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.

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.
   

Bootstrapped collector loads

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

A bootstrapped collector load is a pair of resistors connected in series, with their common point actively driven, often by a unity gain buffer via a large capacitor:

Bootstrapped loads have been popular in audio amplifiers for more than 50 years, although these days they are largely replaced by constant current sources.

The work of a bootstrapped load is easily understood. Because of the unity gain buffer, the right side of the capacitor $C$ (see the schematic above) sees the same potential as the bottom end of $R_2$. As long as the voltage across the capacitor is relatively stable, the voltage across $R_2$ is relatively stable, and so is the transistor's collector current flowing through $R_2$. In particular, the collector current changes only a little with changes in the collector potential (e.g. an audio signal), as if the collector load resistance is large.

Quantitatively, it is obvious that at DC, $R_1+R_2$ is the only load that sets the quiescent collector voltage. To find out AC response, one needs to e.g. write down node equations, which reveal that a bootstrapped load presents a frequency dependent impedance of the form $$Z = (R_1 + R_2) \times (1+s T_z)$$

where $T_z = (R_1 || R_2) C$.

The impedance increases with frequency at 20dB/decade, as would the impedance of an inductor. Effectively, a bootstrapped load is a synthesized inductor with the series resistance $R_1+R_2$ and the inductance $L = R_1 R_2 C$. For example, with R1=R2=1kOhm and C=10uF, the equivalent inductance L=10H.

In a real circuit, this synthesized inductor is not the only collector load - connected in parallel to it are the output impedance of the transistor and the input impedance of the buffer. If this input and output impedances are lumped into Ri:

then the combined collector load has the form $$Z = {R_i || (R_1 + R_2)} \times {{(1+s T_z)} \over {(1+s T_p)}}$$ where $T_z = (R_1 || R_2) C$ as above and $T_p = {{ (R_1 + R_2) \over (R_i +R_1 + R_2) } C}$.

I will look more into the behavior and practical uses of a bootstrapped load in separate posts.

High Precision Composite Op-Amps, Part 5 - Cart Before Horse

 

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

In my previous post on this topic, I gave a couple of practical examples of composite amplifiers with the topology described by John D. Yewen's article in Electronics & Wireless World, February 1987 and promised we can do even better.

One of the issues with Yewen's topology:

is that R1 R2 (in the schematic above) attenuate the signal amplified by U1, which causes U1 to work extra hard, or, more precisely, work with a higher input signal. As was discussed previously on this blog, this affects the linearity of U1's input stage and adds distortion that cannot be corrected by feedback.

One way to address this issue is to use a better opamp as U1, but it is much easier to move the divider to U1's input:

R1 R2 should be large compared to Ri to avoid an unwanted noise gain increase and a loop gain reduction (see the discussion in my previous post), but otherwise this works exactly the same as Yewen's composite, only with lower distortion.

Naturally, this approach also works with frequency dependent dividers:

High Precision Composite Op-Amps, Part 4 - A Practical Composite Chipamp with LM1875

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

In my previous post on this topic, I discussed the role of the voltage divider in John D. Yewen's composite op-amps (see his article in Electronics & Wireless World, February 1987) and improving the composite's loop gain at audio frequencies by making the divider frequency dependent.

Towards the end of the previous post, I promised that this approach works in hardware, too, so here are two practical examples.

The first is a plain Yewen composite with two dissimilar opamps - an OPA134 and an LM1875:

The divider (R4R5) attenuates the output of the OPA134 by 33/(2200+33)≅-36dB, which together with the opamp's GBW of 8MHz places the zero (see my previous post for an explanation) at about 130kHz. It is kind of low, but in testing, placing the zero at a higher frequency made for poor clipping performance. With such a divider, the OPA134 adds about 16dB of loop gain at 20kHz (more at lower frequencies), and this composite produces 0.003% THD at 1kHz, 20W into 8ohm, or about 1/6 of the distortion of a standalone LM1875.

The second example is a composite with the same opamps and a frequency dependent voltage divider C4C5R10:

The improved divider adds a pole at 2kHz and a zero at 150kHz, increasing the loop gain by another 16dB at 20kHz while maintaining stability and clipping similar to that of the first composite. With a careful PCB layout, this composite should be able to deliver 0.001% of THD at 1kHz, 20W into 8ohm.

