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John Caldwell

Dec 21, 2015

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Related

Amp up your cans: How much power do headphones need? (Part
1)

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This post is co-authored by Bharath Vasan.

When we set out to create an operational amplifier (op amp) for headphone applications
(which became the OPA1622 op amp), one of the first questions we needed to
address was just how much power headphones need.

Think of headphones and loudspeakers as a transformer that converts an input
electrical power to acoustic output power. Like all processes, this conversion
of electricity to sound has an efficiency associated with it. And as you might
expect, different headphone styles have different efficiencies. In general,
over-the-ear headphones have lower efficiencies than in-ear headphones.

Headphone manufacturers usually provide the efficiency of their headphones in
terms of the sound-pressure level ([SPL], given in decibels) produced for a
certain input power (typically 1mW). For example, a headphone manufacturer may
specify that their headphones have an efficiency of 100dB/mW, which you should
read as “100dB at 1mW.” Using the reference efficiency provided by the
manufacturer, you can use Equation 1 to calculate the SPL produced for other
power levels:

In Equation 1, PIN represents the input power to the headphones,
and η is the efficiency given at a 1mW reference level. Figure 1 shows the
output SPL for increasing input power for a range of common headphone
efficiencies.

Figure
1: SPL produced vs. input power for various headphone efficiencies

Equation 1 and the plots in Figure 1 include the assumption that the drivers
in the headphones are operating in a linear fashion. Of course, you can’t keep
increasing the input power to the headphones and expect the output SPL to
increase forever (don’t try). At high input powers, nonlinear effects in the
drivers themselves will limit the maximum SPL.

Once you’ve established a target SPL goal, determining the signal levels only
requires some fundamental electrical engineering equations (Equations 2 and
3):

Both of these equations include the nominal headphone impedance,
RHP, also given by headphone manufacturers. Headphones designed for
portable electronics have low impedances (as low as 16Ω) because  a low
voltage signal at the headphones will still deliver sufficient power. Headphones
not intended for portable applications, such as those used in professional
recording studios, may have impedances as high as 600Ω.

Let’s apply all of this information to a design example, calculating the
signal voltage and current necessary to reach a certain SPL for a popular pair
of over-the-ear planar-magnetic headphones. Table 2 lists the design goals and
headphone specifications.

Table
2: Specification goals for design example

Using either Equation 1 or Figure 1, first
determine the necessary input power to reach your SPL goal:

Next, calculate the voltages and currents required to deliver this amount of
power to the headphones:

The combination of a low-impedance headphone with low efficiency and a
very loud maximum SPL goal in this design example illustrated to our team the
challenges ahead in the OPA1622 design. It
was apparent that the amount of current our amplifier would need to deliver to
some headphones would be significant (by op amp standards). With this in mind,
we turned our focus to the output circuitry of the OPA1622. It would need to be capable of delivering large
amounts of current without distortion

In the next three installments of this series, we’ll examine some of the
other challenges we encountered in headphone applications, and how we overcame
them in the design of the OPA1622.

Additional resources

Watch on-demand training courses on stability and more in the TI Precision Labs – Op Amps Low-Distortion Design
and Noise video series.

Download the Analog Engineer's Pocket Reference e-book for
frequently used system- and board-level design formulas (myTI login
required).

Learn more about TI’s precision-amplifier portfolio and find technical
resources.

View TI’s entire audio portfolio with the audio selection tool.

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