An equalizer is a circuit which is capable of amplifying or attenuating a certain frequency-range, and to leave others unaltered. At this stage we can interpret the curve which describes the behaviour of an equalizer: a graph of an amplitude-frequency diagram which gets multiplied by the input signal in order to obtain the output signal. Two preliminary examples will further clarify this concept for us.
When H(f) = constant and in particular equal to 1 on all the spectrum. We'll have, according with the latter statement, the following formula:
Y(f) = X(f)
In other words the circuit doesn't act upon the input signal.
When H(f) = 1 in a particular frequency-range, and elsewhere 0:
The result Y(f) is given by multiplying X(f) and H(f). When H(f) is equal to 0 we get Y(f)=0. When H(f)=1, we get Y(f)=X(f). This is a first example of a band-pass ideal filter. Even if this topic shall be discussed in greater detail further on in the course, we can already begin to see how a transfer function of this kind allows us to extract from the input signal only a certain frequency-range (between 5KHz and 10KHz) which in this case is the range we're interested in. It is called Ideal filter because in reality it is impossible to create circuits that have transfer functions which make such brusque transitions. In actual fact these transitions get smoothed and we'll see how the slope rate speed increases as the complexity, and therefore also the cost, of the circuit in question increases. There are different kinds of equalizers, and we'll be analyzing the most important ones in the next sections.
Peak Bell EQ
Its transfer function is shaped as described in the following diagram:
Bell equalizer
This kind of equalizer has 3 controls:
Gain (reduction/amplification- cut/boost)
Acts upon amplitude A of the bell which can be both positive (amplification) and negative (reduction). Maximum amplification is a parameter which depends on the quality of the circuit: to reach 15 dB gain without added distortions requires sophisticated technology. Generally we find this kind of EQ on mixing-desk channels. The more professional the quality of the mixer, the more its EQ peaks allow high gain-levels without added distortion. In medium-quality mixers, usually the gain-levels are of about 12 dB (bearing in mind that between 12 dB and 15 dB we have a doubling of the signal in electrical terms, and therefore the difference is considerable).
Cut frequency (center frequency)
This is the frequency which has the highest (or lowest) gain on the bell. Generally a potentiometer consents it to vary thus allowing to centre the bell precisely in the frequency-zone we intend to manipulate.
Q Factor
This is a parameter which measures the bell's amplitude, in other words, the amplitude of the frequency-range that is being amplified (or attenuated). It is calculated using the following formula:
Q= fc/(relative bandwidth)
where the relative band-width is measured at 3dB below its peak (see previous diagram). The Q factor is independent from the frequency-zone in which we are considering it. This is evident in a numeric example, bearing in mind that the frequency-scale is logarithmic. Between 20 Hz and 100 Hz the width of the relative band is 80 Hz. If we then move to the higher frequencies, i.e 10000Hz, our bell would extend itself between 9960 and 10040 Hz,in other words we'd have an extremely tight bell indeed (which is in fact impossible to reproduce, for plain physical reasons). So, if we only set the relative range-width value and if, with the control of the central-frequencies, we dragged the filter along the entire frequency spectrum, we'd see how the bell tightens as we reach the higher frequencies and widens as we reach the lower ones. Seeing that once they have been set, we'd like the range's width to remain constant along the entire spectrum, we will add the central frequency to the formula as a moderating factor. Let's now see in practice with numbers how the factors involved vary (w=relative bandwidth):
if fc=100Hz e w=40Hz which means that the bell will have a relevant influence on the range 80Hz-120Hz
We'll have: Q=100/40=2.5
if fc=10000Hz and Q=2.5
We'll have: w=10000/ 2.5=4000Hz which means the range going from 8000Hz to 12000Hz
Here it becomes clear to us that it necessary for w to vary if we want the bell to maintain a constant shape along the frequency-spectrum (seeing that we have put a constant Q factor). Because of the fact that fc has been doubled, maintaining the same Q factor, the range has also been doubled, and in this way the bell's shape has remained intact (we mustn't forget that frequencies are represented logarithmically in order to give a more precise representation of perception by a human ear. With low frequencies a difference of 20Hz is relevant, whereas with high frequencies, a difference of 200 Hz is relevant).
Shelving EQ
This type of equalizer is used in order to have control over the extremities of the audible frequency-spectrum. It has two standard controls:
Cut frequency (roll-off): calculated at the point where the gain-curve decays by 3dB compared to its maximum value.
Gain: applies an amplification or a reduction to the signal-range superior to the cut.
Shelf equalizer
Completely parametric: it is possible to modify all three quantities that characterize the bell equalizer: central frequency (fc), gain (A), Q-factor (Q). Professional mixers have a 4-band parametric equalizer on each channel: lows, middle-lows, middle-highs, highs.
Semi parametric: the Q-factor isn't variable, in other words, the bell's shape is fixed (generally Q is set at a value of approximately 1.5)
Peak: fc and Q values are set and it is only possible to act upon gain. These EQ's are the cheapest on the market and are installed on low-quality mixers.
The following diagrams describe the equalizing section of a low-quality mixer compared to that of a high-quality mixer. We can see how the maximum applicable gain is 12 dB in the first, and 15dB (or even 18dB) in the second. Moreover, the frequency-spectrum is sub-divided into 3 bands (Lows, Middles, Highs) in the low-quality mixers, whereas in the high-quality ones we have 4 bands (Lows, Middle-lows, Middle-highs, Highs). Finally, in the high-quality mixers, the gain-curve of lows and highs can take the form of a bell or of a shelf equalizer, allowing it to have still greater versatility.
Equalizer in a non-professional mixer
Equalizer in a professional mixer
A graphic equalizer consists in a series of single bell equalizers. The width of the bell varies according to the operational context for which the equalizer has been designed.
Table 5.1. Classification of graphic equalizers
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Passive equalizers only use passive components which don't require current and therefore cannot bring about a real increase in gain. Generally when gain is at its highest, the signal doesn't change, whereas it gets attenuated when gain is decreased through a potentiometer or a cursor. Their main defect is that they introduce a slight fall in signal due to the loss of passive components. Active equalizers use active electronic components such as transistors [Transistor ] and thus allow a real gain-increase to take place. However, as a result of active circuiting we have higher levels of added distortion and noise coming through, even though this tends to happen only when using low-quality equalizers. Next we'll be looking at comparing the gain-levels of active and passive equalizers:
Comparison between active and passive equalizers
Related topics on Wikipedia
Example of an ideal filter