Atmel 80C51 Installation and operating instructions

1
Analyzing the Behavior of an Oscillator and
Ensuring Good Start-up
This application note explains how an oscillator functions and which methods can be
used to check if the oscillation conditions are met in order to ensure a good start-up
when power is applied.
Oscillator Fundamentals
A microcontroller integrates on-chip an oscillator to generate a stable clock used to
synchronize the CPU and the peripherals.
Figure 1. Basic Oscillator Architecture
The basic architecture of an oscillator (regardless of its structure) is shown in Figure 1
and built around an amplifier, a feed-back and noise applied on Xtal1 input. The role of
each elements is explained hereafter:
•Amplifier: Used to amplify the signal applied on Xtal1 and to lock the oscillations
exhibit Xtal2. The class A structure is the most popular but new ones are currently
used in order to optimize the consumption or other criterion,
•Feed-back loop: Used to filter the output signal and to send it to the Xtal1 input.
The oscillator stability is linked to the bandwidth of the loop. The narrower the
filter, the more stable the oscillator. Crystals or ceramic resonators are generally
used because they have the narrowest bandwidth and efficiency for the stability of
the frequency.
Amplifier
Feed-back
Loop
Noise +G(f)
H(f)
Xtal1 Xtal2
80C51 MCU’s
ApplicationNote
Rev. 4363A–80C51–07/04

24363A–80C51–07/04
•Noise: Thanks to the noise an oscillator is able to startup. This noise has different
origins:
–thermal noise due to the transistor junctions and resistors,
–RF noise: a wide band noise is present in the air and consequently on all the
pins of the chip and in particular on Xtal1 input of the amplifier. The noise
origin can be industrial, astronomic, semiconductor, ...
–transient noise during the power-up.
The noise is coupled to the amplifier from the inside and outside of the chip through the
package, the internal power rails, ....
Figure 2 shows the typical oscillator structure used in most microcontroller chips. An on-
chip amplifier connected to an external feed-back consists in a crystal or a resonator
and two capacitors (a). Sometimes a resistor is inserted (b) between the amplifier output
and the crystal in order to limit the power applied, avoiding the destruction of the crystal.
Figure 2. Typical Oscillator Structures
a) b)
Xtal1 Xtal2 Xtal1 Xtal2

3
4363A–80C51–07/04
Typical Oscillator
Operation The process involved in start-up and locking of oscillator is explained hereafter (see Fig-
ure 3):
•Biasing process. The power-up is applied and the amplifier output follows the
power until it reaches its biasing level where it can amplify the noise signal on its
input.
•Oscillation. The amplified noise on the output (Xtal2) is filtered by the feed-back
loop which has a pass-band frequency corresponding to the nominal oscillator
frequency. The filtered output noise is amplified again and starts to increase. The
oscillation level continue to grow and reaches the non-linear area.
•Lock. In the non-linear area both the gain and the oscillation level starts to reduce.
•Steady State. A stabilization point is found where the closed-loop gain is
maintained with the unity.
Figure 3. Process Needed to Reach a Stable Oscillation
Each element plays a role and their electrical characteristics have to be understood. The
next sections explain this matter.
Crystal Model and
Operation Crystal and ceramic resonators are piezoelectric devices which transform voltage
energy to mechanical vibrations and vice-versa. At certain vibrational frequencies, there
is a mechanical resonance. Main resonances are called: fundamental, third, fifth, ...
overtones. Overtones are not harmonics but different mechanical vibrational modes.
This crystal is an efficient pass-band filter which exhibits a good frequency stability. The
equivalent model, shown in Figure 4, consists of two resonant circuits:
•C1,L1 and R1 is a series resonant circuit (fs),
• In addition the series circuit, C0 in parallel forms a parallel circuit which has a
parallel resonance frequency (fa) .
Vxtal2
Start Oscillation Steady State
VDD
t
Lock
Biasing
Bias Level

