# Measuring the frequency response of a loudspeaker

Note - this application note is a few years old.  The Pico ADC-216 mentioned has been replaced by the PicoScope 4262.

## Introduction

This application note describes a simple method for measuring the frequency response of a loudspeaker using the Pico ADC-216 oscilloscope. Normally, specialist equipment is needed to make these measurements due to the problems of echoes in the measuring environment. The method described here takes advantage of the triggering modes and built in spectrum analyser of the ADC-216 running with PicoScope.

## Basic theory

The output of a loudspeaker is difficult to measure because it has to be done with a microphone. Measurement microphones are usually omnidirectional which means that they pick up, not only the output from the loudspeaker, but also any background noise and sound reflected from objects around the loudspeaker.

This means that echoes from the walls of the room where the measurements are done corrupt the direct output from the speaker. One solution to this problem is to build an anechoic chamber—a very expensive option. Another technique is to make the measurements outdoors with the test speaker and microphone at the top of a tower. This works well, but only on sunny days when there is no background noise.

A third alternative becomes possible if we can capture the output from the loudspeaker as a digital signal. Once the acoustic signal from the speaker has been digitised it can be analyzed mathematically. Suppose that we feed an impulse into the loudspeaker. The Fourier transform of the impulse is the frequency response, a sum that can be done easily in a computer. So, if we capture the impulse data we can find the frequency response of the loudspeaker. The trick is to choose which part of the impulse to transform. By deliberately truncating the ‘tail’ of the impulse we can effectively cut off the reflections since these arrive at the measurement microphone later than the direct sound. The reflections are removed by a window in time.

This windowing technique is very powerful and is used in many commercial loudspeaker measurement packages. Its chief disadvantage is that it is difficult to calibrate the microphone to show the absolute sound pressure level measured. This is because of the mathematical technique used (FFT) combined with the normal methods for mic calibration (use of piston-phones and so on). Even so the method produces good relative measurements.

If you need to make a set of measurements for comparison you must use identical settings for each. Otherwise the relative levels that you record will not be comparable.

## Measurement considerations

There are a few fundamental rules that apply to this form of measurement.

1. The time to the first reflection determines the window length. This is fixed by the size of the measuring room.
2. The window length determines the low frequency cutoff. The low frequency cutoff of the measurement is always greater than the reciprocal of the window length.
3. Because the data that is captured and processed has a constant number of points per Hz there arevery few data points in the lowest octaves of the measurement. Half the data points will be in the top octave.
4. The width of the impulse determines the bandwidth of the measurement. The wider the bandwidth required the narrower the pulse must be.
5. The energy in the pulse is determined by its width and height. A wide tall pulse will contain more energy than a short narrow one.

Follow this link to see the measurement details.

## Notes on the equipment

Follow this link for notes on the pulse generator and microphone.

## Testimonials

• The kit (2408B) is of obvious quality, easy to setup and calibrate and the free to download software has a reasonable learning curve. Superb kit, superb support, what more can I say.

Rop Honnor
• I have been using my 4224 PicoScope for years. I travel abroad so this has been ideal due to its physical size. Storage of waveforms on my Laptop is very easy allowing me to quickly email waveforms to my Colleagues.

Andrew
• Not many USB scopes works on Win & Mac & Linux too, so that proves me that guys from Pico really cares about us, customers. This made my decision much easier when I was looking to buy an USB scope.

Raul Trifan
• We have been using Picoscope 6404D for quite some time, and are amazed by its accuracy and powerful emulations while working with numerous signal evaluations.

J Mohanty
• PicoLog TC-08: This is a very nice unit that works consistently and reliably.

Jeff Hulett
• It is a great scope. I had a weird problem - it did not work on one of my PC’s. Customer service gave me first class service. If I could give 6 stars for customer service - I would do so.

Niels Larsen
• Perfect Partner for Development of Encoder controlled Stepper Motor Actuators. Since the included software is really stable, this type of device is a great tool for great tasks!

Helmut Schoettner
• A superb piece of equipment worth its weight in gold

Nigel Clinch
• So simple to use & beats any other I have ever used hands down.

John D Samsing
• Rather than webcam our benchtop scope screen, it was suggested we use a PicoScope to share waveforms via screen share.

We were a bit hesitant at first … but it worked flawlessly, and everybody is now out shopping for PicoScopes!

T Lövskog • SVP of Innovation at Additude AB
• Great functionality in a compact size. I really like moving the mouse pointer to a position and having the Time and Voltage display the values at that point. Calibration equipment is a breeze with that feature.

Don Horein

PC oscilloscope and data logger products