Directivity pattern: how to interpret the radiation pattern of speakers

You are only able to precisely plan a PA system if you know the radiation pattern. For only then it is clear which area the speaker covers within its radiation angle. Expert planners often speak of a 'nominal radiation angle', because the radiation angle always relates to a specific frequency. This is necessary, as low frequencies radiate differently from high frequencies. A ground rule is, the higher the frequency, the more directional is the radiation pattern of the speaker. 

The radiation pattern of clusters

The radiation pattern is particularly important if several speakers are supposed to form a cluster. This is almost always the case when several speakers have to cover a specific area from one direction. If you know the radiation pattern you can arrange the speakers in a way that ensures continuous volume on as broad a front as possible. The radiation angles overlap in a way that the sound adds up and no gaps can occur in the cover. For this, a constructive (not destructive) interference is required. Sound waves must not cancel each other out, e.g. because speakers are offset on stage. A couple of centimetres can make the difference between constructive and destructive interferences. Here, the so-called sweet spot is particularly important. That is the area in which people can move about without significantly changing the sound of a speaker. The most important methods to display the radiation pattern of speakers are polar plots and isobaric charts.

In the polar plot, we see 3 values whose interaction is interesting for the positioning of wall speakers. 

1. The (in this case horizontal) radiation angle: 360°, circular
2. The volume in dB: the further out on the circle, the louder the speaker. In our example, each additional inner circle represents a decrease of 6 dB.
3. The frequencies: each colour indicates one test frequency. 

How to interpret the polar plot 

At the northernmost point, i.e. precisely horizontal central in front of the device, speakers are the loudest. Our example shows that even at an angle of 30° to both sides almost all tested frequencies are of consistent volume. Only at 4,000 Hertz the volume decreases slightly. Typically, the low frequencies radiate specially wide. To be precise, if a person stands about 60° to the right of the speaker they will hear a sound with the frequency of 1,000 Hertz just about 5 dB quieter than someone standing right in front of the speaker. A ground rule indicates, a loss of more than 6 dB is too high to say a speaker covers that area. Thus, the speaker in our example has an effective radiation angle of 140° (70° in both directions on the circle). In this case, you can specifically use sketch and protractor when planning PA systems in rooms. The vertical radiation angle can be neglected if the ceiling is of normal height. When dealing with acoustically challenging rooms (halls, houses of worship etc.), it can be beneficial to use speakers which are vertically highly focussed, because they induce fewer sound reflections from floor and ceiling.

In an isobaric chart, we can see the angles on the Y-axis, often marked as 'deg' for degree. The X-axis shows the frequencies. Coloured areas indicate how strong frequencies are in individual radiation angles. In this case, the colour code is graded in steps of 3 dB, from warm colours (no or little loss of sound level) to cold colours (significant loss of sound level). 

How to interpret an isobaric chart

In our specific example you can see that frequencies before 400 Hz are the lower midrange. We perceive this range as specially warm and pleasant. In the example mentioned above, the speaker here only loses 6 dB at a radiation angle of 200°. Therefore, the tested EUL-80 is clearly a speaker with strengths in the bass range and lower-midrange and the lower and middle treble between 4,000 and 6,000 Hertz.

With our magazine for PA technology we hope to make the work of installers, expert planners and newcomers easier and provide inspiration for practical applications and planning. You can also browse through PA-related topics or read here how our colleague Frank Kuhl optimises speaker series for you.