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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING Design Considerations for Common Feedback Amplifiers
Encyclopedia of radio electronics and electrical engineering / Radio amateur designer Recently, there has been another surge of discussions on a topic that can be conditionally called "for" or "against" negative feedback in amplifiers. Unfortunately, these discussions rarely contain any rational argument, while demonstrating a clear lack of knowledge about the "little things" of working and designing systems with FOS. The situation is complicated by the fact that in most cases, devices are cited as justification for objections to the use of feedback, which in fact turn out to be an example of illiterate or unsuccessful use of it. And then, in the worst traditions of school logic, the conclusion is drawn: "feedback is bad!". At the same time, examples of the correct use of FOS seem to be becoming increasingly rare, and most likely due to the virtual absence of modern literature on this issue. That is why it seems to us especially expedient to publish several materials devoted to little-known features of the design of highly linear amplifiers with feedback. Recall that the main reason for the invention of amplifiers with feedback feedback by Harold Black in 1927 was precisely the need to increase the linearity of amplifiers used in multichannel telephone communication systems over one pair of wires. The problem was that the linearity requirements of these amplifiers increase very sharply as the number of channels increases. There are two reasons for this. The first is the number of possible intermodulation products that interfere. The second reason is that with an increase in the signal bandwidth, the losses in the cables also increase, which is why amplifiers have to be placed at a shorter distance (and their frequency response must be adjusted more strongly), and on a 2500 km route their number increases to three thousand. Since the distortion products in the communication line are summed up, the requirements for each individual amplifier are correspondingly stricter. To make it clear how high the class of this equipment is, we note that amplifiers for systems with 10800 channels have a third-order intermodulation distortion level at the end of the passband (60 MHz) of no more than -120 ... -126 dB and a difference tone value of no more than - 130...-135 dB. Higher order intermodulation distortion is even lower. The frequency response of a path containing two to three thousand (!) Amplifiers during its service life (approximately 30 years of round-the-clock operation) changes by no more than a few decibels, mainly due to cable aging. By the standards of conventional equipment, this is fantastic, but in reality it is only the result of the competent use of environmental protection. The problem of increasing the linearity of amplifiers X. Black has been working at Bell Labs since 1921. It was he who developed almost all known methods of distortion compensation, in particular, distortion correction by the so-called direct connection, as well as distortion compensation by summing a distorted output signal with an isolated anti-phase distortion signal . These measures, of course, had an effect, but they were not enough. The cardinal solution to the problem of linearity was precisely the invention of amplifiers with feedback and, most importantly, their correct practical implementation, which was impossible without the creation of an appropriate theory ("there is nothing more practical than a good theory!"). The first step in constructing the theory was made by Harry Nyquist, who found a method still used to determine the stability even before the closing of the feedback loop, based on the type of frequency response and phase response of an open system (Nyquist hodograph). However, not all so simple. Despite the simplicity and apparent obviousness of the principle of operation of the FOS, in order to really obtain the benefits that can be achieved with its use, it was necessary to create a very extensive feedback theory, which is by no means limited to ensuring stability (lack of generation). Its construction was practically completed by the outstanding American mathematician of Dutch origin Hendrik Wade Bode only by 1945 [1]. In order to understand the real complexity of the tasks, we note that even Black's first patent for an amplifier with feedback, which does not describe all the problems, has the volume of a small book - it contains 87 pages. By the way, in total, X. Black received 