Could one of you guys explain what sigma delta dacs and r2r dacs are? Theres been a lot of talk, but I have no idea what it all means 

You could start with:

http://en.wikipedia.org/wiki/Delta-sigma_modulation

There are many ways to look at delta-sigma modulation. The simple 1st order (single difference/accumulation stage) single-bit output looks like this:


(reference: http://stuartowen.com/home/2012/08/13/delta-sigma-adc-basics/#!/single_blog)

It's called delta sigma because the operation has a difference (delta) and an accumulator (sigma). In a nutshell, the single bit output of this delta-sigma (DS) tracks the input through difference/accumulation.

1) The DS takes the difference (error) between multi-bit input and the single-bit output (after a gain and delay).

2) The error is then accumulated.

3) Depending on the current error, and previous state of the accumulator, if new accumulator state is greater than zero, then the decision is to output a positive swing. Otherwise one gets a negative swing.

4) The fact that a single bit is being sent out introduces error which is being tracked by both the difference and accumulation operations.

If one was to analyze this whole thing, one would get a pass-through for the signal + a high-pass filtered or "modulated" quantization noise. The quantization noise high-pass filtering operation frequency response (and gain) depends on the "order" of the delta sigma (or how many difference/accumulation stages it has):


(Frequency Response of effective quantization noise high-pass filtering for simple 1st, 2nd and 3rd order delta sigmas. reference from Wikipedia.)

In the end, the output of the delta sigma is low-pass filtered to remove the high-pass quantization. For this to work well, the original signal highest frequency should be well bellow where the quantization noise starts to creep up.

A couple of things to note:

1) A delta sigma can have multiple difference accumulator stages which determines it's order... not just one.
2) The output of the delta sigma does not need to be single bit.
3) Certain "advanced" sigma delta architectures involve feedback and feedforward gains with more than one quantization stage (like multi-stage MASH architectures)
4) Higher order classic delta sigmas are "cleaner" in the pass-band, but put out more garbage in the stop-band. Which makes the subsequent low pass filter's job more difficult.
5) Certain higher order delta sigmas may have stability problems.
6) Classical analysis of delta sigma assumes uniform distributed quantization noise... And in some cases that is a bad assumption.
7) The oversampling rate of the delta sigma (ratio of highest frequency in the signal to the sampling rate) is usually about 8... higher is bettar.

In the end both R2R (Sample/Hold) and delta sigma DACs put out of band ... and IMO may benefit from "reasonable" analog output filters... which may themselves cause other problems...

Anyhow... for the Matlab inclined here is some quick 1st order ds code:

gain = 0.75; % feedback gain
N = 1000; % display samples
delay = 8; % delay alignment
OSR = 8;< span style="white-space: pre;"> % oversampling factor

% signal
[B, A] = butter(7,0.5/OSR);
x=filter(B,A,randn(1,1e5));

% variables
ds = gain*ones(size(x));
diff = zeros(size(x));
acc = zeros(size(x));

% 1st order delta sigma
for i=2:length(x),
diff(i) = x(i) - ds(i-1);
acc(i) = acc(i-1) + diff(i);
ds(i) = gain*(2*(acc(i)>0)-1);
end

% analog output filter
[B, A] = butter(5,1/OSR);
out = filter(B,A,ds);

close all;

% delta sigma input output spectrum
[H, W] = freqz(x);
[Ho, Wo] = freqz(ds);
figure;
subplot(2,1,1);
plot(W,20*log10(abs(H)));
axis tight; grid on;
title('original signal FR mag')
xlabel('radians');
ylabel('au');
subplot(2,1,2);
plot(Wo,20*log10(abs(Ho)));
axis tight; grid on;
title('unfiltered ds output FR mag');
xlabel('radians');
ylabel('au');

% delta sigma output (unfiltered)
figure;
plot(ds(1:N),'.');
axis tight;
grid on;
title('first order delta sigma');
xlabel('sample');
ylabel('units');

% filtered delta sigma output
figure;
plot(x(1:N)); hold on;
plot(out(1+delay:N+delay),'r');
grid on;
axis tight;
title('first order delta sigma');
legend('input','filtered output');

And some results:

Frequency Responses of DS input and unfiltered output



(Note the out-of-band "modulated" quantization noise on sub-plot 2 sort of matches the Wikipedia linky for 1st order)

DS unfiltered output



DS filtered output

Here are a few excerpts from Pohlmann's Principles of Digital Audio which give a straightforward explanation:

I think it is just like album releases:

* An expert transfer from a tape copy of a young original master tape, done in 16/44.1 (Barry Diament 1980s Close to the Edge) easily beats a less expert transfer directly from a now old and worn original master tape at 24/192 (2013 hdtracks and Blu-Rays).

* Similarly, I'm willing to bet that an expert implementation of a delta-sigma with quality parts, beats a less expert r2r implementation with low quality parts and opamp outputs.