Note that for both versions, the Zobel network (R6C2 and R11C6, respectively) with the values shown is required for stability.

Can we make the composite still better? Yes we can! Stay tuned...

High Precision Composite Op-Amps, Part 3 - More Loop Gain

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

As discussed in my previous post on this topic, the resistive voltage divider in John D. Yewen's composite amplifier (see his article "High-precision composite op-amps" in Electronics & Wireless World, February 1987):

adds a zero to the loop gain, which helps to achieve stability at the expense of the loop gain:

For audio applications, it is desirable to maximize the loop gain, at least in the audio band, but preserve the phase margin. One way to keep that zero and maximize the loop gain at audio frequencies is to make the voltage divider frequency dependent, for example:

Adding an inductor in parallel to R3 adds a pole-zero pair (disregarding the inductor's own series resistance, the pole is at $F_p={1 \over {2 \pi}} {{R_3 || R_4} \over L_1}$, the zero at $F_z={1 \over {2 \pi}} {R_3 \over L_1}$). With the values shown, we get about 12dB of extra loop gain at 20kHz with the same phase margin as without the inductor:

 A 22mH inductor may not be very practical, but a similar effect can be achieved with a resistive-capacitive divider, for example:

Here, the pole is at $F_p={1 \over {2 \pi R_5 (C_1 + C_2)}}$, the zero at $F_z={1 \over {2 \pi R_5 C_1}}$. With the values shown, the loop gain is about the same as with the inductor above:

 

Not bad for one additional passive component. It works in hardware, too - I will show a practical example in my next post.

High Precision Composite Op-Amps, Part 2 - Divide and Conquer

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

My previous post on this topic was on composite opamps from by John D. Yewen's article "High-precision composite op-amps" (Electronics & Wireless World, February 1987):

Appropriately choosing the voltage divider R1R2 at the output of U1 allows to achieve stability (obtain sufficient gain and phase margins) of the composite at the expense of the loop gain. Here, orange traces are the loop gain of the composite from the schematic above, while blue are the maximum possible (whether stable or not) loop gain with the same two opamps:

How can a simple resistive divider make the composite stable? Let me look at the role of the voltage divider in Yewen's composite.

Referring to the schematic above, U2 sees a (differential) input signal that is a sum of (i) the signal at the non-inverting output, where Ri and Rf connect, and (ii) the same signal amplifier by U1 and divided by R1R2.

At low frequencies, U1's gain is large, and U2's input signal is effectively that at its non-inverting input. The loop gain is the product of that of U1 and U2 and falls with frequency at 40dB/decade. At high frequencies, U1's gain is small, and U2's input signal is effectively that at its inverting input. The loop gain is just that of U2, falling at 20dB/decade.

The transition from "low" to "high" frequencies is a zero in the composite's loop gain, located at the frequency where the signal magnitudes at the non-inverting and inverting inputs of U2 are equal - that is, when the gain of U2 followed by R1R2 is unity. For a single-pole U1, that frequency is a fraction of U1's Gain Bandwidth Product (GBW):$$F_{zero}=GBW_{U_1} \times {R_2 \over {R_1+R_2}}$$In the example above, GBW is 10MHz, the divider's attenuation is 22, so the zero is at ${{10 MHz}\over 22} = {455 kHz}$.

That is, Yewen's voltage divider sets the frequency of a zero in the composite's loop gain. The higher the attenuation in the divider, the lower is the zero, and vice versa.

By the way, it is possible and quite practical to replace the fixed divider with a trimpot and adjust the zero to one's liking, e.g. to obtain the necessary phase margin.

Can we make it still better? Yes we can! Stay tuned...

Omicron Headphone Amplifier: Circuit Design

As I mentioned in the previous post, the idea was to build a compact, inexpensive, easy to build low distortion headamp.

One can do compact with discrete SMT circuitry, but that would not be easy to build, hence Omicron is built with opamps.

Common, easily available, inexpensive opamps may or may not be able to drive 32ohm cans directly, so Omicron needs a current booster. An integrated high-speed buffer such as BUF634, LME49600 or LT1010 would do the job, but you can get 10 opamps for the price. So the booster is a classic push-pull emitter follower - just two transistors.

