An Example for High-Level Synthesis of DT SDM Based On Model-Based Designs
In this Chapter, we propose a methodology for model-based SDM design optimization.
This design method is applied to a published design task [34]. Compared with the MASH SDM reported in [34], the SDMs designed by our method achieves much higher SNDR and significantly lower power consumption. This shows that our method can effectively achieve more balanced designs for piratical applications.
4.1 Design Optimization Schemes
A typical SDM design optimization algorithm is reference to [41]
4.2 Example for ΣΔ ADC for 14-bit 2.2-MS/s
The MASH SDM design specs reported in [34] to be achieved are
z Peak SNDR : 72 dB
z Signal bandwidth : 1.1 MHz
According to [34], Vref and VDD are set at 1V and 3.3V for the 0.35-μm CMOS technology.
Design parameter space searched by our model-based optimization scheme is
z B: 1 ~ 4
z OSR: 4~24
z CS: 0.1 ~1.32 pF
z A0: 45 ~ 53 dB
z GBW: 120 ~ 1000 MHz
z SR: 50 ~ 475 V/μs
z Ain: 0.1 ~ 1 V
The results published in [34] and that achieved from our methodology are all listed in Table VII.
TABLE 4.1
COMPARISONS OF OUR DESIGN RESULTS WITH THOSE IN [34]
Design parameters Reference [34] K = 1 Unit
B (second stage) 5 1 -
B (first stage) 1 2
OSR 24 24 -
CS 1.32 1.19 pF
A0 53 53 dB
GBW 1000 120 MHz SR 475 150.8 V/μs
Ain 0.55 0.47 V
SNDR reported in [34] 72 - dB
SNDR(Our model) 75.64 82.897 dB
SNDR(Simulink) 76.585 82.66 dB
POWER(Our model) 207.14 24.0304 mW
1. The optimization result compared to [34] demonstrates that our methodology helps designers to design MASH SDM. The concepts for designing MASH SDM focus on the optimization design of first stage single loop SDM and relax the design parameters on second stage single loop SDM, and the analysis of the optimization result compared to [34] is almost the same as the previous one. In addition, the modified quantization noise needs to be carefully taken into account due to the quantization noise rely heavily on the leakage of MASH SDM.
5
Conclusions
The main contributions in this paper are described in the following. First, an overview of the non-idealities power models of 2nd order single loop SDM and MASH SDM was presented, which shows that mathematical models were quit complete for model-based designs. Then, the quantizer overload model could provide that the obtained results of Ain and SNR from model-based designs could be more similarly to realistic DT SDM, and could indicate the distribution of different nodes of SDM, which maybe helpful in statistical properties. Furthermore, model-based designs can potentially be at the order of 104 times faster, which can search much more design parameters combination than simulation-based designs over the same period. Model-based designs also can explicitly compute each noise and distortion power, which could demonstrate the dominate non-idealities for designers to reduce the non-idealities by adjusting design parameters or using some circuit techniques. The non-idealities power models are currently being developed for other SDM architectures.
Appendix
A.1 an Approach for Extracting Sine Wave Signal from Any Order SDM Output (Behavior Simulation)
The sine wave signal from the SDM output can be extracted by the following equations.
0
The SDM output expresses as Sin(ω(t-c))+N(t), N(t) is the noise in SDM, w(t) indicates window function and c is constant delay depending on the SDM order.
The MATLAB code is written as
signal=(N/sum(w))*sinusx(vout(1:N).*w,fnormal,N);
% Function of sinusx is used to extract sinusoidal Function of sinusx:
function outx = sinusx(in,fnormal,n)
% in: Input data vector
sinx=sin(2*pi*fnormal*[1:n]); % sin(W*N*T) cosx=cos(2*pi*fnormal*[1:n]); % cos(W*N*T) in=in(1:n);
a1=2*sinx.*in';
a=sum(a1)/n;
b1=2*cosx.*in';
b=sum(b1)/n;
outx=a.*sinx + b.*cosx;
A.2 Error Function
Settling noise power model [26] contains many integral equations which can be expended to increase the speed for model-based design. The hardest integral equation for expending is
Fortunately, such error function can be expended by Taylor series as
This alternate form is very useful for increasing the speed for optimization designs.
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