J10 Enhanced Cascode

PAPERSReductionof Transistor Slope Impedance Dependent Distortion in Large-Signal Amplifiers* MALCOLM HAWKSFORD University of Essex, Department of Electronic Systems Engineering, Colchester C04 35Q, UK 0 INTRODUCTION The static characteristics of a bipolar transistor reveal that, under large-signal excitation, there are sources of significant nonlinearity. In an earlier paper [ 1] consideration was given to the IE/VBE nonlinearity, where a family of techniques was presented to attempt local correction of this error mechanism. However, the collector-emitter and collector-base slope impedance of transistors also result in significant distortion, where under large-signal conditions they can become a dominant source of error [2]. The static characteristics show only part of the problem; a more detailed investigation reveals capacitive components which are dependent upon voltage and current levels. Consequently under finite-signal excitation, modulation of the complex slope impedances results in dynamic distortion. It will be shown that the level of error that results from slope distortion is not strongly influenced by negative feedback once certain loop parameters are established. Also, because of the frequency and level dependency of slope distortion, the overall error will contain components of both linear and nonlinear distortion that are inevitably linked to individual device characteristics. It is therefore anticipated that a change of transistor could, in principle, lead to a perceptible change in subjective performance, even when the basic dc parameters are similar, In this paper consideration is given to a class of voltage amplifiers employing a transconductance gain cell gm, a gain-defining resistor Rg, and a unity-gain isolation amplifier, together with an overall negativefeedback loop. This structure is typical of most voltage and power amplifiers. However, although it is more usual to focus attention on input stage and output stage distortion, we shall consider in isolation the distortion due only to slope impedance modulation and assume other distortions are controlled to an adequate performance level. It will be demonstrated that significant 5 distortion results from-Rope modulation, and a design * Manuscript received 1987 June 22. J. Audio Eng. Soc., Vol. 36, No. 4, 1988 April methodology is presented to virtually eliminate its effect, even when the slope parameters are both indeterminate and nonlinear and when signals are of substantial level. We commence our study by investigating the role of negative feedback as a tool for the reduction of slope distortion and to show that although effective, in isolation, it is not an efficient procedure. I NEGATIVE FEEDBACK AND THE SUPPRESSION OF SLOPE IMPEDANCE DEPENDENT DISTORTION Consider the elementary amplifier shown in Fig. 1, where the principal loop elements are transconductance gm, gain-defining resistor Rg, and feedback factor k. The nonideality of the transconductance cell is represented by an output impedance Zn, where ideally Zn = o% but in practice is finite and signal dependent. (Any linear resistive component of Zn is assumed isolated and lumped with Rg.) In general, Zn is a composite of the slope parameters of the output transistors in the transconductance cell. It can also include a reflection of any load presented to the amplifier. However, we assume here a perfect unity-gain buffer amplifier to isolate the slope distortion of the transconductance cell. Although Zn is signal dependent, our analysis will assume small-signal linearity so that performance sensitivity to Zn can be established. However, the circuit topologies presented in Sec. 3 are not so restricted and can suppress the nonlinearity due to Zn modulation. For a target closed-loop gain _/there is a continuum of k and Rg for a given gm, where the target closedloop gain _ for Zn = oDis defined, gmRg 1 + kgmRg as _ - (I) Hence for a given k, gm, and _/, Rg is expressed Rg - gm(1 - _k) (2) 213 it is an interesting example of a distortion that is not reduced by moving from a zero-feedback to a negativefeedback topology. respectively. the base and emitter bulk resistances are assumed lumped with Rs and RE. the independence of E on k and Rg for a given 'y and gm is true for distortion resulting only from Zo. (6) and(7) revealthat to reduce the dependence on slope distortion. (5). a factor not considered in the present discussion. For analytical convenience. 