### Ceramic Resonator Application Notes

```CERAMIC RESONATOR PRINCIPLES
Principles of Operation for
Ceramic Resonators
1/2 π
Equivalent Circuit Constants: Fig.1.2 shows the symbol for a
fr
fa
Qm
(Q m
ceramic resonator. The impedance and phase characteristics measured
between the terminals are shown in Fig.1.5. This figure illustrates that the
resonator becomes inductive in the frequency range between the
frequency fr (resonant frequency), which provides the minimum
impedance, and the frequency fa (anti-resonant frequency), which
provides the maximum impedance. It becomes capacitive in other
frequency ranges. This means that the mechanical oscillation of a twoterminal resonator can be replaced with an equivalent circuit consisting of
a combination of series and parallel resonant circuits with an inductor L,
a capacitor C, and a resistor R. In the vicinity of the resonant frequency,
the equivalent circuit can be expressed as shown in Fig.1.4.
The fr and fa frequencies are determined by the piezoelectric ceramic
material and its physical parameters. The equivalent circuit constants can
be determined from the following formulas:
Considering the limited frequency range of f r ≤ f ≤ f a , the impedance is
given as Z=R e +jwL e (L e ≤=0) as shown in Fig.1.5. The ceramic resonator
should operate as an inductor Le (H) having the loss Re (Ω).
Fig.1.1 shows comparisons for equivalent circuit constants between a
ceramic resonator and a quartz crystal resonator. Note there is a large
difference in capacitance and Qm which results in the difference of
oscillating conditions when actually operated. The table in the appendix
shows the standard values of equivalent circuit constants for each type of
ceramic resonator.
Higher harmonics for other modes of oscillation exist other than the
desired oscillation mode. These other oscillation modes exist because the
ceramic resonator uses mechanical resonance. Fig.1.6 shows these
characteristics.
FREQUENCY
CERAMIC RESONATOR
2.50MHz
4.00MHz
1.0x10 3
385
4.2
4.4
33.3
36.3
17.6
8.7
912
1134
147
228
455KHz
8.8x10 3
14.5
256.3
9.0
2734
12
L 1 (µH)
C 1 (pF)
C 0 (pF)
R 1 (Ω)
Qm
∆ F (KHz)
=
=
=
=
L1 C1
L1 C1C0/( C1+C0) = Fr
1/2 π Fr C1R1
1/2 π
1 + C1+C0
Mechanical Q)
8.00MHz
72
5.9
39.8
4.8
731
555
CRYSTAL
2.457MHz
4.00MHz
7.2x10 3
2.1x10 3
0.005
0.007
2.39
2.39
37.0
22.1
298869
240986
3
6
453.5KHz
8.6x10 3
0.015
5.15
1060
23000
0.6
8.00MHz
1.4x10 4
0.027
5.57
8.0
88677
19
Figure 1.1 Comparisons of equivalent Circuit Constants for Ceramic and Crystal Resonators
1M
500k
100k
50k
C1
L1
fr
Phase ø (Deg.)
Figure 1.2) Symbols for 2-Terminal Ceramic Resonator
104
Impedance Z (Ω)
Impedance between 2 terminals
Phase (φ) = tan-1 X/R
Z = R + jX ( R: real number, X: imaginary number)
Impedance Z (Q)
105
103
fa
102
Main Vibration Mode
10k
5k
Thickness Mode
1k
500
100
50
10
5
1
0 000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.00
R1
Frequency (MHz)
10
Figure 1.6) Spurious Characteristics for a Typical Ceramic
Resonator (455 KHz)
430
440
450
460
470
Frequency (KHz)
C0
R1
L1
C1
C0
:
:
:
:
Equivalent Resistance
Equivalent Inductance
Equivalent Capacitance
Inner Electrode Capacitance
+90
Figure 1.3) Electrical Equiv. Circuit for a Cer. Resonator
CL1
CL2
L1
L2
0
Re
Le
C
L
C
L
(Colpitts Oscillator)
-90
C
(Hartley Oscillator)
R e : Effective Resistance
L e : Effective Inductance
Figure 1.4) Equivalent Circuit for a Ceramic Resonator in
the Frequency Range of f r ≤ f ≤ fa
Figure 1.5) Impedance and Phase Characteristics for
Ceramic Resonators
Figure 1.7) Basic configuration for an LC Oscillation Circuit
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Basic Oscillating Circuits
Colpilts Circuit
Generally, the oscillating circuits can be grouped into the
following three types:
1. Positive feedback
2. Negative resistance element
3. Delay of transfer time or phase in the case of ceramic resonators,
quartz crystal resonators, and LC oscillators, positive feedback is the
circuit of choice.
