1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
|
.PS
if "plotlib" != "1" then { copy "plotlib.pic" }
if "dpictools" != "1" then { copy "../sources/dpictools.pic" }
if "Zalgebra" != "1" then { copy "../sources/Zalgebra.pic" }
maxpswid = 20
maxpsht = 200
textht = 11/72*2/3
textoffset = 3/72
# display conveniences:
box invis wid maxpswid*0.999 ht maxpsht*0.999
[] at last box.nw+(1,-1)
# Generated data
define decay { 1 - expe(-($1)) }
pi = atan2(1,1)*4
ampl = 1
wlen = 1
omega = 2*pi/wlen
phase = -90/360*2*pi
n = 51
for j = 1 to n do { t = (j-1)/10;
xvals[j] = t;
yvals[1,j] = decay(t)
y1[j] = yvals[1,j]
yvals[2,j] = expe(-t)*ampl*cos(omega*t+phase)
y2[j] = yvals[2,j]
yvals[3,j] = (t)*expe(-t)
P[j]: (xvals[j],yvals[2,j])
y3[j] = yvals[3,j]
}
# Moore's law data
Transistors[1]: 1971,2250
Transistors[2]: 1972,2500
Transistors[3]: 1974,5000
Transistors[4]: 1978,29000
Transistors[5]: 1982,120000
Transistors[6]: 1985,275000
Transistors[7]: 1989,1180000
Transistors[8]: 1993,3100000
Transistors[9]: 1997,7500000
Transistors[10]: 1999,24000000
Transistors[11]: 2000,42000000
Transistors[12]: 2001,25000000
Transistors[13]: 2003,221000000
Transistors[14]: 2006,291000000
Transistors[15]: 2009,774000000
Transistors[16]: 2010,2.046e9
Transistors[17]: 2012,3.1e9
nT = 17
# "4004" "8008" "8080" "8086" "286" "386" "486" "Pentium" "Pentium II"
# "Pentium III" "Pentium 4" "Itanium" "Itanium 2" "Core 2 Duo" "Core i5"
# "Itanium 9300" "Itanium 9500"
graphwid = 3.5
graphht = 2.65
define bp__ { /72*scale }
G1: graphb( graphwid,graphht,xvals,yvals,3,n,1 ) with .Box.nw at last[].sw+(0,1)
{"G1" at G1.s below }
# {box invis wid 15bp__ with .e at G1.Box.w + (-0.4,0) "G1" }
G2: graphb( graphwid,graphht,xvals,y1,1,n,0 ) with .Box.nw at G1.Box.sw+(0,-0.5)
{"G2" at G2.s below }
G3: graphb( graphwid,graphht,xvals,y2,1,n,10 ) with .Box.nw at G1.Box.ne+(0.5,0)
{"G3" at G3.s below }
G4: graphb( graphwid,graphht,xvals,y3,1,n,0 ) with .Box.nw at G2.Box.ne+(0.5,0)
{"G4" at G4.s below }
B1: grlinlin( graphwid,graphht,P,n,10 ) with .nw at G2.Box.sw+(0,-1)
{"B1" at B1.s below }
B2: grlinlin( graphwid,graphht,P,n,11 ) with .Box.nw at last [].Box.ne+(0.5,0)
{"B2" at B2.s below }
D3: grloglin( graphwid,graphht,Transistors,nT,212 ) \
with .Box.nw at B1.Box.sw+(0,-1)
{"D3" at D3.s below }
D4: grloglin( graphwid,graphht,Transistors,nT,002 ) \
with .Box.nw at last [].Box.ne+(0.5,0)
{"D4" at D4.s below }
# A Bode diagram shows the magnitude of the response in dB and the phase
# in degrees, both with respect to the logarithm of the frequency, so
# two separate linear vertical scales are required and a logarithmic
# horizontal scale.
# A second-order resonant system produces a suitable frequency-response test.
# The transfer function of a canonical second-order resonance is given by
# w_n^2
# --------------------------
# s^2 + 2*zeta*w_n*s + w_n^2
# where w_n is the natural frequency and zeta the damping ratio.
# Let the input frequency be f Hz or w = 2*pi*f rad/s and represent
# the input signal in the frequency domain by complex number s = 0 + j*w
# or by the pair (0, w). The above (complex) function is evaluated for
# different values of s.
define SecondOrd { $2: Zprod((0,$1),(2*zeta*w_n,$1))
$2: Zsum((w_n2,0),$2)
$2: Zdiv((w_n2,0),$2) }
w_n = 60 * 2 * pi # 60 Hz in rad/s
zeta = 0.1
fmin=w_n/(2*pi) / 5
fmax=w_n/(2*pi) * 5
# Calculate dB gain and phase responses over a set
# of frequencies spaced uniformly on the log scale
w_n2 = w_n^2
logfmin = log(fmin); logfmax = log(fmax)
n = 100; lastph = 0
for i=0 to n do {
lf = (i/n)*(logfmax-logfmin) + logfmin
logfrq[i+1] = lf
w = exp(lf) * 2 * pi
SecondOrd(w,Z);
# Z: Zprod(Z,Z) # 4th order resonance
GH: ZtoB(Z)
dbgain[i+1] = GH.x
phase[i+1] = GH.y
if (abs(lastph) > 90) && (GH.y*lastph < 0) then {
phase[i+1] += sign(lastph)*360 }
lastph = phase[i+1]
}
npts = n+1
# Graph sizes
graphwid = 5
graphht = 3
# Plot gain and phase vs freq
D: bodepl( graphwid,graphht,npts,logfrq,dbgain,phase ) \
with .Box.nw at D3.Box.sw+(0,-1)
# Plot gain vs freq
G: bodepl( graphwid,graphht,npts,logfrq,dbgain,phase,1 ) \
with .Box.nw at last [].Box.sw+(0,-1)
# Plot phase vs freq
P: bodepl( graphwid,graphht,npts,logfrq,dbgain,phase,2 ) \
with .Box.nw at last [].Box.sw+(0,-1)
.PE
|