1. (2) is satisfied to set the target gain _. it is important to observe that Zn reduces with increasing frequency due to device dueto closed-loopstabilityrequirements.k. is A = gmZnRg Zn + Rg + kgmZnRg (3) PAPERS gm is to be anticipated for a given output [1].. Audio Soc. Elementary amplifier topology using transconductance 214 cell and gain-defining resistor. especially as the choice of Rg is often the principal distinction between low-feedback and high-feedback designs [5].sofrequency capacitance and that gm also reduces with that there are fundamental constraints on the effectiveness of slope distortion reduction using overall negative feedback. [___ Fig. However. 3 in both single-ended and complementary formats. Fig. ol. -_/ 'Y + In practice whereby gmZn E - (6) gmZn > > _ for a well-behaved amplifier. the product {grnZn} must increase. particularly high at frequency. and an estimate is made of the output impedance Zo for a range of circuit conditions. for finite Zn. where Zeeand Zcbrepresent collector-emitter and collector-base slope impedances. 4 illustrates a small-signal transistor model of the common-emitter cell. respectively.36.No. and when considered in isolation. The output impedance Zc observed at the collector of the common-emitter ellis givenby c where E represents the ratio of error signal to primary signal and can be visualized according to Fig.4. J. 2. V April . In this section the output impedance of the common-emitter amplifieris analyzedin termsof the small-signal parameters for a range of source resistances Rs and emitter resistances RE. in power amplifier circuits. for 0 _< k _< 1/'y. The error contribution due to Z n can be estimated by evaluation of the transfer error function [3]. 1988 Eng. As an aside we are assuming gm to be linear. / //. In practice a reduction of Rg places a heavier current demand on gm. 2 OUTPUT IMPEDANCE OF COMMON-EMITTER AMPLIFIER The common-emitter amplifier is shown in Fig. (2) for selected target gain 'y and transconductance gm.HAWKSFORD where. [4] E defined by A E 1 (5) examined as a transconductance cell and current mirror. i 1 . thus a greater distortion contribution from + Rs(1 - -Vin _ primarysignak---. Transfer error function model of voltage amplifier in Fig. 2. provided the condition of Eq. 1. Also. gmZn A 1 + gngm/' Y (4) This result demonstrates that the dependence of the transfer function A on Zn is independent of the selection of feedback factor k._/_(/__ _ V o error signal -"_ _ L_V_3 Fig. (4) into Eq. the output stage will exhibit distortion under load. E-_ -'Y gmZn (7) Zc - Vo OLio 1 ct ( Zee + RE + --Zee [RE Zbe ) et)] (1 + hfe) (8) Theresults of Eqs. and hfe is the collector-base current gain.._. then 'Y/gm _ Rg _ o% The actual closed-loop gain A. In the next section the common-emitter amplifier is and eliminating Rg defined by Eq. Substituting A from Eq. . However. . (11). Soc. 4. thus the grounded-base stage as used in the cascode will offer superior results in terms of output impedance. Eq. especially as Zcbfalls with frequency. zc = (Zee + RE)(ZbcZcb Rsh) + (1 + hfe)Zce(REZcb.Zcb where. 5. and results in lower overall distortion that is virtually frequency independent.RE >> Zbe/(1 + hfe). RE >> Zbe/(1 + hfe). Applying inequalities to Eq.to( 1 --oQ I RE (a) (b) RE -rs I E .REk current division factor is (9) This case is typical of the current source and grounded-base amplifier as used in the cascode configuration. RE i× i° [ R ' amplifier 215 Fig.hfe)Zce + Zcb + Zbe (10) or.Zce) -[- MRs + RE) (11) The expressions for Zc reveal significant complexity. (a) Single-ended current mirror. 4) Case 4: Rs >> Zb_. Zc _ (1 + afc)Zee + Zcb Rj--I- kE j (12) R_RE +I Rs +RE (15) that is. alteratively. 4. (1 1). 4 a new form of distortion correction is proC F 'n bo(l o [ % Zbe IB () v° I b __ __ _ I . Hence. 3) Case 3: Rs >> From Eq. hfe}. eliminating a. To simplify the results. consider a family of approximations for Zc for specific cases of Rs and RE.(1 q. (11) reveals hRE >> Zbe(Zcb -Jr zee). (1 1) reduces to Zc ZceZcb Zce -}. Common-emitter gain cells.. Eq. RE = O. so that the dominant contributors to the output impedance can be determined. Audio Eng. ---. which is compounded by the signal dependence of the small-signal parameter set {Zce. I Ri posedZee and Zcb even when impedance dependence on both that reduces output nonlinear. (b) Complementary current mirror. 