I've been spending a fair bit of time trying to understand what is influencing the VRef mods by simulating the circuit in LTSpice.
In the earlier posts on the topic it appeared that the stock filter was same design as described in two Brown Burr/TI application notes. The app notes suggest that while the circuit is stable with any capacitance, there is a relationship between the filter components that needs to be maintained to prevent a peak in noise gain occurring. This suggests that simply throwing bulk capacitance at the board may not the complete answer to instability in the VRef supply.
The simulation circuit I've working with is very basic, and uses a model of the OPA365 from the TI website.
This screen grab shows the setup for simulating glt's 16-cap mod published on hifiduino blog.
Noise analysis is useful and quickly indicates the degree of peaking in each configuration.
Transient analysis is used to check waveform on the output of the Vref. I've settled on using a sine current load of 6mA, which might be a little low, and test the setups at several different frequencies.
Be warned, I'm a bit of hack with LTSpice so there is likely to be errors in my methodology.
I'm using the 16-Cap mod as an example, simply because it's typical of the straight stock+cap mod. It will sound far better than a stock, unmodified board.
First the noise analysis which clearly shows peaking. This is better than stock, which peaks at 25kHz/181nV in my sims, and with manual calculations.
Next step is transient analysis. This shows the "ramp up" when the cap is first loaded. From what I can determine the "ramp up" is directly related to the noise peaking. If I do fft analysis of only the steady state portion the "peak" disappears. In a real situation the load will not be a steady sine load, so the "ramp up" behaviour is likely to influence overall performance. The ripple in this example is about 3.15mV peak to peak.
FFT of the transient response
Next step is to perform an FFT on the transient response, to visualise the frequency components. In this case the test frequency matches the centre frequency of noise peaking.
The level of ripple is around 2-3 times worse than testing done away from the peak. With a 1kHz tone the peak level for this configuration is -85dB, which is a 25dB difference.
Transient response changes with frequency
As the frequency of the load on the VRef changes the transient response also alters. The big cap mods have relatively low levels of ripple - 0.45mV once the waveform settles - but the "ramp up" is slow, and messy. I'm not sure what impact this low level instability will have, if any.
The stock+1000uF mods behave in the same way, excepting that the peak occurs at a slightly higher frequency. Increasing the capacitance moves the peak to a lower frequency and reduces the amplitude but does not eliminate the peaking.