44363A–80C51–07/04
Figure 4. Crystal Models.
Figure 5 plots the module and phase of the impedance crystal and shows both the
series and parallel resonance frequencies.
Figure 5. Phase and Module Versus the Frequency
The behavior of the crystal depends on the frequency and is summarized in Table 1.
Table 1. Nature of the Impedance Versus the Frequency
Frequency f < fs f=fs fs < f < fa f=fa f>fa
Z(f) Capacitive
C1 Resistance R1 Inductive L1 Resistance Rp Capacitive C0
Phase(°) -90 0 +90 0-90
Q2Q1 R1 L1 C1
C0
9.998
.
10
6
9.999
.
10
6
1
.
10
7
1.0001
.
10
7
1.0002
.
10
7
1.0003
.
10
7
1.0004
.
10
7
1.0005
.
10
0
25
50
75
100
9
6.034
0
f()
)
11 × 9.998 10
6
⋅
f
6 6 7 7 7 7 7 7
90
45
0
45
90
90
90 −
)) 360
6.28
⋅
Parallel
Z(f)
dB
φ(f)
d
egree
f
f
C1
R1
L1
Rp C0
fs
fa
Series
fs 1
6.28 C1 L1
⋅⋅
:=
fa fs 1 C1
C0
+⋅:=

5
4363A–80C51–07/04
The impedance phase is related to the frequency and each elements of the model plays
a role in specific frequency ranges. The main electrical characteristics of these elements
are summarized hereafter.
Table 2 gives some typical crystal characteristics.
Note: 1. Fundamental Mode
2. Third Overtone Mode
“Series” Versus
“Parallel” Crystal There is no such thing as a “series cut” crystal as opposed to a “parallel cut” crystal.
Both modes exist in a crystal. Only the oscillator structures (Pierce, Colpitts, ..) will oscil-
late the crystal close to the fs or between fs and fa resonance frequencies. The first
structure is called a series resonant oscillator and the second a parallel resonant
oscillator. It should be noted that no oscillator structure is able to oscillate at the exact
fa frequency. This is due to the high quality factor at fa and the difficulty to stabilize an
oscillator at this frequency.
Table 2. Examples of Crystal Characteristics
Frequency
MHz R1 ohms L1 mH C1 fF C0 pF fs MHz fp MHz Qs Qp
32 35 11.25 2.2 7 32 32.005 646k 3.11
30(2) 20 11 2.6 6 30 30.0065 102k 6.14
30(1) 40 33.94 0.83 3.8 30 30.00328 160k 3.48
20 50 20 3.2 10 20 20.0032 497k 2.98
16 80 11.641 8.5 3 16 16.022 146k 3.42
10 20 0.025 10 20 10 10.00025 159.2k 80
8 7 0.0862 4.6 40 8 8.00026 618k 17.4
6 8 0.0848 8.3 40 6 6.000356 533k 37
2 100 520 12 4 2 2.003 66K 198
fs 1
6.28 C1 L1
⋅⋅
:=
Series resonance
frequency Quality factor
Qs L1 6.28
⋅ fs ⋅
R1
:=
Parallel resonance
frequency Quality factor
ESR
Qp 1
C0 6.28
⋅ fp ⋅ R1 ⋅
:=
fa fs 1 C1
C0
+⋅:=
ESR R1 1 C0
CL
+





2
⋅:=
fp fs 1 C1
2C0 CL
+ () ⋅
+





⋅:=
Qp 1
CL 6.28
⋅ fp ⋅ ESR ⋅
:=
With External Load, CL
frequency
Quality factor

64363A–80C51–07/04
Overtone or
Fundamental Mode Vibrational mode is used to reduce the crystal cost. Above 20MHz it is costly to produce
such crystals tuned on the fundamental mode. To avoid that, an overtone mode is used
to tune the oscillation frequency. To work properly, this vibrational mode needs a spe-
cific schematic where a frequency trap is installed on the oscillator output to short-circuit
the fundamental mode and force the overtone mode. The trap is an LC filter installed
between the Xtal2 and the ground. The frequency on this filter is calculated on the fun-
damental mode using the Thomson equation (see Figure 6).
Figure 6. A LC trap is Used for an Overtone Oscillator
Drive Level The characteristics of quartz crystals are influenced by the drive level. In particular,
when the drive level increases, the frequency and the resistance change through non-
linear effects. In extreme cases an inharmonic mode may replace the main mode as the
selective element and cause the frequency of the oscillator jump to a different fre-
quency. With an overdrive level, the crystal substrate itself may be damaged. Typical
characteristic of frequency vs. drive levels is shown in Figure 7.
Figure 7. Frequency Shift vs. Drive Level
Drive level is a measurement of the total power dissipated through the crystal operating
in the circuit. Typical drive levels are between 50 uW and 1000 uW (1 mW). Drive levels
should be kept at the minimum level that will initiate and maintain oscillation. It should be
less than half of the maximum drive level. Excessive drive may cause correlation difficul-
ties, frequency drift, spurious emissions, "ringing" wave forms, excessive ageing, and/or
fatal structural damage to the crystal.
Ftrap
1
2π×
Ltrap Ctrap ××
-----------------------------------------------------------=
0
X1
C1 C2 Ctrap
Ltrap
Xtal1 Xtal2