1) Case 1: Rs = O.Rszce) + Zbe(Zcb q. Such distortion is demonstrated in Sec. 2) Case 2: Rs = 0.Zcb. No. Small-signal model of common-emitter showing slope impedances zee and Zcb. (10) approximates to h = (1 + hfe)Zce and the denominator of Eq. J. Zc _ Zcb · (13) In selecting a circuit topology it should be noted that Zcb> Zee.PAPERS SLOPE DISTORTION IN LARGE-SCALE AMPLIFIERS where the collector/emitter ct = 1 + and gbegce 't. Zc -_ Zbe. Zcbis still signal dependent and represents a significant distortion mechanism where large signals are encountered. Zc is Zce in parallel with Zcb/ (1 + hr0 and represents the worst-case output impedance condition. RE = O. Vs In Sec.Rsh Zcb Z!b + Zce Zbe + (1 Zbe + (14) + hfe)R Rs s _.Zcb. 3. Zbegcb q. Vol. Nevertheless. 1988 April Fig. for Rs >> Zbe. 36. and noting Zbe< < Zce. Zc is parallel combination of Zee and Zcb. Zbe. thus the common-emitter stage offers a minimal slope distortlon contribution. experimentation has revealed the desirability of ac bypassing of the base bias resistance of the groundedbase stages [see capacitors C in Fig. with the driver stage adding a degree of slope dis'tortion under large-signal excitation. a substantial increase in collector impedance is possible and that this is achieved even when z¢_ and Zcbare dynamic. 6(b)]. Two circuit approaches have been identified to meet the requirement of base and collector current summation without direct connection tO the c011ector_ These are based on a local feedforward and feedback strategy. 6(b).HAWKSFORD PAPERS 3 REDUCTION OF NONLINEAR SLOPE IMPEDANCE DEPENDENT DISTORTION The output impedances of the grounded-base and common-emitter amplifier cells are bounded by the device slope impedances Zcb and Zc¢. This technique both reduces output device power dissipation and aids a further increase in the slope impedances.2 Feedback Topology The conventional cascode as illustrated in Fig. Audio Eng. respectively. No. with typical component values and transistor parameters. (8) reveals that the factor ct in the denominator restricts the output impedance. is still substantial advantage. while in Fig. with only the output collectors swinging the full range of output voltage. There are many possible topologies offering minor variations.1 Feedforward Topology The feedforward topology is a derivative of the Darlington transistor that is occasionally employed in power amplifier current mirrors [6]. (16) reveals that. 4 NOISE CONTRIBUTION OF GROUNDED-BASE STAGE WITH BASE CURRENT SUMMATION In this section brief consideration is given to the . The conventional Darlingtonconnection of parallel collectors compromises this ideal. then the expression for collector output impedance would become vo eric + (1 = Vo io an upper bound on Zcu is ratio of RE to the emitter of of current will although there transistor output impedance as seen at the output device. respectively. 36.contribution of noise from the common-base stage in the cascode for the two basic topologies shown in Fig. 3. so that lower values should be anticipated. If a modified circuit topology could be realized such that the base current is summed with the collector current but without incurring an extra load on the collector. 6(c) the basic current paths are illustrated which apply even when Zceand Zcb are nonlinear. (16). This both enhances circuit operation and eliminates any tendency toward high-frequency oscillation due to the positivefeedback loop formed by the base-emitter connections. 1988 April . In practical topologies this is compromised by a small margin. However. 2. Soc. as demonstrated by cases 2 and 3 in Sec. Zcb Reduction The methods based on feedforward and feedback addition of the output device base current can be compounded to offer further performance advantage. 5 two circuit examples are presented which yield similar performance. It should be noted that the collectoremitter voltage variation of the drivers is small. which is a significant improvement over the common-emitter stage as Zcb> Zce. Vol. though each uses the same basic concept. 4. As a practical detail. 6(a) offers an output impedance approaching Zcb. It is not intended to analyze each variant. In each circuit the base current of the output device is returned to the emitter via the emitter-collector of the driver stage. it is only the output device whose collector is required to swing over the full output voltage. 6(b)] can lower the operating current of the common-base stage. The new topology is shown in Fig. 3. yet with an enhanced output impedance realized by removing the respective currents in Zce and zcb from the output branch of the complementary stage. 