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 load is connected to both A (via R2) and the current dumper (via L1).

The feedback for A is taken from the output of the current dumper. It is easy to see that for the feedback signal, A, R1 and C1 form an inverting integrator. As usual, the integrator adds a phase shift of 90° (on top of inverting) and amplification, with gain falling by 20dB/decade as frequency increases, reaching unity at

F0 = 1/(2π×R1×C1) 

With the values shown in the schematic above, F0 ≈ 4.82MHz. The gain of this integrator at any other frequency is

G = F0 / Fx

For example, at 20kHz the gain is 4,820 / 20 = 241, or 47.6 dB with the values shown. As in any other negative feedback amplifier, the integrator's gain works to reduce the open-loop distortion of the current dumper by a factor of  (1+G).

The residual distortion from the output of the current dumper is fed to to the load via L1, which adds 90° of phase lag. Since L1's impedance increases with frequency, the distortion level at the load falls with frequency at 20dB/decade. The same residual distortion is amplified by the integrator and appears at its output (and, via R2, at the load). Here, the level also falls with frequency at 20dB/decade, but the phase shift is 270° (180° to account for inverting and 90° for integrating), that is, 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 cancelled.

According to Walker, perfect cancellation occurs when L1=R1×R2×C1. In the language of the AES paper, "For the linearity of Trl and Tr2 to be immaterial then L must equal RRC". This conclusion, however, is based on a number of assumptions, among which are that A has large gain at all frequencies, that the amplifier has closed-loop unity gain and that L1 has zero DC resistance. The cancellation condition can be generalized for a more realistic setup, but the details will have to wait for another post.

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.