, ' ,,.,EDITED BY THE RESEARCH LABORATORY OF N. V. PHILIPS' CI.OEILAMPENFABRIEKEN, EINDHOVEN, NETHERLANDS

Transcription

1 J -~-~--:-- --'-- ~~-~.~- -~~... - /. './ - _... ' I~. VOD: '5. NR i. FEBRUARY 1950 Researèh Reports.. EDITED BY THE RESEARCH LABORATORY OF N. V. PHILIPS' CI.OEILAMPENFABRIEKEN EINDHOVEN NETHERLANDS R 125 PhilipsRes. Rep. 5! A ;NOTE ON THE MAXIMUM FE~DBACK' OBTAINÁBLE IN AN AMPLIFIER' OF THE CATHODE-FEEDBACK' TYPE \ i ' ' ~ : \.. by J. te WINKEL ~'I The' total feedback on the last valve in a feedback amplifi~r is calculated for the case that the feedback voltage is derived from an ' impedanceinserted between the cathode of the Iast valve and earth (cathode feedback). This quantity is shown to have an upper limit which depends only on the frequency and on the ratio 'of the trans- 'conductance and input capacity of this last valve; the total feedback also appears to be invariably less than theproduct of the îndividual : feedback of the valve and the feedback around the main loop. Résumé \ On a calculé la contre-rëaction totài.e appliquëe au dernier tube d'un amplificateur à contre-rëaction dans Ie cas spêcial oü la tension. de contre-rëaction est dêrivêe d'une impëdançc insërëe entre la cathode du dernier tube 'et la terre (contre-rëaction par cathode).. On montre que cette quantité!lune limite supërieure déterminée par la frêquence et par le rapport entre la pente du dernier tube et sa _. capacitë de grille à cathode; on montre également que la contre- rëaction est toujours infërieure ' au produit de la' contre-réaction individuelle du tube et la contre-rêaction obtenue pour' le circuit principal. : Zusammen~assung I' 'I.~.... Man berechnet den Rückkopplungsfaktor fill die letzte Röhre eines rückgekoppelten Verstärkers fill den Fall dab die Rückkopplungs-. spannung abgenommen wird von einer Impedanz zwischen der Kathode der letzten Röhre und Erde (Kathodenrückkopplung)... Es wird gezeigt dab diese GröBe einen Grenzwert besitzt der nur ' abhängt von 'der lfrequenz und von -dem Verhältnis der Steilheit ' der letzten Röhre und deren Eingangskapazität; es wird gleichfalls gefunden dab der berechnete Rückkopplungsfaktor immer niedriger ist als der Produkt der Faktoren fill die letzte Röhre an sich und fill den Hauptrückkopplungskreis. '...~. I 'Lin~ amplifiers used. in carrier-telephone-communication systems : ~generally require a large amount of feedback firstly to reduce the harmonic. distortion caused by the output valve sufficiently to avoid mutualinter- fèrence of the channels amplified simultaneously and secondly to reduce. '

2 M. 2 J. te WINKEL. variations in the amplifier gain caused by changes in the various valves... A circuit diagram of a _conventional amplifier having one single feedback. loop is shown in fig. la. If the bandwidth required is large however a slightly modified circuit as shown in. fig. lb is to be preferred. This is known as the cathode-feedback circuit and other conditions being equal allows more feedback 1). In. a strict sense it is no longer a single-loop circuit because the first and last válves haveindividual feedback through' the impedance between their c~thodes and earth. In most cases as shown in fig. lb the individual feedback on the last valve is increased further since the requirements' in regard to output distortion are generally more severe than those for gain stability. ; I[ ]1 II[ Fig. 1. a: Single-loop feedback circuit; b. Cathode-feedback circuit. Circuit elements only necessary for d.c. supply are not shown. Unlimited application of feedback may cause the circuit to become unstable.bode has shown 2) that 'to achieve stability the feedback has to be limited. to a value that depends on the bandwidth the number of valves the safety margins and the so-called figur~ of merit of the valves i.e. the quantity e[c where s represents the transconductance and C the sum of input and output capacitances. The object of the pr~sent note is to point out that for the cathodefeedback circuit there is an additional Iimitafion of the total feedback on the last valve which largely offsets the advantages claimed for this type of circuit.. In order to demonstrate this the circuit diagram of fig. lb has been redrawn in fig. 2 showing only the last valve explicitly. All other valves v'. I