7 to stimulate development. this result is an upper bound that assumes that all the base current is returned to the collector. (8)-(10) established where Zcu = R E +Zce + (1 + hfe)Zce(ZcbR E - zceRs) (16) gbe Zcb q- Rs_' An examination of Eq. a bypass current Ix [see Fig. and can be used independently or cumpounded to give further enhancement.:)mportant to note that a small fraction of output transistor base current is not returned to the emitter and is dependent on the 2i6 Topologies for Zce. In circuit applications where the common-emitter stages operate at a high bias current to improve IE/VBE linearity. A simple modification to the basic circuit can return the base current of the grounded-base stage to the emitter of the common-emitter stage. Consequently the advantages of the Darlington are retained. [7]. though a family of topologies is presented in Fig.. However. while circuit symmetry ensures that noise in Ix does not flow in the output branch. It is clear that because the common-emitter stage offers a relatively high output impedance at the collector. In both cases let i2n be the mean square noise current in the collector of the common-emitter stage and let the common-base stage have respective noise voltage and noise current sources e2nand in 2.3 Compound Feedback/Feedforward ZCU ot)io Hence from Eqs. Again. the equivalent voltage noise generator of the commonbase stage yields a negligible contribution to the output d. This fractional loss lower the bound suggested by Eq. 3. 8. howeveri. It is. Consequently signal current flowing in both Zceand Zcbnow formlocal loopswhichdonot includethe outputbranch. an examination of Eq. In Fig. Audio Eng. Soc. Slope distortion reduction using feedback topology. (b) Enhanced cascode. 4. Vol.PAPERS SLOPE DISTORTION IN LARGE-SCALE'AMPLIFIERS v s ih! vs ib! ibl . (a) Conventional cascode. 36. 1988 April 217 . -v_ (Observe base current RE k (a) (b) · [ '_ % (c) Fig.) offeedforward addition ofoutputstage base currents using a two-stage ib 2 (b) topology. 5.. Two examples paths ibl and ih2. (c) Illustration of signal current paths ice. ionin zee. No. 6. zcb. J.ibl +ih2 Io ibl Io ib 2 ib2 -v_ (a) Fig. Audio Eng. while in Fig. 8(a) almost all in must flow in the 2 collector. _. resulting in only a fraction. an inspection of the noise current paths reveals that in Fig. Circuit examples using two-stage common-emitter amplifier with a common-base output stage. h Rs RE Rs RE (a) (b) Fig. Vol. However. (b) Enhanced cascode. 1988 April . 7. 218 d. Consequently with the enhanced topology there is virtually no extra noise generated by the addition of the com__mon-basestage. 4. Soc. i t I t Fig. (a) Conventional cascode.HAWKSFORD PAPERS noise current. appearing in the collector (assuming similar transistor hfe' S) . Noise sources of common-base stage. No.. hence effective load. 36. 8(b) virtually all the noise current circulates locally through the common-emitter stage. 8.in2/[1 + 1/hfe + hfeRE/(Rs + RE + Zbe)] 2. Hence the output noise current is also i2n. the error signal due to the modulation of output impedance Zn was not dependent on the level of feedback. though they follow the same basic frequency dependence. [10]. The enhanced topology has specific application in large-signal voltage amplifiers and. or at 50 kHz this requirement rises to more than 40 dB. reaching an unacceptable 1. and an offset-null potentiometer is provided since no servo amplifier is used. Audio Eng. It is interesting to observe that if negative feedback alone were used to reduce error dependence on Zn by the same factor as the enhanced cascode. whereby useful distortion reduction can be achieved for large-signal voltage amplifiers. thus vindicating the adoption of the enhanced topology. In particular. more fundamentally. These tests are sufficient to validate the technique. 36. An appendix outlines how slope impedance distortion reduction can improve the performance of voltage/power amplifiers by enhancing the interface between amplifier stages which alternate their signal referencebetweengroundand supplyrail. 9(c). However. Although the reduction of large-signal-related errors arising from slope distortion has been the central thesis. A third area of application is RIAA disk preamplifiers that use a transconductance cell and a passive equalization-defining impedance [9]. 