f OSC =
1/2 π
L1 * [(CL1 * CL2)/( CL1 + CL2)]
Hartley Circuit
f OSC =
1/2 π
C (L1+ L2)
In a ceramic resonator oscillator, the inductor is replaced by a ceramic
resonator, taking advantage of the fact that the resonator becomes
inductive between resonant and anti-resonant frequencies. The most
commonly used circuit is the Colpitts circuit.
Among the positive feedback oscillation circuits using LC, the tuning
type anti-coupling oscillation circuit, by Colpitts and Hartley, are
typically used. See Fig. 1.7.
The operating principle of these oscillation circuits can be seen in Fig.2.1.
Oscillation occurs when the following conditions are satisfied.
Loop gain: G = α • β ≥ 1
Phase amount: φ Τ = φ 1 + φ 2 = 360˚ • n (n = 1,2,…)
In Fig.1. 7, a transistor, which is the most basic amplifier, is used.
The oscillation frequencies are approximately the same as the resonance
frequency of the circuit consisting of L, CL1, and CL 2 in the Colpitts
circuit or consisting of L1, L2, and C in the Hartley circuit. These
frequencies can be represented by the following formulas.
In a Colpitts circuit, an inversion of φ 1 = 180˚ is used, and it is inverted
more than φ 2 = 180˚ with L and C in the feedback circuit. The operation
with a ceramic resonator can be considered as the same.
α(φ1)
40
30
Amplifier
Gain
Phase Shift: φ1
Possible to Oscillate
90
Phase
20
A
Feedback Network
Transfer Function: Β
Phase Shift: φ2
CL1
Oscillating conditions
Loop gain G = α • β≥1
Phase Shift φT = φ1+φ1 = 360˚ • n(n = 1,2, …)
0
Gain
-10
-20
CL2
Ceramic Resonator
10
Phase (deg)
Loop Gain (dB)
Rf
-90
-30
-40
3.90
β(φ2)
4.00M
VDD = +5V
CL1 = CL2 = 30pF
IC: CD4069UBE
4.00
4.10
Frequency (KHz)
Figure 2.1) Principles of Oscillation
Figure 2.2) Basic Oscillation Circuit with Inverters
40
Impossible to Oscillate
30
90
Ceramic
Resonator
Loop Gain (dB)
β(φ2)
IC
Zin [1M(Ω)] - j/w[8 • 10 9(F)]
0.01µΩ
10
Phase
Phase (deg)
α(φ1)
20
0
-10
Z0 = 50Ω
Vector Voltmeter
CL2
Vin
-20
CL1
-90
Gain
S.S.G.
-30
-40
3.90
Loop gain G = α • β≥1
Phase Shift φT = φ1+φ1 = 360˚ • n(n = 1,2, …)
4.00M
VDD = +2.7V
CL1 = CL2 = 30pF
IC: CD4069UBE
4.00
4.10
Frequency (KHz)
Figure 2.4) Measured Results of Loop Gain
and Phase Shift
Figure 2.3) Measuring Circuit Network for Loop-Gain and Phase Shift
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APPLICATIONS
CMOS Inverter: A CMOS inverter can be used as the inverting
amplifier; the one-stage type of the 4069 CMOS group is most useful.
Because of excessive gain, ring oscillation or CR oscillation is a typical
problem when using the three-stage buffer type inverter, such as the 4049
group. ECS employs the RCA CD4O69UBE as a CMOS standard curcuit,
as shown in Fig. 3.2.
Typical Oscillation Circuit: The most common oscillator circuit for a
ceramic resonator is a Colpitts circuit. The design of the circuit varies
with the application and the IC to be used, etc. Although the basic
configuration of the circuit is the same as that of a crystal controlled
oscillator, the difference in mechanical Q results from a difference in
circuit constants. Some typical examples follow.