347 patents, a significant part of which is related specifically to the implementation of amplifiers with OOS. In comparison with such a volume of work, all the claims of modern "subverters of the foundations" who have not created anything even close in level, and often have never even read (or have not understood) the works of Black, Nyquist and Bode, look at least overly self-confident. Therefore, the question is not about using the OOS (in reality, it always exists, just not always explicitly), but that this use is competent and brings the desired result. So, which of the "not described in the textbooks" should you pay attention to when designing and evaluating the circuit design of amplifiers with feedback? First, we recall that in the formula for the transfer coefficient (transfer function) of a feedback system H(s) = K(s)/[1+b(s)K(s)] complex numbers and functions appear, namely:
To obtain correct results, calculations must be carried out according to the rules of arithmetic of complex numbers [2], which is often forgotten even by the authors of textbooks. For example, at a loop gain phase angle close to ±90°, ±270°, the amplitude non-linearities of the original amplifier are almost completely converted into phase ones (i.e., into parasitic phase modulation, albeit weakened by |bK| times). In this case, parasitic amplitude modulation practically disappears, and the results of intermodulation distortion measurements can be 20 ... 30 dB more optimistic than the spectrum analyzer (and hearing in the case of UMZCH) actually shows. Unfortunately, this is exactly the case with most OUs and many UMZCHs. A good example is the current feedback amplifier described by Mark Alexander [3]. The real level of intermodulation distortion (in the English abbreviation - IMD) of this amplifier on a two-tone signal with frequencies of 14 and 15 kHz according to the spectrum analyzer is approximately 0,01%, which is in good agreement with the plot of harmonic distortion versus frequency (approximately 0,007% at a frequency of 15 kHz ). If the intermodulation distortion of this amplifier is measured using the standard (only amplitude modulation) method, then the resulting IMD values will be much lower. At a frequency of 7 kHz, we get only a negligible 0,0002%, and at 15 kHz - about 0,0015%, which is significantly lower than the real values (about 0,005 and 0,01%, respectively). This effect was also mentioned in passing by Matti Otala [4]. Next moment. It is important to understand that the FOS cannot reduce the absolute value of the distortion and noise products brought to the input in comparison with the situation when the FOS loop is open and the signal levels at the output are the same in both cases. At sufficiently high frequencies, the gain of any amplifier drops; as a consequence, the difference signal in the amplifier with feedback also increases. Therefore, in the region of higher frequencies, the input and subsequent cascades will inevitably begin to show their nonlinearity, since the increase in the difference signal in an amplifier with feedback is possible to almost double the input value [5] due to the phase shift. We also note that with a closed feedback loop, distortion products, especially of a high order, such as the “teeth” of switching the arms of the output stage, are similar to high-frequency input signals and the input low-pass filter cannot help here. That is why, in order to prevent a catastrophic expansion of the spectrum of intermodulation distortions with the introduction of FOS, it is highly desirable to provide a faster decay of the envelope of the spectrum of distortion products without FOS than the rate of decay of the loop gain. This condition, unfortunately, is not only little known (Bode only hints at it, considering it obvious), but is also extremely rarely fulfilled. For the same reason, the frequency correction introduced for stability should not lead to a deterioration in the linearity of the amplifier over the entire frequency range, up to the unity gain frequency and even somewhat higher. The most obvious way to achieve this is to perform a correction in such a way as to directly reduce the value of the input signal, as was done in the famous M. Otala amplifier (Fig. 1). Note that the "quenching" of the difference signal at the input by the R6C1 circuit used here ultimately gives a much better result than the template frequency correction circuit of the op-amp type, despite the presence in the emitter circuits of differential stages of boost capacitors C2, C4, C6, which greatly increase the dynamic nonlinearity.
