Importance of low distortion

When talking about the distortion of audio electronics such as a DAC or a power amplifier, low order harmonics, particularly 2nd and 3rd, are often considered "harmonious" and "benign". In contrast, high order harmonics, which are not harmonically related to the fundamental tone, are considered noxious. This argument usually supports the idea that tube amps sound better, because tubes only add low order distortion, or that low- or zero-feedback amplifiers sound better because feedback adds higher order harmonics.

Let's conduct a little experiment. Let's say we test an amplifier that adds 0.01% of the 2nd harmonic (H2) and 0.001% of the 3rd (H3):

The distortion is not particularly high and is all low order, harmonious and benign, perhaps even euphonic.

Now let's play a simple chord, A-C#-E:

Oops. In addition to H2 and H3, our benign test amplifier sputters a bunch of intermodulation products, musically unrelated to the chord, with levels comparable or in some cases above those of H2 and H3. These are not euphonic and would not be masked by music. Worse, they will mask the music itself.

So, an amplifier with low order and relatively low level, "benign" distortion may be euphonic with a single tone but not so euphonic with a chord. Practically speaking, such an amplifier would have genre preferences: it might sound fantastic on simple music such as solo vocal, but would get confused with anything moderately complex, and it would mush a full orchestra or, say, a Rammstein recording.

Current Dumping: Fine Print

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

In the previous post, I explained how current dumping works on an intuitive, qualitative level. Let's go into the next level of detail.

A current dumping amplifier is a feedback amplifier consisting of a low distortion, low power amplifier A and a high-power, distorting buffer ("current dumper", here Tr1 and Tr2)  inside a common negative feedback loop:

Negative feedback reduces, but not completely eliminates, the distortion that the current dumper adds to the signal. From my earlier post, the share of that distortion that remains at the output (point D at the schematic above) after the negative feedback is applied is given by the Error Transfer Function $${ETF={1 \over {1- A \times B}}}$$ where $A$ is the transfer function (basically, the frequency-dependent gain) of the integrator composed of A,R1,C1, and $B$ is the transfer function of the feedback network. In this case, the feedback network has unity gain and is connected to the inverting input of the integrator, so $B=-1$, and $${ETF={1 \over {1+ A}}}$$ Therefore of the total open loop distortion $\epsilon$ of the current dumper, at point D we observe $$\epsilon _D={\epsilon \times ETF}=\epsilon {1 \over {1+ A}}$$ Since the current dumper adds distortion $\epsilon$, for this to happen, the input of the current dumper (point A at the schematic above) should see "pre-distortion" $$ \epsilon _A = {\epsilon_D - \epsilon}={{\epsilon {1\over {1+ A}}}-\epsilon}=-\epsilon{A \over {1+ A}}$$ At the load, $\epsilon_A$ and $\epsilon_D$ combine in reverse proportion to the impedances of R2 and L1: $$\epsilon_{LOAD}\propto {\epsilon_A Z_{L_1} + \epsilon_D Z_{R_2}}$$ Note that the load impedance affects the absolute level of the combined signal at the load but not the proportion of $\epsilon_A$ to $\epsilon_D$.

Combining the last three equations and dropping the common denominator $1+A$: $$\epsilon_{LOAD}\propto {\epsilon (Z_{R_2} - A  Z_{L_1})}$$

Clearly, the perfect cancellation of the current dumper's distortion occurs when $$Z_{R_2} = A  Z_{L_1}$$

For the implementation above, under ideal conditions, $Z_{R_2}= {R_2}$, $Z_{L_1}= s {L_1}$, $A=1/{(s R_1 C_1)}$, and the perfect cancellation means

$$R_2={L_1 \over {R_1 C_1}}$$

which is the result from [1]: "For the linearity of Tr1 and Tr2 to be immaterial then L must equal RRC".

However, by going through the algebra above, we obtained a more general and quite remarkable result: a perfect distortion cancellation requires the ratio of $Z_{R_2} /  Z_{L_1}$ to mimic the amplifier's loop gain $A$. This gives us the freedom to make current dumping work under less than ideal conditions and in different implementations than above. Stay tuned.

