FEEDBACK can occur inadvertently or be applied deliberately; it can be positive or negative, voltage or current feedback. A typical case of positive feedback is the ordinary electron-tube oscillator, where the plate circuit is tightly coupled to the grid circuit so that the gain of the circuit is infinitely in creased.
Feedback through the tube capacitances can be such as to set up self-oscillation; this, again, is positive feedback. Positive feedback is associated with increased gain, negative feedback with ...
Fig. 701. Block diagram showing the application of negative feedback.
... decreased gain. Yet the application of excessive negative feedback can cause an amplifier to oscillate at a low frequency (motor boating) or at a high frequency, but it is not the negative feed back itself that has caused the instability but the phase change in the amplifier resulting in the feedback becoming positive at low or high frequencies.
Fig. 701 shows any amplifier with a gain of A. In the absence of feedback E11 = E12 and A X E1 = Eo. Now feed back a portion Beta of the output voltage Eo. Obviously Beta cannot be greater than unity and if the whole of E0 were fed back the input to the amplifier would be so great that overloading would be inevitable. f3 is there fore a fraction of E0. The gain of the amplifier with f3 E0 feedback is Eo Eo En E12 + /3Eo
Another way of expressing this is to say that the amplification after feedback is:
A 1 +f3A
... where A is the gain of the amplifier without feedback.
Similarly: distortion without feedback distortion with feedback =
.... so there is the basic principle: negative feedback decreases the gain of an amplifier and decreases the distortion in the same proportion. In case the sign preceding the factor f3A or f3Eo is thought to be wrong when compared with formulas given in standard textbooks, remember that for negative feedback f3 is negative. The amplification formula is frequently given as:
A I - {3A
... but, if f3 itself carries a negative sign, the factor must become
+f3A.
Negative feedback stabilizes the gain of an amplifier and consequently improves the frequency response. Without feedback the gain will vary with frequency due to the presence of capacitive and inductive reactances and so will the phase shift. It is easy to design an amplifier with a flat response from, say, 100 to 10,000 cycles without feedback. Below and above this range the gain will fall and the phase shift will increase. If the phase shift becomes greater, negative feedback, when applied to the amplifier, tends toward positive feedback, so the gain lost by negative feedback is reduced and the width of response without loss of gain is greater. Considered this way it will be obvious that to depend entirely on phase-changed feedback to give a wide response is not sound practice, for so much feedback may have to be used that negative is changed to positive feedback at low and high frequencies, causing oscillation and instability. Feedback can make a poor amplifier somewhat better but the true purpose of negative feedback is to make a good amplifier very much better.
This is possible because of other attributes. Negative voltage feedback decreases the effective plate resistance of the output tube or tubes in the same ratio as it reduces gain.
Provided the feedback voltage is in series with the input voltage (as shown in Fig. 701) the input resistance of the amplifier will be multiplied by the same factor, (1 + [3A). Stability Phase shift in the amplifier will result in instability if the amount of feedback or the phase change is too great. A single stage of resistance-capacitance coupling, with adequate screen and bias bypassing, will have a phase change of not more than +90° at the highest and lowest frequencies. If the bypassing is not adequate, the phase change can increase up to a maximum that is always a little less than +180°. If there is more than one stage, then the total phase change will be the sum of the phase changes of each stage. An output stage with transformer has a phase change that reaches a maximum of 90° at low frequencies and 180° at high frequencies.
A tube without associated reactances changes the phase exactly 180° for all frequencies and a direct-coupled amplifier can have not only a very wide frequency response, but no phase change at the low frequency end except the reversals effected by the tubes themselves. If, therefore, feedback is used, all that is necessary is to make sure that the feedback has the correct phase to provide negative feedback and low frequency instability or motorboating cannot arise.
Phase shift and time constants
With an R-C amplifier involving phase change in each stage it is necessary to keep the phase change as small as possible, otherwise instability will occur with quite small amounts of feedback. To avoid this calls for much longer time constants than those given in Tables 8 to 10. Attenuation of the response at each end in creases phase shift; longer time constants contribute to wide frequency response. If, in the interests of economy, the time constants are kept short and it is hoped to widen the response by applying negative feedback, it will be found that the desired amount of feedback may not be attainable owing to instability resulting from the large phase change introduced by the interstage coupling. In other words, the great advantages of negative feedback are only achieved if the amplifier to which the feedback is to be applied has been properly and generously designed in the first place.
