Configured speaker systems come with a number of specifications that are important to consider at design stage. This seems like a good place to start, as the engineering is intended to optimize for these parameters. The following table lists some of these parameters using the Adam S3H as an example.
Why the Adam S3H? Because I am an Adam Audio (and Dynaudio) fanboy. They have excellent monitoring systems. Furthermore, Adam and Dynaudio thoroughly publish their lab data to back up their claims. This means that it serves as excellent learning material.
In all fairness, I would have liked to use Dynaudio as an example however, the files do not display the information in a way that is as useful for this particular article. It is highly likely that we will use Dynaudio and Genelec as examples in later articles. All images used in this article are from the Adam S3H product page.
Adam S3H Overview
The S3H is an active midfield Studio Monitor. It is comprised of two 7″ woofers, a 4″ mid-range driver and a ribbon tweeter (for high frequencies). The system also uses two ports for extended bass response. Let’s get into some system specifications. A complete system specification is available on the product page.
Frequency Response and Spectragram
The frequency response of a system is defined as a ratio of the output to the input as a function of frequency. This is also sometimes known as the magnitude-frequency response. It is given so that a user can have some indication of how a system will perform over the range of human hearing (20 Hz – 20 kHz). It is quite possible to create a system that is strictly concerned with human speech and the associated bandwidth (250 Hz – 6 kHz). Furthermore, there are lab playback systems for microphones and speakers that are meant to work within the the range of human hearing, strictly above (supersonic) and strictly below (infrasonic).
The plot above corresponds with the frequency response of the Adam Audio S3H. The frequency response of high performance systems, is usually accompanied by a ± dB value and a normalized and averaged frequency plot. The value of ±3 dB or less is considered the goal for high fidelity systems as larger deviations are perceptible to human listeners, especially in critical listening environments. So a question worth considering is: How precise do you really need to be with your speaker system? As we will see very soon, this ±3 dB value is valid for the listening position depending on a few factors including the direction the speaker is radiating. 
A related measurement to the frequency response is a spectragram. A spectragram shows the frequency response over time of some waveform. In this case, the waveform is the impulse response which is the result of taking the inverse FFT of the frequency response. If you do not understand what impulse response is, please feel free to look at my previous articlewhich is about impulse responses in the digital domain. The same theory and application still applies.
This spectragram reveals that the lower frequency values of 50 Hz decay out to >20 ms. This is for a few reasons but, I suspect that the main contributing factor is the two ports used for extending the bass response. The physical phenomenon will be discussed in another article. Essentially, ports act as resonators and this is the downside of using them. This can also be displayed by a waterfall plot (below) but I find this less useful even though it shows the full decay envelope. 
Directivity matters when designing a speaker system and it is largely dictated by use case. As an example: Public Address systems at ball parks and train stations are arranged to use speakers of a given directivity. The highly directional response is required so that late acoustic reflections at a number of listening positions do not interfere with the direct sound such that intelligibility of the broadcast signal is compromised. Another example is speaker arrays acting as one source in live sound rigs.
Highly directional speakers are not always the best fit for a given use case. In the case of high fidelity systems such as studio monitors, the implementation within a critical listening environment is the key factor. That is to say that studio acoustics, should be created/designed with consideration to a specific monitoring system and its directivity as well as the frequency response. Ideally, these systems are custom fits every time. So the questions is: What is the playback configuration that this speaker will be used in? Will this be used within a speaker array such as for live sound? Will this be used within a surround sound setup? Is this speaker meant for far field or near field monitoring?The S3H is a midfield monitor.
The horizontal plane directivity and vertical plane directivity are shown in the following figures.
One of the reasons I like Adam Audio is that they create great speakers at a great price and they actually give measurement data sets associated with a given design. I just want to take a moment to point out some key characteristics of this monitor and why these plots exhibit these general behaviors. The testing methods involved for speaker systems will be discussed at length in a future article.
