Custom Design of a High-Fidelity Hearing Aid

In this project you are asked to design a custom hearing aid that amplifies sound non-uniformly over the hearing spectrum to compensate for frequency dependent hearing deficiencies. One of your group members will be the client for whom the hearing aid will be designed.

Hearing loss typically occurs non-uniformly over the audio frequency range. Thus, each client is tested with a series of tones. The volume of each tone (frequency) is adjusted to level that can barely be heard by the client. The value is recorded for each frequency used in the test. The hearing loss at the threshold of hearing can be quantified in terms of the gain required to bring the client's threshold of hearing to that of the normal threshold of hearing. For example at a given frequency, if a tone at a normal threshold of hearing level is 30 dB, and the client has a threshold at 36 dB, then a gain of 6 dB is required to resort the persons sensitivity to that of a normal ear.

You must design an amplifier circuit to compensate (as much as possible) for hearing losses at different frequencies. Assume the input is the sound impinging on a microphone. The microphone converts changes in acoustic pressure to voltage changes. The microphone output is fed into a broad-band amplifier, which is designed to amplify the weak signals from the microphone uniformly over the audio range. The transfer function of the combined microphone and broadband amplifier results in a flat spectral magnitude over the region of interest. The circuit you must design is concerned with the relative amplification/attenuation over the hearing spectrum to compensate for the losses in the ear. The signal from your circuit is fed into an audio amplifier to drive the earphone. The transfer function of the combined earphone and audio amplifier also results in a flat spectral magnitude. A constant gain (volume) over the entire spectrum can be adjusted through the audio amplifier driving the earphone. The output impedance of the broad-band amplifier, which feeds into your circuit, is 50 ohms. The input impedance of the audio amplifier, which feeds into your circuit, is 2 Megaohms.

**Figure 1. **Top-level block diagram of entire hearing-aid unit.

The client for whom you will be designing the hearing-aid circuit can assess their hearing loss with the sounds files (wav files) located at

http://www.engr.uky.edu/~donohue/audio/fsear.html

The tones can be played directly from the Web page or down loaded first. If you are connected through a slow link, you should download the tones first. Tones from 40 Hz to 15000 Hz are provided, however, depending on the quality of your speakers or headphones, you may not be able to use some of the higher and lower frequencies. From the instructions on this Web page you should be able to obtain specifications for your amplifier. In addition to specifications at the tones you use, your amplifier should not pass DC and should be below -3 dB at 21000Hz.

Let's define a *goodness* factor on which to judge how well your circuit performs. Let be the transfer function associated with your circuit, on a dB scale let be the difference between the normal threshold of hearing and your client's threshold of hearing (i.e. normal(dB) - client (dB)). Ideally, we should have the product of the magnitudes of these functions equal to 1 for all frequencies in the range of interest:

for all w in the range of interest

Expressed in terms of dB:

for all w in the range of interest

Since you cannot test the ear at all frequencies, you must determine a set of test points to use that reasonably sample the audio range. Given that *N* discrete points were used in testing the clients hearing loss, the bias error for the combined ear and hearing-aid system is given by the average error in terms of dB:

The variation about the normal criterion is expressed as:

Good performance for the design can then be described in terms of minimizing m * _{e}* and s

For the design you can use any references and computer programs. Your design is limited to use at most 6 op amps and no inductors (capacitors and resistors).

The final and preliminary report must define the problem your design solves. This involves determining the information that is important to your design and stating the problem in more mathematical terms. The more clearly and simply the problem is stated, the easier the design task will be. Ideally the report should be as short as possible and still communicate all the details needed by someone who is designing the custom circuit (Note that the people building the circuit do not need to know that this circuit is going to be used in a hearing aid. All they need to know are specifications on the circuit). Determine based on your clients hearing loss pattern and state the specifications for your circuit. The restated problem should sound almost like a homework problem (i.e. I must find a circuit whose transfer function has the following characteristics ...). The final and preliminary report must also include a block diagram of your top-level design (for your circuit - not the hearing-aid) and a discussion of the function and purpose of each element. Once your top-level design is completed for the preliminary report, the tasks required to complete the design and final report must be identified and assigned to members in your group. Your main resources are time and the skills of your team members. Since some tasks will depend on the completion of other tasks, you need to set target dates for each subtask to guarantee the final deadline is met. Performance results should include computation of and values for your final circuit along with a plot of the absolute error as a function of frequency to demonstrate how well your design conforms to the original specifications. A plot of the magnitude response generated from SPICE must also be included and explained (the values you use in your final performance evaluation must be those computed from SPICE using the non-ideal op-amp model). The equations, computer programs, and approximations used in solving for the critical parameters of your circuit must be described. The final and preliminary report must be done on a word processor.

