Introduction

First of all, I would like to introduce myself and provide a general overview of the contents I’ll be developing throughout this article: an insight into some of the interesting work we’ve been carrying out here at Aratechlabs with polar patterns.

I am Daniel Seix, CTO of the company, and while not a sound engineer myself (so not really suitable to give any recording advice), I’ve been exposed to firsthand microphone measurement data and learned some interesting facts about microphone polar patterns that are worth sharing for all of us to enjoy. I will try my best to explain Aratechlabs’s approach to process microphone’s raw technical data obtained from measurements in anechoic chambers, its strengths and weaknesses where they are worth noting, and some use cases and examples.

A special thanks to microphone brands that have kindly provided us with fresh measurement data of the models they wished to include in Arapolarmic , AEA and Audio-Technica . I wish more of them would so helpful. We also measured several of Violet Design microphones ourselves.

Table of Contents

1 – A Simple Microphone Directivity Model.
2 – What Actual Measurements in an Anechoic Chamber Look Like.
2.1 – An Example: Amethyst, Violet Design.
3 – What we can do about it. Generalization.
3.1 – Symmetry.
3.1.1 – Violet Design’s Amethyst Revisited.
3.2 – Angle Correction.
4 – What About Scale?
4.1 – An Example: PRO25AX, Audio-Technica.
5 – Caveats.

A Simple Microphone Directivity Model.

First of all, I will describe a fairly simple mathematical model that explains the directivity behaviour of microphones. I will not dive into it a great depth, just as much as should be useful to follow remaining parts, but I’ve built an interactive applet, embedded at the end of this section, that will let you play a bit with different settings.
You can read more about microphone directivity in our post microphone directivity tutorial.

There are several kinds of microphones, and each model has its distinctive polar patterns, carefully designed to achieve different goals. Here’s an article about Using microphone polar patterns effectively that explains some of this in further detail, with some theoretical background, and also more to the point for those of you interested in actual recording tips.

My fairly simple model approximates the behaviour of a microphone by just considering the part of the capsule intersecting with the plane of rotation: a segment that represents the length of the diameter of a cylindrical capsule, or better still, the width of a rectangular one – or its height, for that matter, should the rotation be vertical, – assuming the shape of the capsule is symmetrical at both sides of the aforementioned segment.

What explains the pickup falloff is the fact that the sound wave reaches each point along this segment at a slightly different phase.

Frequently, part of such falloff is also due to this sonic labyrinth thing. That is something that blew my mind when I first read about it, so I’ve modeled a simple one to play with. A sonic labyrinth is an artifact that forces part of the sound reaching the capsule from behind through a twisted path, meaning that a sound coming from that direction will be phase cancelled by a greater amount.

Included in Arapolarmic’s library there is a microphone model, Violet Design’s The Finger, that has an adjustable sonic labyrinth accessory that they call “the reflection ring”.

It is worth noting that polar patterns often have a hidden part, which depends on the scale chosen to display them. Have in mind that the charts plot negative dB values but distances are always physically positive (never mind if the scale represents from 0 to -20 dB, its length won’t be negative) and being strict about that would be quite confusing. The end result is that any datum below the minimum scale value is trimmed out of the plot for the sake of clarity (more on that later).

A curious fact about those negative scales is that due to the trimming and the logarithmic quality of decibel measures, the same data will take a somewhat different shape at different scales, even though the readings will be the same – that is as long as they lay within the chosen scale, notice that a different subset of data will be trimmed out for each scale.

Click in the image below to access the interactive applet. This applet might be too heavy for mobile devices so it is recommended to run it in computers or laptops.

What Actual Measurements in an Anechoic Chamber Look Like

You might expect that microphone measurements come out exactly as the model predicts, but unfortunately that is not the case. There are many things the model does not take into account, such as the physical interference of the body of the microphone itself, the slight misalignment of the mic respect the theoretical axis in the chamber – even the capsule can be a little misaligned inside its casing, remember that many microphones are assembled by hand, – and whatever issues arising in an experimental environment. The actual data is no longer theory.

An Example: Amethyst, Violet Design

Realize that some plots are not perfectly symmetric, yet we can still get a good idea of what the data are telling us.

What we can do about it. Generalization

It is reasonable to expect some minor variations in the output of each single instance of every microphone model, so if we are going to publish diagrams that are intended to be valid representations of the response of any mic like itself, then some – let’s say – normalization of the data is necessary. For that we have to rely on the theoretical model.

Symmetry

A quick inspection of the mic reveals a cylindrical capsule, so in our ideal world its directional response would be symmetric.

With respect to polar patterns symmetry, a very simple operation is more than enough. It consists of dividing the data in two parts along the zero degrees axis and obtaining the arithmetic mean of the values at each side of it. See the example in the next section.

It looks nice and comfy, but every case must be examined closely as we’ll see later.

Violet Design’s Amethyst Revisited

The result of both halves’ arithmetic mean is certainly more appropriate for representing the output of several microphone items than the original single microphone chart was. It fits the ideal model for all microphones better, while keeping the essence of its unique character.

Angle Correction

There are times, though, where the previous operation reveals a significant change in the shape of the plot. See an example:

The new chart displays wider and shallower dead zones, as well as some little bumps that weren’t there in the first place. Something is obviously wrong.

The original plot shows two outstanding minimum values, one at each side of the axis, but they are averaged at a slight offset from one another in the new one, which is all too wrong – the model we are pursuing is symmetric; it does not have deaf spots at oddly distributed angles.

But how nice, the error is measuring itself for us! A look at the data reveals that the misalignment amounts to -8.1 degrees, and everything makes sense again after the correction:

What about Scale?

I introduced the issue of scale towards the end of section 2, but having a real example will surely enlighten things a bit.

An Example: PRO25AX, Audio-Technica

In this example I have highlighted the parts that would be trimmed out in a dashed line style.

Just by looking at their shape, the -30 dB chart seems to be more directional than the -40 dB one, but remember that they plot exactly the same dataset.

While in a theoretical model the trimming of part of the plot is not such an issue, as readings will sometimes go all the way to -∞, and you can always get the exact value – check it out in the applet; – with real measurements things are quite different. Having a dead angle of nearly -50 dB is quite remarkable and it is important not to leave it out. Just make sure of reading the scale when comparing different charts.

Caveats

This post has shown you a way that allows you to modelize the raw data obtained when, for example, a measurement of a microphone directivity is carried on in an anechoic chamber.

Take into account that this methodology is not related to quality control in microphone manufacturing where measurements are made for many units of them. When statistical process control is applied to determine if there are statistical significant difference between the produced units, other statistical tools and techniques are applied.

Now you can monitor in real time the directivity of microphones in your mobile device using Arapolarmic , through the representation of the polar patterns over the microphone using Augmented Reality.

Take into account that by now we provide symmetric polar charts for a single plane of rotation, the horizontal one, and assuming the response should be symmetric there is no problem using the same plots all around their axis (for example dynamic microphones or most of small diaphragm condenser). But there are special cases.

You should take into account that the body of large diaphragm microphones blocks the sound a bit, so the response from below them will be slightly different.

Another special case are ribbon microphones where the capsule is way higher than wide, so the response in the vertical plane will be more directional. We will try to solve the issue in upcoming versions of the tool.