3 .. AMPLIFIER OF THE CATHODE-FEEDBACK TYPE are included in the network N which feeds a current i through the impedance Z (usually a capacitance) between 'grid and cathode of the last valve and also through the feedback impedance R. If the valve.is assumed to be a penthode. with transconductance s the output' current is then io=isz. The voltage acrossr which is fed back to the input is equal to.. l+sz (L + LO) R = LoR. sz. 3. I + Fig. 2. Essential parts of the cathode-feedback circuit. Further let the input and output voltages be ei and eo the output load. Ro and the amplification fa~tor Without' any feedback around the main loop p. Then from which the amplification with feedback p' can be derived: f1= R 1+sZ l+f1-'---. 'Ro sz The feedback on the last valve could be calculated by opening the feedback loop at the grid of this valve. However it is more convenient to.calculate instead the quantity S defined by ds to which Bode has given the' name sensitivity. This procedure is also

4 j '.. '4 J te WINKEL ' r '. J' more justifie( theoretically because the sensitivity give: 'directly the ratio in which the output distortion is reduced. For the circuit analysed here however feedback and sensitivity are equalê} Putting I'. R 1+sZ /3=--- s -z t ' one can write Logarithmic differe~tiation' gives S~milary Further pp 1 p = p/3 ~ dp' = 1 '(dp + d(3)_ dfj. p' 1+ p/3 p /3 ' B dfj 1 ds 'P=-l+sZ-;': df.i 1 ds ' -= -'.. P 1+ SZk s 'I for /-~includes the amplification of the last valve which is proportional tos/(l + 8' 1 ) Zk being the impedance determining the individual feedback on fhis 'valve. ' ' ':' ' Thus Generally Z ~'Zk; therefore the reciprocal of the first term 'of.this expression shows the feedback on the last valve which would normally he expected i.e. the product of the feedback around the main loop and the' individual feedback on the valve. The significance of the second term... of the expression however is not ~appar~nt at first sight. The derivation IP.ven shows that it results from the differentiation of fj: which contains the factor (1 + sz)/sz; this factor represents the ratio of the current. through the feedback impedance R and that through the output load Ro;- The main conclusion to' be drawn froin the expression for l/s isnów that its seco~d term will li~it' the sensitivity for the last valvè to the ' value 1 + s Z which limit could' 'only be reached if it we~e possible to increase the feedback around the main JooP indefinitely. '. ' It is seen that this limit depends only on die last valve ÎJ;l the circuit. In general Z will represent the grid-cathode capacitance of the valve but i~ should be possible to increase this impedance in certain'. frequency. ' I \'

5 . -'i.- '..~ '...: 'J'_. 5. '~r~gionsat ~he'e:l):penseof ~the~s by adding othe~ ~ircûit elém~n~s parallel. to th~ capacity In any case the general level of the maximum feedback' 'obtainable on the lást valve will depend only on the ratio of its trans- : con:ductance and input capacity which quantity is closely related to. the figure of merit 'previously referred to In practical 'cases where the feedback required on the last valve is : large the additional limitation discussed above may he severe. For in- I stance for a transconduct'ance of 8 ma/v and an input capacity of 12 pf the limiting val~e at ~ frequency of 3 Mc/sec will amount to 11+ s ZI =.35'4 or 31 db and the actual feedback realized will be still less depending on the fe~dback obtainable around the main loop. The.feedbaèk on the other valv~s will not of course be affected and the i~crease III feedback all?w_edby the cathode-fe~dba~k circuit is fully ~ffective. ' Eindhoven September 1949 \ REFERENCES 1) H. W. Bode Network analysis and feedback amplifier design Van Nostrand.New York 1945 p ~ 2) Bode loc. cit. Chapter XVII. 3) For a full discussion on the relation between feedback and sensitivity see Bode: loc. cit. Chapters IV-VI.. \ I /.