# Input Capacitors for Headphone Amps

Some headphone amplifiers have an optional input capacitor. This article discusses the tradeoffs involved in choosing this capacitor’s value, or for choosing to eliminate it entirely.

The comments in this article were made with the amp circuits on this site in mind, as they are the only ones I have extensive personal experience with. In some other circuits, the input capacitor is absolutely required due to the design of the circuit, so it cannot be eliminated. You must understand your amplifier’s design before you try to apply this article’s information to it.

### The Problem

An input capacitor is not required in the amps on this site in the ideal situation. They receive an incoming AC signal (music), and they amplify it for the headphones. Very straightforward.

But in real life, music sources have some DC offset: the AC signal is shifted by some constant DC level. The amplifier multiplies the source’s DC offset by the amp’s gain, and adds some offset of its own. If this total offset is large enough, it can damage headphones, so a source that has an acceptably low DC offset can still become a problem when used with an amplifier.

DC offset is a problem because it can heat up the driver coil to the point where damage occurs. Even if that does not occur, DC offset robs the driver of some of its dynamic range, which raises its distortion. With excessive DC offset, this can cause the driver to overextend, damaging it.

A conservative limit is 20 mV across the driver. If your amp has a gain of 10, then the source must have a DC offset of no more than 2 mV, and that’s assuming that the amp has no DC offset of its own.

### How Do You Measure DC Offset?

Put your meter on the DC millivolts scale and measure from ground to each of the amplifier’s output channels.

It’s most useful to measure this while it is plugged into the source. If your amp uses mini jacks (1/8"), put a mini-to-mini cable in the jack and measure from the long “sleeve” part to the “tip” and “ring” parts out at the end of the plug. With 1/4" jacks, it’s a bit tougher because 1/4" to 1/4" cables aren’t very common. Instead, it’s simplest to measure between the solder lugs on the inside of the amp. If you don’t want to open the amp up and can’t find a 1/4" patch cable, a 1/4" to dual RCA adapter will also work: just measure from the inside of each RCA jack to the outer shell.

You can also measure DC offset at the source. Remember to multiply this by the amp’s gain when deciding if it’s acceptable.

### A Common Solution

Since one never knows how much DC offset the various sources out there will have, a conservative design choice is to add a capacitor in series with the input. A capacitor will strip the DC offset from an AC signal in this orientation.

If adding a capacitor fixes the problem, why not always use an input capacitor? That’s the subject of the remainder of this article.

### RC Filter Weakness 1: Bass Roll-Off

Together with the input impedance of the amp (R), the input cap (C) forms what is called a high-pass RC filter. “High-pass” means that it passes high frequency signals without attenuation; as the frequency gets lower, attenuation increases. In the amplifiers that I talk about on this site, R is R2. The first curve in this graph is a high-pass filter’s attenuation curve.

An RC filter has a “corner frequency,” the point where the filter attenuates the signal by 3 dB. Above this point, the attenuation asymptotically approaches 0 attenuation in a high-pass filter. Below this point, the filter attenuation increases by 6 dB per octave. (An octave is a frequency doubling.) The formula for finding this corner frequency is:

Let’s work an example. Consider what happens if you use an 0.1 µF input cap with an amp that has a 100 kΩ input impedance:

f = 1/(2 · π · 100,000 · 0.0000001)
1/(2 · π · 0.01)
1/0.0628
15.9 Hz

This means that the filter has attenuated the signal by 3 dB at about 16 Hz. At 8 Hz, the signal will be down by 9 dB, then down by 15 dB at 4 Hz, and so on. Up at the lowest audible frequency (20 Hz), the signal will only be attenuated by about 2 dB with this filter. A few dB of attenuation isn’t a big problem by itself, but that’s not the end of the story.

### RC Filter Weakness 2: Phase Distortion

A worse problem with RC filters is the phase distortion, not the roll-off. With a corner frequency of 16 Hz, there will be significant phase distortion up through about 100 Hz. (The second curve in this graph shows the phase distortion.) This distortion “smears” the bass line.

If you want to understand this issue in more detail, I recommend that you download the demo version of the Micro-Cap circuit simulator. You draw a schematic of your circuit in it, and then you can run a simulation on it to get an idea of how that circuit will behave in real life. Here is the file used to generate the above graph, so it’s already set up for you. Just tweak the component values and say “Analysis | AC” to get graphs for attenuation and phase distortion.

The accuracy of the simulation is a combination of how well you understand your circuit, the simulator, and electronics in general. If you do not understand these things, chances are excellent that the simulator will tell you lies. Depending on your mood, these lies can be entertaining or enraging.

Bottom line, you end up wanting a corner frequency way below 20Hz to keep phase distortion down to a reasonable level.

### RC Filter Weakness 3: Capacitor Distortions

Phase distortion is an essential part of the way capacitors work. You see it in the simulation results because even an ideal capacitor would have phase distortion.

Real capacitors have additional distortion mechanisms due to material imperfections. Film types have lower distortion than electrolytic and ceramic types. Film caps made with separate film and foil are better than those made with metalized film. Also, the dielectric film material matters: in decreasing order of preference for use in an audio signal path, the main types are polypropylene, PPS and polyester. You shouldn’t go any farther down the scale than polyester for signal path caps under any circumstances.

The better the capacitor, the bigger it tends to be, physically. The previous section also shows us that higher cap values are also better than lower values, which increases physical cap size as well. Since board space is limited, you may have to compromise on the input capacitor’s quality. If your board space limits you to a choice between a 1.0 µF metalized polyester and an 0.1 µF polypropylene, the polyester might actually be the better all-round choice.

### Conclusion

If you don’t put an input cap in your amp, you avoid these issues entirely. There’s no phase shift, no bass roll off, and no decrease in sonic clarity. Just realize that you risk damaging your headphones if you do this. A source that has a low DC offset today may develop a problem tomorrow.

I've only skimmed the surface of this issue. For more details on how to pick capacitors, I recommend the following resources:

Picking Capacitors — by Walter G. Jung and Richard Marsh

The Sound of Capacitors — by Steve Bench

Input Capacitor Equations — is a 1-sheet PDF giving the equation

as advice for the size of this capacitor, along with a mathematical defense and other useful tidbits.