Unfortunately the effects of power supply non-idealities are not included in the LM3886 model, hence, not part of the simulation. It should be relatively obvious, however, that if the supply to the LM3886 is bouncing, the LM3886 may behave in unintended ways. The most common cause of supply bounce is parasitic inductance. As mentioned earlier, the self-inductance of a piece of wire or PCB trace is approximately 1 nH/mm. Hence, excessive trace length between the supply bypass capacitors and the IC will result in significant supply inductance. This inductance will restrict current flow into the IC. This may cause the IC to, effectively, brown out on fast current spikes. This can lead to high frequency instability.
The data sheet is a bit ambiguous on the exact requirements for bypassing. On page 20, it is mentioned that a 10 µF tantalum capacitor with a 100 nF ceramic cap in parallel from each supply pin to ground is all that is needed. Then in the following paragraph, it is mentioned that if the supply bypass capacitors are greater than 20 µF, HF instability is only an issue if the supply lead inductance exceeds 1 µH (corresponding to about 1 m of trace length). The larger tantalum cap is intended to provide a low supply impedance at audio frequencies. The 100 nF ceramic cap ensures that the supply impedance remains relatively low at RF frequencies beyond the self-resonance frequency of the tantalum capacitor. In addition to the smaller capacitors by the LM3886 supply pins, larger capacitors are needed by the power entry to the circuit board. National recommends a minimum of 470 µF per supply rail.
As mentioned earlier, the purpose of the supply bypass network is to keep the supply impedance as low as possible throughout as wide a frequency range as possible. In the 15+ years that have passed since the release of the LM3886, there has been a tremendous development, in particular, in the field of multi-layer ceramic capacitors (MLCC) and electrolytic capacitors. Hence, it seems prudent to explore the limits of the supply bypassing and explore the performance that can be achieved by using more modern components.
The figure below shows the resulting supply impedance for one supply rail, as seen by the LM3886, for the recommended supply bypass network. The network consists of a 100 nF film cap by the IC pin, then a 10 uF tantalum capacitor, followed by a generic 1000 uF electrolytic can where the power enters the PCB. I assumed that the board is connected to the power supply by 20 cm (8") of 0.5 mm2 (AWG 20) wire and that the supply is an ideal supply (Zout = 0 Ω).
The capacitor parasitics used in the simulation were those measured on actual components using an HP 4194A Impedance/Gain-Phase Analyzer. The supply impedance shows a slight effect of the 1000 µF electrolytic cap around 5 kHz and the resonance of the lead inductance and the 100 nF film cap is apparent at 5 MHz. The impact of the 10 uF tantalum capacitor is difficult to spot. It may be responsible for the slight change in slope near 100 kHz.
Let's explore the limitations of the system. The LM3886 supply pins are rather long. There is at least 7~8 mm exposed outside the plastic package and probably another 7~8 mm as part of the lead frame inside. Hence, the inductance between the IC die and the first bypass cap is about 15 nH. This may even be a tad optimistic. The inductance of the IC supply leads dominates the supply impedance at HF. At 10 MHz, the impedance of the 15 nH inductor is about 1 Ω (at 100 MHz, 10 Ω), hence, this is the lower limit on the supply impedance at HF. At DC, the limit is set by the resistance of the wires, connectors, and terminal blocks on the supply inlet to the board. Hence, the lowest impedance possible at LF, in this setup, is 20 mΩ, not including the DC resistance of the IC pin itself.
The commonly recommended supply bypassing strategy of small-medium-large capacitors in parallel works by employing the progressively increasing self-resonance frequencies (SRF) of the bypass capacitors. At frequencies higher than the SRF of the capacitor, the impedance of the capacitor is dominated by the impedance of its parasitic inductance, i.e. the capacitor "has turned inductive". The idea behind the traditional bypassing scheme is to ensure that when the large cap "has turned inductive", the medium cap takes over and dominates the total supply impedance. Similarly for each of the following caps in the decoupling network. This strategy is valid as long as the inductance of the IC pin is lower than the inductance of the traces and parasitic inductances of the bypass capacitors. In cases where the IC pin inductance dominates, the game changes. For the LM3886, a more appropriate bypassing strategy is to get as much energy storage as close to the IC pin as possible. With the parts available in present day, it is possible to improve greatly upon the bypassing scheme recommended in the LM3886 data sheet.
Above simulation uses a 4.7 µF X7R ceramic capacitor (TDK P/N: FK20X7R1H475K) and a 22 µF OSCON electrolytic capacitor (Panasonic P/N: 35SEPF22M) along with the same generic 1000 µF electrolytic can from the previous simulation. The simulation shows a significant improvement in the 100 kHz to 10 MHz frequency range. The ceramic caps and the OSCON caps needed for proper bypassing of the LM3886 will set you back a grand total of about $3.50 in today's Digikey prices. That seems like money well spent.
It is worth noting that increasing the 1000 µF capacitor to 10000 µF has very little impact on the supply impedance. In fact, reducing the capacitance to around 100 µF is possible without any adverse negative impact. The data sheet recommendation of 470 µF or larger is very reasonable. This allows sufficient margin to maintain a good, low supply impedance, even with the relatively large component tolerances found on electrolytic caps. I recommend 1000 µF as it is commonly available at a reasonable price point.
For the ceramic capacitors, it is worth spending a little extra to get the X5R or X7R dielectric ceramic capacitors rather than the cheaper Y5V ceramic. The voltage coefficient of Y5V is horrid! At half the rated voltage, expect the capacitance to be about 30 % of the marked value. It's down to 20 % of the marked capacitance at the rated voltage for a Y5V cap. The voltage coefficient of X5R and X7R is not pretty either, but unlike Y5V, you can expect the capacitance to be about 50 % of the marked value at 50 % of the rated voltage. Therefore, if possible, I also suggest getting capacitors rated for operation at 100 V rather than the commonly used 50 V types. For additional information on the different dielectrics, see this white paper and Wikipedia.
Section 3: Grounding