Correcting nonlinearity of transistor amplifiers

2 960 I R E T R A N S A C T I O N S ON A U D I O 103 Correspondence Comments on “Nonlinear Distortion Reduction by Complementary Distortion”* In his recent paper,’ Dr. Macdonald states that “complete cancellation [of dis- tortion] is impossible because of distortion of the original distortion, and that over-all distortion reduction is only possible over a limited range of input signal amplitude.” It appears to this writer that this conclusion is basedupon the mathematicalmodelchosen, and not upon physical reasoning. Consider the system of Fig. 1, in which two comple- mentarily distorting transducers having nonlinear transfer functions TI and Tz are connected in tandem. The over-all gain of the pair is to be linear and is taken as unity since this corresponds to the case considered by Dr. Macdonald. The condition to be attained is that TIT:. = 1. (1) Correcting Nonlinearity of Transistor Amplifiers* I n a recent paper,’ it was shown that a significant reduction in the nonlinear dis- tortion of an amplifier is obtained by adding a network, possessing a complementary non- linear transfer function, in tandem with the amplifier. If the network is connected to the input of the amplifier, predistortion of the signal results, tending to cancel distortion originating in the amplifier. Practical meth- ods of realizing predistortion in vacuum tube amplifiers have been illustrated2 using a network composed of resistors and semi- conductor diodes. These methods can be ap- plied to transistor amplifiers, and anexample of this technique is described below. The nonlinearity of a common-emitter amplifier can be appreciated by plotting the transfer resistance characteristic of the transistor, under operating conditions, against input voltage. Transfer resistance can be defined3 as The complementary circuit is shown in Fig. 2 (b), in which the nonlinear element is iden- tical t o t ha t of Fig. 2(a), and the GM ampli- fier is presumed to have a high output im- pedance. To calculate T, we presume an out- put voltage of eo. Hence, the output current is iout = f ( 4 ( 7 ) so tha t and where Vi, is the sum of the bias and signal voltages, and I , is the resultant collector current for that particular condition. This is illustrated in Fig. 1 for a 2N188A transistor under normal operating conditions and for different values of R,, the driving source re- sistance. Over the operating range, an al- most constant relationship exists between the characteristics representing R,= 0 and R,= 2000, given by Fig. 1. If we represent TI as a power series in eo, i.e., Rt - Rt - + 30 ohms. (R, = 2000) (R, = 0 ) then to satisfy (1) we have This is due to the almost constant ratio be- tween the collector current I , and the base current IB and corresponds in this case to a ratio of approximately IC I8 - = 66. Ideally, the transfer resistance should be constant over the whole of the working range as illustrated by the line AB. An ap- proach to this ideal can be achieved if R, is made to vary appropriately with the input voltage. The required resistance vs voltage characteristic of R, can be obtained directly from Fig. 1. For any pair of points on a line of constant collector current, such as CD, the vertical intercept of CD, multiplied by the ratio I c / I ~ , gives the required value of R, for that particular condition. At the same time, the horizontal intercept gives the ap- I I (b) Fig. 2. In ( 3 ) , T2 is defined in terms of its output voltage rather than its input voltage. There is no special merit in defining Tz in terms of its input voltage el. In particular, if a non- linear network approximating T I can be realized, then a similar network can be used to simulate Tz to the same degree of accuracy by simple transfer function inversion tech- niques. Consider, for example, the case in which a two-terminal nonlinear network N such as a combination of diodes and resistors is con- nected as shown in Fig. 2 (a). The R x ampli- fier is presumed to have very low input im- pedance. The input current is controlled by the nonlinear element i i n = j ( e o ) . (4) The over-all transfer function is Equating ( 5 ) and (8 ) , we see tha t R.tfGJf must be unity. I t is noted, that with this general ap- proach, the distinction between predistor- tion and postdistortion disappears, since we may assign the roles of correcting element and element to be corrected arbitrarily to either TI or Tz. Furthermore, the range of input amplitude over which the system may be expected to work is limited only by a zero in the derivative of el with respect to eo, since this would imply infinite gain in the complementary element. F. D. WALDHAUER Bell Telephone Labs. Murray Hill, N. J. * Received by the PG:, March 10.1960. * J. R. Macdonald, Nonlinearityndistortion re- duction by complementary distortion, I R E TRANS. ON AUDIO, vol. AU-7, pp. 128-133; September-Octo- ber, 1959. 2 G W Holbrook “Reducing amplifier distor- - 4 tion,” ‘EZ~cironic Tech.: vol. 37, pp. 13-20; January, t o m .,”-* 8 G. W. Holbrook and B. A. Bowen “Some factor; affecting nonlinear distortion in transislor amplifiers, 1958 IRE Canadian Conuention Record, pp. 388-396. 10-1 I I c = l m A P 5 0 QO- IVin-VOLTS (negative) ~ 0 2 0.4 0.6 Fig. 1-Transfer resistance. t-12V f2“ 4c 6b 8b 100 PERCENTAGE OUTPUT POWER Fie. 2-Compensated amplifier. propriate value of voltage to be developed across R,. The required nonlinear characteristic of R, is of the same general form as tha t ob- tained in a suitably biased semiconductor diode, Such an arrangement is illustrated in the interstage network sho~vn in Fig. 2. In this circuit the interstage coupling is formed by the semiconductor diode W , in series Ivith R1 and shunted by R?. Bias is obtained from the voltage divider, Ra and Rd, forming the bias resistor of a second stage. The improvement in nonlinear distor- tion obtained by this circuit is also illus- trated in Fig. 2 . This shoxvs the relative values of total harmonic content present when using the compensating network and when the network is replaced by a linear resistor eqrlal in value to R?. Cnder these conditions the compensated amplifier has a gain of slightly more than 1 db greater than the uncompensated case. By use of inter- stage netLTorlcs composed of semiconductor diodes connected in a “back to back” condi- tion, similar results have been obtained with Class :i and Class AB push-pull output cir- cuits. G. VL‘, HOLBROOK