A relative angle of 0° is also known as on-axis. This is the response of the speaker facing a listening position that is directly in front of the speaker. We can assume that the distance between the source and the receiver for this plot is 4 meters (the same distance specified in the frequency response chart). From a broad perspective we can see that the ±3 dB holds true for the on-axis measurement position (as is in keeping with the frequency response chart above). However, ±3 dB does not hold true if we are standing at a listening position that is 4 meters away from the speaker and to the side of it at the relative angles of ±30→±180°.
There are a few contributing factors to the creation of this directivity response. Overall, the uneven distribution is due to a few main factors   :
- A speaker driver does not radiate consistently over a directivity range of ±180°.
- A speaker driver does not radiate uniformly over the range of frequencies.
- The drivers that make up a speaker system will cause interference effects at a given point in space. (This is why driver alignment is important.)
- The drivers may not radiate in phase. (This can be compensated for in some crossover network designs to a degree.)
- The wave produced by a driver is also reflected off of the enclosure yielding further interference effects. (This is why enclosure design must be simulated carefully.)
This means that the wave (as it arrives at the listening position) over the range of listening positions, will be subject to a number of interference effects and a given driver may not radiate sound in a given direction, at a given frequency at all. The fact that the ±3 dB aspect of the S3H holds true for a horizontal and vertical distribution within ± 15° makes this monitor an excellent choice for a midfield monitoring solution in stereo and certain surround formats. This recommendation only holds true as long as your listening environment’s acoustics is catered to this specific speaker.
You may notice that for the horizontal directivity plot, there is a narrowing of the radiation at 2 kHz. It is not obvious as to why this occurs there but the result is that this monitor (in a given speaker configuration) has a constrained sweet-spot for a listening position. Outside of that sweet-spot there exists an audible drop in response for that narrow bandwidth. This introduces coloration and inaccurate monitoring for the user. In the vertical directivity plot, there exists a narrowing at 3 kHz. This corresponds with the cross over frequency of the mid-range driver and the tweeter. Again, this will introduce coloration outside of the listening position. 
You may notice that this plot has a lower frequency limit of 100 Hz. This is due to the fact that a 100 Hz wave has a wavelength of roughly 3.4 meters. At these wavelengths, we can assume that a speaker system (or a given driver) acts as an omni-directional source as the wave can diffract around the enclosure and certain interference effects are minimal. Conversely, the speaker acts with more directional/specific radiation characteristics at higher frequencies as the wavelength is smaller than the enclosure or the driver. This is why, as the plot tends towards 20 kHz the drop in off-axis response is more exaggerated.
Phase Response and Group Delay
In loudspeaker systems, the audible frequency range is created by combinations of drivers. That is to say that low frequencies are produced by a woofer, mid ranges are produced by a smaller woofer and high frequencies are created by a tweeter (which takes a few forms). How these devices work will be discussed in another article.
*** This section will be difficult if you do not understand anything about Fourier Analysis of signals and basic signal analysis. Click the link to read my other articles on these subjects. This section really deserves its own article. I aim to create a separate article that teaches this particular aspect in accordance to digital filter design.***
Every device that takes an input signal (like a speaker) and produces some corresponding output (like a speaker) may or may not affect the amplitude and phase of the sinusoidal component frequencies of that signal. This can be illustrated using a phase-frequency plot. 
Speaker drivers are not linear phase devices. This means that different component frequencies of the input signal will experience differences in phase at the output. This is especially important when these signals are summed (at the listening/receiver position) as the interference effects may affect the frequency response. Due to the fact that speaker drivers cannot occupy the same physical space on the speaker, then the drivers must be carefully aligned. Furthermore, the input signal may have to be compensated for in order to achieve linear phase.
Linear phase simply means that (across the entire frequency spectrum of interest), the phase alternates between –nπ and nπ as a single straight line with an arbitrary slope. n is simply an integer multiple. Usually this phase gradient is represented as a wrapped slope between -π and π.
Why is linear phase important? In short, linear phase systems preserve the shape of the input signal. Luckily, humans are not highly sensitive to changes in phase response (insofar as it does not dramatically effect the frequency response) for normal playback use. The task of achieving linear phase is almost impossible with speaker systems, let alone single drivers. However, I want to point out an amazing feat of engineering from the team at Adam Audio. The phase curve is near linear at the cutoff frequencies of 250 Hz and 3 kHz.