7
4363A–80C51–07/04
The maximum drive, PMax, is specified by the crystal manufacturer. The maximum
RMS current which can flow in the crystal and it is given by the following expression:
where ESR is equivalent resistance at the parallel frequency, fp.
For example, 0.1 Watt Maximum power with an ESR of 32 ohms gives a 56mA maxi-
mum RMS current.
The RMS voltage across the crystal can be evaluated in the same manner:
where UMrms is the maximum RMSvalue.
For example, if PMrms is 0.1Watt and ESR =32Ohms, the maximum RMS voltage
accross the crystal is 1.8V. In case of overdrive power, a resistor must be connected
between the amplifier output and the crystal as shown in Table 2.
Class-A Amplifier Figure 8 gives an example of a class-A amplifier. Resistance Rf is used to bias the out-
put stage to VDD/2. Cxtal1 and Cxtal2 are the parasitic capacitors due to input and
output amplifier pads plus the parasitic capacitances of the package. Rout is the equiv-
alent output resistance of the amplifier. The equivalent schematic is true only for the
linear area of the gain and for small signal conditions. This linear operation occurs dur-
ing the startup when the power is applied. The transfer function is often first order and
low-pass filter type.
Figure 8. (a) Typical structure of a class-A amplifier. (b) Equivalent schematic. (c) Gain
response.
Next section explains the two specific amplifier areas needed to startup and lock an
oscillator.
IMrms PMrms
ESR
:=
PMrms ESR IMrms
2
⋅:=
UMrms PMrms ES
R
⋅:=
VDD
VSS
Rf
G(f)
f
VSS
G0
Cxtal1 Cxtal2
Rout
vin vout
a) b) c)
G0
Xtal1 Xtal2
Xtal1 Xtal2

84363A–80C51–07/04
The Two Operating Areas Figure 9 illustrates the transfer function of a CMOS amplifier. An amplifier such as that
shown in Figure 8 has two operating regions. These regions determine the oscillator
operation at start-up and during steady state while oscillations are stabilized. Figure 9
shows these two regions:
•Region A, is the linear region. The gain is constant, and vout is proportional to
vin:
The dynamic range of this linear region is typically +/- 1 volt around the quiescent
point Q at 5v VDD.
•Region B, is the non-linear region. The gain is no longer linear, and becomes
dependent on the vout level.The higher the vout, the lower the gain. The
amplification is automatically reduced while the output oscillation increases until a
stabilization point is found (amplitude limitation).
Figure 9. Gain Curve and the Two Amplification Region
The oscillations start gradually. The noise on its input is amplified until the level reaches
VDD. If conditions (gain and phase) as specified above are fulfilled, startup is normally
guaranteed at circuit power-on time. Indeed, during power-on, noise over a large spec-
trum appears and is sufficient to start-up the system. Only a few microvolts or millivolts
are needed but the startup time is inversely proportional to this level. Typical waveform
of an oscillation is shown in Figure 10.
Figure 10. Start and Lock of a Feedback Oscillator
vout f () Gf () vin f )()× =
A
ve
vs
VDD/2
VDD/2
Linear region
Non-Linear region
Non-Linear Region
B
B
Vxtal2
Start and lock Steady State

9
4363A–80C51–07/04
Series and Parallel
Oscillators Some oscillator architectures force the crystal to operate around the series frequency
and some others to work around the parallel frequency. This section gives information
about these working modes.
series resonant
oscillator This structure used a non inverted amplifier to force oscillation at its the natural series
resonant frequency fs. The crystal phase is zero, the resistance is minimum (R1) and
the current flow is maximum.
Figure 11. Series Resonant Structure
The feedback (X1) filters the oscillation frequency and send this signal in phase to Q1
input.
Parallel Resonant
Oscillator This structure used an inverted amplifier to force oscillation between fs and fa reso-
nance frequencies where the crystal impedance appears inductive (L1). This structure is
called Pierce. To have this frequency resonant, fp, the imaginary part of the crystal
impedance must be zero. So only capacitive reactance can cancel the inductive one.
This is why the C1 and C2 capacitors are added on Xtal1 and Xtal2 (see Figure 12).
Figure 12. Parallel Resonant Structure
The resonance frequency is given hereafter:
where CL is the capacitive load equivalent to the C1 in parallel to C2.
The equivalent series resistance (ESR) is a little higher than for fs and is given with the
next expression:
Considering the expression of fp, CL plays an important role to have the required oscil-
lation frequency. CL is the loading capacitor used during the crystal calibration by the
crystal manufacturer to tune the oscillator frequency. If an accurate frequency is
Q2Q1
X1
Q
2
Q1 R1
Xtal1 Xtal2 Xtal2 Xtal1
Q2Q1 CL
L1
ESR
Q2Q1
X1
C1 C2
Xtal1 Xtal2
Xtal1 Xtal2
fp fs 1 C1
2C0 CL
+ () ⋅
+





