Cathode Follower follows  Audio?

Introduction

Cathode Follower stages (CF) are widespreadly used in the audio design but with  an high rate of controversial.

What’ the reason?

The opponents recognize in th CF an harsh sound and ascribing the reason to the presence of 100% of Feedback Factor. Therefore the use of this circuit topology (as well as any amplifier with overall feedback) must be avoided in a true hi-fi amplification system.

The supporters claim that this concen is unjustified because the involved Negative Feedback acts only locally then sonic degradation is assent. Further CF stages have unique properties as  good current and impedance matching capabilities.

But, do the cathode follower unaffects the sonic texture really, or its use must be evaluated with care?

In this article I’ll try to reply this question.

The “Looped” Block

Any feedback amplifier can be modeled with the block diagram in Fig. 1 (right side).

I assume the exempliphying hipothesys the the open-loop amplifier A have a non-linear behaviour modeled with a second order input-output characteristic:

           (1)

When you apply the Negative Feedback you obtain:

   (2)

By solving  eq.(2) with respect to e_in  you obtain:

(3)

where:

The square-root in eq.(3) can be approximated with the following expression:

(4)

Then the signal in output to the feedback amplifier is a power-series expansion of the input signal: a very interesting result!

In fact altough the amplifier A in its open-loop state  yields only second-order effects, the feedback amplifier in reducing  the distortion extends dramatically the harmonic spectrum, i.e. the feedback amplifier has less distortion of the open-loop one but the harmonic spectrum of the former is richer in harmonics.

            You have other factors that make worse this situation.

First, the feedback factor g is frequency dependant and decrease with and, for  the same definition of  factor   a the high order terms in eq.(4) increase with the frequency. This reflect one of major troublesome aspect of feedback amplifier because you can see g the magic term for this circuit topology (for example with g you can artificially affect the closed loop gain, the input and output impedance and so on).

Second, the complexity of eq.(4) increases when you realistically assume that the input-output relationship for the open-loop amplifier have an higher order.

This artful behaviour of negative feedback amplifiers could be one of the aspects correlated with the timbric alteration that some people seem to notice during the listening in critical situations.

The Cathode Follower Stage

Fig.2

I’ll lead a similar analysis for the circuit topology depicted in Fig.2.

By assuming:

(5)

since:

(6)

through algebraic calculi you obtain the following expression for the voltage eg:

(7)

where:

The eq.(7) underlines that the cathode folllower stage presents a non-linear behaviour exactly alike an overall negative feedback amplifier  (really, after the results obtained with the eq.(7) you can state that a more complex relationship between the voltages V_in and V_out  exists).

Fig.3

            Fig.3, depicts the harmonic spectrum of a CF stage build with a 6DJ8 vacuum tube. You can observe a large harmonic content counterbalancing a relatively low THD. Some audio designers are deeply convinced about the harfulness of this behaviour then refuse tout-court this circuit topology. Others share this worry  but observe that the degenerative phenomenon summarized by eq.(7) yields effects only when signal swings are elevated and therefore if border effects are evaluated attentively the benefits surclass the disadvantages.

In accordance with this last viewpoint a CF stage can result irreplaceable in the impedance matching, in the reactive loads driving  and when you want  a low cost driver in a grid currents context (classes A₂, AB₂).

Conclusions

Is the Cathode Follower audio-compliant?

You can reply in a more solid manner at this point. The input-output relationship of this stage is the same of a true feedback amplifier and therefore harmful in the potential but this worry is motivated when voltages and/or currents are high. In the signal amplification domain, i.e. in the design of Phono and Line Preamplifiers, this cannot be matter of concern. When large signal are involved as in the power amplification its use must be attentively evaluated and compromises are inevitable.