Acoustic Impedance and Your Audio Electronics

Just as is the case in electronics, acoustic impedance can cause signal reflection at a microphone/speaker.

Acoustic impedance is a great topic for all the electronics engineers who just happen to be audiophiles (myself included). Impedance is not simply a phenomenon that defines signal behavior in electronics. In fact, any propagating wave disturbance has an associated impedance, including acoustic waves and mechanical waves.

The idea of impedance suddenly rears its head when we worry about impedance matching in a system where energy is converted between different forms. For example, acoustic impedance and electrical impedance matching in an audio system is not a simple matter of matching speeds of sound and electrical impedance on interconnects. If you’re in the business of designing a new precision audio system, you’ll need to consider your mechanical and acoustic design alongside your electronic design.

Electrical and Acoustic Design

Interestingly, because audio systems are so ubiquitous, and because a poorly designed system receives so much attention, the EMI and noise requirements in these systems are extremely stringent. Compared to a low-level high-speed digital system, a minor hum in an audio system could cause a user to quickly forsake your product for a competitor’s. With such a digital system, we only worry that noise is within the receiver’s noise margin; as long as a “0” or “1” is received correctly, any residual noise is effectively ignored. In a precision audio system, noise should be brought below the threshold of human hearing.

The relevant frequency range in an audio system for audio reproduction (i.e., sending a signal through a speaker) is much lower than in a typical digital system. Ultra-fast digital signal bandwidths span up to the GHz range, while audio signals only span up to 20 kHz (the edge of the human hearing range). In digital recording equipment for audible signals, ADCs run at comparably lower frequencies than their counterparts in other electronic systems, reaching 176.4 kHz for high fidelity systems. Even if you’re working with ultrasonic audio recording systems, your sample rate probably won’t hit much higher than the Msample/s range.

Although the frequencies are lower, there is one point in audio design that is sometimes overlooked: acoustic impedance and its effects on impedance matching. The acoustic impedance of an audio element will determine how much power can be transferred from a speaker into air, and from air into a microphone.

Acoustic Impedance Bridging

Whether you consider the bones in your eardrum or the shape of a trumpet, acoustic impedance matching provides the same function as electrical impedance matching. It prevents reflections and provides maximum transfer of acoustic energy into/out of a receiver/transmitter. Acoustic impedance is just the product of the speed of sound in air and density. The mechanical impedance of the speaker is already designed to provide acoustic impedance matching to the surrounding medium within a specified bandwidth. Contrary to typical analog/digital electronics applications, standard impedance matching is not used.

In audio systems, a technique called “impedance bridging” is used to purposefully mismatch the electrical impedance of an amplifier from the load impedance. An example of this dynamic source impedance bridging with a high-Z load is shown in the circuit diagram below.

Impedance bridging between an audio amplifier and a load

A real audio element will have either very high or very low impedance (not the typical 50 Ohms), and it will contain some crossover networks. An audio amplifier is basically a current-limited voltage source, thus it has low impedance and maximum voltage needs to transfer to the load, rather than maximum power. Similarly, a transducer connected to a pre-amp is also a low impedance current-limited voltage source, and the pre-amp also needs to receive maximum voltage. This justifies the use of impedance bridging rather than impedance matching to ensure maximum voltage transfer throughout the signal bandwidth.

The output/input amplifier is dynamically impedance mismatched to a particular transducer in the device. This purposeful mismatch forces the load (i.e., the transducer or receiving) to receive nearly 100#% of the output voltage without maximum power transfer. To summarize, the point of impedance bridging and acoustic impedance matching is as follows:

• Purposefully mismatch the transducer from the amplifier to ensure maximum voltage is dropped across a driven transducer. Electrical transmission line effects don’t apply at these frequencies.

• Design the speaker/transducer itself to have matched acoustic impedance and ensure maximum transfer of mechanical power into the surrounding medium.

The idea of typical electrical impedance matching at audible frequencies in an audio system does not apply here, unless you're the telephone company with mile-long transmission lines.

What If I’m Not Designing Audio Equipment?

If you’re not designing audio equipment, and you simply need to detect an acoustic wave at a specific frequency, you’ll get the highest power transfer from a transmitter (or into a receiver) with electrical impedance matching. There are a number of reasons for this.

First, the outputs from drivers not used for audio is not dynamic and will have a fixed value; you want to match your receiving transducer to this particular value, especially if you are detecting a single frequency (e.g., an ultrasonic frequency at 1 MHz). Second, this application does not rely on reproducing a broad bandwidth voltage signal at the transducer; it only relies on passing a strong signal at a single frequency to a transmitter/receiver.

Tools for Audio Electronics Design

Perhaps the most important tools for designing audio electronics are frequency sweeps, noise analysis, transfer functions, and small signal analysis for the amplifier section. Amplifiers, microphones, and other components all add some noise to the signal passed through an audio system. Any kind of noise analysis you can perform with verified component models will help you understand how the noise floor appears at the speaker in your system. A recording system just operates in reverse, and you’ll want to simulate how frequencies from 20 Hz to 20 kHz (or at higher frequencies for ultrasonics) will appear at an ADC in the presence of noise.

If you’re a fan of audio systems with analog equalizer dials, transfer functions for different knob settings are quite important. There is a whole field of audio equalizer design, which can get rather complex when you start designing a multiband equalizer. The transfer function and gain in specific frequency bands will determine how a signal is modified in the frequency domain and is reproduced for the listener in the time domain.

Old-school audiophiles are fans of graphic equalizers

Because your audio system needs to include a precision amplifier, it’s critical that you quantify THD+N (measured in dBc) seen at the speaker and the dynamic range of the system. If you can translate the signal at the speaker into a power output using your speaker data sheet, you can determine how loud the system will be before saturation. The amplifier you select needs to run in the linear range while outputting a signal through a low impedance transducer, and your THD+N measurement needs to be as low as possible.

You can quantify THD and THD+N in your system using a noise simulation alongside small-signal analysis at different input signal levels. Note that this needs to be performed throughout the relevant frequency range, so a frequency sweep needs to be performed at each input signal level. This is a time-consuming task, but it allows you to qualify that the system is designed properly before building a prototype.

Whether you’re designing a precision audio system or any other electronics system, the PCB layout and design features in Allegro PCB Designer and Cadence’s full suite of design tools are the ideal choice for building and simulating your new product. You’ll have a full suite of design tools for acoustic impedance matching and PCB layout for your new product. You’ll also have access to a set of tools for MCAD design, verified component selection, and data management.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.