⋅:=
ESR R 11
C 0
CL
-------+


×2 CL C
1 C 2×
C 1 C 2 +
---------------------=,=

10 4363A–80C51–07/04
required CL must be respected. Here are some standard values are 13, 20, 24,30, and
32 pF.
Analysis Method Two methods of oscillator analysis are considered in this application note. One method
involves the open-loop gain and phase response versus frequency. A second method
considers the amplifier as a one-port with negative real impedance to which the filter is
attached. The second one will be preferred for very low frequency (32KHz).
The next sections explains the basics of these two methods and how to use them.
Open-loop Gain and
Phase This first method analyzes the product of the gain of the amplifier and the feed-back
loop.
Figure 13. Basic Oscillator Architecture
The general equation to start-up the oscillation process is shown hereafter. Let’s
express vout(f):
the transfer function between vout(f) and vn(f) is:
the start-up condition can now be evaluated with the Barkhausen criteria:
and lock condition can be expressed:
This start-up condition depends on the product of the gain and feed-back but also on the
frequency. The lock condition is controlled by the non-linear area of the amplifier output.
The gain is automatically reduced while the output oscillation increased until a stabiliza-
tion point is found.
Amplifier
Feed-back
Loop
Noise +G(f)
H(f)
vout(f)
vin(f)
vn(f)
vout f () Gf () Hf f ()× vout f ()× Gf () vn f ()× +=
vout f
()
vn f ()
------------------
Gf
()
1
Gf () Hf ()× –
--------------------------------------=
Gf
() Hf ()×1>
Φ Gf () Hf ()×()0 =
Gf
() Hf ()×1 =

11
4363A–80C51–07/04
To analyze the oscillation conditions, it is useful to use a Spice simulator. Some free-
ware are available on the Web and only the basic functions of Spice are required. Figure
14 shows a typical oscillator Spice circuit use to demonstrate the AC small signal
analysis.
Figure 14. Typical crystal oscillator structure.
As seen previously, the open-loop gain is analyzed to check the oscillation conditions.
To do that the feed-back loop is broken. The crystal has to be loaded with the same
impedance than the input impedance of the amplifier.
Figure 15 shows the Spice circuit used to analyses the oscillation conditions. A 16MHz
crystal is used for this analysis and CP1 and CP2 are tuned to have the oscillation con-
ditions (G> 0dB, Phase=0).
Figure 15. Spice Circuit Used to Analyze the Oscillation Conditions
Figure 16 plots the gain and the phase of the open-loop circuit. At 16.001MHZ the gain
is greater than unity (38dB) and the phase is zero. The oscillation conditions are met
ensuring a good oscillator startup.
38pF
Xtal1 Xtal2

12 4363A–80C51–07/04
Figure 16. Gain and Phase response for the open-loop gain.
This method allows to check the maximum capacitive loads and the maximum electrical
characteristics of the crystal.
Figure 17 (a) plots the gain and phase when Cp1 and CP2 are too big. The gain is now
too small to guarantee a proper startup. The phase begins to shift and is no longer zero.
Figure 17 (b) plots the gain and phase when the equivalent resistance of the crystal (R1)
is too big. The gain is now negative and the phase is not zero. The oscillation conditions
are not met and this oscillator will not start.
Figure 17. Gain and phase for two conditions
a) Cp1 and Cp2 are too big (56pF), b) R1 is too big = 40ohms.
Table 3 resumes the case studies analyze with the spice model and tool.
0
100
-55
187
G
ain(dB) Phase(°)
0
36
72
108
144
180
0
20
30
10
-10
Gain
Phase
Phase = 0°
Gain = 38dB
16.001MHz 16.007MHz
40
.00100MHz 16.00188MHz
V
(VXtal1)/V(VXtal10))
0
6
.5
1
.1
15.99503MHz 16.00796MHz
DB(V(VXtal1)/V(VXtal10))
0
-21.4
8.3
G=0.3dB
G=-3dB
Phase > 0
a) b)

