Class-D audio amplifiers with negative feedback

There are many different designs for audio amplifiers. Class-D, or switching, amplifiers generate their output signal in the form of a high-frequency square wave of variable duty cycle (ratio of on time to off time). The square-wave nature of the output allows a particularly efficient output stage, with minimal losses. The output is ultimately filtered to remove components of the spectrum above the audio range. Mathematical models are derived here for a variety of related class-D amplifier designs that use negative feedback. These models use an asymptotic expansion in powers of a small parameter related to the ratio of typical audio frequencies to the switching frequency to develop a power series for the output component in the audio spectrum. These models confirm that there is a form of distortion intrinsic to such amplifier designs. The models also explain why two approaches used commercially succeed in largely eliminating this distortion; a new means of overcoming the intrinsic distortion is revealed by the analysis. Copyright (2006) Society for Industrial and Applied Mathematics

Using Needs Assessment to Understand Continuing Disability in Patients with Enduring Mental Illness. Implications for Considerations of Service Development

Particular strengths of the MRC Needs for Care Assessment Schedule have been used to investigate the treatment status of patients with persistent psychiatric disability in ways that other needs assessment tools are unable to. One hundred and seventy-nine such patients from three settings; a private sector psychiatric hospital, two public sector day hospitals situated in the same town, and a high security hospital, were found to have a high level of need. Although there were differences between settings, overall these needs were well met in all three. The high level of persistent disability found amongst these patients could not be attributed to failure on the part of those treating them to use the best available methods, or to failures to comply or engage with treatment on the patient's part. In some two thirds of instances persistent disability was best explained by the fact that even the most suitable available treatments have to be considered only partially effective.