Code covered by the BSD License

# Delta Sigma Toolbox

### Richard Schreier (view profile)

• 1 file
• 4.58904

14 Jan 2000 (Updated )

High-level design and simulation of delta-sigma modulators

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

realizeQNTF(ntf,form,rot,bn)
```function ABCD = realizeQNTF(ntf,form,rot,bn)
% ABCD = realizeQNTF(ntf,form='FB',rot=0,bn)
% Convert a quadrature noise transfer function (ntf)
% into an ABCD matrix for the desired structure.
% Supported structures are
%	FB	Feedback
%	PFB	Parallel feedback
% 	FF	Feedforward  (bn is the coefficient of the aux DAC)
%   PFF Parallel feedforward
%   FBD	FB with delaying quantizer  NOT SUPPORTED YET
% 	FFD	FF with delaying quantizer  NOT SUPPORTED YET
% rot =1 means rotate states to make as many coefficients as possible real
%
% The order of the zeros is used when mapping the NTF onto the chosen topology.

% The basic idea is to equate the value of the loop filter at a set of
% points in the z-plane to the values of L1 = 1-1/H at those points.

% Handle the input arguments
parameters = {'ntf';'form';'rot';'bn'};
defaults = {NaN, 'FB', 0,0};
for i=1:length(defaults)
parameter = char(parameters(i));
if i>nargin | ( eval(['isnumeric(' parameter ') '])  &  ...
eval(['any(isnan(' parameter ')) | isempty(' parameter ') ']) )
eval([parameter '=defaults{i};'])
end
end

% Code common to all forms
ntf_p = ntf.p{1};
ntf_z = ntf.z{1};
order = length(ntf_p);

A = diag(ntf_z);
A(2:order+1:end) = 1;
if strcmp(form,'PFB') | strcmp(form,'PFF')
% partition the NTF zeros into in-band and image-band
fz = angle(ntf_z)/(2*pi);
f0 = fz(1);
inband_zeros = abs(fz-f0)<abs(fz+f0);
n_in = sum(inband_zeros);
imageband_zeros = ~inband_zeros;
n_im = sum(imageband_zeros);
if any(imageband_zeros(n_in+1:end)~=1)
error('Please put the image-band zeros at the end of ntf.z');
end
if n_im >0
A(n_in+1,n_in)=0;
end
end
D = zeros(1,2);

% Find a set of points in the z-plane that are not close to zeros of H
zSet = zeros(order*2,1);
for i = 1:order*2
z = 2*rand(1,1)-1 + 1i* (2*rand(1,1)-1);
while any(abs(z-[ntf_z; zSet])<0.1)
z = 2*rand(1,1)-1 + 1i* (2*rand(1,1)-1);
end
zSet(i) = z;
end
% Evaluate L1 = 1-1/H at these points
L1 = 1 - 1./evalTF(ntf,zSet);

switch form
case 'FB'
B = zeros(order,2);
C = [zeros(1,order-1) 1];
% Compute F = C * inv(zI-A) at each z in zSet
F = zeros(length(zSet),order);
I = eye(order);
for i = 1:length(zSet)
F(i,:) = C * inv(zSet(i)*I-A);
end
B(:,2) = F\L1;
if rot==1
ABCD = [A B(:,2); C 0];
for i = 1:order
phi = angle(ABCD(i,end));
ABCD(i,:) = ABCD(i,:)*exp(-1i*phi);
ABCD(:,i) = ABCD(:,i)*exp(1i*phi);
end
[A B2 C D2] = partitionABCD(ABCD);
B(:,2) = B2;
end
B(1,1) = abs(B(1,2));
case 'PFB'
B = zeros(order,2);
C = [zeros(1,n_in-1) 1 zeros(1,n_im-1) 1];
% Compute F = C * inv(zI-A) at each z in zSet
F = zeros(length(zSet),order);
I = eye(order);
for i = 1:length(zSet)
F(i,:) = C * inv(zSet(i)*I-A);
end
B(:,2) = F\L1;
if rot==1
ABCD = [A B(:,2); C 0];
for i = 1:order
phi = angle(ABCD(i,end));
ABCD(i,:) = ABCD(i,:)*exp(-1i*phi);
ABCD(:,i) = ABCD(:,i)*exp(1i*phi);
end
[A B2 C D2] = partitionABCD(ABCD);
B(:,2) = B2;
end
B(1,1) = abs(B(1,2));
case 'FF'
B0 = [1;zeros(order-1,1)];
B = B0; B(end) = bn;
% Compute F = inv(zI-A)*B at each z in zSet
F = zeros(order,length(zSet));
I = eye(order);
for i = 1:length(zSet)
F(:,i) = inv(zSet(i)*I-A) * B;
end
C = L1.'/F;
if rot==1
ABCD = [A B; C 0];
for i = 2:order-1
phi = angle(ABCD(end,i));
ABCD(i,:) = ABCD(i,:)*exp(1i*phi);
ABCD(:,i) = ABCD(:,i)*exp(-1i*phi);
end
[A B C D2] = partitionABCD(ABCD);
end
B = [-B0 B];
case 'PFF'
B0 = [1;zeros(order-1,1)];
B = B0; B(n_in+1) = 1;
% Compute F = inv(zI-A)*B at each z in zSet
F = zeros(order,length(zSet));
I = eye(order);
for i = 1:length(zSet)
F(:,i) = inv(zSet(i)*I-A) * B;
end
C = L1.'/F;
if rot==1
ABCD = [A B; C 0];
for i = 2:order-1
phi = angle(ABCD(end,i));
ABCD(i,:) = ABCD(i,:)*exp(1i*phi);
ABCD(:,i) = ABCD(:,i)*exp(-1i*phi);
end
[A B C D2] = partitionABCD(ABCD);
end
B = [B0 B];
otherwise
error(sprintf('%s error. Sorry, form "%s" is not supported.\n', ...
mfilename, form));
end

ABCD = [A B; C D];
```