Since the design of an amplifier can be calculated, the conditions for stability can also be calculated. These can be displayed in a Nyquist diagram. The method is fully described in standard textbooks and technical journals; a useful summary will be found in Langford Smith's Radiotron Designer's Handbook, Fourth Edition, pp. 356 et seq. This guide also gives references to the best articles on the subject. As it is the aim of the present work to avoid mathematical computation, some notes on practical steps to avoid or overcome instability are given in the next section.
Application of negative feedback
The simplest application of feedback to a single stage is found in the cathode-loaded or "cathode follower" tube, shown in Fig. 702-a. This is simply a case where an ordinary triode plate cathode circuit has had the plate load transferred from the plate to the cathode end of the circuit. The basic circuit, as shown, postulates a conductive grid circuit, and when the tube is used as an amplifier, suitable negative bias must be applied, say by a bias battery.
To call the tube an amplifier is, however, hardly correct, for the gain of the stage is less than unity since there is inherent 100% negative voltage feedback. The output source impedance is very low, the input impedance high and distortion is practically nonexistent, so the value of the cathode follower lies in its action as an impedance transformer. The output terminal impedance is approximately equal to the reciprocal of the mutual conductance of the tube, in parallel with the cathode load. If this is used to feed a low value load impedance also, the power will be severely limited, and the distortion will rise too.
The cathode follower can be R-C coupled to the next stage by inserting a coupling capacitor and shunt resistance. It will be appreciated that the whole of the de losses and the power output must be dissipated by the cathode resistor.
One way of solving both the bias and output coupling problems is to replace the cathode coupling resistor with the primary of an output transformer, as shown in Fig. 702-b, the secondary being connected to the load, which would normally be a speaker. This usage, because of the low output impedance characteristics of the cathode follower, gives extremely good speaker damping but as there is no gain in such an output stage it follows that the necessary amplification must be made up by an additional stage of voltage amplification at quite a high level. The power output of the tube will be the same as that when used normally but, as the gain is less than unity, the input voltage required for normal operation must be multiplied by the amplification factor of the tube. The de resistance of the transformer primary will contribute toward the bias resistance required, but an additional bias resistor, with appropriate bypass capacitance may need to be inserted between the cathode and the transformer primary. See Fig. 702-c.
Figs. 702-a, -b. Simple current feedback: (a) cathode follower; (b)
cathode follower arrangement in which the primary of the output transformer
replaces the cathode resistor.
Simple current feedback
A simple way of applying feedback (in this case, current feed back) to any R-C stage is to omit the cathode bias resistor bypass capacitor. In Fig. 702-a, if the grid circuit is returned to ground,the cathode resistor will be the bias resistor, but this will generally produce far too much bias on the tube causing it to operate at a very low plate current. To overcome this, the cathode load can be divided, as in Fig. 702-d, where R1 and R2 form the cathode load (replacing the plate load) and R2 is the bias resistor proper. C2 may or may not be needed as a bypass. The grid return would then be taken to the junction of RI and R2. The blocking capacitor, C1, may be the plate coupling capacitor from the previous stage. If the load resistor is divided equally between plate and cathode circuits, the phase inverter circuit of Fig. 305 ...
Figs. 702-c, -d. Cathode circuit arrangements: ( c) bias resistor in
series with primary of output transformer; (d) split cathode load,
Fig. 703. Method of connecting a series feed resistor.
... is formed. The split-load phase inverter 1s therefore partly a cathode-follower stage.
Triode-connected tetrodes and pentodes
The foregoing points refer to triodes. With tetrodes or pentodes, if the plate and screen grids are connected to the same B-plus
Fig. 704. Applying feedback across a single tube output stage.
supply directly, they will behave like triodes because the cathode load is common to both plate and screen circuits. For pentode operation -the screen must be given an independent potential, most easily done by a series-feed resistance, suitably bypassed to cathode as shown in Fig. 703.
