THD Cancellation in Push-Pull Stages  

Fig. 1 The true Push-Pull Stage

You can also find a push-pull stage, mainly in Japanese realizations, as driver for single_ended amplifiers with power  tubes of the transmitting variety, Fig. 2.

Fig. 2 A Push-Pull Driver for a Single Ended Output Stage

         In a true push-pull stage the signal on the secondary of the output transformer it’s caused by a process that includes also a differentiation; this permits the theoretical cancellation of even harmonics and, for triodes, also a sensitive reduction in the THD and InterModulation Distortion (IMD).

         From Fig. 1, you have:

ip1= h1*Vin+h2*Vin^2+h3*Vin^3+…+  (17)

ip2= -h1*Vin+h2*Vin^2-h3*Vin^3+…-   (18)

 since

Vin1= -Vin2= Vin.

By differentiating (18) and (19) you’ll have:

id=ip1-ip2= 2*h1*Vin + 2h3*Vin^3 = (2*h1*Vp + 3/2*h3*Vp^3)sinwt – ½*h3*Vp^3sin3wt +… (19)

 and therefore the perfect cancellation of even harmonics is obtained.

An ideal push-pull with triodes presents the maximum output power when:

 RLp-p= 2*ri  (20)

 where  ri is the internal resistance exhibited from each triode. Besides:

 RLp-p <2*ri produces higher distortion and lower power, while

RLp-p >2*ri produces both lower distortion and power.
 

 From a theorethical point of view it’s interesting to observe that  the reduction in the THD when RLp-p increases, is not indefinite because very high value for RLp-p can cause an increase in the 3^rd harmonic that being the most significative component in the output spectrum can produce an increase in the T.H.D. Fig. 3 shows this phenomenon on a simulated push-pull stage.

More interesting appears instead the possibility to analyze the spectral behaviour in presence of structural asymmetries. In fact a real push-pull amplifier will  always present asymmetries as umbalancing in the bias current, slightly different driving signals,  different half-primary impedance and so on.

Fig. 3 3rd harmonic vs. THD in a Push-Pull Stage
 

If the unbalancing is of small entity it cannot produce harmful effects from a sonic point of view since the most effect consists in the production of even harmonics, further some designers are convinced  that these asymmetries can be useful because they would eliminate the  harsheness that an “unbalanced” spectrum with only odd armonics shows. I believe that the reproduction of a more pleasant sound not always means a sound close to the real event, in fact an alterated harmonic spectrum can in some cases color the sound in a manner that could apper

Fig. 4 The Frequency Distribution Histogram of 2nd Harmonic

us very pleasant. Pro-audio amplifiers can take advantage from a colored sound but hi-fi amplifiers must aim to a neutral  and indistorted sound.

Nevertheless a study of the asymmetries in an output push-pull stage could return useful on the attempt to reduce or null the output distortion with the HCT by mixing its harmonics with those produced by previous stages of the amplifier. For this study  I have built a push-pull  output stage with 300B Vacuum Tube with the following bias point:

Vp=300Vcc, Vg=-61Vcc, Ip=60mA;

Fig. 5 The Frequency Distribution Histogram of 3rd Harmonic

and simulated a MonteCarlo Analysis with MicroSim DesignLab Ev. Rel 8.0 with a 10% Uniform Deviation in the half-primary inductance of the push-pull transformer when RLp-p is 1kW, 1.5k W, 2kW, 3kW rispectively.

Subsequently I have processed the output data with MathCad Pro 6.0 in order to   produce Frequency Distribution Histogram (FDH) of 2^nd and 3^rd harmonics. In Figg. 4 and 5  X-axis represents the value (in Volts) of harmonics and y-axis represent  the number of samples. This means, for example, that in Fig. 4b  about six samples with 2^nd harmonic values between 0.2 and 0.4V when RLp-p=1.5k.

 The samples close to  the origin (with a very low voltage therefore)  represent the better case since they refer to a null unbalancing condition  (during a MonteCarlo with a given number of iterations Pspice always performs at first a simulation to nominal value of the varying parameter – that is in this case the semiprimary inductance ). When an unbalancing of this level occours, Fig. 4 reveals a good insensibility of the 2^nd harmonic to load variations. In fact the FDHs preserve always the same qualitative shape. The increase of the load resistance is surely the primary cause that produces an amplitude  reduction  of the 3^rd Harmonic samples, Fig. 5. Therefore you can see a push-pull stage as a rigid structure since in the best condition of operation produces practically only odd harmonic that  could be eliminate hardly increasing the value of load resistance; on the contrary when unbalanced it produces even harmonics insensitive to the load variations. Nevertheless small unbalancing , in the case of triodes don’t result harmful, even theoretically it’s possible to make a push-pull stage also with different triodes [1].

[1]  F. Langford-Smith   Radiotron Designer’s Handbook  R.C.A., p. 509 Chap. XII, pp. 580-81 Cap. XIII, Cap XIV 4^th Ed., 1953.