The foregoing explains the desirability of a large margin of linearity in stages preceding those where the main drop in the frequency response is formed - in amplifiers with feedback, this is necessary first of all in order to prevent a significant expansion of the spectrum of distortion products. In order to increase the linearity of the input stages, it is often recommended to use field-effect transistors in them, however, this recommendation makes some sense only when using discrete field-effect transistors with a high cutoff voltage (more than 5 V) and setting the appropriate mode (about half of the initial current, however, amplification of such a stage small). Amplifying cascades on bipolar transistors with the introduction of local feedback, providing the same effective transconductance and operating at the same current as cascades on field-effect transistors, always provide significantly better linearity, especially at high frequencies, due to a better ratio of through capacitance to transconductance [6 ]. The use of standard op amps with a "field" input, in which the input transistors operate in a mode that is approximately 0,6 ... in which no more than 0,7 ... 0,1 V drops on the emitter resistors. In high-speed op-amps with a "bipolar" input, the voltage drop across the emitter resistors is usually not lower than 0,2 ... 300 mV, so the linearity of their input stages is higher, and their input capacity is less. It is for these reasons that high-linearity, high-speed field-input op amps (such as the OPA500 and AD655) are typically built as a combination of bipolar transistor stages with input source followers. To increase the linearity of the input stages, it is most effective to use local frequency-dependent feedback, which simultaneously provides the necessary decrease in the frequency response and the increase in linearity (for example, with inductors in the emitter circuits of the input stages [7]). Frequency-dependent local environmental protection reduces the depth loss of the overall environmental protection in the operating frequency band; it is applicable both in voltage amplification stages (for example, in op-amps LM101, LM318, NE5534 [8]), and in output stages (for example, in op-amps OR275, LM12 and in UMZCH TDA729x and LM3876 / 3886 microcircuits). Thus, when developing an amplifier with feedback, it is necessary to ensure acceptable (at least not worse than a few percent) linearity and better stability of characteristics without feedback precisely in the frequency region where the loop gain is small, and not at low frequencies, where the loop gain is high. A number of measures to improve the linearity at low and medium frequencies (for example, the introduction of the so-called tracking link in a cascode amplifier) simultaneously leads to a deterioration in the stability of the characteristics and (or) a decrease in the linearity at HF. Therefore, their introduction into amplifiers with feedback is impractical. In the case of using local OOS, in order to obtain good results, it is necessary to optimize their frequency characteristics, since each of them not only increases the linearity of this cascade, but also reduces the loop gain in the general OOS circuit. This task is not trivial, one cannot do without very accurate computer modeling and optimization. As a rule of the first approximation, we can assume that close to the optimal option is the one in which the contribution of all stages to the resulting distortion of the amplifier with OOS (with a closed OOS loop!) Is approximately the same. Further, for amplifiers with common feedback, it is critically important that there are no dynamic tracking drops in the feedback loop. This means that dynamic non-linearities are unacceptable, leading to abrupt changes in characteristics, for example, due to blocking or saturation (quasi-saturation) of transistors, or due to the appearance of grid currents in lamps when a signal is applied through a coupling capacitor. If for some reason such phenomena cannot be excluded, it is necessary to take measures to level their influence in frequency regions where the loop gain is small (especially in the unity gain frequency region), using, for example, local environmental protection. An excellent example is the NE5534 push-pull output stage [8] based on transistors of the same conductivity structure. It would seem that the cascade is very non-linear: the upper shoulder is an emitter follower, the lower one is a transistor with a common emitter. Nevertheless, due to the increase in the depth of the local FOS with frequency, even traces of "steps" are absent in the OS (of course, provided that the board is correctly routed). Therefore, the main source of distortion in this amplifier most often turns out to be precisely the overload of the input stage, which does not contain (in order to minimize noise) emitter resistors! Be that as it may, this op-amp does not have an increase in distortion in the audio frequency band even with a gain with an NFB of 40 dB (P = 0,01), when the depth of the total NFB at 20 kHz does not exceed 30 dB. Distortions in this case do not exceed 0,005% (and this is with an output signal swing of 20 V from peak to peak), and their spectrum is practically limited by the third harmonic. At the same time, connecting a load up to 500 ohms has almost no effect on distortion. Of the other circuit defects, dynamic hysteresis (created by most circuits designed for "smooth" switching of the shoulders of push-pull output stages) is especially dangerous, as well as the "central cutoff" that occurs at high frequencies - a step (a standard disease of output stages on compound transistors according to the Shiklai scheme or on basis of the "parallel" amplifier). From the point of view of stability, these defects are equivalent to the appearance of an additional phase shift, reaching up to 80° ... 