Single-stage feedback
Negative feedback over the output stage only is easy to arrange and cannot introduce instability. It may include the output trans former or not, as desired. Fig. 704 shows feedback from the plate of the output tube to the interstage transformer. The ratio…
Fig. 705. Applying feedback across n push-pull output stage.
Fig. 706. Applying feedback across the output stage and output transformer.
… of R1 to R2 determines the amount of voltage fed back and blocking capacitor C should be chosen to give the minimum possible reactance phase shift for those frequencies normally on the flat part of the response curve without feedback.
The arrangement is simply duplicated in mirror image for a push-pull output stage, as shown in Fig. 705, but note that the input transformer must have separate secondaries as the two feedback resistors R1 cannot be merged. Bias resistor R3 is, of course, common to both tubes and does not normally require bypassing. Precisely similar circuits can be used for tetrodes or pentodes. If it is desired to include the output transformer in the feedback circuit, the feedback potential divider is hardly necessary since there is appreciable stepdown in the output transformer.
The ground terminal of the input transformer can be taken directly to one terminal of the output transformer secondary, as shown in Fig. 706. In this case a push-pull output stage does not require a two-winding input secondary, the center tap of the secondary winding being taken to the output secondary. The phase of feedback must be watched, for connection of the output trans former secondary the wrong way will result in positive feedback.
Fig. 707. Applying feedback across two stages.
Fig. 708. The secondary of the output trans former is part of the feedback
loop.
Fig. 709. Rf bypass to ground in an early stage increases stability
in feedback amplifiers.
Two-stage feedback
Examples of feedback over two stages are shown in Figs. 707 and 708. Feedback can be taken from the output plate to the previous stage cathode (Fig. 707), or from the output transformer secondary to the previous stage cathode (last part of Fig. 708 and first part of Fig. 707) or grid (Fig. 708). It is desirable to be able to adjust the feedback voltage, as in the arrangement of Fig. 704, so a potential divider is connected across the secondary winding, represented by R1 and R2 in Fig. 708. In a developmental or experimental amplifier this can conveniently be a potentiometer or one of the resistors can be variable, which will allow a preset of either minimum or maximum feedback.
All these arrangements are equally suitable for push-pull working and, provided the reactances (and phase shift) of the first stage are suitably arranged, instability will not occur with reason able amounts of feedback.
Fig. 710. A capacitive shunt is sometimes placed across the' primary
of the output transformer.
Fig. 711. The diagram shows a capacitive shunt across the feedback resistor.
By methods similar to those of Figs. 704, 705, etc., feedback can be applied over three stages, or more, but instability will become troublesome unless certain precautions are taken. As has been explained, this is because of cumulative phase shifts due to bass and treble cutoff in the successive stages of the amplifier. Super sonic oscillation may not be heard in the speaker yet it may rise to such a value as to burn out the speaker voice coil. The first step in designing any multistage amplifier is to make sure that the output stage has no tendency whatever to oscillate at high frequencies in the absence of feedback. The oscilloscope is the best indicator of parasitic oscillations. Similarly there must be absolutely no tendency whatever to motorboating through common impedance coupling in the plate supply. The amplifier must be rock-steady without feedback under all possible working conditions so that, if instability appears when feedback is applied, it is known for certain that it is feedback that has caused the oscillations; otherwise the cause and cure can never be found.
Amount of feedback
The desired amount of feedback may not be possible if the design of the amplifier is inadequate. Instability can certainly be cured by reducing the amount of feedback and the easiest way ...
Fig. 712. Bass cut filter for feedback amplifiers.
... out may be to make sure that the performance of the amplifier with reduced feedback is adequate. Otherwise, simple corrective devices include connecting a very small capacitor between the plate of an early stage and ground (Fig. 709) shunting the primary of the output transformer by a suitable capacitor (value to be found by experiment) (Fig. 710) or shunting the feedback resistor by a capacitor (Fig. 711).
