SAR_ADC开关切换能量详细推导--附带matlab代码

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SAR_ADC开关切换能量详细推导过程以及matlab代码。


matlab代码：

1. %%
   
2. clear;
   
3. clc;
   
4. 
   
5. % initial parameters
   
6. n=10;
   
7. c_unit=1;
   
8. v_ref=1;
   
9. 
   
10. % preallocating
    
11. energy_conv=zeros(1,2^n);
    
12. energy_saving=zeros(1,2^n);
    
13. energy_mono=zeros(1,2^n);
    
14. energy_vcm=zeros(1,2^n);
    
15. 
    
16. % calculating
    
17. for x=0:(2^n-1)
    
18.     b=decimal2binary(x,n);
    
19.     energy_conv(x+1)=energy_calculate_conv(b,n,c_unit,v_ref);
    
20.     energy_saving(x+1)=energy_calculate_saving(b,n,c_unit,v_ref);
    
21.     energy_mono(x+1)=energy_calculate_mono(b,n,c_unit,v_ref);
    
22.     energy_vcm(x+1)=energy_calculate_vcm(b,n,c_unit,v_ref);
    
23. end
    
24. energy_avg_conv=sum(energy_conv)/2^n;
    
25. energy_avg_saving=sum(energy_saving)/2^n;
    
26. energy_avg_mono=sum(energy_mono)/2^n;
    
27. energy_avg_vcm=sum(energy_vcm)/2^n;
    
28. 
    
29. % plot
    
30. hold on;
    
31. plot(0:(2^n-1),energy_conv,'k-s','MarkerIndices',1:32:2^n);
    
32. plot(0:(2^n-1),energy_saving,'r-x','MarkerIndices',1:32:2^n);
    
33. plot(0:(2^n-1),energy_mono,'b-^','MarkerIndices',1:32:2^n);
    
34. plot(0:(2^n-1),energy_vcm,'c-v','MarkerIndices',1:32:2^n);
    
35. hold off;
    
36. 
    
37. % note
    
38. title('\fontname{Times New Roman}Switching Procedure Comparision');
    
39. xlabel('\fontname{Times New Roman}Output Code');
    
40. ylabel('\fontname{Times New Roman}Switching Energy [CV^2_{ref}]');
    
41. legend('Conventional','Energy-saving','Monotonic','Vcm-based');
    
42. set(gcf,'color','white');
    
43. set(gca,'FontSize',12);
    
44. set(gca,'FontName','Times New Roman');
    
45. set(gca,'XLim',[0 2^n-1]);
    
46. set(gca,'YLim',[0 max(energy_conv)]);
    
47. grid off;
    
48. box off;
    
49. 
    
50. 
    
51. %%%%%%%%%%%%%%%%%%%%%%%%% fucntion defination %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
52. % function to convert decimal to binary
    
53. function convert_result=decimal2binary(d,n)
    
54.     % initial parameters
    
55.     binary=zeros(1,n);
    
56.     i=n;
    
57.    
    
58.     % judge
    
59.     while i~=0
    
60.         if d<2^(i-1)
    
61.             binary(n-i+1)=0;
    
62.         else
    
63.             binary(n-i+1)=1;
    
64.             d=d-2^(i-1);
    
65.         end
    
66.         i=i-1;
    
67.     end
    
68.    
    
69.     % result
    
70.     convert_result=binary;
    
71. end
    
72. 
    
73. % function to calculate conventional method of an arbitrary code
    
74. function energy_result=energy_calculate_conv(b,n,c_unit,v_ref)
    
75.     % initial parameters
    
76.     energy_1=2^(n-1)*c_unit*v_ref^2;
    
77.    
    
78.     % preallocating
    
79.     block_1=zeros(1,n);
    
80.     block_2=zeros(1,n);
    
81.     energy_step=zeros(1,n);
    
82.    
    
83.     % circle
    
84.     for i=2:n
    
85.         a=zeros(1,n);
    
86.         for k=1:(i-1)
    
87.             a(k)=(1-2*b(k))*2^(n-k)*(2*b(i-1)-1)/2^i;
    
88.         end
    
89.         block_1(i)=sum(a);
    
90.         block_2(i)=2^(n-i)*(3-2*b(i-1));
    
91.         energy_step(i)=block_1(i)+block_2(i);
    
92.         energy_sum=sum(energy_step);
    
93.     end
    
94.    
    
95.     % result
    
96.     energy_result=energy_sum*c_unit*v_ref^2+energy_1;
    
97. end
    
98. 
    
99. % function to calculate energy-saving method of an arbitrary code
    
100. function energy_result=energy_calculate_saving(b,n,c_unit,v_ref)
     
101.     % preallocating
     
102.     block_1=zeros(1,n);
     
103.     block_2=zeros(1,n);
     
104.     energy_step=zeros(1,n);
     
105.    
     
106.     % circle
     
107.     for i=3:n
     
108.         a=zeros(1,n);
     
109.         for k=1:(i-1)
     
110.             a(k)=-1/2^(i-1)*(1-2*b(i-1))*2^(n-k-1)*(1-2*b(k));
     
111.         end
     
112.         block_1(i)=sum(a);
     
113.         block_2(i)=2^(n-i);
     
114.         energy_step(i)=block_1(i)+block_2(i);
     
115.         energy_sum=sum(energy_step);
     
116.     end
     
117.    
     
118.     % result
     
119.     energy_result=(energy_sum+3*2^(n-3))*c_unit*v_ref^2;
     
120. end
     
121. 
     
122. % function to calculate monotonic method of an arbitrary code
     
123. function energy_result=energy_calculate_mono(b,n,c_unit,v_ref)
     
124.     % preallocating
     
125.     block_1=zeros(1,n);
     
126.     block_2=zeros(1,n);
     
127.     energy_step=zeros(1,n);
     
128.    
     
129.     % circle
     
130.     for i=2:n
     
131.         a=zeros(1,n);
     
132.         for k=1:(i-1)
     
133.             a(k)=1/2^(i-1)*2^(n-k-1)*b(k)+1/2^(i-1)*b(i-1)*2^(n-k-1)*(1-2*b(k));
     
134.         end
     
135.         block_1(i)=sum(a);
     
136.         block_2(i)=2^(n-2*i+1);
     
137.         energy_step(i)=block_1(i)+block_2(i);
     
138.         energy_sum=sum(energy_step);
     
139.     end
     
140.    
     
141.     % result
     
142.     energy_result=energy_sum*c_unit*v_ref^2;
     
143. end
     
144. 
     
145. % function to calculate vcm-baesd method of an arbitrary code
     
146. function energy_result=energy_calculate_vcm(b,n,c_unit,v_ref)
     
147.     % preallocating
     
148.     block_1=zeros(1,n);
     
149.     block_2=zeros(1,n);
     
150.     energy_step=zeros(1,n);
     
151.    
     
152.     % circle
     
153.     for i=2:n
     
154.         a=zeros(1,n);
     
155.         for k=1:(i-1)
     
156.             a(k)=1/2^(i-1)*(2^(n-k-1)*(b(k)-0.5)+b(i-1)*2^(n-k-1)*(1-2*b(k)));
     
157.         end
     
158.         block_1(i)=sum(a);
     
159.         block_2(i)=2^(n-i-1);
     
160.         energy_step(i)=block_1(i)+block_2(i);
     
161.         energy_sum=sum(energy_step);
     
162.     end
     
163.    
     
164.     % result
     
165.     energy_result=energy_sum*c_unit*v_ref^2;
     
166. end
     
167. %%
     

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