The Theory of Transient Intermodulation Distortion

The existing theory of transient intermodulation distortion (TIM) is extended to cover the calculation of the duration of intermodulation bursts. It is shown that feedback values in excess of some 40 dB will cause large internal overshoots within the amplifier. The clipping of these overshoots due to the limited dynamic margins of the amplifier driver stages is shown to give rise to long periods during which the amplifier is in cut-off condition. The duration of these periods is calculated and the mathematical results are verified with digital and analogue simulation. Finally, the relationships of TIM, slew rate, and power bandwidth are discussed.

 The application of strong negative feedback in audio amplifiers has become standard practice over the last decade because transformerless transistor amplifier circuits have enabled its easy use. In the tube amplifier era it was the output transformer which, due to its complex transfer function, precluded the use of much more than some 20-30 dB feedback. Even then, amplifier designers were discussing a particular “veil” which seemed to appear in the sound when the feedback was very strong. At the same time, amplifiers having small-signal frequency ranges greater than 1 MHz were advocated as being the only ones giving adequate sound quality. The theory presented here will justify these conclusions to some extent. Later, the inherent nonlinearity of early transistor amplifiers forced designers to use strong negative feedback to cope with the requirements of low harmonic and intermodulation distortion. Even when the importance of this basic reason decreased in later years, the apparent ease of the use of feedback as a cure-all for almost all amplifier sicknesses continued and commercial power amplifiers having some 60-100 dB feedback are not rare today. At the same time, the debate of “transistor sound” versus “tube sound” continued and has become an object of intensive research. It should be strange in principle that a tube amplifier and a transistor amplifier having equal performances and specifications which are much better than necessary for the ear, should sound remarkably different. The only solutions of this apparent dilemma seem to be that

1. the present amplifier measurements are partly irrelevant in respect to the audible amplifier characteristics; and/or

2. the present amplifier measurement methods do not reveal all of the major sound degradation effects.

Recently, at least one basic distortion mechanism, which does not appear with present amplifier measurement methods, the transient intermodulation distortion (TIM), has been discovered. It is a side effect of the use of a too strong negative feedback, which makes the modern transistor amplifiers, in particular, very susceptible to it. The basic theory of TIM is straightforward and clear [l]. TIM has been shown to be relatively common in commercial audio amplifiers [2] and the ear seems to be very sensitive to it [3]. Methods for its elimination have been outlined [4] and several “TIM-free’’ amplifiers have been constructed [5] -[8]. An intensive public discussion of the effect has recently begun in several countries, The purpose of this paper is to extend the theory of TIM to the calculation of the amplifier cut-off time, to explain some of the basic behavioral models for this phenomenon, and to try to establish practical limits to the application of feedback in audio amplifiers. The relationships of TIM and some other amplifier properties will also be discussed shortly.

 

Basic Configuration

We will examine the basic feedback amplifier circuit of Fig. 1. Here p is the purely resistive feedback path around the amplifier A which has an open-loop gain Ao . C is the preamplifier which is imagined to incorporate the transfer function of the signal source, so that for the purpose of the analysis the input signal VI may be assumed to have infinite bandwidth. It is essential to note that though V, itself may have signal components of very high frequency, the preamplifier C acts as a low-pass filter, moderating the signal in such a way that the amplifier A input signal V, includes only components in the usual audio passband.

The preamplifier frequency response is assumed to be that shown in Fig. 2. Two alternative responses are shown; one corresponding to linear response and the second corresponding to treble boost. The power amplifier frequency response is assumed to have the form of Fig. 3. Because of stability considerations, idealized -6 dB/octave slopes are assumed in the open-loop response. This may not always be true in practical amplifiers where the phase margin is not always n/2, and where different frequency compensation techniques may be combined to shape the response of Fig. 3. The results of the analysis may, however, be used as general guidelines, and the effects of the departures from the idealized model should be carefully analyzed separately.

by Matti Ottala and Eero Leinonen