Step response in audio

The loudspeaker step response is a plot derived from the impulse response, and holds useful information regarding the quality of the loudspeaker. The step response is a qualitative measure of a loudspeaker’s time coherence. Usually, an audio system is comprised of more than 2 drivers. Depending on their position on the baffle, and the position of the acoustic center of each individual speaker, they might be, or might not be, aligned.

For example, let’s imagine a 2-way speaker with a tweeter and a mid-bass. If the sound from tweeter reaches the listener first, and the sound from the mid-bass reaches the same position, but after a short delay, then the two drivers are not time coherent. Some people want to reach for the perfect time alignment. Some argue that a small delay between the drivers doesn’t affect the perceived audio quality of the system. Regardless on which camp you are in, a loudspeaker step response measurement will give you the facts.

Typical step response plots

Before I make the step response measurements, let’s analyze some charts that you will typically bump into.

loudspeaker step response

This is a typical chart you will see on a 2-way speaker. There is an initial sharp positive peak in the step response, followed by an undershoot, and then, a larger, more slow rising, positive peak. The first peak is produced by the tweeter, and the second is produced by the mid-bass. Although the drivers are connected with the same polarity, and the speakers are placed flush on the same baffle, their acoustical centers are not aligned. The speakers are not time coherent, and the mid-bass lags the tweeter by a few fractions of a millisecond.

This 2-way loudspeaker step response is very common. Although there is a short delay between the two drivers, don’t be surprised if you will find such response on expensive loudspeakers. Achieving a perfect step response, might compromise the frequency response. As a result, most manufacturers tend to not shoot for perfection in this area.

Let’s take a look at another example that is also common :

step response single driver

You might find this step response plot in 2 situations :

  • You a measuring a single speaker driver. There is an initial peak, and no follow-up, because there is no additional driver.
  • You are measuring a loudspeaker which has the speakers perfectly aligned. There is only one peak in the step response because the speakers are time coherent. You can consider that the 2 peaks overlap. This is the perfect step response some strive for : “the right triangle” step response.

Prerequisites

Before we get to the actual measurements, you will need some measuring equipment. This is what I used :

  • Dayton audio EMM-6 – Budget microphone, good quality, comes with calibration file. Around 50$
  • Focusrite Scarlett 2i2 – Good audio interface , 2 inputs / outputs, 96 kHz sample rate. Around 150$. Other sound cards can be used, regardless if they are internal or external.

The setup is exactly like you would make a frequency response measurement. I already wrote an article on How to make a full range frequency response measurements using ARTA. Basically, place the microphone at 1 meter and do an impulse response. From the impulse response you can derive the frequency response, but you can also extract the step response.

Loudspeaker step response measurement using ARTA

To serve as a device under test, I’m going to use the 2-way loudspeaker I recently made. You can find more info about it here. But let’s return to the loudspeaker step response measurement. Basically, if you read the article linked above, you’ll be able to make an impulse response measurement using ARTA. And your screen should look like this :

impulse response arta

You can see at the top, I circled the button you need to press, to switch to the step response window. After maximizing that window, it should look like this :

step response audio

Next, we have to zoom in on what we are interested in. This is the first section of the graph. You can fiddle with the controls, or follow these exact instructions :

  • Gain up 2 times.
  • Click Max Zoom 2 times.
  • Scroll left 5 times.

Then the graph should look like this :

zoomed step response

Now we have a front row view of the step response. We can left click and right click to place markers. ARTA will show the exact time between the two markers. As a result, if we place a marker on the first peak (tweeter) and another marker on the 2nd peak (the mid-bass), we can extract the delay between the 2 drivers.

step response markers

As you can see, the delay between the 2 drivers is 0.3 ms. This is not a perfect step response. But, if you read the article describing the build process of this pair of loudspeakers, you can see that both drivers cancel each other out at the crossover frequency. You can observe a null in the frequency response, if you reverse the polarity of the tweeter.  Trying to achieve a better step response will result in a deeper null, but that doesn’t mean that the audio quality of this speaker is degraded.

Step response of M-Audio BX 5

To give you another example, let’s analyze the step response of a popular studio monitor : M-Audio BX5.

step response m-audio bx5

Judging by the step response graph, the M-Audio BX5 has a delay of 0.34 ms between its two drivers. A smudge more compared to our DIY speakers. In conclusion, even some respectable loudspeaker has some kind of time incoherence between its drivers. It’s not the end of the world.

Conclusion

If you measure the frequency response of a particular speaker, you are actually a click away of looking at its step response. We already saw 2 examples where the step response revealed that there is a slight time incoherence between the 2 drivers of the loudspeaker. In audio, it’s always a game of balancing things out. Sure, you can strive for a perfect step response, but you are probably setting yourself up for a bad time when it comes to the frequency response.

However, these plots can reveal some flaws with the system if the delay is too big. Perfect step response or not, in the end, how the speaker sounds is what’s important.


References

  1. Testing Loudspeakers by Joseph D’Appolito (Audio Amateur Pubns,1998).
  2. Image source : link.