# Speaker Tests Polar Response by Richard C. Heyser (May 1975)

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 By Richard C. Heyser THE DIRECTIONAL characteristics of a speaker are important in determining not only the modifications in timbre and quality that occur as one moves around in front of the speaker, but also the gross effects of sound reflection due to room and boundaries. Since angular dependence is important to the sound one hears, Audio provides measurement of this property. Because it is almost impossible to find any simple combination of frequencies that will properly represent the way one subjectively perceives the changes of timbre that occur with change of angle, Audio abandoned the conventional practice of plotting amplitude response versus angle for single frequencies. The parameter chosen for angular measurement comes from the fact that most program material is dynamic and aperiodic in nature. No single sine wave measurement could be expected to properly represent such program material. Audio uses the total energy in the 20 Hz to 20 kHz band which a loudspeaker generates for a perfect impulse and plots this as a function of angle. We call this the polar energy. The basis for this measurement is the one-meter frequency response. The square of the amplitude of the frequency response is a measurement of the total energy density for a single frequency, while the total energy for all components from 20 Hz to 20 kHz is the sum of this density throughout the frequency range. This amounts to the area under the curve formed by plotting the square of the amplitude response on a linear vertical axis versus a linear horizontal, frequency axis. To make this measurement, we integrate the square of the frequency response between the 20 Hz to 20 kHz limits. Angular Energy Measurement This energy measurement is a single number and represents how much work could be done against a microphone (or an ear) for a given input power, distance, and angle. This energy value is converted to a logarithmic basis in dB to relate this relative measure of this energy to a familiar form identifiable with psychoacoustic properties. In making this measurement, the speaker under test is mounted on a rotatable platform on an adjustable tripod assembly. The platform is driven by a motor and rotates in a fashion similar to a record turntable, but much slower. A precision potentiometer picks off the angle of the platform, and the pot's output is used to position a pen on a recorder. Each computation of energy takes one second. The plotter is programmed to draw straight lines between each energy value and its corresponding angle as the speaker is rotating on the platform, and a measurement is made every 1.5 degrees. The reference angle for all measurements was arbitrarily chosen as the front axis of the speaker, so that if one is directly in front of the speaker, one is also at the defined zero degree point. Incidentally, this tripod configuration is also used for the anechoic frequency response and the energy-time measurements. As a matter of good practice, the frequency response is observed for every reasonable angle one might assume in listening. Thus, while we normally only present only the zero-degree, anechoic frequency response, we have an excellent idea of the behavior off axis and present any special plots and observations which might be of value. Polar Response Plot The term "polar" refers to the use of a polar coordinate system using magnitude and angle. The magnitude is shown as distance from the center of the plot and is the relative measure of energy in dB. Since this measure is logarithmic, the center of the plot is not zero energy, but some value below peak response, such as -25 dB, since we have arbitrarily chosen zero dB as the value of energy at the outer-most circle of the plot. In making up the curve, the value in dB corresponding to the center of the chart is automatically taken into account. Thus, a curve which passes through or remains at the center of the chart through a substantial angular range doesn't necessarily mean no sound will occur at that angle, but simply that the level of the sound will be at least 25 dB below peak (to use the above example). This is the result of choosing a scale factor which shows the major effects of listening angle change on a chart of reasonable size. Most stereo or quadraphonic program material is oriented either left or right, rather than up or down. For that reason, we plot the energy response in the horizontal plane (or azimuth) in preference to the vertical plane (or elevation) when a single plot is shown. The major sonic effects in vertical angle can be seen in the three meter room response since the floor and ceiling boundaries influence the early sound to a great extent. The polar plot is presented as a view looking down on the speaker so that "leftness" and "rightness" are in proper perspective. Thus, one good way to use this data is to imagine the chart placed on top of the speaker with the indicated front axis aligned with the front of the speaker. Looking down on the chart will show the location of the relative energy levels for wide band material. An excellent test signal to check this is off-channel FM noise, which is quite close to white