to have values that mantain a precise relationship. When we need to change the impedance value (in other words, to make an *impedance matching*), we can recur to a transformer without changing the other electrical quantities. By varying the number of primary and secondary spires we obtain our required final impedence.

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By induction we mean the electromagnetic action of an electric component on another component finding itself in its magnetic field's range of action.

Charge of a capacitor