Basics of Hard to drive Speakers

Basics of Hard to Drive Speakers

While writing a blog on EPDR I realized I needed to explain what a hard to drive speaker was, and why EPDR does not really help you.

In the typical parlance of audiophiles, a hard to drive speaker is one with unusually low impedance and / or phase angles. The reason for this has to do with how voltage is divided between the amplifier’s output, and the speaker. Without using complex math, here’s the basic voltage divider formula. We’ll use R (resistance) instead of Z (impedance) to keep things simple. Let \(V_{out}\) be the amplifier’s attempted output and \(V_{spkr}\) be the voltage that actually makes it to the speaker terminals:

\[ V_{spkr} = V_{out} * \frac{R_{spkr}}{R_{amp} + R_{spkr}} \]

Consider with a very good amplifier the amplifier’s output impedance ( \(R_{amp}\) )is very low, so if \(R_{amp} = 0\) therefore \(V_{spkr} = V_{out}\) because the right side becomes equal to 1. This is ideal, and the electrical output remains constant regardless of frequency. However, as \(R_{amp}\) rises and/or \(R_{spkr}\) drops, \(V_{out}\) starts to go along with the impedance curve, which can be a roller coaster. This is why tube amps don’t do so well with electrostatic speakers and their 1 Ohm loads in the treble, or really any speaker with < 4 Ohm areas.

Here’s the fundamental problem with EPDR : None of the formulas involved address the amplifier’s output impedance, or peak current delivery or anything else related to the voltage and current at the speaker terminals. The value and derivation of EPDR is entirely about transistor heat. Howard never crosses the line to claim it isn’t about heat, but he also tries to use this understanding as another, better impedance measurement, and it can’t be. And this is where the confusion has come from. JOB’s point however that EPDR can help understand which speaker is more likely to cause an amplifier to clip is valid. How many times have you heard an amp actually disconnect due to overheating however?

Another thing to note is that an amplifier’s output impedance is the end result of the power supply, output stages and feedback design.

Damping Factor

Quickly, amplifiers rarely publish or measure output impedance, but instead publish “damping factor.” It’s calculation is \(DF = 8 / R_{amp}\)

So an amplifier with a DF of 100 has an output impedance of 0.08. Important to note that DF is usually reported in the bass but is often lower (higher R) in the treble.