Other than dead silence, feedback must be the most hated thing in professional audio. Feedback has been with us since the first microphone was placed in front of a speaker and is something every audio technician learns to manage. As long as loudspeakers are returning sound information back to presenters and performers the potential for feedback will remain. This month, we’ll define the cause of feedback, and then see how some aspects of monitor speaker design can contribute to causing feedback.
Feedback Defined
One can ask for feedback on a presentation, set the feedback percentage for delay effects, use “negative feedback” in an electronic circuit or anger a singer with a squealing monitor wedge. In all definitions of feedback, the core concept hinges on the return of information, electrical signals, or sound waves back to the original source after a period of time. For the delay effect, the feedback may arrive many tens or hundreds of milliseconds (ms) after the initial signal. By contrast, feedback in an electronic circuit (such as an opamp) is returned back to the source nearly instantaneously. Sound returning back to a microphone from a monitor lies somewhere in between, usually taking a 5 to 15 milliseconds.
Feedback is defined as follows. Return some component of the sound after a period of delay and subsequently re-combine the returned signal with the original source. Three key parameters then define the nature of the interaction between the original and returned signal. These are the phase shift, polarity and gain relative to the original signal. Feedback in the audio world will occur at a specific frequency will occur if three things happen:
• First, the frequency must be in phase, or nearly in phase, at the point where the original signal and returned signal meet. If the return signal is out of phase with the initial input, it will cause cancellation, not reinforcement, and feedback will not occur.
• Second, the polarity of the two signals must be the same. If two signals arrive in phase, but the polarity of one is positive (+) and the other negative (-) they will cancel.
• Third, the amplitude of the frequency must increase with every trip around the feedback “loop.” Another way of saying this is that the gain for a feedback frequency, as it makes the loop from wedge to microphone over and over, must remain greater than one.
As an example, if the gain of a loop is 1.5, the signal feedback signal will be 1.5 times the original on the first trip around the loop and 1.5 x 1.5 = 2.25 times on the second trip around the loop. On the tenth trip around the feedback loop, the gain is almost 58 times the original signal! This explains why a feedback frequency can get very loud very quickly.
Let’s compare what happens in an electronic circuit with what occurs in a monitor wedge to understand further how these three concepts (phase, polarity and gain) work together in defining feedback. For electronic circuits, the phase shift is very small for all audio frequencies, because the delay around the loop is essentially zero. Often times the gain of the electronic feedback signal is substantial. The reason one can send a “hot” signal back into the original circuit is that the electrical polarity is negative, or inverted, relative to the original signal. Fed back into the circuit, the inverted polarity signal acts to correct distortion and improve the circuit behavior. Feedback is a good, useful thing in many circuit applications.
By contrast, the time it takes sound to travel in the air between the monitor wedge and the microphone causes a propagation delay of a few milliseconds — an eternity in electronic circuit terms — but very short in human terms. This delay introduces phase shift and that phase shift is different for every frequency. For a given delay time, low frequencies that have long wavelengths experience low phase shift. High frequencies, with their shorter wavelengths, experience more phase shift.
Due to the delay from monitor to microphone, all frequencies arrive at the microphone with different relative phases. Some frequencies will end up completely in phase, some will be completely out of phase, and some will fall in between. Changing the polarity from positive to negative will only cause a swap of which frequencies are in phase and which frequencies are out of phase. This means a polarity swap will reduce some feedback frequencies at the expense of causing other ones. That said, polarity swap between adjacent wedges is sometimes effective for mitigating low frequency feedback when there are multiple open microphones.
A monitor wedge and microphone combination has comparatively low gain, meaning the typical cardioid microphone doesn’t pick up as much of the monitor’s volume. This means the gain between the monitor and microphone is usually well below one. The point where feedback begins is where the gain between wedge and microphone increases over one.
Shortly before a wedge “takes off” into full-blown feedback, you will often hear a hollow “ringing” sound. The ringing from a monitor that occurs just before feedback happens as the gain between monitor and microphone creeps upwards towards unity. The closer the gain is to unity, the greater number of repeats between the wedge and microphone required for the frequency to die out. Consider an example where the gain is 0.95. After 15 round trips, the gain is only reduced to 0.46. It takes 45 cycles between microphone and monitor to reduce the gain to 0.1. If a monitor is consistently exhibiting the ringing immediately before feedback, a slight change in the performer’s location, a music stand, air temperature, or humidity might be enough to send the wedge squealing.
Driver Effects on Coverage Pattern
Now that the conditions for feedback are clear, we can discuss how the design of monitor loudspeakers influences the likelihood of feedback. We already mentioned that swapping monitor (or microphone) polarity has little overall effect on feedback. Similarly, while we have some control over the gain through microphone choice and placement, eventually the wedge can be turned up sufficiently to feed back.
This leaves us with phase shift effects from the loudspeaker’s design to influence how feedback proof a monitor will be. More specifically, the differences in phase shift that result from the directional behavior and the physical spacing distance between the low and high frequency loudspeaker transducers.
