Amplifiers for use in audio applications and many instrumentation applications must have a closely linear frequency response from DC (0 Mz) to a high frequency, typically of the order of 20 kHz in the case of audio amplifiers, preferably well beyond.
One way of obtaining the required linearity is to design a set of cascaded amplifying stages, with the output of one amplifying stage feeding the input of an adjacent amplifying stage in the sequence, to obtain an amplifying circuit with a open loop gain much larger than required at DC, and, apply an outer negative feedback loop to the system which is frequency independent over the desired operating range, thereby producing an amplifier with a lower closed loop gain and an extended linearity in comparison to the open loop characteristics. Such an amplifier is shown schematically in FIG. 1 with two cascaded stages .mu..sub.1 and .mu..sub.2 inside a DC feedback loop with gain 1/.beta.. FIG. 2 illustrates this general principle, showing typical gain versus frequency on a log-log plot for a single pole compensated Op. Amp. Curve A shows a typical frequency response of the cascaded amplifier stages .mu..sub.1 and .mu..sub.2 shown in FIG. 1 with the negative feedback .beta.. The frequency response is linear up to a frequency f.sub.o whereafter the frequency response D decreases at an increasing rate and for stability must usually be engineered to decrease at a uniform 20 db/decade (halving each octave) or not considerably more. Curve B shows the gain of the circuit in FIG. 1 with frequency-independent feedback loop .beta. installed, reducing the gain to a value much less than the open loop gain and thereby extending the linear frequency response to a value f.sub.c much larger than f.sub.o.
An operational amplifier, hereafter referred to as an Op. Amp., is an electronic circuit or device which amplifies a signal which is the difference between the separate signals on its inverting and non-inverting input terminals (or +& - inputs). The output from the output terminals is typically symmetrical about a ground reference, and the device is powered by symmetrical positive and negative supply rails: exceptions are well known, along with the methods for making them behave in a similarly useful way to the typical case Op. Amps.
An Op. Amp is typically used as a linear amplifier for which feedback means are provided to its input terminals from its output terminal, in order to maintain a linear relation between the input signal and the amplified output signal. Without feedback, Op. Amps typically have a very high gain .mu. measuring from 10,000 to 100,000 or more.
Feedback means for linear operation is typically a resistive voltage divider from the output, with the inverting input connected to the junction of the voltage divider. The ratio characteristic of the voltage divider, by which it reduces the output voltage for feedback purposes, is known conventionally as .beta., and regarded as a fractional gain. When the + input is grounded, and a signal applied to the bottom of the voltage divider constituting the feedback means, the Op. Amp will invert the signal on the output, and have a closed a loop gain of 1/.beta. for all practical purposes. The signal actually amplified is very small, approximately -1/.mu. times the output signal. The term .mu..beta. is known as the Loop Gain. The limiting case is where .beta.=1, and Loop Gain equals .mu., otherwise of course Loop Gain is less than .mu.. Conversely, when the bottom of the voltage divider is grounded, and a signal connected to the + input, the Op. Amp will non-invert, and have a closed loop gain of 1+1/.beta..
Both the inverting and non-inverting configuration of an Op. Amp are used commonly, each having different advantages for various purposes. For practical purposes, linear amplification using Op. Amps must use one or the other, or more rarely both.
Both configurations are subject to the same limitations which place an upper limit on the .mu. of Op. Amps which can be usefully stabilised. This limitation imposes restrictions on the performance of Op. Amps. and restricts the usefulness of negative feedback in maintaining linearity and reducing distortion or errors on the output. Consequently a great deal of design effort is put into giving Op. Amps as high a .mu. as possible, consistent with stability or reliable operation under given feedback conditions and this depends also on expected loads the Op. Amp has to drive. With power amplifiers the problem is especially acute.
All operational amplifiers degrade in performance when required to deliver current into a load, and this applies especially to high quality audio power amplifiers, discrete or integrated. The better quality required the more difficult the design and production problems, and the greater the expense. It is generally agreed that high open loop gain is the only way to enhance the performance of an otherwise sound design.
