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| 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(shè)計低電壓運算放大器和精密傳感器應(yīng)用比較 |
| 文件頁數(shù)： | 26/28頁 |
| 文件大?。?/td> | 168K |
| 代理商： | AND8054 |
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26
Appendix II: Method II:
Solve N(j
ω
o
)
REAL
= N(j
ω
o
)
IMAGINARY
= 0
The oscillation equation sometimes can be determined
directly from the characteristic equation by substituting
s = j
ω
ο
into
s and arranging the N(j
ω
ο
) into its real and
imaginary parts. However, this method is usually not
feasible for circuits which are fifth order and higher
oscillators. This procedure is essentially a subset of the
Routh test, because the first two rows of the Routh array will
correspond to N(j
ω
o
)
REAL
and N(j
ω
o
)
IMAGINARY
. If the
characteristic equation N(s) = j
ω
ο
= 0, the poles of the
characteristic equation will be on the imaginary axis at
±
j
ω
ο
with an oscillation frequency of
ω
ο
. The Method II
procedure is shown below for second and third order
oscillators [13].
Second–Order Circuits
N2(s)
a0s2
a1s
a2
a0s2
a1
a0s
a2
a0
Let s = j
ω
ο
be the frequency at which N
2
(s) = 0. The
condition for oscillation is meet when the a
1
term is set to
zero, and the s–term is removed. The frequency of
oscillation is found from:
o
a2
a0
Third Order Circuits
a0s3
Let s = j
ω
ο
be the frequency at which N
3
(s) = 0, and arrange
the equation into its real and imaginary parts:
N3(s)
a1s2
a2s
a3
N3(j o)
(–a1
2
o
a3)
j o(–a0
2
o
a2)
0
Thus, the real and imaginary parts equal zero when:
–a1
2
o
a3
0 and –a0
2
o
a2
0
Solving the above equations for
o2
gives:
2
o
a3
a1
a2
a0
Summary of Method II Equations
Oscillator
Order
N(s)
Oscillation
Condition
o
áááááááááááááááááááááááááááááá
á
áááááááááááááááááááááááááááááá
á
ááá
2nd
ááá
á
ááááááááááá
ááááááááááá
á
ááááá
ááááá
á
a1
ááááááááá
ááááááááá
á
o
a0
á
3rd
á
á
á
a0
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