HCMOS Inverter Circuit: Recently, the high speed CMOS (HCMOS)
is increasingly being used for circuits allowing high speed and low power
consumption for microprocessors.
There are two types HCMOS inverters: the un-buffered 74HCU series
and the 74HC series with buffers. The 74HCU system is optimum for
ceramic resonators. See Fig.3.3
Design Considerations: It is becoming more common to configure
the oscillation circuit with a digital IC, using an inverter gate. Fig.3.1 on
the following page shows the configuration of a basic oscillation circuit
with a CMOS inverter.
INV.1 operates as an inverting amplifier for the oscillating circuit.
INV.2 is used as a waveform shaper and also acts as a buffer for the
output.
The feedback resistance Rf provides negative feedback around the
inverter so that oscillation will start when power is applied.
If the value of Rf is too large and the insulation resistance of the input
inverter is low, then oscillation will stop due to the loss of loop gain. Also,
if Rf is too great, noise from other circuits can be introduced into the
oscillation circuit. Obviously, if Rf is too small, loop gain will be
decreased. An Rf of 1MΩ is generally used with a ceramic resonator.
Damping resistor Rd has the following function although it is
sometimes omitted. It makes the coupling between the inverter and the
feedback circuit loose; thereby, decreasing the load on the output side of
the inverter. In addition, the phase of the feedback circuit is stabilized. It
also provides a means of reducing the gain at higher frequencies, thus
preventing the possibility of spurious oscillation.
TTL Inverter Circuit: The value of load capacitance CL1 and CL2
should be greater than those of CMOS due to impedance matching. In
addition, the feedback resistance Rf should be as small as several KΩ.
Note that the bias resistance Rd is required to properly determine the DC
operating point.
Frequency Correlation: The oscillator circuits shown on the
following page are ECS standard test circuits. The inverters used in these
circuits are widely accepted as industry standard because their
characteristics are representative of those found in microprocessors
within the same family (CMOS/HCMOS/TTL). Naturally, applications
will differ in what IC is used, and as can be expected, oscillator circuit
characteristics will vary from IC to IC.
Usually, this variation is negligible and a ceramic resonator part
number can be selected simply by classifying the processor as CMOS,
HCMOS or TTL.
Given that the standard ECS ceramic resonators are 100% frequency
sorted to the test circuits on the following page, it is relatively easy to
correlate the frequency of oscillation of our standard circuit to that of a
customer specified circuit.
For example, if the microprocessor being used is a Motorola 6805at a
frequency of 4MHz, then the correct ECS part number would be
ZTA4.OMG (frequency sorted to the CD4O69UBE CMOS test circuit).
Circuit parameters should be selected as below:
lag of 180˚. These values should be properly selected depending on the
application, the IC used, and the frequency. If CL1 and CL2 are lower
values than necessary, the loop gain at high frequencies is increased,
which in turn increases the probability of spurious oscillation. This is
particularly likely around 4-5MHz where the thickness vibration
mode lies.
Oscillation frequency (fOSC) in this circuit is expressed approximately
by the following equation.
f OSC =
fr
1 + (C1 / C0 + CL)
VDD (+5V)
Where, fr: Resonance frequency of the ceramic resonator.
C1: Equivalent series capacitance of the ceramic resonator.
C0: Equivalent parallel capacitance of the ceramic resonator.
CL =CL1 • CL2/CL1 +CL2
40
IC: MC68HC05C4
38
39
20
Rf
This clearly shows that the oscillation frequency is influenced by the
loading capacitance. Caution should be taken in defining its value when a
tight tolerance for oscillation frequency is required.
CL1
CL2
C1 = 30pF
C2 = 30pF
R1 = 1MΩ
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By actually setting up this circuit as well as the standard test circuit
shown in Fig.3.1 below, it is possible to establish the average shift that can
be expected when using the ZTA4.OMG with a 6805 processor. The actual
data is shown below:
RESONATOR SAMPLE #
IC: MC6805C4
IC: CD4O69UBE
3994.21
3997.49
4000.87
3998.18
4001.09
3998.37
3991.80
3995.46
3997.96
3995.96
3998.87
3996.01
1
2
3
4
5
X
Figure 3.1) Basic Oscillation Circuit with
CMOS Inverter
From this data, it is possible to predict that the standard ZTA4.00MG
resonator will have an approximate +0.06% frequency shift from the
original 4.00MHz ±0.5% initial tolerance. This is of course a negligible
shift and will not affect circuit performance in any way.
