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參數資料
| 型號： | AND8054 |
| 廠商： | ON SEMICONDUCTOR |
| 英文描述： | Designing RC Oscillator Circuits with Low Voltage Operational Amplifiers and Comparators for Precision Sensor Applications |
| 中文描述： | RC振蕩器電路設計低電壓運算放大器和精密傳感器應用比較 |
| 文件頁數： | 27/28頁 |
| 文件大?。?/td> | 168K |
| 代理商： | AND8054 |
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AND8054/D
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27
Appendix III: Routh’s Stability Test
Routh’s Stability Test [12] can be used to test the
characteristic equation to determine whether any of roots lie
on the imaginary axis. Routh’s test consists of forming a
coefficient array. Next, the procedure substitutes s = j
ω
o
for
s, and the summation of the row is set to zero. If the row
equation produces a nontrivial solution for
ω
o
, the procedure
is complete and the frequency of oscillation is equal to
ω
o
.
If the row equation does not yield an equation that can be
solved for
ω
o
, the procedure continues with the next row in
the Routh array. This technique arranges the numerator of
the characteristic equation (i.e. denominator of the transfer
equation) into the array listed below.
A
1
LG
(s)
N( s)
D( s)
T(s)
A
A
N( s)
a0sn
a1sn
an
1
a2sn
an
2
a3sn
3
...
1s
sn
sn–1
sn–2
sn–3
.
.
.
a0
a1
b1
c1
.
.
.
a2
a3
b2
c2
.
.
.
a4
a5
b3
c3
.
.
an
an–1
bn–2
cn–3
s0
f1
where the coefficients b
1
, b
2
, b
3
, etc., are evaluated as
follows:
a1a2
a0a3
a1
b1
b2
a1a4
a0a5
a1
b3
a1a6
a0a7
a1
The evaluation of the b’s is continued until the remaining
terms are equal to zero. The same pattern of cross
multiplying the coefficients of the two previous rows is
followed in evaluating the c’s, d’s, etc...
c1
b1a3
b2a1
b1
c2
b1a5
b3a1
b1
This process is continued until the
n–
th row has been
completed. The Routh stability criterion states:
1. A necessary and sufficient condition for stability is
that the first column of the array does not contain
sign changes.
2. The number of sign changes in the entries of the
first column of the array is equal to the number of
roots in the right half s–plane.
3. If the first element in a row is zero, it is replaced by
ε
, and the sign changes when
ε
→
0 are counted
after completing the array.
4. The poles are located in the right half plane or on
the imaginary axis if all the elements in a row are
zero.
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