Head, Elec. Engrg. Dept. Royal Military College of Canada Kingston, Ont., Can. IRE TRANSACTIONS OAT A ITDIO May-June Distortion Reduction by Com- put transfer characteristic. This result shows tha t whenever one can conveniently adjust plementary Distortion”” and stabilize the operating aoints of a cir- I t is stimulating and valuable when a paper arouses sufficient interest that readers take time to write comments on it. .in au- thor almost prefers negative comments than none a t all, since this response a t least indi- cates the paper has been read. Therefore, I x ish to begin my reply to the correspond- ents who discussed my paper [l] by thank- ing them for their helpful comments, which not only serve to illuminate the subject in question further but give me the oppor- tunity to make a few additional informal re- marks. Greiner [ 2 ] mentions that practical tech- niques for complementary distortion reduc- tion have been used by him and others for some years and presents an amplifier-cath- ode follower combination as an example. It would be most valuable to the readers of these T R A ~ S A C T I O ~ S interested in the pres- ent subject if he would, in future corre- 2N107 +I work in this field by himself or others or n@d;3@c$ - L---->- J tative complementary results of measurements distortion reduction made on cir- his perhaps submit a short paper giving quanti- cuits. I believe no one would question his remark that the use of a single-tube volt- age amplifier followed by a cathode follower can yield less nonlinear distortion than the voltage amplifier alone. Because of the generally considerably lower distortion of a \Tell-designed cathode follower than a single- tube voltage amplifier, it is surprising that the serial combination of the two can, ac- cording to Greiner, yield less distortion than the cathode follower (presumably operating at the same output level) alone. Such a re- sult must require rather special operating conditions, and Greiner has performed a use- ful service by pointing out its possibility. Even more useful lvould be specific meas- ured results substantiating the effect in question. The author was drawn to speculate about complementary distortion reduction by fleeting references (now lost) in the litera- ture 011 “second harmonic cancellation,” and by the surprising results of harmonic and intermodulation distortion measurements made 011 an active audio filter built in 1955 [ 3 ] . ‘This device uses circuits involving cathode followers in combinations somewhat similar to that advocated by Greiner, and it was found that careful adjustment and stabilization of B + and B - voltages and heater current allowed greatly reduced out- put second harmonic and intermodulation distortion to be obtained as compared to that with unadjusted bias voltages and cur- rents. It is interesting to compare Fig. 8 of this paper [3] (intermodulation distortion vs output voltage) with Fig. 2 of the comple- mentary distortion paper [ l] (total harmonic distortion vs a quantity which is propor- tional to output \-oltage amplitude if the total distortion is not very high). I n spite of the difference between intermodulation and harmonic distortion, there is great simi- larity between the curves, indicating, as stated i n the text [ 3 ] , that proper operating r.R.z---- 1 2N188A spondence, either give references to published * Received by the PGA, April 29, 1960. cuit, adjustment fdr minimum output dis- tortion should be made to take advantage of whatever built-in complementary dis- tortion reduction is possible. Two recent publications which explicitly use nonlinear complementary distortion networks to pro- duce reduced over-all distortion are cited Greiner’s second point is that i t is not impossible to obtain complete harmonic dis- tortion cancellation by complementary dis- tortion as stated in my paper. I agree with Greiner’s conclusion; in the paper, my con- trary conclusion was not sufficiently re- stricted to stand correct as written. The pa- per showed tha t an infinite number of complementary correction terms were rra- quired to cancel completely a given distor- tion by the techniques proposed in the paper. It should have been made clear :!;at there is no necessity to have a one-to-o !e correspondence between correcting terms ill the completementary series and cotnple- mentary distortion networks. In ideal cases, a single correction network (see later discus- sion) may be used to realize the required transfer characteristic. I t is generally believed that negative feedback can only reduce but not eliminate nonlinear distortion. An ingenious feedback arrangement due to Guanella [6] has been shown theoretically and experimentally j71 to allow complete cancellation of nonlinear distortion and interference. Thus, here is another method different in kind from complementary distortion reduction which shows that, unlike taxes, distortion need not always be with us. Klipsch [8] has stated that while com- plementary distortion reduction can be ac- complished for single frequencies, the resto- ration or undoing of modulation distortion occurring with multiple input frequencies is impossible. I am grateful to him for bringing up this matter since his statements repre- sent a rather commonly held viewpoint which probably should have been discussed in my paper. Actually, complementary dis- tortion can produce the effect of unmodulat- ing (not demodulating) an intermodulation signal and can thus m.ork as well with mul- tiple as n-ith single frequency input signals. Consider second harmonic distortion fol- lowed by postdistortion complementary dis- tortion correction. The output of the original distorting circuit may be written as el =ale I +a2ea2. IYith an input signal consisting of two sinusoids of frequencies SI and fi, the eo2 term produces in the output el signal com- ponents having frequencies of. ( f a - f ~ ) and (f2-fl). I t is often thought that once such modulation terms appear, nothing can be done about it. This is not so. hfter the out- put el has been passed through a perfect postdistortion circuit of gain bl, the result- ing output will be just albleo and will contain no distortion of any kind [l]. Rather thar unmodulating the modulated signal, a man- fest impossibility and the root of Klipsch’s comment, the postdistortion circuit gener- ates a nex distorted signal which has modu- lated components of the proper amplitudes and phases in relation to those at its input - . 1.11, 151.