Use Of The Cmos Unbuffered Inverter In Oscillator Circuits, elektronika, elektronika, INWERTERY

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Application Report
SZZA043 - January 2004
Use of the CMOS Unbuffered Inverter in Oscillator Circuits
Moshiul Haque and Ernest Cox
Standard Linear & Logic
ABSTRACT
CMOS devices have a high input impedance, high gain, and high bandwidth. These
characteristics are similar to ideal amplifier characteristics and, hence, a CMOS buffer or
inverter can be used in an oscillator circuit in conjunction with other passive components.
Now, CMOS oscillator circuits are widely used in high-speed applications because they are
economical, easy to use, and take significantly less space than a conventional oscillator.
Among the CMOS devices, the unbuffered inverter (’U04) is widely used in oscillator
applications. This application report discusses the performance of some TI ’U04 devices in
a typical crystal-oscillator circuit
.
Contents
1
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2
Theory of Oscillators
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2.1
Characteristics of Crystals
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
Buffered and Unbuffered CMOS Inverters in Oscillator Circuits
. . . . . . . . . . . . . . . . . . . . . . . . .
6
4
Characteristics of a CMOS Unbuffered Inverter
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
4.1
Open-Loop Gain
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
4.2
V
O
vs V
I
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
4.3
I
CC
vs V
I
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
4.4
Variation of Duty Cycle With Temperature
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
5
Characteristics of LVC1404
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
6
Practical Oscillator Circuits
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
6.1
Selection of Resistors and Capacitors
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
6.1.1
R
F
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
6.1.2
R
S
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
6.1.3
C
1
and C
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A. Laboratory Setup
Practical Design Tips
16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
A.1
Laboratory Setup to Measure Open-Loop-Gain Characteristics
. . . . . . . . . . . . . . . . . . . . . . . .
18
A.2
Laboratory Setup to Measure I
CC
vs V
I
Characteristics
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
Appendix B. LVC1GU04 in Crystal-Oscillator Applications
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
B.1
LVC1GU04 in 25-MHz Crystal-Oscillator Circuit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
B.2
LVC1GU04 in 10-MHz Crystal-Oscillator Circuit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
B.3
LVC1GU04 in 2-MHz Crystal-Oscillator Circuit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
B.4
LVC1GU04 in 100-kHz Crystal-Oscillator Circuit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
Trademarks are the property of their respective owners.
1
SZZA043
Appendix C. LVC1404 in Crystal-Oscillator Applications
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
C.1 LVC1404 in 25-MHz Crystal-Oscillator Circuit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
C.2 LVC1404 in 100-kHz Crystal-Oscillator Circuit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
List of Figures
1
Oscillator
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2
Electrical-Equivalent Circuit of a Crystal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
3
Pierce Oscillator Using CMOS Inverter
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
4
Open-Loop-Gain Characteristics of LVC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
5
Open-Loop-Gain Characteristics of AHC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
6
Open-Loop-Gain Characteristics of AUC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
7
V
O
vs V
I
Characteristics of LVC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
8
V
O
vs V
I
characteristics of AHC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
9
V
O
vs V
I
Characteristics of AUC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
10
I
CC
vs V
I
Characteristics of LVC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
11
I
CC
vs V
I
Characteristics of AHC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
12
I
CC
vs V
I
Characteristics of AUC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
13
Duty-Cycle Variation in LVC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
14
Duty-Cycle Variation in AHC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
15
Duty−Cycle Variation in AUC1GU04
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
16
Pinout Diagram for LVC1404
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
17
Logic Diagram of LVC1404
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
18
Open-Loop-Gain Characteristics of LVC1404
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
19
Pierce Oscillator Circuit Using Unbuffered CMOS Inverter
. . . . . . . . . . . . . . . . . . . . . . . . . .
13
20
Effect of R
S
on Oscillator Waveform (No Load)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
21
Effect of R
S
on Oscillator Waveform (R
L
= 1 k
)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
22
Effect of R
S
on the Frequency Response of Feedback Network
. . . . . . . . . . . . . . . . . . . . .
15
23
Effect of R
S
on the Phase Response of Feedback Network
. . . . . . . . . . . . . . . . . . . . . . . . .
15
24
Oscillator Circuit Using a Schmitt-Trigger Input Inverter
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
A-1
Open-Loop-Gain Measurement Setup
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
A-2
I
CC
vs V
I
Measurement Setup
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
B-1
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 25 MHz)
. . . . . . . . . . . . . . . . . . . . . . . . .
19
B-2
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 10 MHz)
. . . . . . . . . . . . . . . . . . . . . . . . .
20
B-3
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 2 MHz)
. . . . . . . . . . . . . . . . . . . . . . . . . .
21
B-4
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 100 kHz)
. . . . . . . . . . . . . . . . . . . . . . . .
22
C-1
Output Waveform of Oscillator Circuit Using LVC1404 (Frequency = 25 MHz)
. . . . . . . . .
23
C-2
Output Waveform of Oscillator Circuit Using LVC1404 (Frequency = 100 kHz)
. . . . . . . .
24
List of Tables
B-1
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 25 MHz)
. . . . . . . . . . . . . . . . . . . . . . . . .
19
B-2
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 10 MHz)
. . . . . . . . . . . . . . . . . . . . . . . . .