References

1. P. J. Walker and M. P. Albinson, "Current Dumping Audio Amplifier," presented at the 50th AES convention, March 1975.
2. S. Takahashi and S. Tanaka, “Design and Construction of a Feedforward Error Correction Amplifier,” JAES vol. 29, pp. 31-37, Jan/Feb 1981.

Current Dumping Revisited

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

Current dumping is a way of constructing a power amplifier where a low-power, low-distortion amplifier is used to correct the distortion of a higher-power, but less linear, amplifier ("current dumper"). The underlying assumption is that it is easier to construct a low power, low distortion amplifier than a high power, low distortion amplifier.

Current dumping was introduced by quintessential English audio company Quad and was used in a series of Quad's power amplifiers starting with the Quad 405. Quad's founder, P. J. Walker, presented the concept at the 50th AES convention in 1975 [1].

There has been much interest and public discussion of current dumping in late 1970s and early 1980s. While most reviewers used more or less complicated math to explain why and how current dumping works, the basic implementation is easy to understand on an intuitive level.

The following schematic is from Walker's original AES paper:

Here, A is the low power, low distortion amplifier, and Tr1 and Tr2 form the "current dumper". The feedback for A is taken from the output of the current dumper. The load is connected to both A (via R2) and the current dumper (via L1). 

Any distortion appearing at the output of the current dumper Tr1 Tr2 (point D in the schematic) is fed to the load via two parallel branches:

• Via L1
• Via the integrator A R1 C1, followed by R2:

 

If these two branches feed the load with the distortion of equal amplitude and opposite in phase, the load will see zero distortion - this is the big promise of current dumping.

Intuitively, since L1's impedance increases with frequency at 20dB/decade, the distortion it feeds to the load falls with frequency at the same rate and lags in phase by 90°. The same distortion coming via the integrator also falls with frequency at 20dB/decade, has a 90° phase lag, and is inverted - that is, its the phase is opposite to the distortion coming via L1. Since the levels are proportional and phases are opposite, with the right choice of R2, the residual distortion from the current dumper can be nulled.

The circuit is particularly easy to analyze if the gain of A is assumed to be infinite. In this case, the inverting input of A (labeled F) is at the ground level (that is, zero distortion signal) due to the feedback via C1. If the distortion is nulled perfectly, the load (labeled L) is also at the ground level. The current via R1 is equal to that via C1, and the current via L1 is equal to that via R2. A little algebra quickly shows that this can only happen when the DC resistance of L1 is zero, and its inductance is L1=R1×R2×C1. In the language of the AES paper, "For the linearity of Tr1 and Tr2 to be immaterial then L must equal RRC".

It is worth nothing that the gain of the integrator A R1 C1 is the loop gain of the amplifier, and that R1×C1 is the time constant corresponding to the frequency where the loop gain becomes unity (in magnitude; a 90° phase lag remains). For a perfect distortion cancellation, the impedances of L1 and R2 at that frequency must be equal.

Let's make a reality check and see if the ideal distortion cancellation can be implemented with reasonable parts. A typical Miller-compensated audio amplifier behaves like an integrator A R1 C1 above and reaches the unity loop gain at the frequency of about 1 MHz (see my previous post for an explanation). 1MHz corresponds to R1×C1 of about 0.16 μS. (Walker's own values, shown on the schematic above, give the unity-loop-gain frequency of 4.8MHz, which I believe is rather optimistic with the parts that were available in 1975.)

A typical air core inductor of the type commonly found at the output of such an amplifier will have an inductance in the low single μH range, so let's use Walker's 3.3μH. With R1×C1=0.16 μS, the cancellation condition above gives us 21 ohm for the value of R2. If we want the whole current dumping amplifier deliver, say, 100W peak power (50W RMS on a sinewave) into a 8 ohm load, our low-power, low-distortion amplifier A would only need to provide about 140mW into R2 at 20kHz, and less at lower frequencies. That looks rather realistic.

What is unrealistic are the assumptions of infinite gain for A and a zero DC resistance for the inductor. Still, the cancellation condition can be generalized for a more realistic setup, but the details will have to wait for another post. Stay tuned.

References:

1. P. J. Walker and M. P. Albinson, "Current Dumping Audio Amplifier," presented at the 50th AES convention, March 1975.
2. P. J. Walker “Current Dumping Audio Amplifier,” Wireless World, vol. 81, pp. 560-562, Dec. 1975.