Finally, everyone is expected to keep an engineering notebook. This is like a technical diary that can be used to track the evolution of the project. Each time your group meets, you must record what was accomplished in the meeting (i.e. We decided on the top-level design shown below. Joe agreed to do the Matlab program and have it ready by Friday. Since Bill wasn't here we decided that he should find the circuits and their design equations by tomorrow ...). If you spend time individually or as a group doing anything related to the project, this should be dated and recorded in your notebook (i.e. I found several useful circuits in the textbook that can be used in our project. These circuits and their transfer functions are ...). If you do any kind of calculation, algebraic manipulation, or computer program, write it in the notebook, even if the work is incorrect, leave it in the notebook. You can indicate your error in the next entry and correct it then. If you work with a spreadsheet program or Matlab, generate a printout of what you did, or a sample of what you did (for Matlab see help on the command "diary"). The notebook should NOT be typed; however, your work should be organized, dated, and legible. It must also be handed in with the project. There is no excuse for a late engineering notebook when the project was handed in on time. You will loose double points for a late engineering notebook. All work presented must be in chronological order (i.e. do NOT give a series of short statements of what you did each day, and then stuff all your derivations, programs, plots, etc. in the back of the notebook).

If your project is properly completed it should include at least:

- A block diagram of your circuit that explains the functions of the sub-circuits and how they connected.
- Schematic diagrams of your circuit (or sub-circuits) with actual component values.
- A listing of design equations used for your circuits.
- A plot comparing the transfer function magnitude of your circuit with the desired transfer function magnitude.
- Computed values for the bias_error and variance_error of your final circuit.

If any of the above components are missing, a significant amount of points will be deducted from your score.

Please follow the format given below for the preliminary report:_________________

Section I - Problem Definition (2 points)

- Describe desired (ideal) transfer function (use numbers and graphs!!!)
- Present performance criterion that must be satisfied or optimized and limitations on your design.

Section II - Top-Level Design (2 Points)

- Present block diagram of your top-level design
- Describe purpose and function of each block

Section III - Time-Table. (2 Points)

- Break-down project into smaller sub-tasks
- Distribution of effort (primary responsibility for each member)
- Tentative time schedule for sub-tasks in order to complete project by required date

Note: Score will be scaled down for documents that are poorly organized or poorly written.

Please follow the format given below for the final report:_______________________

Section I - Problem Definition (3 points)

- Describe desired (ideal) transfer function (use numbers and graphs!!!)
- Present performance criterion that must be satisfied / optimized.

Section II - Top-Level Design for Final Solution (4 points)

- Present block diagram of top level design
- Describe purpose and function of each block
- Explain changes from proposed solution (if any)

Section III - Technical Description and Schematics of Circuits (5 points)

- Present schematic of each block in top level design
- Describe critical parameters for each circuit and present equations indicating their relationship to circuit components

Section IV - Optimization of Circuit Parameters (4 points)

- Identify critical circuit parameters used to minimize error
- Explain the process used in adjusting these parameters

Section V - Performance Results (5 points)

- Present final and (explain how computation was performed)
- Plot of final transfer function in SPICE (label axes, always!)
- Plot of difference between SPICE points and ideal transfer function
- Conclude about how well (or poorly) your design performed (what would you do differently if you had more time to improve), and how well you were able to stick to your original plan in the proposal

8 points for your individual engineering notebooks

Note: Score will be scaled down for documents that are poorly organized or poorly written.