20
B-3
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 2 MHz)
. . . . . . . . . . . . . . . . . . . . . . . . . .
21
B-4
Effect of R
S
on Duty Cycle and I
CC
(Frequency = 100 kHz)
. . . . . . . . . . . . . . . . . . . . . . . .
22
2
Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043
1
Introduction
Resistors, inductors, capacitors, and an amplifier with high gain are the basic components of an
oscillator. In designing oscillators, instead of using discrete passive components (resistors,
inductors, and capacitors), crystal oscillators are a better choice because of their excellent
frequency stability and wide frequency range. A crystal basically is an RLC network that has a
natural frequency of resonance.
2
Theory of Oscillators
In principle, an oscillator can be composed of an amplifier, A, with voltage gain, a,
and phase
shift,
α,
and a feedback network, F, with transfer function, f, and phase shift,
β
(see Figure 1).
V
1
V
2
Amplifier, A
a,
Feedback Network, F
f,
Figure 1. Oscillator
For
|
f
|
|
|
1 the oscillating condition is fulfilled, and the system works as an oscillator.
f and a are complex quantities; consequently, it is possible to derive from equation 1
j
|
f
|
|
|
exp
1
(1)
the amplitude
|
f
|
|
|
1
(2)
and the phase
2
(3)
To oscillate, these conditions of amplitude and phase must be met. These conditions are known
as the Barkhausen criterion. The closed-loop gain should be
≥
1, and the total phase shift of 360
degrees
is to be provided.
2.1
Characteristics of Crystals
Figure 2 is an electrical-equivalent circuit of a quartz crystal.
Use of the CMOS Unbuffered Inverter in Oscillator Circuits
3
SZZA043
C
L
R
C
0
Figure 2. Electrical-Equivalent Circuit of a Crystal
The quantities C and L are determined by the mechanical characteristics of the crystal; R is the
resistance of the resonant circuit at the series resonance, and C
o
represents the capacitance of
the leads and electrodes. C
o
is much larger than C and is affected by the stray capacitances of
the final circuit. Because R is negligible, the impedance of this circuit is given by equation 4.
j
2
LC
1
Z
(4)
2
LCC
o
(
C
o
C
)
A series-resonance frequency is attained when the impedance, Z, approaches 0, Z
→
0
1
=
f
ser
2
LC
(5)
A parallel-resonance frequency is attained when the impedance, Z, approaches
∞
, Z
→
∞
C
f
=
f
1 +
par
ser
C
(6)
o
An oscillator circuit using the parallel resonance mode of the crystal is less stable than the
equivalent circuit using the series resonance, because of the dependence on the external circuit
parameter. For series resonance, the crystal appears as a series-resonant resistance, R. For
parallel resonance, the crystal appears as an inductive load.
In the oscillator circuit, the crystal acts as the feedback network. For proper operation, the input
impedance of the amplifier should be well matched to the low series-resonant resistance of the
crystal. For HCMOS devices, because of the high input impedance, a crystal operated in series
resonance would be completely mismatched. The solution is to operate the crystal in
parallel-resonance mode. But, parallel resonance has a poor frequency response compared to
series resonance because of the dependence on C
o
(stray capacitance or circuit capacitance).
Connecting a capacitance in parallel (C
P
) with the crystal can reduce the influence of C
o
on the
parallel-resonance frequency. From the equation of the parallel-resonance frequency
1
C
=
f
1 +
+
par
C
C
2
LC
(7)
p
o
4
Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043
By choosing C
P
> C
o
(C
o
is approximately 3 pF to 5 pF, and C
P
typically is 30 pF).
C
P
>> C (C is in the range of femtofarads)
1
f
par
≈
2
LC
(8)
Now, the parallel-resonance frequency is approximately equal to the series-resonance
frequency.
A popular application of the parallel-resonance circuit is the Pierce oscillator circuit (see
Figure 3) in which the parallel combination of C
1
and C
2
constitutes C
P
.
C
C
=
1
+ C
2
C
P
C
(9)
1
2
C
1
and C
2
form a capacitor voltage divider that determines the degree of feedback. The
feedback factor is given by
C
1
C
2
f
(10)
R
F
CMOS Inverter
C
1
C
2
Crystal
Figure 3. Pierce Oscillator Using CMOS Inverter
The optimal value for C
p
determines the quality and frequency stability of the crystal oscillator.
Usually, the crystal manufacturer’s data sheet specifies the recommended load for the crystal
(C
L
). C
p
represents the load for the crystal, and this should be equal to C
L
, as specified in the
crystal manufacturer’s data sheet.
In an oscillator circuit, the CMOS inverter operates in the linear mode and works as an amplifier.
The phase shift provided by the inverter is 180 degrees. To meet the oscillating condition, the
crystal oscillator must provide an additional 180 degrees of phase shift. If C
1
= C
2
, current
through them is identical and 180 degrees out of phase from each other. Hence, for C
1
= C
2
, the
crystal provides a phase shift of 180 degrees.
The feedback resistor modifies the input impedance of the CMOS inverter. For an inverter with
an open-loop gain much higher than 1, the input impedance becomes
Use of the CMOS Unbuffered Inverter in Oscillator Circuits
5
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