noise in uniform spectral density after compensation for demodulator de emphasis. One very important characteristic to look for in the polar response is left/right symmetry, and a surprising number of speaker systems are not symmetrical. If no precautions are taken with such systems, they will never be truly balanced in their stereo reproduction when listened to in their normal symmetric left/right placement. The general subjective effect of this will be a badly wandering center-stage stereo image when one moves left or right of center in the listening area. In most cases, this can be cured by rotating one or both speakers to give a balanced sound. A highly directional response is an allied problem that is occasionally observed. Such speakers are generally excellent for corner locations since most listening is then done in an on axis configuration, but they will seldom give satisfactory stereo imagery if flush mounted against a wall and with a wide stereo base. Conversely, a speaker with a "flower petal" polar pattern should not be placed in a corner. The side lobes of radiated energy will scatter off the corner walls and cause severe interference with the direct sound. Strange peaks and dips in polar energy, particularly if they are not symmetric about the front axis, indicate diffraction or scattering. The fronts of all too many speaker enclosures are designed more for cosmetically pleasing lines than through proper acoustic theory, perhaps because one looks at a speaker for longer periods of time than one listens to it. These acoustic blemishes frequently show up in the polar response, and if exceptionally bad, they may result in listener fatigue and general dissatisfaction with the stereo or four-channel image. Acoustically hard reflecting surfaces should be positioned in line with polar energy peaks only if substantial sound scattering is to your liking. There are many who prefer the broad-base stereo effect due to such reflections, and some speaker systems are designed with this type of reproduction as a goal. Many other listeners prefer a less-diffused sound image. Regardless of one's taste in the matter, the polar energy plot is an indicator one can use to decide if a speaker is compatible with the room in which it will be used. Phase II IN KEEPING WITH the finest editorial traditions of Murphy's First Law, it seems that my December Audio article describing loudspeaker phase measurements was printed out of phase. The paragraphs defiining the term "minimum phase" were split apart and redistributed so that the intended conclusion of the article was tucked neatly into the central portion of the text. The type gremlins also scrambled a point I was trying to make about the fact that it is not necessary to have a peak in speaker response in order to have the sound we call a resonance, but that we can also have this sound due solely to certain types of phase changes even if the system measures "flat." apologize for any confusion which these errors may have caused. (And I apologize both to our readers and to Mr. Heyser for these errors. Those who would like a sheet showing the correct order of the article's paragraphs should write me. -Editor.) Importance of Phase After many decades of being ignored, phase response is now becoming acknowledged as a very important consideration in high quality sound reproduction. Audio has received several letters requesting some description of the physical aspects of non-minimum and minimum phase response networks. In partial repayment for the inadvertent confusion the disordering of my phase response article may have caused, I would like to summarize two very important physical reasons why it is important to know if an audio system is of minimum-phase type in its reproduction. First is the consideration of accuracy in the reproduction of transients. If a system is minimum phase, then the best transient response always occurs when the frequency response is adjusted to be the flattest possible. Most amplifiers are minimum phase; most loudspeakers and magnetic tape recorders are non minimum phase. Second is the consideration of naturalness. The sounds we hear in our everyday experience contain subtle cues which we use to identify naturalness. All of us from birth become very adept at processing this "software" without ever realizing we are doing this. If an audio system alters these cues in such a way that they are contrary to what is expected from natural sound, then we may find the reproduced sound to be unnatural. Such alterations can occur with non-minimum-phase transmission systems. If, for example, in reproduced sound the overtone structure from every instrument in an orchestra is heard slightly before the musical fundamentals which give rise to these overtones, then we may sense that something is wrong with the reproduced sound without really being able to say exactly what bothers us. It just doesn't sound natural. There are other physical considerations of minimum-phase behavior but any discussion of them or even an elaboration on the details just outlined would fill a good-sized book. -R.C.H. --------------------- (adapted from Audio magazine; May 1975) Also see: IM Distortion in Speaker Systems (Mar. 1976)
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