1988 April A theory was presented to demonstrate that for a given input cell transconductance and closed-loop gain. Such device-specific distortion can. MOSFETpower amplifiers can benefit by using a more optimum current source to drive the output stage since this reduces dependence on both gate-to-source voltage errors as well as slope impedance modulation errors [8]. The more optimum current source will lower distortion and increase EQ accuracy as the current source exhibits a lower output capacitance. a test circuit was constructed to validate the technique and to permit an objective assessment. 9(a) and (b). the same level ' of distortion due to modulation of Zn should be anticipated.9% at 50 kHz. although distortion products are of a lower order. However. if overall feedback was applied together with an appropriate increase in the gain-defining resistor Rg. with the eomparative output stage variants highlighted in Fig. Such factors are often impractical to achieve. and moves against the loop gain requirement for stability. 4. which reflects the popularity of this topology. especially as the cost overhead is minimal compared with the conventional cascode. the latter particularly affecting low-frequency performance. where zcb _ Zee. 6 CONCLUSION This paper has presented a method of reducing the performance dependence on transistor collector-emitter and collector-base slope impedance parameters. thus making negative feedback less effectual in suppressing slope-dependent nonlinearity. The total harmonic distortion results are given in Table 1. ifRg is raised. they are still frequency dependent. The conventional cascode exhibits a marked improvement. though clearly they are a limit to linearity for the enhanced circuit. where performance is almost independent of both Zee and Zcb.PAPERS SLOPE ISTORTION D INLARGE-SCALE AMPLIFIERS 5 MEASURED PERFORMANCE OF ENHANCED TOPOLOGY ADVANTAGE To highlight the performance advantage of the modified common-base stage and to demonstrate the significance of slope distortion at large signal levels. together with the indication that the two stages of amplification are of inherent low distortion.This later distortion would be particularly evident with the enhanced cascode.) However. contribute to the subjective performance and 219 . Of particular significance is the almost frequency-independent nature of the distortion. together with a higher output resistance. (Note that a unity-gain buffer amplifier would be required. Soc. resulting in a reduced distortion from modulation in gm. the reduction of linear distortion at lower signal levels is also welcome. and represent a substantial performance enhancement irrespective of whether overall feedback is contemplated in a final design. Three variants of the circuit were constructed and tested with ascending levels of modification. shows a distortion reduction greater than 40 dB at 50 kHz with a very desirable 31. Consequently for the test circuits of Section 5. while the common base stage is Zcb. the signal current level operating in the transconductance gain stage will fall. J.8-dB improvement at 1 kHz over the basic circuit. the distortion dependence on transistor slope impedance inevitably rises with both frequency and output voltage level. No.. This difference in performance arises from the basic common-emitter stage having an output impedance --_Zee. with appropriate circuit additions. hence the tracking of the distortion figures. at 1 kHz an increase in loop gain of more than 30 dB is required. This performance level was masked by slope distortions in the conventional circuit. the enhanced cascode. Slope distortion has been shown to involve several factors that depend on both transistors and the associated circuit elements in a particular application. The circuit is dc coupled and no overall feed_t_ack i§ used. All measurements were performed with a sinusoidal input and an output voltage of 80 V peak to peak. The ehhanced topology is shown in Fig. The techniques described in this paper should also find application in circuits that require enhanced supply rail rejection. where distortions are consistently reduced by 20 dB compared with the no-cascode circuit. to power amplifiers. where modulation of gm is now the limiting distortion mechanism. provided gm and target gain 'y remained constant. Vol. This result is a function of the voltage-dependent nature of the device capacitance and represents a severe dynamic distortion. The results show that the basic circuit exhibits a distortion rising with frequency. in principle. However. The output voltage is derived using a 10kfl gain-defining resistor Rg. No.011 0. % 0. Test frequency. 