INV.1
VDD
Output
INV.2
IC
IC
Rf = 1MΩ
IC: CD4069UBE (MOS)
X: Ceramic Resonator
Rd: Damping Resistance
Rd
CL1
X
CL2
VDD
14
FREQUENCY RANGE
VDD
190 ~ 249KHz
250 ~ 374KHz
375 ~ 429KHz
430 ~ 699KHz
700 ~ 1250KHZ
1.25 ~ 1.80MHz
1.80 ~ 6.30MHz
6.31 ~ 13.0MHz
+5V
+5V
+5V
+5V
+5V
+5V
+5V
+12V
CD4069UBE (RCA)
1
3
2
4
7
Rf
Rd
OUTPUT
CL2
CL1
Figure 3.2) CMOS Standard Circuit
VDD +5VDC
FREQUENCY RANGE
14
TC74HCUO4 (TOSHIBA)
1
2
3
4
7
Rf
Rd
OUTPUT
CL1
CL2
Figure 3.3) HCMOS Standard Circuit
190 ~ 374 KHz
375 ~ 429 KHz
430 ~ 699 KHz
700 ~ 999 KHz
1000 ~ 1250 KHz
1.251 ~ 1.80 Mhz
1.80 ~ 6.30 MHz
6.31 ~ 13.0 MHz
13.01 ~ 19.99 MHz
20.00 ~ 25.99 MHz
26.00 ~ 32.00 Mhz
C L1
330pF
220pF
120pF
100pF
100pF
30pF
30pF
30pF
CIRCUIT CONSTANT
C L2
Rf
470pF
1M
470pF
1M
470pF
1M
100pF
1M
100pF
1M
30pF
1M
30pF
1M
30pF
1M
Rd
0
0
0
0
5.6K
0
0
0
C L1
470pF
330pF
220pF
150pF
100pF
100pF
100pF
100pF
30pF
15pF
5pF
CIRCUIT CONSTANT
C L2
Rf
470pF
1M
330pF
1M
220pF
1M
150pF
1M
100pF
1M
100pF
1M
100pF
1M
100pF
1M
30pF
1M
15pF
1M
5pF
1M
Rd
5.6K
5.6K
5.6K
5.6K
5.6K
1.0K
680
220
0
0
0
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FREQUENCY RANGE
VDD
14
SN74LSO4N (T.I.)
1
3
2
7
4
Rf
Rd
OUTPUT
CL2
CL1
Figure 5.1) TTL Standard Circuit
1.251 ~ 1.499 MHz
1.500 ~ 1.99 MHz
1.80 ~ 2.49 MHz
2.50 ~ 3.99 Mhz
4.00 ~ 4.99 Mhz
5.00 ~ 6.30 Mhz
6.31 ~ 6.99 Mhz
7.00 ~ 8.99 MHz
9.00 ~ 11.99 MHz
12.00 ~ 13.99 Mhz
14.00 ~ 17.99 Mhz
18.00 ~ 21.99 MHz
22.00 ~ 25.99 Mhz
26.00 ~ 32.00 MHz
Rd
22KΩ
22KΩ
22KΩ
10KΩ
10KΩ
10KΩ
10KΩ
10KΩ
10KΩ
22KΩ
22KΩ
22KΩ
22KΩ
22KΩ
VCO (Voltage Controlled Oscillator) Circuits: VCO circuits are
used in TV’s and audio equipment because the signals need to be
processed in synchronization with pilot signals transmitted from
broadcasting stations. Oscillation circuits, such as LC and RC were
originally used; however, ceramic resonators are now used since they
require no adjustment and have superior stability over the older type
circuits. Resonators for VCO applications are required to have a wide
variable frequency
Circuits for Various IC/ LSI:
Ceramic resonators are being used in a wide range of applications in
combination with various kinds of IC’s by making good use of the
previously mentioned features. Following are a few examples of actual
applications.