100°. In a number of op-amps and some models of powerful amplifiers, to overcome these shortcomings, RF bypass circuits are used (multichannel OS). The question of choosing the type of frequency response of loop amplification is quite well covered in the classical literature, for example, in [1]. The choice of the optimal number of amplification stages, taking into account their relative speed, and the design of systems with multichannel FOS are considered in detail in [9], so we will only give brief information below. Since the “slowest” UMZCH node is most often a powerful output stage, the optimal number of cascades in the UMZCH from the point of view of linearity and depth of the OOS is certainly not less than three (as Bode established, with approximately equal speed of the cascades, a three-stage amplifier is optimal). In the case of performing correction with circuits bypassing the cascades on the RF, the number of cascades is limited only by the complication of the device. The division of the general FOS loop into several local loops, promoted by a number of authors, is inexpedient despite the simplification of the design. Coverage by "local" feedback of more than one stage in the amplifier, as shown by Bode, leads to the loss of potentially achievable linearity. For example, two cascades connected in series with a local NFB of 30 dB each will have obviously worse linearity than the same two cascades covered by a total NFB of 60 dB in the same frequency band. Of course, there are some exceptions to this rule. So, for the formation of the frequency response of the loop gain, it is useful to use frequency-dependent local feedback, when in the region of the operating frequencies of the amplifier they are practically turned off and do not reduce the achievable depth of the overall feedback. Another example - in microwave amplifiers made on discrete components, the excess phase shift introduced by active elements and passive circuits begins to exceed the natural one, determined by the frequency response decay, and the achievable depth of the overall OOS is small. In this case, it is more practical to use chains of intertwined local FOSs instead of a general FOS. The phase stability margin at high frequencies for UMZCH should not be chosen less than 20 ° ... 25 ° (lower - unreliable) and it is unprofitable to increase more than 50 ° ... 70 ° (noticeable losses in the amplification area, i.e. in speed and OOS depth). To increase the depth of the OOS in the operating frequency band, it is advisable to introduce a loop amplification section with a steepness of about 12 dB per octave into the frequency response. It is even better to form the frequency response of a loop amplification such as a Bode cut or a Nyquist stable one (with a phase shift beyond 180 °), however, their correct implementation is rather complicated and therefore not always justified. That is why UMZCH with a Nyquist loop amplification frequency response, as far as is known, are not mass-produced. The designs described in the literature have significant operational limitations (in particular, the inadmissibility of high-frequency signals entering the input, poor output voltage clipping). Removing these restrictions is possible, but cumbersome. Another often overlooked very important feasibility factor is the design of cascades covered by feedback. It should ensure that there are no parasitic resonant peaks at the frequency response decay and beyond the passband, forcing, in order to ensure stability, to artificially lower the speed of the amplifier as a whole (see the examples of the frequency response of open-loop feedback amplifiers shown in Fig. 2). The presence of parasitic peaks in the frequency response sharply reduces the depth of the OOS achievable without self-excitation. Curve 1 demonstrates the possibility of providing a large (10 dB) stability margin at a unity gain frequency of about 2 MHz. The depth of the OOS at 20 kHz is at least 40 dB. Curve 2 has a parasitic peak, the quality factor of which is about 20 (actually, it can be more). In order for an amplifier with such a frequency response not to be excited (with a stability margin of only 2 ... 3 dB), the loop gain and the CNF bandwidth of such an amplifier will have to be reduced by a factor of 20 compared to curve 1, and the frequency of probable self-excitation will be a hundred times higher than the nominal unity gain frequency!
Summing up a brief review, we note that any design is a set of compromises, so it is very important that the applied solutions are mutually linked, and the design is a single whole. With regard to UMZCH, for example, there is no particular reason to specifically achieve a depth of feedback above 80 ... 90 dB in the audio frequency band, since the main source of distortion products in this case will no longer be active elements, but constructive ones, for example, interference from push-pull output stages. It is clear that in such a case, it is more important to carefully refine the design, as is done in one of the author's designs [10] or in foreign amplifiers of the Halcro and Dynamic Precision brands. Literature
Author: S. Ageev, Moscow; Publication: radioradar.net
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