Ptc.Controls.Worksheet.Printing.EngineeringPages+EngPagesPaginato
12)
PV/R = 0.68/(1 + 1.55s) where R = 1/s for unit step input
PV = 0.68/(1 +1.55s)(1/s)
PV = 0.68/[s(1 +1.55s)]
Taking the inv Laplace transform
pv(t) = XXXXXXXXXXe^-0.645t) (Time domain response)
Using the final value theorem:
Value = = 0.68 (Final value)
13)
Given transfer function: 3.16/[s(1+2s)]
From calculations and graphing (see next page) we get:
Phase margin = 22°
Gain margin = 24dB
Stable = Yes
Frequency (MHz)
S
(d
B
)
-80
-60
-40
-20
0
20
40
60
80
ang( S[2,1] ) (deg)
-180
-135
-90
-45
0
45
90
135
180
Frequency (MHz)
XXXXXXXXXX
Gain vs Phase
S ang( S[2,1] )
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Line
D
Typewritten Text
1)20log 3.16
D
Typewritten Text
D
Typewritten Text
2) - 20dB/decade
D
Typewritten Text
3)-20dB/decade
D
Typewritten Text
D
Typewritten Text
D
Line
D
Line
D
Line
D
Typewritten Text
W0dB
D
Typewritten Text
D
Line
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
W-180°
D
Typewritten Text
D
Typewritten Text
D
Line
D
Line
D
Typewritten Text
24dB
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
2)-90°
D
Line
D
Typewritten Text
1) 0°
D
Typewritten Text
-135°
D
Typewritten Text
-180°
D
Typewritten Text
CF = 0.5
s
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Text Box
GH = 3.16/ [(1 + 2s)s]
Gjw = 3.16/ [ jw(1 + 2jw)]
= 3.16/ [jw(1 + jw/0.5)]
Start Freq (SF) = 0.5/10 = 0.05
s ; Entry Point = 20 log 3.16/0.05 = 36dB
Entry slope -20dB/decade due to s term in denominator.
Corner Freq (CF) = 0.5
s; slope after CF -40dB/decade
Entry phase is -90° due to s term in denominator.
At CF, phase shift is -90° - 45° = -135°; At 10*CF, Phase shift = -180°
D
Text Box
Rad/s
D
Typewritten Text
D
Typewritten Text
(10dB)
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
D
Typewritten Text
Calculations:
D
Typewritten Text
Frequency (MHz)
S
(d
B
)
-80
-60
-40
-20
0
20
40
60
80
ang( S[2,1] ) (deg)
-180
-135
-90
-45
0
45
90
135
180
Frequency (MHz)
XXXXXXXXXX
Gain vs Phase
S ang( S[2,1] )
D
Line
D
Text Box
SF=0.05
s
D
Line
D
Text Box
36dB
D
Line
D
Text Box
CF=0.5
s
D
Line
D
Text Box
16dB
D
Line
D
Line
D
Text Box
5
s
D
Line
D
Line
D
Line
D
Line
D
Line
D
Text Box
-24dB
D
Line
D
Text Box
w0 = 1.2
s
D
Line
D
Text Box
-158°
D
Text Box
0dB
D
Line
D
Line
D
Text Box
24 dB
D
Line
D
Text Box
Phase margin = -180° XXXXXXXXXX°) = 22°
Gain Margin = 24dB
System is stable because at -180° phase shift, gain = -24dB
D
Text Box
Rad/s
D
Text Box
SP = 36dB