Applications for Microprocessors: Ceramic resonators are
optimum as a stable oscillating element for various kinds of
microprocessors: 4 bit, 8 bit, and 16 bit. As the general frequency
tolerance required for the reference clock of microprocessors is ±2% - 3%,
about circuit constants because they vary with frequency and the LSI
circuit being used. Fig. A shows an application with a 4 bit
microprocessor, and Fig. B shows an application with an 8 bit
microprocessor.
Miscellaneous: Other than the above mentioned uses, ceramic
resonators are widely used with IC’s for voice synthesis and clock
generation. For general timing control applications, oscillation frequency
is usually selected by the user based on the IC manufacturer’s
recommended operating frequency range. The selection of this frequency
with a given IC will dictate what circuit values and which ceramic
representative when selecting a ceramic resonator part number.
As mentioned earlier, there are many applications for ceramic
resonators. Some of the more application specific oscillator circuits
require that unique ceramic resonators be developed for that application
and IC.
Remote Control IC: Remote controls have increasingly become a
common feature. Oscillation frequency is normally 400-500 KHz, with
455KHz being the most popular. This 455KHz is divided by a carrier
signal generator so that approximately 38KHz of carrier is generated.
+5V
CIRCUIT CONSTANT
C L2
Rf
2000pF
4.7kΩ
1500pF
4.7KΩ
1000pF
4.7KΩ
1000pF
4.7KΩ
680pF
4.7KΩ
470pF
4.7KΩ
470pF
4.7KΩ
330pF
4.7KΩ
220pF
4.7KΩ
220pF
2.2KΩ
150pF
2.2KΩ
100pF
2.2KΩ
68pF
4.7KΩ
47pF
4.7KΩ
C L1
1500pF
1500pF
1000pF
1000pF
680pF
470pF
470pF
330pF
220pF
220pF
150pF
100pF
68pF
47pF
+5V
VDD (+5V)
100KΩ
VDD
40
RESET
IC: MC68HC05C4
61
44
42
43
26
41
24
25
22
38
6805
23
39
20
Rf
VSS
TMP47C420F
9
11
12
E
ExTAL
xTAL
4.00M
18 19 20 21
fOCS
30pF
30pF
4.00M
CL1
30pF
C1 = 30pF
C2 = 30pF
R1 = 1MΩ
30pF
Figure A) TMP47C420F (TOSHIBA)
CL2
(1) MC6805 (Motorola)
(2) HD6805 (Hitachi)
Figure B) 6805s by Various Manufacturers (Timing Control)
Figure C) By Various Manufacturers (Timing Control, 8bit)
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OSCILLATION RISE TIME
against load capacitance (CL) and supply voltage. It is noteworthy that
the rise time is one or two decades faster for a ceramic resonator than for
a quartz crystal. (This point is graphically illustrated in Fig. 6.3)
Oscillation rise time means the time when oscillation develops from a
transient area to a steady area at the time the power to the IC is activated.
With a ceramic resonator, it is defined as the time to reach 90% of the
oscillation level under steady conditions as shown in Fig.6.1.
Rise time is primarily a function of oscillating circuit design. Generally,
smaller size of ceramic resonator will cause a faster rise time. The effect of
load capacitance becomes more apparent as the capacitance of the
resonator decreases. Fig.6.2 shows an actual measurement of rise time
Starting Voltage: Starting voltage means the minimum supply voltage
at which an oscillating circuit can operate. Starting voltage is affected by
all circuit elements. It is determined mostly by the characteristics of the
IC. Fig.6.4 shows an example of an actual measurement for the starting
10
ON
VDD
5
IC: TC74HCU04P
VDD = +5.OV
CL1 = CL2 = 100PF
OV
2
Crystal
0.9 x Vp-p
Rise Time (msec)
1
Vp-p
t=0
Rise Time
Time
0.5
Ceramic
0.2
0.1
0.05
Figure 6.1) Definition of Rise Time
0.02
Oscillation Rise Time (ms)
0.01
(IC: CD4069UBE, Resonator: ZTA4.0MG)
1.0
0
0.5
1.0
2.0
5.0
10
20
Oscillation Frequency (MHz)
0.5
Figure 6.3) Rise Time vs. Oscillation Frequency for both Ceramic and Crystal Resonators
0
0
2
5
8
Supply Voltage (V)
Starting Voltage (V)
Oscillation Rise Time (ms)
(a) Supply Voltage Characteristics
(IC: CD4069UBE, Ceramic Resonator: ZTA4.0MG)
1.0
0.5
+5
(IC: CD4069UBE, Resonator: ZTA4.0MG)
+4
+3
+2
+1
0
0
20
40
60
80
0
0
20
40
60
100
CL(pF)
80
100
Supply Voltage (V)
(b) CLCharacteristics (CL = CL2)
Figure 6.4) Starting Voltage Characteristics Against CL (CL1 = CL2)
Figure 6.2) Example of Actual Measurements for the Charac. of Oscillation Rise Time
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CHARACTERISTICS OF CERAMIC
RESONATOR OSCILLATION
Supply Voltage Variation Characteristics: See Fig.1 below for an
example of an actual measurement of stability for a given oscillation
frequency.
