Three Simple Rules for Creating an Effective Gain Structure
By Douglas Self
Douglas Self has a worldwide reputation as a leading authority on audio amplifier design, but it is perhaps less well known that he has devoted a good deal of study to small-signal circuitry, including many years as the chief design engineer at one of the major mixing console manufacturers, where his achievements included winning a Design Council Award. His rigorous, skeptical, and thoroughly practical approach to design has been applied to the small signal area as well, and some of the results can be found in his recent book, The Design of Active Crossovers. Senior designer of high-end audio amplifiers and contributor to Electronics World magazine, Douglas has worked with many top audio names, including Cambridge Audio, TAG-McLaren Audio, and Soundcraft Electronics.
Below is an excerpt from his recent book The Design of Active Crossovers.
There are some very basic rules for putting together an effective gain structure in a piece of audio equipment. Breaking them reduces the dynamic range of the circuitry, either by raising the noise floor or lowering the headroom.
1. DON’T AMPLIFY THEN ATTENUATE.
It is all too easy to thoughtlessly add a bit of gain to make up for a loss later in the signal path, and immediately a few dB of precious headroom are gone for good. This assumes that each stage has the same power rails and hence the same clipping point, which is usually the case. Figure 1 shows a fragment of a system with a gain control designed to have +10 dB of gain at maximum. There is assumed to be no noise at the input. A and B are unity gain buffers and each contributes −100 dBu of its own noise; Amplifier 1 has a gain of +10 dB and an EIN of −100 dBu.
The expectation is that the level control will spend most of its time set somewhere near the “0 dB” position where it introduces 10 dB of attenuation. To keep the nominal signal level at 0 dBu we need 10 dB of gain, and Amplifier 1 has been put before the gain control. This is a bad decision, as this amplifier will clip 10 dB before any other stage before it in the system, and this introduces what one might call a headroom bottleneck.
On the positive side, the noise output is only ‒96.8 dBu, because the signal level never falls below 0 dBu and so is relatively robust against the noise introduced by the stages.
2. DON’T ATTENUATE THEN AMPLIFY.
Since putting our 10 dB of amplification before the gain control has disastrous effects on headroom, it is more usual to put it afterwards, as shown in Figure 2. Now noise performance rather than headroom suffers; the amount of degradation depends on the control setting, but as a rule it is much more acceptable than a permanent 10 dB reduction in headroom. The signal-to-noise ratio is impaired for all gain control settings except maximum; if we dial in 10 dB of attenuation as shown then the signal reaching Amplifier 1 is 10 dB lower, at −10 dBu. The noise generated by Amplifier 1 is unchanged, and almost all the noise at its output is its own EIN amplified by 10 dB. This is slightly degraded by the noise of block B to give a final noise output of −89.2 dBu, worse than Figure 1 by 7.6 dB. If there are options for the amplifier stages in terms of a noise/cost trade-off and you can only afford one low-noise stage then it should clearly be Amplifier 1.
3. AMPLIFY AS SOON AS POSSIBLE.
Get the signal up to the nominal internal level as soon as it can be done, preferably in the first stage, to minimise its contamination with noise from later stages. Consider the signal path in Figure 3, which has a nominal input level of ‒10 dBu and a nominal internal level of 0 dBu. It has an input amplifier with 10 dB of gain followed by two unity-gain buffers A and B. As before, all circuit stages are assumed to have an Equivalent Input Noise level of −100 dBu, and the incoming signal is assumed to be entirely noise free. The noise output from the first amplifier is therefore −100 dBu + 10 dB = −90 dBu. The second stage A adds in another −100 dBu, but this is well below −90 dBu and its contribution is very small, giving us −89.6 dBu at its output. Block B adds another −100 dBu, and the final noise output is −89.2 dBu.
Compare that with a second version of the signal path in Figure 4, which has an input amplifier with 5 dB of gain, followed by block A, a second amplifier with another 5 dB of gain, then block B. The signal has received exactly the same amount of gain, but the noise output is now 1.7 dB higher at −87.5 dB, because the signal passed through block A at −5 dBu rather than 0 dBu. There is also an extra amplifier stage to pay for, and the second version is clearly an inferior design.
In active crossover design the problem is not usually quite so marked as in the examples above, because any level controls are usually trims rather than full-range volume controls, but the principles still stand.
Let us examine a typical scenario; assume that you want to make a fourth-order Linkwitz–Riley filter, and you are planning to use two cascaded second-order Sallen and Key Butterworth filters of the equal-C type to make component procurement simpler. For a second-order Sallen and Key filter to be equal-C the stage gain has to be 1.586 times (+4 dB) and when you cascade two to make the fourth-order Linkwitz–Riley filter you have a total gain of 2.5 times (+8 dB) to deal with. There are three possibilities: Firstly, you can attenuate the signal by 8 dB before the filters, but the low level in the first filter will almost certainly degrade the noise performance. Secondly, you can attenuate the signal by 8 dB after both filters, but now there are higher signal levels, in particular 8 dB higher at the output of the second filter, and headroom problems may occur at this point. Thirdly, and usually best, is some compromise between these two extremes. For example, putting 4 dB of attenuation after the first filter, and then another 4 dB of attenuation after the second filter will reduce the headroom problems by 4 dB.
Alternatively, putting 4 dB of attenuation before the first filter, followed by 4 dB of attenuation after it, will reduce the noise contribution of the first stage. The aforementioned assumes you do not need to add buffers between the attenuators and the filters to give the latter a low source impedance. If you are seeking the best possible performance, then probably your best option is to not use Sallen and Key equal-C filters in the first place, but stick to the more usual unity-gain sort.