At low and mid frequencies, the wavelengths of sound are several feet long, much bigger than the driver diameter. As the frequencies get higher, the driver’s dimensions become comparable to the wavelength of sound being reproduced. At 1,200 Hz, the wavelength is about one foot, or approximately a driver diameter of the typical 12-inch monitor wedge woofer. In this frequency range, the driver’s coverage angle starts to narrow. As frequencies get higher, the driver grows progressively more directional.
The driver becomes more directional because of phase shift, specifically the phase difference between sound that comes from different points on the speaker cone. Imagine standing off to the left of the monitor woofer and listening. Sounds from the left side of the speaker cone will arrive sooner than sounds from the right side of the speaker cone. This is because you are farther from the right side of the speaker cone than the left side. At low and mid frequencies, this difference in distance is of little effect. The wavelengths are long compared to the cone diameter and therefore the phase difference is minimal. However, when the wavelengths become shorter, comparable to the dimensions of the cone, the phase shift between different points on the cone becomes greater. The radiation of the left and right side of the cone is now less in phase, and the result is that the woofer’s coverage angle starts to narrow.
The directional response of a compression driver and horn is even more complicated at 1,200 Hz. Generally the horn will have less pattern control at 1.2 kHz than at higher frequencies. Unfortunately, the way the directional control changes at as the frequency increases is complicated, and will be somewhat different for every high frequency horn design.
Adding the Crossover
It also happens that 1.2 kHz is approximately the crossover frequency between the woofer and the horn in a typical high end monitor speaker. The loudspeaker designer therefore has to combine a woofer with narrowing coverage and a horn with widening coverage in a way that provides the smoothest possible coverage through the crossover point, which is a region where both drivers bear the burden of reproducing sound.
Even if the loudspeaker designer is very skilled, and mates the drivers with differing coverage patterns in the best possible way, there remains the matter that the drivers are still separated a physical distance at the crossover point. As you move the microphone in the vicinity of the loudspeaker wedge, you change the relative distance from each driver, and therefore the relative phase shift relationship between the drivers. In some locations the drivers will be more in phase, and in other locations they will be more out of phase, all depending on the relative distances between the two drivers and the microphone.
These phase shift effects are best illustrated graphically. Let’s look at three figures to make the frequency response differences due to driver spacing more easily understood. Each figure represents a two-way loudspeaker with the horn mounted next to the woofer. There are four plots in each figure:
• Upper left plot shows the individual drivers’ frequency response
• Lower left plot is the horizontal coverage pattern of the speaker viewed from above
• Lower right plot is a 3D projection of the horizontal response coverage
• Upper right plot is view the horizontal coverage pattern on end
Fig. 1 represents the directional response of a Linkwitz-Riley 4th order filter (LR4) with perfect point-source drivers. Fig. 1 is the idealized case for directional response between two separated drivers. Notice that the coverage is by no means uniform everywhere. There are substantial dips at specific listen angles, but the maximum response is on-axis. As our sources are physically spaced apart, this represents best our speaker coverage pattern can be with point source drivers.
Fig. 2, by contrast, shows the same LR4 filter with real drivers. The summed response is awful, there is now a giant hole in the response almost directly on-axis. This demonstrates that textbook crossover filters, when coupled to real world drivers, can often produce unsatisfactory results.
Finally, Fig. 3 shows the response of the real world drivers using carefully designed crossover filters. The end result is similar to Fig. 1, but the crossover filters bear no resemblance to the simple LR4 case used in Figs. 1 and 2. One filter is second order; the other is third order and overall, it’s a more complicated system. The end result requires substantial loudspeaker design knowledge and measurement to achieve. Still we have not eliminated the location-dependent phase shift effects, but minimized them as much as feasible.
Conclusion
We have systematically defined feedback, and discussed the factors that cause its occurrence. We then discussed how loudspeakers have changing coverage directly in the frequency region where crossover points are common. Finally we showed how the combination of loudspeakers and different crossover filters can produce dramatically varied response results based on listening position.
A fair question to ask, in light of the graphs above, is why not exclusively use coaxial monitor loudspeakers? As a coaxial system places both drivers as physically close together as possible, that solves all our problems, correct? Unfortunately, the decision to use coaxial transducers is not so clear-cut. Coaxial designs can have more limited power handling and narrow coverage at certain frequencies. While certain aspects of coaxes are advantageous for monitors, they are not a monitor panacea.
Monitor engineering is a messy business. The monitor mixer is responsible for many different mixes, battling feedback, communicating with performers and presenters, and generally juggling chain saws. It is tempting to utilize wedge loudspeakers of questionable pedigree for monitor duty, when in reality monitors should probably be the most carefully designed loudspeakers in a production company’s inventory. Low stress, feedback-free shows are worth the expense of investing in carefully designed monitor speakers.
Phil Graham is FRONT of HOUSE’s regular technical contributor and resident scientist.
Images courtesy of Charlie Hughes at Excelsior Audio/excelsior-audio.com.
