subtitle : The output impedance and the impedance graph

#### What is impedance?

The term impedance appears quite often on the specifications of audio products. The word is sometimes used interchangeably with ‘resistance’, and while there are definite similarities in meaning, the two terms are distinct.

The term ‘resistance’ refers to the general property of obstructing current flow through a circuit. A popular analogy is that of a water pipes: just as the pipe with a wider diameter lets water flow more readily, so does the circuit with less resistance allow more electricity to flow. A tighter diameter will impede the flow of water, which is analogous to reistance in electricity.

When measuring electrical resistance however, we find that there are some objects whose resistance is constant regardless of whether the current is DC or AC, and that there are others whose resistance is dependent on the frequency of the signal. This necessitates a distinction in terminology, and the latter is called impedance.

As the term impedance is used in audio products, audio products have frequency-dependent resistance. And, as both resistance and impedance measure the same quality of hampering a current, they are quantified in the same unit, the Ohm(Ω).

To summarize:
Impedance refers to frequency-dependent resistance; practically all electrical equipment are built using inductors (L) and capacitors (C) as opposed to resitance alone (in an AC config), hence the term impedance is used for distinction.

#### Impedance bridging (impedance matching)

Now that we’ve covered impedance, let’s move on to impedance bridging and impedance matching. Strictly speaking, impedance bridging and impedance matching are separate concepts, but as they are used interchangeably in the audio world, we too will use them interchangeably.
So what is impedance bridging?

The circuit above represents a simplified audio system with loudspeakers connected to an amplifier: Vs represents the voltage from electrical source, Zs represents the internal impedance of the amplifier, ZL represents the load (speakers) impedance, and VL represents the voltage through the loudspeakers.
If we assume that Vs is 10V, and that Zs and Zl are 2Ω and 8Ω respectively, it follows that VL is 8V; the mathematical formula for this is:
VL = Vs X (ZL / (Zs + ZL))

That is, the voltage through the speakers (VL) is inversely proportional to the internal impedance of the amplifier and proportional to the impedance of speakers themselves. In other words, a smaller output impedance from the amplifier will drive a load better, and a larger load impedance will make the sound larger.
As a real-life example, when using a Y-splitter to listen to music with a friend, there is a noticeable, sudden drop of volume when your friend plugs in his earphones. The reason for this is because the second pair of earphones decrease the load impedance, leading to a lower voltage and thus a lower volume.
To summarize:
A lower internal / output amplifier impedance and a larger load impedance leads to a better signal strength.

#### Impedance curves for earphones / headphones

Dynamic earphones and headphones tend to have a fairly consistent impedance curve across frequencies.

Impedance graphs for AKG K370 (in red) and Sennheiser HD228 (black)

The impedance graphs for the two products above show little difference between 20Hz and 20KHz, at both ends of the audible spectrum. Other products tend to show a minor peak near the bass and a gradual decline as the frequency increases, but the difference usually not significant.

On the other hand, products that make of balanced armature drivers exhibit uneven impedance graphs with noticeable changes in impedance as the frequency changes.

Impedance curves for Ultimate Ears triple.fi 10 pro (in red) and Etymotic research ER-4P

In case of the triple.fi 10 pro, the impedance peaks around 1KHz and bottoms out at 10KHz; in contrast, the ER-4P’s impedance increases with frequency.
The problem is that with equipment such as triple.fi 10 pro and ER-4P whose impedance changes significantly with frequency, the sound also changes based on the output impedance.

Frequency response graphs for UE 10 Pro paired with different amplifers (Diffuse Field EQ)
Red: UE 10 Pro + Nuforce Mobile Amplifier
Blue: UE 10 Pro + HeadRoom Balanced Desktop
Green: UE 10 Pro + E-MU 0404 USB (Headphone Out)

As you can see from the graph above, when paired with amplifiers with high output impedance (usually voltage amplification, as in E-MU 0404 USB), the triple.fi 10 pro displays a weaker treble, whereas pairing with low output impedance (usually current amplification, as in NuForce Mobile) results in a treble boost.

Note
In my review of the triple.fi 10 pro, I stated that despite the frequency response graph (which had a rather excessive bass), the unit sounded balanced – this was precisely due to the effect mentioned above. At the time, the testing and the listening were done using different amplifiers, specifically the Headroom Desktop and Cowon S9, respectively. The portable player was able to bring out the treble since it had a lower output impedance, which had had relatively less treble when coupled to the high output impedance of the Desktop amp.

Silicon tubes used; no Diffuse Field EQ applied for an accurate comparison

In contrast, the ER-4P shows a stronger treble with high-impedance amplifiers (usually voltage amplification, as in E-MU 0404 USB), and a weaker treble with low-impedance amplifiers (usually current amplification, as in NuForce Mobile).

The root cause of this problem is the earphones and headphones dramatically changing impedance with frequency, but barring that, lower output impedance is desirable in DAPs and amplifiers as the difference is proportional to the impedance.
To summarize:
Products with impedance that falls with frequency (triple.fi) will have less treble from larger output impedance, and more treble from a smaller output impedance.
In contrast, products with impedance that rises with frequency (ER-4P) will have more treble from larger output impedance, and less treble from a smaller output impedance.
Note
Sometimes resistor adapters are marketed as making the sound ‘better’ universally. While the sound does, in fact, change due to the increased load impedance, the character of change is determined by the impedance characteristics of the product, and resistors will not increase bass or treble on all products.

#### How much output impedance do products have?

If you’ve understood everything thus far, then you’re probably wondering what the output impedances are like on products on the market today. So I went through the products that I have and measured the output impedance on some of them.

On desktop products, the output impedance tends to be larger than on their portable counterparts as they are frequently used with high-impedance headphones and operate out of a wall socket.
On portable products, the output impedance tends to be smaller as they are used with earphones and must operate on a battery, which cannot provide the high voltage necessary for a large output impedance.