Crossover Basics - Driver Response

The Decibel or dB

Decibels (dBs) are a curious way to measure electrical and acoustic energy. Curious, and terribly convenient! For us, we use relative electrical dBs to discuss how filters work, and absolute acoustic dBSPL to measure speaker output.

When discussing the effects of a filter on a signal, we'll use relative dBs. That is, there's no set standard, but we talk about something being +4dB or -18 dB. This is useful because we can map this to speaker outputs no matter the volume settings. It is how we will discuss how a filter works, without worrying about the absolute output levels.

On the other hand, when we discuss the acoustical outputs we'll use dBSPLs which are in absolute terms, but using a set input level. Don't worry too much if this is confusing, we'll make it more clear as we go along.

The LM-1 Crossover Revisited

As mentioned in my first installment on Crossover Basics, the effects of a crossover filter are additive to the speaker driver.

We are going to use the LM-1 crossover and focus on the tweeter response in detail. Let's refresh your memory about the crossover, here it is on the left.


We'll focus on the tweeter filter section. This includes C1, L1, R1, and R2. The woofer section will seem neglected by comparison, but we cover it in more detail in other blog posts, including the Zobel.

Let's go over the transfer function. That is, how the voltage at the tweeter is different from the amplifier output because of the crossover. 0 dB means there was no change, the input and output are the same. The woofer response (in red, below) is almost exactly 0 dB until around 700 Hz when the low-pass filter kicks in. The tweeter on the other hand is more complicated. Let's discuss.

Anytime you see a chart this clean, you can be sure you are NOT looking at acoustical measurements. The blue line is tne tweeter filter's response. Except for the level shifting, this seems like something straight from my previous post on Crossover Basics. First, notice the level of the tweeter. It has been "padded" or "lowered" 6 dB below input. This is accomplished by the 4.2 Ohm R1. R1 is effective at all frequencies. Everything gets shifted down about 6 dB because of it. It's not exactly always constant, but let's pretend it is for right now, which is very close to true.

In addition to the padding there is a high pass filter reducing the midrange and bass at about 8 dB/octave below 2kHz. We discuss pads by an absolute number, like "6 dB" because it's effect is constant at all frequencies but we talk about high and low-pass filters with rates. In this case, 8 dB/octave means every time you cut the frequency in half, you will loose 8 dB. This is the actual "high-pass" section at work. This is C1,L1,R2. Notice that after about 4 kHz the high pass filter effectively stops working. It's as if it wasn't there anymore.  Above this level the only parts still involved in the high frequency response are the tweeter and R1. 

Putting it All Together

The point of this post is that these changes are not in isolation, but rather in combination with the driver so let's take a look at how the padding resistor and thigh high pass filter combine withe the acoustical response of the driver to produce the final outcome.

Notice the scale is now different. We are now looking at dBSPL, or sound pressure dBs. It is most common to take the frequency response measurements of a driver at 2.83 Volts input with the microphone at 1 meter distance. As you can see, below, this particular tweeter outputs about 90 dB at 2.83 volts above 4kHz or so.  2.83V is a common reference standard because at 8 Ohms this is about 1 Watt.

The top black line represents the tweeter with no filter at all. The green line represents the tweeter with just R1 added. It's not exactly 6 dB down everywhere due to the tweeter's impedance curve, but it's close enough for us! You'll learn more about this in the next post which covers the Zobel. The red line represents the addition of the high pass filter section, C1, L1 and R2. You can see it pivots around 3 kHz.

By carefully selecting the filter knee (-6dB point) and it's Q, or steepness we can get a little bit of EQ thrown in for free. Take a look at the original response (black) at around 2 kHz. You see the broad bump centered there? The bump is pretty much gone thanks to the high pass filter. We have not only added the high pass filtering, but we also tamed a little over-activeness int he tweeter without increasing the part count.

Padding

In the chart below you can see the final LM-1 design in red, vs. the a redesign without R1:



It may not be obvious from this, especially since this author likes to use far-field as his reference, but the LM-1 without padding would shriek.

In designing a crossover, I find it easiest to start low and work my way up. The low pass filter will reduce the sensitivity of the woofer at the crossover point. After this, we must adjust the tweeter to match and then add the high pass filter.

The total amount of padding (dB loss) depends on a number of things, including:

• Innate woofer efficiency
• Woofer low pass filter and baffle step compensation
• Innate tweeter efficiency
• Tweeter high pass filter

Unfortunately there is no simple, accurate way to go from a manufacturer's sensitivity specs to appropriate filter design.

The crossover designer must balance all four of these issues at the same time which is why in-cabinet measurement and simulation are so important. I encourage you to grab the LM-1 simulation files and attempt this for yourself.

Also note, that doing the reverse, padding the woofer, is generally discouraged because the power dissipation needed to lower a woofer a few dB is pretty large and requires big resistors and will waste a larger amount of amplifier energy. If your tweeter is too insensitive you probably need to change tweeter or woofer. It is pretty rare to find any design that does not require any tweeter padding.

Summary

With this posting, you now have learned:

• How crossover filter's add to driver output to create the combined effect of both. 
• How you can use leverage a high pass filter to also work as an EQ for you. 
• Why tweeters usually have resistors to pad them down. 

In my next post, Crossover Basics - The Zobel,  we'll go over the LM-1 woofer response but spend particular attention on the often misused or misunderstood circuit, the Zobel.

Cheers!