CSTCW24M0X53-R0 Datasheet, PDF (13/32 Pages) Murata Manufacturing Co., Ltd. – Ceramic Resonator

P17E.pdf
2012.10.31 ^{Note • Please read rating and CAUTION (for storage, operating, rating, soldering, mounting and handling) in this catalog to prevent smoking and/or burning, etc.}
• This catalog has only typical specifications because there is no space for detailed specifications. Therefore, please review our product specifications or consult the approval sheet for product specifications before ordering.
Principles of CERALOCK^{® 2}
2
Notes
(Note 3)
Fig.ᶙ shows the equivalent circuit of an emitter
grounding type transistor circuit. In the figure, Ri
stands for input impedance, R0 stands for output
impedance and – stands for current amplification
rate.
When the oscillation circuit in Fig.2-6 is expressed
by using the equivalent circuit in Fig.ᶙ it becomes
like Fig.ᶚ. Z1, Z2 and Z are as shown in the table
for each Hartley type and Colpitts type circuit.
The following 3 formulas are obtained based on
Fig.ᶚ.
As i1 ≠ 0, i2 ≠ 0, i3 ≠ 0 are required for continuous
oscillation, the following conditional formula can be
performed by solving the formulas of (1), (2) and (3)
on the current.
ЌR0Z1Z2=(Z1+Ri)Z₂₂–{Z1(Z2+Z)+


R0Z1Z2=(Z2+Z+Z1)Ri}(Z2+R0)
ɹɹ
ʜʜʜʜ (4)
Then, as Z1, Z2 and Z are all imaginary numbers,
the following conditional formula is obtained by
dividing the formula (4) into the real number part
and the imaginary number part.
1
R
R0
-
R0 1
+
(Imaginary number part)
Z1Z2Z+(Z1+Z2+Z)RiR0=0
ɹɹ
ʜʜʜʜ (5)
(Real number part)
ЌR0Z1Z2+Z1(Z+Z2)R0+
Z2(Z+Z1)Ri=0ɹɹɹɹ

ʜʜʜʜʜʜʜ (6)
Fig.ᶙ
R0
Z
1
-
R
R0 1
2
+
3
1
Z2
Z1
Hartley Type
Colpitts Type
Z1
jωL1
1 / jωCL1
Z2
jωL2
1 / jωCL2
Z
1 / jωC
jωL
Fig.ᶚHartley/Colpitts Type LC Oscillation Circuits
ЌR0i1+(R0+Z2) i2–Z2i3=0
ʜʜʜʜʜʜʜʜ (1)
Z1i1+Z2i2–(Z2+Z+Z1) i3=0

ʜʜʜʜʜʜʜʜ (2)
(Z1+Ri) i1–Z1i3=0

ʜʜʜʜʜʜʜʜʜʜʜ (3)
Formula (5) represents the phase condition and
formula (6) represents the power condition.
Oscillation frequency can be obtained by applying
the elements shown in the aforementioned table to
Z1,Z2 and Z solving it for angular frequency ω .
(Hartley Type)
1
(L1L2)
C{1+
(L1
L1 · L2
+ L2) CR
R0
}

ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ
ʜʜʜʜ
(7)
(Colpitts Type)
1
L
CL1·CL2
CL1+CL2
· {1+
L
(CL1+CL2)
R
R0
}

ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ
ʜʜʜʜ
⁽⁸⁾
In either circuit, the term in brackets will be 1 as
long as Ri and R0 is large enough. Therefore
oscillation frequency can be obtained by the
following formula.
(Hartley Type) fosc. =
1
ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ

ʜʜ (9)
(Colpitts Type) fosc. =
1
ɹɹɹɹɹɹɹɹɹɹɹɹɹ^Cɹ^L1ɹ^{· C}ɹ^L2ɹɹʜ (10)
CL1+CL2
11