# Guitar Speakers and their Power Handling

### How an Electrodynamic Loudspeaker Works

### Thermal Damage

From the aspect of power dissipation, a guitar speaker can be modeled as a resistor. Most guitar amp enthusiasts are familiar with the equation for electrical power and how it can be used to determine the power dissipated across a resistor. Resistors can be thought of as transducers that intentionally convert electrical energy to heat in order to create a voltage drop. Resistors have a power rating that indicates how much power they can dissipate before being damaged and this rating is analogous to the speaker power rating.

### Mechanical Damage

### How the Speaker Power Rating is Determined

### Guitar Amplifier Power Output Ratings

*Power Output: 50W into 8ohm at 5% THD*

This type of power output rating is obtained by using a sine wave from a signal generator (usually 1 kHz) as the input signal. The 5% THD (total harmonic distortion) figure means that the sine wave was able to generate 50W of power output with relatively low distortion (near the threshold of clipping or overdrive). THD measurements were one of the first conventions used to objectively compare the fidelity of audio amplifiers.

Guitar amps are unconventional audio amplifiers. While most audio amplifiers are designed to keep distortion as low as possible, guitar amplification has evolved to where overdrive distortion is usually a requirement. For example, the Marshall® JCM800 2203 is a 100W tube amp that has a highly regarded overdrive sound. The owner's manual lists the power output as follows:

*Typical power at clipping, measured at 1kHz, average distortion 4% 115 watts RMS into 4, 8, 16 ohms. Typical output power at 10% distortion 170 watts into 4 ohms.*

This example shows that for many guitar amplifiers, the power output rating (100W in this case) is not a maximum power output rating, but more of a ballpark clean power output specification.

### RMS and Overdrive Distorion

#### General Equation for the RMS value of a periodic function

$$V_{RMS} = \sqrt{\frac{1}{T} \int_{0}^{T} [V(t)]^2 dt}$$

where the **Square** portion of the equation is

$$[V(t)]^2$$

and the **Mean** portion of the equation is

$$\frac{1}{T} \int_{0}^{T} [V(t)]^2 dt$$

and the **Root** portion of the equation is

$$\sqrt{\frac{1}{T} \int_{0}^{T} [V(t)]^2 dt}$$

Guitar amp output ratings are usually based on a sine wave at low distortion, but if the volume is turned up further or a gain boosting effect is used, the sine wave becomes more overdriven and can approach the shape of a square wave. The RMS value of a square wave is equal to its amplitude, while the RMS value of a sine wave is equal to its amplitude divided by the square root of two.

### Tube vs. Solid State Outputs

For tube outputs, it's important to match the load impedance to the amp's output impedance. For solid state outputs, it's important to use a load that is greater than or equal to the rated minimum load impedance and to know the amp's power output at that load. For example, the Fender M-80 is a solid state amp rated for 69 W(RMS) at 5% THD into 8 ohms and 94 W(RMS) at 5% THD into 4 ohms (the minimum load impedance).

With solid-state amps, overdrive distortion generated by the power-amp is not generally considered musically pleasing, so most people will not exceed the amp's low THD power rating. Tube power amps, on the other hand, are often played well beyond their low THD rating.

### Amps with Multiple Speakers

#### Formula for calculating the equivalent overall impedance of speakers wired in parallel

$Z_{\text{total}}$ = Equivalent Overall Impedance

$Z_1$ = Impedance of speaker 1, etc.

$$ Z_{\text{total}} = \frac{1}{\frac{1}{Z_1} + \frac{1}{Z_2} + \frac{1}{Z_3} + \ldots + \frac{1}{Z_n}}$$#### Example: Two Speakers in Parallel

$$Z_{\text{total}} = \frac{1}{\frac{1}{Z_1} + \frac{1}{Z_2}} = \frac{1}{\frac{1}{16Ω} + \frac{1}{16Ω}} = \frac{1}{\frac{1}{2}} = 2Ω$$#### Formula for calculating the equivalent overall impedance of speakers wired in series

$Z_{\text{total}}$ = Equivalent Overall Impedance

$Z_1$ = Impedance of speaker 1, etc.

$$ Z_{\text{total}} = Z_1 + Z_2 + Z_3 + \ldots + Z_n$$#### Example: Two Speakers in Series

$$Z_{\text{total}} = Z_1 + Z_2 = 4Ω + 4Ω = 8Ω$$### Choosing Guitar Speakers to Last a Lifetime

There is no standard method used by all amp manufacturers when selecting an appropriate speaker power rating. If you want to choose a speaker to last a lifetime, you will want to choose a speaker that can handle the maximum amount of preamp and power amp overdrive distortion that can possibly be put into it and safely avoid exceeding the speaker's thermal limits. In the case of single speaker setups, this means choosing a speaker rated for at least twice the rated output power of the amp. For multiple speakers, choose twice the rated power that would be distributed to it.

You might decide to go with a lower power rating because you know that you will never be cranked at full power and love the sound of a lower power rated speaker. In the same way you may choose a speaker with a much higher power rating because of the way it sounds.

#### A Real World Example: Speakers for a Fender® '65 Twin Reverb® Reissue

1) Determine the rated output power of the amp.

*Amplifiers have two power ratings: power consumption and power output. The power consumption is always much higher than the power output. In this case the output power is 85 watts RMS and the power consumption is 260 watts.*

2) Determine the output impedance for that output power rating.

*In this case it is 4 ohm*.

3) Determine the number of speakers.

*In this case there are two 12" (8 ohm) speakers wired in parallel for an overall impedance of 4 ohms.*

For this amp, speaker choices to last a lifetime should be rated for at least 85 watts each. There are a lot of speaker choices rated for 100 watts and this rating would be very safe. Actually, the stock speaker for this amp is the Jensen C12K and it is rated for 100 watts.

### Choosing Guitar Speakers to Last a Lifetime

You might decide to go with a lower power rating because you know that you'll never be cranked at full power and love the sound of a lower power rated speaker. In the same way you may choose a speaker with a much higher power rating because of the way it sounds.

A Real World Example: Speakers for a Fender® '65 Twin Reverb® Reissue

1) Determine the rated output power of the amp.

*Amplifiers have two power ratings: power consumption and power output. The power consumption is always much higher than the power output. In this case the output power is 85 watts RMS and the power consumption is 260 watts.*

2) Determine the output impedance for that output power rating.

*In this case it is 4 ohm.*

3) Determine the number of speakers.

*In this case there are two 12" (8 ohm) speakers wired in parallel for an overall impedance of 4 ohms.*

For this amp, speaker choices to last a lifetime should be rated for at least 85 watts each. There are a lot of speaker choices rated for 100 watts and this rating would be very safe. Actually, the stock speaker for this amp is the Jensen C12K and it is rated for 100 watts.

*By Kurt Prange (BSEE), Sales Engineer for Antique Electronic Supply - based in Tempe, AZ. Kurt began playing guitar at the age of nine in Kalamazoo, Michigan. He is a guitar DIY'er and tube amplifier designer who enjoys helping other musicians along in the endless pursuit of tone.*