Staggered response
A more satisfactory method is to stagger the response of the several stages. In a three-stage amplifier, for example, by giving...
Fig. 713.
Treble cutoff filter is placed between plate and ground.
... the intermediate stage a narrower response than the other two, the phase shifts of the various stages will occur at different frequencies.
Although the final response may not be as wide as one would have hoped for, the somewhat narrower response may permit a degree
Fig. 714. Treble step filter is shunted across the plate load.
of feedback not otherwise obtainable, thus securing important feedback advantages with but slight loss of transmission characteristics (a convenient term for the frequency-amplitude characteristic of the amplifier). 1.
[1. H. W. Bode has evolved a method of some precision (see: Bell System Technical Journal, July, 1940, p. 421: "Relations Between Attenuation and Phase in Feedback Amplifier Design" and "Network Analysis and Feedback Amplifier Design"; D. Van Nostrand Co.) whereby· the appropriate response characteristics are determined in a mathematical device called the complex frequency plane, which can be applied to provide an amplifier with good feedback and good stability. A simplified treatment assuming that the attenuation characteristics are straight lines is described by V. Learned (Proceedings of the IRE, July, 1944, p. 403: "Corrective Networks for Feedback Circuits"), but this needs some skill in application. ]
Modification of the normal amplifier response involves shifting the frequency at which either bass or treble cutoff operates. Simple bass cutoff can be achieved by suitable choice of the cathode and screen bypass capacitors (C1 and C2 in Fig. 712), treble cutoff by the network between plate and ground in Fig. 713. But for the best results it is necessary to provide a "step" in the bass and treble attenuation. A bass step can be introduced by a network of the type shown in Fig. 712, a treble step by an R-C network shunted across the plate load as in Fig. 714.
It may be thought that the information just given is not very practical because specific values are not given. This is true but an empirical statement that such and such values of components are required is also of little practical value. It must be realized at all times that feedback is not just something that provides an easy way out for the shortcomings of careless design. It has been made clear that the response of the amplifier has a direct bearing on the behavior of the feedback loop. The amplifier is part of the feedback loop for the signal enters the amplifier, passes through it and is fed back to the input; the loop contains the whole circuit from original input to fed-back input. So, then, every reactance in the amplifier has to be considered in relation to the design of the complete feedback loop and the only way to do that is to calculate the complete circuit. This involves mathematical processes.
Stabilized feedback amplifier
----------- Bass attenuation and phase-shift nomogram--- Time constant in seconds = R X C where R is in ohms and C is in farads or R is in megohms and C is in microfarads.
It is obvious that the response of the amplifier must be known both as to voltage and phase change. Treble and bass boost or
Fig. 715. Ideal response of a stable feedback amp.
attenuation are also involved. The circuits which achieve this are filters, and filters are associated with what are usually called tone controls. These matters are dealt with in the next section.
The ideal response for a stable feedback amplifier is shown in Fig. 715. The dotted response curve represents the response expected from a well-designed three-stage resistance-coupled amplifier. At 6 db per octave attenuation of each stage, the attenuation over the three stages is 18 db per octave. The example given shows a flat response from 50 to 20,000 hz, with appreciable response at 20 and 40,000 hz. If substantial feedback, say, of the order of 30 db is applied to such an amplifier, phase shift of the attenuated response outside the desired limits of 50 to 20,000 hz will cause instability. To overcome this, the attenuation immediately out side the designed limits must be sudden and severe, as shown by the solid line, followed by a step, as indicated by the level parts of the solid response curve. Such attenuation characteristics are usually only obtainable by using L-C or L-C-R filters. In most cases these refinements are not necessary, as the degree of feedback is usually less; but where a three or more stage amplifier is to be improved by substantial feedback (in the present illustration there is also a nearly 10 db margin of safety, to guard against conditional instability) severe attenuation with a step filter is essential. It will be noticed that for a flat response from 50 to 20,000 hz the de signer of a successful feedback amplifier is concerned with the response over a range as wide as 3 to 300,000 hz. The danger of in stability is lessened by strict attention to the phase shift of each stage over the whole frequency response. Reference can be made to the phase shift nomogram shown.