An associated metric with phase response is group delay. Group delay is the delay time of the amplitude envelope of sinusoidal component frequencies. This can be an audible to the listener. If the delay time is constant (for a given range of frequencies), then the effect is inaudible over the range of frequencies. Usually frequencies will have relative differences in delay time. 
If this characteristic is audible it is commonly referred to as time-smear. It turns out that audibility of this is not constant over the range of human hearing. Here are some known values of the audibility of delay time over the range of human hearing.
- 8.00 kHz : 2.0 ms
- 4.00 kHz : 1.5 ms
- 2.00 kHz : 1.0 ms
- 1.00 kHz : 2.0 ms
- 500 Hz : 3.2 ms
This data was first compiled in 1978 by Blauert and Laws . Unfortunately, there is nothing more recent or specific to verify or contest this. So the question for you as an engineer is: Is this group delay audible and does it conflict with the average use case? Is this phase response corrupting my frequency response and can I counteract any behaviors in order for any effects to be less audible?
Total Harmonic Distortion
Total Harmonic Distortion (THD) is a metric that can be used to estimate the degree to which a system does not accurately reproduce the input signal. Systems such as guitar cabinets may actually use this within the design but high fidelity systems such as the Adam S3H aim to keep this figure as low as possible. Sometimes you will see THD+N which further considers Noise internal to a system.
I do not wish to discuss the measurement method for this metric in this article. However, I want to give a fundamental overview of what THD is. THD is measured for a given frequency by comparing the input wave of a single frequency (a sine wave) to the output. Sometimes, the system produces harmonics (or inharmonic partials). The amplitudes of each added frequency component are combined (at the output). Usually this is turned into a percentage of the input value. THD+N is the result of measuring the output signal excluding energy at the input frequency of interest.
The plot (above) by Adam Audio actually shows the THD over a range of frequencies. This plot also shows some other distortion metrics, however, these are not commonly measured or published in metrics. Please note that the y-axis scale is reported in dB relative to a 1 Va input. 
This plot shows the level of THD when a signal of 1 Va is used as input. This yields a 90 dB SPL output for this speaker configuration. In other words, when a 90 dB SPL signal is created by the speaker, then at 1 kHz (example) the THD of the input signal is roughly 65 dB below. This is likely inaudible. Manufacturers sometimes publish THD as a percentage or in dB values. Also, some manufacturers give THD at 1 kHz while other give for a frequency band.
Transducers, and therefore whole speaker systems, are not linear devices (or anywhere close to it). They will exhibit these distortion effects over a range of amplitudes and frequencies. The key role of the amplifier and crossover network is to compensate for this or stop the driver from operating in the ranges of amplitude and frequency that cause this. As a designer you may ask: How much of this can I really afford? Where will it occur? How can I mitigate this behavior?
Power Consumption, Weight, and Size Constraints
Perhaps the first thing that comes to mind for most system designers is the physical constraints on a system. Not everyone has the space requirements to fit two Adam Audio S6X’s. As beautiful and truly awe inspiring as they are it might not be practical for most listeners. The speakers are 97kg each and 940mm x 720mm x 490mm.
Design matters and the fundamental questions are: Who is using this speaker system? Why is this speaker system being used? What are the environmental factors that my speaker system may be subjected to? Humidity, dust, portability, method of power are all important and are a root cause for many design trade-offs.
Electro-acoustics is a study at the crossroads of certain classic engineering disciplines. Therefore, it is common to find mechanical, electrical and acoustics engineers working together to design a given system. The specification of high-fidelity systems can offer anyone new to this sub-domain a general set of considerations when designing a system.
Design dictates performance and user experience. Therefore, it is important to know what you need from your electro-acoustic system. In the next article for this series, I want to explain measurement methods for electro-acoustic systems. How can we objectively compare and contrast systems? What are some key factors that one may consider in design? What should I expect to see when I measure a system? Until then:
Be good to each other and take it easy…
Will Fehlhaber is an Acoustics Engineer and Audio Programmer from the UK and Bay Area.