9.9 Conventional cascode.T. (b) Complementary J. Vol. However. There are numerous circuit possibilities for enhancement.039 0. Test circuit with three output stage variants.47 0. Total harmonic distortion. . 1988 April . 36.16 Enhanced cascode.T 50Y common-emitter output stage. which are candidates for adoption in transconductance-based amplifiers.T_ 'T' ' 7 (a) (b) :loon off_tnun PNPZTX753 Zk4 100n 220R I00n 560. cascode output stage. the two Table 1. Soc.010 0.51 1. Thepaper has presented a familyof primitive circuit topologies based on the same principle as the enhanced cascode. 4. Audio Eng.012 0.+VO 1Ok lo_ _T_ .016 +50Y +50Y lOOn _.11 0.14 0.. which results in small deviations from the target transfer function. (c) Complete test circuit with 220 (a) Complementary enhanced cascode.. kHz 1 10 20 50 No cascode. % 0.39 0. (c) Fig.HAWKSFORD PAPERS reflects the mutual interrelationship of transistors and circuit construction. % 0. about the genesis of the Pip. Albinson. Soc." HFN/RR. 30." J. [10] O. 7 ACKNOWLEDGMENT The author wishes to gratefully acknowledge the assistance of Paul Mills from the Department of Electronic Systems Engineering for his support in constructing and compiling the measured data on the three circuit derivatives." Audio Amateur.). [7] P. 36. Two-stage voltage amplifier with Vsrepresenting power supply voltage variation. Soc. 8 - Vo/Vs Vo/Vin (18) supply rail I . J. vol. 25 (1985 Dec. Hawksford.kmgmRg (17) Let 8 be the ratio of output to input transfer functions for inputs Vs and gin . "Current Dumping Audio Amplifier. p. pp. vol. preprint 1995. Soc. vol.current mirror Vin nl R8 Fig. R.). m the current gain of the current mirror. and k the feedback factor. (Abstracts). to disassociate Zcbfrom the output impedance at the collector. APPENDIX SUPPLY RAIL REJECTION AS A FUNCTION OF INPUT STAGE AND CURRENT MIRROR SLOPE IMPEDANCES In this appendix the sensitivity of a two-stage negative-feedback amplifier is determined as a function of the slope impedances Znl and Zn2 of the two stages. "Power Amplifier Output-Stage Design Incorporating Error-Feedback Correction with Current-Dumping Enhancement. 960 (1983 Dec.. "A MOSFET Power Amplifier with Error Correction. 12.). M. pp. "Feedback. Rg a gain-defining resistor. Soc.17 (1984 Jan. vol. Jones.)." J./Feb. 31. Cambrell.Rg/Zn2 ) 4. 23. Soc. P.PAPERS SLOPE ISTORTION D INLARGE-SCALE AMPLIFIERS basic principles to be observed are 1) Adequately high effective emitter resistance RE to disassociate Zee from the output impedance at the collector.. vol. 8 REFERENCES [l] M.. Audio Eng. no. pp. together with a distortion characteristic that is considerably less frequency dependent. No. mgmRgVin to express Vo as a function of 4-Rg[m/Znl 4. 32. 4. Cherry. 30. 409 (1975 June). J. pp. [9] Y. [2] E. 282-294 (1982 May). [4] M. pp. 10 where gm is the transconductance of the input stage. Audio Eng. Audio Eng.). p. Soc. Sensitivity." presented at the 74th Convention of the Audio Engineering Society. J. 7-12 (1986). vol." presented at the 50th Convention of the Audio Engineering Society.r2/Znl ) (1 4. J. K. "The Lang 20W Class-A MOSFET Amplifier." HFN/RR (Letter to the Editor). 30. 35-40 (1985 Dec. 10. pp. 85. 1524. Audio Eng. p. 1988 April 221 . Vol. 503-510 (1981 July/Aug. 2. M. Cherry and G. Observation of these two principles then enables a transformation of the signal level from low voltage to large voltage without incurring a significant distortion penalty due to dynamic modulation of the transistor slope parameters. Hawksford. 2. Hawksford. vol. [3] M. vol. Cordell. pp. Soc.J. without adding extra circuitry to collector. vol." J. Walker and M. no. Lang.r2/ZnlZn2]V s Vo - (l 4. "Distortion Correction Circuits for Audio Amplifiers. J. vol. r2 the input impedance of the current mirror (r 2 < < Znl). "Audio Preamplifier with no TID. [6] E..". Using linear analysis both Vin and Vs.. Audio Eng. 58-60 (1979 Aug." J." Wireless World. and Sta- bility of Audio Power Amplifiers. [5] K. Miloslavskij. 