Why am I blowing it up with a 200 watt amplifier.

by Pat Brown

In this article, Pat Brown answers this question, “Why am I blowing it up with a 200 watt amplifier.”

I received an excellent question via email that I think may be of general interest.

The Scenario

A bass guitar rig is exhibiting thermal failure (i.e smoke!) when driven hard during shows. The box has one 15″ driver and one 10″ driver. The power rating of the 15″ driver is 500 watts. The power rating of the 10″ driver is 75 watts. Both are 8 ohms and are connected in parallel. The head has a 200 watt rating.

The sum total of the driver power ratings is

500 W + 75 W = 575 watts

The guy wants to know how he is blowing it up with a 200 watt amplifier. Good question!

Let’s draw the schematic to address the problem.

Note that I have calculated the Maximum Input Voltage (MIV) for each driver from its power and impedance ratings. The MIV is the voltage at the threshold of power compression (3 dB in any 1/3-octave band). I am assuming that the power rating of each device is based on this voltage, but in the real world it may not be.

Since these two devices are in parallel, they will each have the same voltage developed across them. The 15″ loudspeaker will handle a higher voltage, but that doesn’t buy you anything since the 10″ driver will be over-powered before you ever get there. Even though this box is thought to have a 575 W rating, it can only handle 24 VRMS, which is the MIV of the 10″ driver.

Point: You can’t determine the system power rating by summing the power ratings of the individual drivers.

That only works if they are all identical devices, and with multi-way loudspeakers they never are. By that logic I could parallel a 1 watt driver with the others and have a system power rating of

500 W + 75 W + 1 W = 576 W

Of course the system would stop functioning when the voltage reaches about 3 VRMS due to the 1 W driver. A chain is only as strong as its weakest link.

The Amplifier Voltage

The head only has an 8 ohm rating. The calculated output voltage is 40 VRMS. We don’t really know what the voltage does at 4 ohms, but my guess would be that it stays about the same. The reasons are:

1. The average impedance of each driver is typically higher than the “rated” impedance.

2. Amplifiers are essentially voltage sources if you don’t overload them.

So, I would expect the amplifier voltage to remain at 40 VRMS, which is more than the 10″ driver can handle. If the head has a limiter, it  is possible that the RMS voltage from the head is actually higher than the 40 VRMS calculated from the power rating, especially since bass guitar notes can have pretty low crest factors (like sine and square waves).

System Power Rating

So what is the box’s “power rating.” If the maximum input voltage is 24 VRMS, the power rating would be

W = E²/R = 24²/4 = 144 watts

But this rating depends on the driver impedance. If the actual load is higher, the power rating will be lower.

W = E²/R = 24²/8 = 72 watts

The bottom line is that the box’s MIV is 24 VRMS. That’s what I need to know to not smoke it. I don’t really care about the box’s power rating and I normally don’t take power ratings of either amplifiers or loudspeakers at face value without investigating where the numbers came from.

The “take away” here is that one should be very suspect of power ratings that are not accompanied by voltage ratings. Of course the application of this extends far beyond bass rigs.    pb