Special thanks to Engineer Mr. Xu from XK-Audio for his patient guidance; and to amirm, the moderator of AudioScienceReview Forum, for authorizing the usage of his measurements, which made this article possible.Understanding this article requires basic knowledge of complex numbers and high-school-level electricity knowledge.

Essentially, headphone drivers are just electric components, and headphone systems are just complex circuits. To analyze the electroacoustic performance of headphone drivers, we can consider all the components from the last stage of amplifier to the headphone driver as an active local circuit. This article will unveil one of the most important parameters of headphones —

**the impedance**.

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### Impedance and Impedance Curve

**Impedance**describes the opposition that an electronic component presents to the flow of current. It consists of

**resistance**and

**reactance**, where reactance is further divided into

**inductive reactance**and

**capacitive reactance**. Impedance can be described mathematically as follows:

For dynamic and planar magnetic headphone drivers, the capacitive reactance is usually much smaller than the linear resistance and inductive reactance, i.e., X≈XL. Therefore, the impedance of headphones can be approximated as being composed only of resistance and inductive reactance, i.e.,

**impedance curve**.

**Guess which headphone's impedance curve it is!**The answer will be revealed at the end of the article.

### Impedance of Planar Magnetic Headphones

Planar magnetic headphones use conductive traces printed on a diaphragm and drive the diaphragm using electromagnetic induction. A planar magnetic headphone driver consists of magnets and a diaphragm with conductive traces. The magnets produce a magnetic field, and the conductive traces carry the signal current, which creates a force that drives the diaphragm, causing it to vibrate and produce sound. The following images show two typical planar magnetic driver structures.### Impedance of Dynamic Headphones

Dynamic headphones bind a voice coil to a diaphragm and use electromagnetic induction to drive the voice coil, which in turn drives the diaphragm. A dynamic driver consists of a magnet, a voice coil, and a diaphragm. The magnet produces a magnetic field, and the voice coil carries the signal current, generating a force that drives the diaphragm, causing it to vibrate and produce sound. The following images show a typical structure of dynamic driver.## Resonance and Self-Induction in Dynamic Headphones

You may have noticed a great peak in dt880's impedance curve at low frequencies. This is because dynamic drivers tend to resonate near certain frequencies, causing a large amount of electromagnetic and mechanical energy to convert back and forth. This phenomenon is known as**resonance**, and the frequency at which it occurs is the resonant frequency, aka

**f0**, which is of great interest to audiophiles and acoustic engineers.

According to Engineer Mr. Xu from XK-Audio, the first generation of Avalon headphones, similar to the dt880, experienced a significant increase in impedance at certain low frequencies due to resonance, negatively affecting sound quality. The second generation of Avalon learned from the first generation's experience, increased resistance, and used an ultra-large diaphragm (d = 70 mm) to make the impedance curve flatter, resulting in a high-impedance dynamic headphone.

These two effects will also cause the voltage sensitivity calculated from impedance and power sensitivity to be lower than the actual situation. Therefore, when evaluating the "difficulty" of driving dynamic headphones, voltage sensitivity is more meaningful than power sensitivity. The calculation method and derivation process can be found in ths article

*The Algebraic Relationship Between Sensitivity and Impedance*

The impedance curves of some modern dynamic headphones can be flatter, such as the Aune AR5000.

### Does Output Impedance Affect Frequency Response Curves?

**In most cases, no.**The frequency response distortion caused by the high output impedance of tube amplifiers is negligible!

The following section can be skipped by general readers. There is an old Chinese saying: "To know what is so, and to know why it is so." This section is for true audiophiles.

## Algebraic Relationship

The output section of an amplifier and the headphone driver form a series circuit, causing the voltage distribution across the headphone unit to vary at different frequencies. If the impedance curve, linear resistance, and frequency response curve of the headphone and the tube amp are known, we can accurately calculate the frequency response of the headphone on this tube amp.If at a certain frequency, the linear resistance of the headphone is R, the reactance is X; the linear resistance part of output impedance the tube amp is r, and the reactance is x, then while under the same total equivalent voltage, the decibel sound pressure level, aka dBSPL, driven by the tube amp will be:

## Frequency Response Simulation

In this program, I used the frequency response and impedance curve of the Beyerdynamic dt1990 measured by amirm from ASR Forum and reduced the overall linear resistance by 230 Ω to create a hypothetical "low-impedance dt1990" to

**amplify the effect of output impedance on headphone frequency response**. I also assumed a tube amp with an output impedance of Z=300+0.01∗frequency+100/frequency (very few tube amps have such high output impedance nowadays).

We then get the following output, where the blue line is the original frequency response of our hypothetical "low-impedance dt1990", and the red line is the frequency response of the "low-impedance dt1990" driven by a high-output-impedance tube amp.