In a circuit like that, there are two major sources of distortion under designer's control. The obvious one is the output stage, where transistors experience large variations of voltage and current, leading to nonlinearity and to distortion. Since we only need 100mW - that's 80mA peak into 32ohm or 11V peak into 600ohm - and it is not a battery-powered headamp, Class A or AB with sufficient quiescent current is an easy choice. Unfortunately, even Class A by itself does not deliver the distortion we have in mind, so we will place it inside a feedback loop.

Quite a few headamps use a current booster inside the feedback loop of an opamp. It works well at low frequencies, below 1kHz or so, but at higher frequencies the opamp's gain goes down, and distortion goes up. This produces familiar looking charts:

and familiar sound: feedback redistributes distortion to upper audio frequencies, adding brightness, making sibilants unnatural and muddling the midband with intermodulation products. We want to avoid this trap and push distortion below the noise level using more loop gain. So instead of a single opamp, Omicron uses two (two half of one dual opamp) in each channel.

The other source of distortion is the opamp's input stage. Its has a delicate job of comparing a portion of the amplified signal with that from the source, and its own distortion is indistingushable from the useful signal. Better opamps may have more linear input stages, but are not necessarily common, easily available or inexpensive. Thankfully, there is another way. Increasing the loop gain (which we need anyway) decreases the differential input voltage that the input stage sees, making its job easier and distortion - smaller.

That was for the differential component of the input voltage, but there is also the common mode component. In a typical non-inverting configuration, the differential voltage may be zero, but inverting and non-inverting inputs would be flying up and down with the full amplitude of the input signal. This generates measurable and audible distortion, which we want to avoid. So Omicron is an inverting amplifier.

Inverting, of course, reverses the absolute phase. There are many people who say they can hear absolute phase, and prove this by flipping the phase switch on their amp or reversing speaker connection. However, this is not a blind test and can be (and probably is) biased. A more subtle test was offered by Stereophile on their first Test CD:

Track 8 on the CD features an "absolute phase" demonstration. The sound starts out with its overall polarity one way around, but finishes with its polarity inverted. According to many writers, especially Clark Johnsen in his book The Wood Effect, the sound of human voice and many instruments will be more natural with the polarity correct—ie, so that an acoustic compression that reaches the microphone will be reproduced as an acoustic compression that reaches the listener's ear—than it will the other way. We have no idea which way 'round on Gordon's recording is correct, but as we have inverted the polarity somewhere in the middle, you will be able to hear for yourself if there is an audible difference between the two states. And can you identify where the change in polarity occurs?

If you believe that absolute phase is important, get the CD and listen to the track and find where the change in polarity occurs. If you can do it, then you may want to rewire your headphones 😉

So here is the actual schematic of one channel of Omicron:

Each channel of Omicron is a composite amplifier built with two halves of an NE5532 and a two-transistor complementary emitter follower (EF) as a current booster. There are two feedback loops - one global and one for the second opamp and the EF. This configuration was selected after comparing a number of alternatives, including a single opamp with a current booster, a Yewen style composite, a Samuel-Groner-super-opamp-style composite, and a few others.

Going left to right:

• R1R3R5C1C2 is the global feedback loop.
• R1C1 is the input LPF. The amplifier is relatively wideband, with -3dB point of its frequency response at several 100's kHz (measurements will follow).
• C2 provides lead compensation, improving phase margin.
• D3-D6 and R10 adjust the loop gain in case of clipping or slewing, helping recovery.
• R7R8R9C4C5C6 is a local feedback loop with two-pole compensation.
• Q1Q2 and associated parts are the output current booster. R13 and R14 set the quiescent current, D7 and D8 provide thermal compensation.
• L1R43R45C45 is the output filter that both helps stability with capacitive loads and protects Omicron from EMI ingressm from the headphones' cable. 
  

Gain is x2.5, which works for both low- and high-impedance headphones. Input impedance is relatively low at 2kOhm - modern sources will handle it easily. The amplifier does not include a volume control in order not to be tied to a specific part; a 10kOhm pot with linear characteristic can be used - together with the input impedance and the effect on gain, it produces a control characteristic which is closer to true logarithmic than many audio pots.

Stay tunes for measurements and construction details of Omicron.