"Looped" Amplifiers

 

Fig. 1

 

From  the Block Diagram in Fig. 1 you have:

Vout= G1*ein + G2*ein^2  (G2<<G1)   (1)

        where

ein= vin-ef= vin – b*(G1*ein + G2*ein^2) (2) 2)

 

By solving with respect to ein you obtains:


                                                                  (3)

where:

g= 1+b*G1, a= (4*b*G2)/g^2         (4)

The square root can be appoximated with the following expression:


                                                                 (5)

Backward substitutions show a very interesting result: although A yields only 2nd  order effects, the Feed-Back amplifier reducing the THD extends drammatically the harmonic spectrum. This artful behaviour of amplifiers with NFB could be correlatated  with timbric alteration that some people seem to notice during the listening with “looped” amplifiers in critical situations.

  

 The Cathode Follower

Fig. 2


Thanks to relatively low output inpedance approximatively equal to 1/gm and good current capabilities, designers use this circuit for impedance matching, as driver and ,more rarely, as output stage (also in the OTL configurations).

          By assuming:

ik= h1*eg + h2*eg^2

since:

vout= ZL*ik


through algebraic calculi you obtain the following expression:

                                                     (6)

where:

a= (4*ZL*h2)/(ZL*h1+1).

 

Fig. 3


Therefore, also under the qualitative profile a cathode follower presents a non-linear behaviour very close to that of  the block diagram in Fig. 1.

           Fig. 3 shows harmonic spectra about two different cathode followers when the output signals have  both 1% of THD. You can observe a large  harmonic content counterbalancing a relatively low THD. Some designers are deeply convinced about the harmfulness of this behaviour expecially in a sonic context, therefore they refuse the use of Cathode Follower because they outline that, as a stage having 100% of Negative FeedBack, sonic deterioration is superior to electrical benefits. Others, also attributing this structure a potential sonic degradation of the processed information, above all when signal swings are elevated, admit the superiority of benefits with respect to disadvantages. Really a good Cathode Follower can result essential for matching impedances and driving capacitive loads. Further a low cost Class A2 driver it’s unthinkable without a Cathode Follower. I believe that cathode followers don’t have the dynamic compression sensation often recognizable in poor designed common cathode amplifiers. Nevertheless signal peaks can be cut with modalities that you can find both in solid state stages and full amplifiers with overall feedback.  A simple common cathode stage always saturate softly.