The fundamental limitation on .mu. is associated with the work of Bode and Nyquist, whose conclusions are commonly summarised as follows: At low frequencies the input and output signals are precisely related in phase; 0.degree. for non-inverting, and 180.degree. for inverting configuration. At high frequencies however the output lags or retards in phase due to many unavoidable mechanisms in active devices like transistors, as well as parasitic capacitances. At the same time, and for similar reasons, the .mu. of an Op. Amp falls off with frequency, and at a progressively faster rate. At some frequency the output will be phase shifted by 180.degree., and if the Loop Gain (1/.mu..beta.) is not less than one at this point, and amplifier will oscillate and be useless for other purposes. Most often, loads on the Op, Amp's output induce this condition, and then it is said to be unstable. Loop Gain=1/.mu..beta. (for inverters), so the more feedback applied to an Op. Amp, or the larger the fraction .beta. in the feedback network, the closer the amplifier is to instability. The worst case is when .beta.=1, and the amplifier is at Unity Gain (voltage follower), Integrated Op. Amps are commonly made with internal frequency compensation so they are stable at Unity Gain. Still others are said to be decompensated, and have a minimum 1/.beta. (AV) at which they are stable. Further types can be compensated externally as desired. In all cases there is a stability margin or safety factor, expressed in terms of the phase shift when .mu..beta.=1. Different standards apply for different classes of use, but 135.degree. is one accepted standard for common commercially available low level integrated Op. Amps (commonly known as "mini-DIP" in the 8 pin DIP form, but available in many other packages, e.g.: 14 pin DIP, 16 pin DIP, SIP, surface mount etc), giving a stability margin of 45.degree..
Frequency compensation comprises the various methods for making on Op. Amp's .mu. roll of with frequency at a (nearly) uniform rate, so that .mu. crosses the unit gain (.mu.=1) point at a convenient frequency which will guarantee a suitable stability margin.
Since reducing an Op. Amp's .mu. degrades its performance, frequency compensation is always a question of arriving at an acceptable stability margin, leaving as high a .mu. as possible. A satisfactory minimum of frequency compensation is thus chosen.
Special care is required in power amplifiers, since instability can rapidly destroy output devices, and often the loads to which they are attached. The problem is especially acute in high quality audio amplifiers, whose performance practically depends on their .mu., while their stability must be guaranteed under unpredictable load conditions.
Stability problems can be local or global and have many causes, all of which are exacerbated by higher open loop gain however it is produced, for example by adding more stages, or stages with inherently more voltage gain or by adding current buffers. In particular, it is generally thought impossible to construct a linear amplifier from two cascaded operational amplifiers inside the same linear DC feedback loop in which each operational amplifier operates at its open loop gain at DC. The resulting open loop gain of such a circuit is the product of the separate open loop gains at DC, and must roll off at higher frequencies at a rate of at least 40 dB per decade. Theoretical texts and practical experience typically suggest that such a combination cannot be stabilised and could not produce a useful linear amplifier with a useful power bandwidth.
It is well-known and demonstable experimentally that differentiated feedback is radially more effective than DC or restive feedback in correcting errors generated within the Op. Amp itself, otherwise known as distortion. In practice, differentiated feedback is commonly used in conjunction with DC feedback for frequency compensation, and also for reducing distortion. This is most usually done using capacitance, though inductors can sometimes be used.
It is known, although not commonly practised, to use nested differentiating feedback loops for stabilisation of multi-stage amplifiers. European Patent Application 92200283.7 (publication No 0499308A1) describes the use of nested capacitive feedback to stabilise amplifiers with 3 and more cascaded stages. Similar techniques have been previously described by Cherry (Australian Patent 521165) to result in an audio amplifier of low distortion and very high open loop gain. However such designs have been restricted in their practical applications, being rather complex to design and construct, and difficult to troubleshoot. No such techniques have previously been demonstrated to product a stable amplifier when the amplifier stages themselves have gain and impedance characteristics typical of complete stand along operational amplifiers. Such techniques have been restricted at best to stabilising amplifier stages, each being of relatively low gain and limited transconductance within an operational amplifier. Technical Handbooks supplied by Op. Amp manufactures (National Semiconductor Linear Applications Databook application notes AN272, AN 446, page 1063 for example) invariably describe cascaded op amp circuits with a substantial DC feedback component applied to the second Op. Amp, resulting in some improvement in distortion over a single Op. Amp, but limited in scope compared with what might be achieved if a composite open Loop Gain at DC approaching the product of the gains of the two Op. Amps could be reliably stabilised.