The following describes the general characteristics of oscillation in the
basic circuit. Contact ECS International for detailed characteristics of
oscillation with specific kinds of IC’s and LSI’s.
The stability against temperature change is ±0.3 to 0.5% within a range
of -20˚C to + 80˚C, although it varies slightly depending on the ceramic
material. Influences of load capacitance (CL1, CL2) on the oscillation
frequency is relatively high as can be calculated from the formula for fOSC.
The fOSC. varies by approximately ± 0.1% because of the capacitance
deviation of ± 0.1% in the working voltage range. The fOSC. also varies
with the characteristics of the IC.
-40
min.
0
40
80
120
0
2
5
8
Supply Voltage (V)
Temperature (˚C)
0
1
4
CL1/CL2 (pF)
(c) CL2 Characteristics
(b) Supply Voltage Characteristics
(a) Temperature Characteristics
2
-0.5
-0.1
-0.5
VDD = +5V
CL1 = 30pF
+0.5
fOSC Drift (%)
max.
min.
0
fOSC Drift (%)
fOSC Drift (%)
max.
oscillation level against temperature, supply voltage, and load
capacitance (CL1, CL2). The oscillating level is required to be stable over a
wide temperature range, and temperature characteristics be as flat as
possible. This change is linear with supply voltage unless the IC has an
internal constant voltage power source.
+0.1
VDD = +5V
+0.5
Oscillation Level: Below are examples of actual measurements of the
+0.5
fOSC Drift (%)
fOSC Drift (%)
VDD = +5V
CL2 = 30pF
+0.5
0
1
2
4
VDD = +5V
0
10
20
40
100
CL(pF)
CL2/CL1(pF)
Figure 1) Examples of an Actual Measurement of
Stability for a given Oscillation Frequency
-0.5
-0.5
(e) CL Characteristics
(CL1 = CL2)
(d) CL1 Characteristics
V1H
V2H
+8
VDD = +5V
+6
VDD = +5V
CL1 = 30pF
+6
V1H
V1H
+5
+7
V2H
+5
+5
+2
+1
-40
Temperature (˚C)
0
40
80
120
0
V2L
VIL
-1
(a) Temperature Characteristics
Oscillating Level (V)
+3
Oscillating Level (V)
Oscillating Level (V)
V2H
+4
+6
+4
+2
1
5
V1L
8
(c) CL2 Characteristics
V2L
V1L
-1
(b) Supply Voltage Characteristics
+6
VDD = +5V
+5
V1H
V2H
V1H
Oscillating Level (V)
Oscillating Level (V)
V2L
Supply Voltage (V)
+5
+3
+2
V1L
+1
0
4
CL1/CL2 (pF)
-1
+1
V2H
+4
2
0
+2
2
VDD = +5V
CL2 = 30pF
+3
+1
+3
0
+6
+4
1
2
4
V2L
-1
+4
+3
+2
+1
Figure 2) Examples of an Actual Measurement of
Output Levels
10
40
CL(pF)
CL2/CL1(pF)
-1
(d) CL1 Characteristics
20
0
100
V2L
V1L
(c) CL2 Characteristics
(CL1 = CL2)
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