30. Audio Eng. 2) Addition of base current to collector current.1/Zn2 4. The basic circuit is shown in Fig. "The Essex Echo: Reflexions. "Output Resistance and Intermodulation Distortion of Feedback Amplifiers.). '29. J. Audio Eng..). [8] R.. 178198 (1982 Apr. (Abstracts). Also in low-feedback designs greater local feedback enhances the wide-band distortion characteristics of gm and helps aid an overall distortion profile which is less frequency dependent.D. motorcycling and motormechanics. the distortion is processed completely by the feedback loop. and a member of the Review Board of the AES Journal. Dr. Vol. (19) is also shown to be independent of Rg. observe how Ra and Zn2 form a potential divider to supply injected distortion. No. Since his appointment at Essex. The Ph. This is particularly important in power amplifier applications.HAWKSFORD and PAPERS Eq. where research on amplifier studies. and Ph. but as Rg-->oo. in high loop gain applications where gm is _= 1 + 1 1 + r2 mZn_ ( [Z_ 1 Znl)] 1 gm (19) define The results show that the slope impedances gether the high-frequency high-frequency characteristics may large.D. Hawksford studied at the University of Aston in Birmingham and gained both a First Class Honors B . Hawksford has had several AES publications that include topics on error correction in amplifiers and oversampling techniques for ADC and DAC systems. distortion a the falling particularly gain required toif of gm to suppress wide-band power supply injection. where his principal interests are in the fields of electronic circuit design and audio engineering. 222 J. Dr. program was supported by a BBC Research Scholarship where work on the application of deltamodulation to color television was undertaken. digital signal processing and loudspeaker systerns has been undertaken. 4. become withlimiting factor. a Chartered Engineer. Fellow of the AES. His leisure activities include listening to music. For example.Sc. In lowfeedback applications. Audio Eng. His supplementary activities include designing commercial audio equipment and writing articles for Hi-Fi News--activities that integrate well with visits to Morocco and France. 36. where in class AB operation Vs is wide band (> >20 kHz) and a nonlinear function of the input signal due to output stage commutation. Hawksfordis a memberof the lEE. the suppression of supply rail rejection together with gm. The advantages of maximizing both Znl and Zn2 and using separate power supplies for voltage amplifier and output stage in power amplifiers are evident. Soc..Dr. THE AUTHOR I. he has established the Audio Research Group. However. the slope impedance dependent distortion is suppressed more by the presence of Ra than by the presence of gm. U.. 1988 April .K. Malcolm Hawksford is a senior lecturer in the Department of Electronic Systems Engineering at the University of Essex. Documents Similar To J10 Enhanced CascodeSkip carouselcarousel previouscarousel nextDrum shuffleHigh Efficiency Audio Power Amplifier Van Der Zee12 Bar Blues DrumsToto - Rosanna drum sheet musicTransistor CookbookJ4 Distortion Correction Circuitsapplication of op ampKnowledge-based parametric design of mechanical products based on configuration design methodElectronics Lab 9Feeling and FormCEAmpSu10CHH-b.e-LAB-2Texas Blues ShuffleThe Real Folk Blues Drum ScoreLaboratoria 1 Electronica 2-AMPLIFICADOR 30WSssssssss Sssssssss25. VLSI syllabusPar Darling Ton320 Lecture 23LF398_2 datasheet Syllabus 1st Year38683607-AmplifierAmplifierIECEP ELEXAmplifierAnalog Electrical Multiple Choice TestDesign and Simulation of Low Noise Amplifiers at 180nm and 90nm Technologies3-130715032206-phpapp02Copyright10. PICs y Amp. Op..pdfMore From Алексей ГрабкоSkip carouselcarousel previouscarousel nextGnossienne No 5Gnossienne No 1 and 3Chopi (Danza Paraguaya) (Las Tres Palomas) [3a. en Sol#] [4a. en Si] [5a. en Sol#]Gymnopedie 2Erik Satie Gnosienne 1Je te veuxVassiliev Konstantin WorksErik Satie Gnossienne No 3Gymnopedie 3No 6, Though Far From JoyErik Satie Gnossienne1gymnopedie1_Gnossienne No 4Simon Steen Andersen Insideout Side in...gnnosienne2Leguizamon-Castilla- El Silbador (Arr. P. Marquez)SongbookVinogradovaJens-Peter Braun - O ChoraoCs Amps SpeakersGubaidulina, Sofia - Toccata, For GuitarJ12 Distortion Reduction MC Current DriveKamil Bartnik - I Wanna Know the Name of Love for Two GuitarsBartok Bela_Gyermekeknek, Tr BrodszkyQuine, Hector - Guitar TechniqueKarl Wieland Kurz - Il Giardini Del Sogno - Ed. HoppstockDIY.JE-990.DOA.V1AUp SamplingQuine, Hector - Guitar TechniqueXp CookbookFooter MenuBack To TopAboutAbout ScribdPressOur blogJoin our team!Contact UsJoin todayInvite FriendsGiftsLegalTermsPrivacyCopyrightSupportHelp / FAQAccessibilityPurchase helpAdChoicesPublishersSocial MediaCopyright © 2018 Scribd Inc. .Browse Books.Site Directory.Site Language: English中文EspañolالعربيةPortuguês日本語DeutschFrançaisTurkceРусский языкTiếng việtJęzyk polskiBahasa indonesiaSign up to vote on this titleUsefulNot usefulYou're Reading a Free PreviewDownloadClose DialogAre you sure?This action might not be possible to undo. Are you sure you want to continue?CANCELOK