## How to flatten peaks in the frequency response?

Implementing an audio peak filter circuit in your passive crossover design can sort out unwanted bumps in frequency response. These are normally called parallel notch circuits. The circuit is composed of a capacitor, an inductor and a resistor, all wired in parallel. Normally, there are certain formulas to calculate the values of the components. However, in real life these calculations do not work, and serve more as a starting point.

Anyway, we are going to skip that all together, since we are going to make the audio peak filter circuit happen in XSim. To serve as a device under test, we are going to use the Dayton Audio RS125-8 (Amazon affiliate paid link). First of all, I taken the necessary measurements and created the FRD and ZMA file. If you don’t know what I’m on about, check out these articles :

Since we have the files, we are going to load them up in XSim and create a simple circuit.

### XSim

If you don’t have XSim, you can go ahead and download it from here. Now that we got that out of the way, let’s see how the response looks like, with the files loaded and all.

As you can see, there is quite a considerable peak at around 1400 Hz. Normally, the speaker should be flat, as the manufacturer specifications suggest. However, the measurements were made on a baffle with straight edges. For this reason, those peaks are likely an edge diffraction effect.

Now that we know what we have to fix, let’s add the parallel notch filter.

We have the circuit in place. Don’t worry about the values of the components just yet. We’ll get to that in a second.

### Audio peak filter circuit

Now you are looking at the frequency response, and correctly observing that the circuit hasn’t affected the curve. That’s fine. This is true because the value of the resistor is 10 mOhm. Now let’s try to explain what each component does :

• The resistor determines the effectiveness of the filter. Larger resistor, means deeper notch, a more aggressive reduction in output.
• The product of the capacitor and inductor determine the frequency where the filter takes effect.
• If you want a broader frequency span to be affected, decrease the capacitor value and increase the value of the inductor. The produce of the 2 values needs to stay the same so that the target frequency remains the same.
• If you want to affect a narrow frequency span around the target frequency, increase the value of the capacitor. Consequently, decrease the value of the inductor, so that the target frequency remains unchanged (capacitor x inductor produce needs to stay the same).

Finally, we got the theory out the way. Let’s move on to a practical example.

### Notch filter circuit – step by step

Like I said, we are not going to do any calculations. Therefore, we are going to take advantage of this piece of software.

#### Step 1 – Increase the value of the resistor

Increase the value of the resistor by a considerable margin. Let’s say 100 Ohms. Now you should see a deep notch in the frequency response. So, the notch marks the target frequency.

#### Step 2 – Adjust the capacitor and inductor

As you play around with the value of the inductor and the value of the capacitor, you will see the notch move from left to right.

We have the notch in place, at around 1400 Hz. You can take note of the produce of the inductor and capacitor. L x C = 0.62 * 20.5 = 12.71.

#### Step 3 – reduce the value of the resistor

We gave the resistor a ridiculous value, just to keep an easy eye on the notch. However, the whole point is to have a linear response. Go ahead and lower the value of the resistor to a more respectable value.

The resistor value is lowered. However, that value is not set in stone. Most likely we are still going to change its value when we will fine tune the circuit.

#### Step 4 – Fine tuning

In the final step, alter the value of the capacitor and inductor, but keep their produce the same. As a result, the target frequency is still 1400 Hz but, the only difference is that more or less frequencies around the 1400 Hz mark are affected.

After quite a bit of fiddling I manage this response. Not exactly ruler flat, but way better than that 6 dB hump.

### Conclusion

Depending on your exact setup that you are working on, implementing an audio peak filter circuit can have various results. Sometimes it smooths the response flat, while other times it creates a wrinkly response. However, what’s important is that by using XSim you get to make a precise circuit with good results. Furthermore, the execution of the filter is pretty straightforward and easy follow.

#### References

1. Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005).