The general model introduced in Fig.4.10 is commonly used to design stable high-order modulators. If a chain of integrators is used to form the loop filter, two main modulators typologies exist [1, 5, 8]:
a cascade of M delaying integrators is used to form the filter, where the feedback and the input signals are being fed to each integrator input with different weight factors a_i and b_i (Fig.4.11).
The transfer function of the signal filter, L_0, is:
while the feedback filter L_1 can be derived as:
where a_i and b_i>0. The NTF results:
Note that the NTF zeros must lie at 푧=1 (i.e. DC). The weight factors a_i can be used to introduce finite non-zero poles into the NTF and to determine the zeros of L_1 (z). The a_i factors can be found
a cascade of M delaying integrators is used to form the filter, where the feedback and the input signals are being fed to each integrator input with different weight factors a_i and b_i (Fig.4.11).
The transfer function of the signal filter, L_0, is:
while the feedback filter L_1 can be derived as:
where a_i and b_i>0. The NTF results:
Note that the NTF zeros must lie at 푧=1 (i.e. DC). The weight factors a_i can be used to introduce finite non-zero poles into the NTF and to determine the zeros of L_1 (z). The a_i factors can be found