13
4363A–80C51–07/04
Table 3. Oscillation Conditions versus Cp1, Cp2 and R1
CP1 and CP2 are generally chosen to be equal maintaining a gain in closed loop equal
to the unity.
Negative feed-back
resistance The second method analyzes the real part on the input impedance of the amplifier and
compares it with the real part of the pass-band filter. The impedance seen on the input
amplifier is negative under certain conditions and cancelled the crystal resistance. In
that case there is no more lost of energy and oscillations are stabilized.
Figure 18 shows the equivalent model of an oscillator. The crystal is equivalent to a RLC
filter corresponding to the motional arm. Z3 in the equivalent impedance accross Xtal1
and Xtal2 pins including the C0 crystal capacitor and Cx3. Z1 and Z2 are the input and
output impedances including the two external capacitors Cp1 and Cp2 used to adjust
the oscillator operating point.
Figure 18. a) Oscillator Equivalent model b) Equivalent model around the resonance.
Figure 18 shows in what conditions the oscillator will oscillate. To have an oscillation
stable in steady condition, the lost of energy in the crystal has to be cancelled. This con-
dition occurs when:
Cp1(pF) Cp2(pF) R1(ohms) Oscillation Conditions
33 33 10 Yes
33 33 40 No
56 56 10 No
0 00
R1 L1 C1
Z1
Z3
Z2
Crystal
Xtal1 Xtal2
Amplifier
R1 C1L1
Rin Cin
Crystal
Amplifier
a) b)
Rin R 1 –=

14 4363A–80C51–07/04
and at the frequency:
Cin is the equivalent capacitor seen between Xtal1 and Xtal2 and is equal to:
where Cx1 and Cx2 are the global capacitors seen on the input and output pins. Cx3 is
the capacitor seen between Xtal1 and Xtal2 pins.
To ensure a good startup of the oscillator, Cx1 and Cx2 have to be correctly adjusted. In
order to define them, the amplifier impedance must respect the conditions on Rin and
Cin parameters:
•Rin: Cx1 and Cx2 has to be adjusted to have Rin > R1:
•Cin: Cx1 and Cx2 have to be adjusted to obtain a negative imaginary part and
finally a input capacitor.
gm is the amplifier gain.
An example is given hereafter. The main characteristics of this case study is:
•Amplifier: gm=0.01A/V, Cxtal1=5pf, Cxtal2=8pF, Cxtal3=5pf
•Crystal: R1=80, L1=11.64mH, C1=8.5fF, C0=5pF
f
1
628
L 1
C 1 Cin ×
C 1 Cin +
-----------------------
××,
------------------------------------------------------------=
Cin C 0 Cx 3
Cx 1 Cx 2×
C 1 xCx 2 +
---------------------------++=
Rin Zc
()
Cx 1 Cx 2×() gm – ×
gm Cx 3×()
2ω2
Cx 1 Cx 2 Cx 2 Cx 3 Cx 1 Cx 3× + × + ×()
2
× +
-----------------------------------------------------------------------------------------------------------------------------------------------------------=
Im Zc
()
gm
2
Cx 3ω2 Cx 1 Cx 2 + () Cx 1 Cx 2 Cx 1 Cx 3 Cx 2 Cx 3× + × + ×()
2
×× + × –
ω gm Cx 3×()
2ω2
xC 1 Cx 2 Cx 2 Cx 3 Cx 1 Cx 3× + × + ×()
2
× + ()×
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------=
CIm Zc
()
628,
f ×
--------------------=

15
4363A–80C51–07/04
Figure 19. Oscillator Example
Table 4 shows two cases: first, there is no external additional capacitors and second two
capacitors are adjusted to the oscillation frequency.
When there is no capacitor Rin is less than R1 (80 ohms) and no oscillation occurs.
With Cp1=Cp2=5pf, Rin is -175 ohms and is greater than R1 and the condition to have
oscillations is met. As with the previous method, Cp1 and Cp2 can be tuned and the
electrical characteristics can be checked. Table 4 resumes the case studies.
Table 4. Cp1 and Cp2 capacitors with R1=80ohms.
Conclusions Two methods have been presented to analyze and to check the oscillation condi-
tions.They have shown the possibility to predict the added capacitors in versus the
electrical characteristics of the crystal or resonator devices. It will help to specify the
margin of the crystal and resonator devices.
Cp1(pF) Cp2(pF) Rin(ohms) Cin(pF) Oscillation Condition
00-608.26 No
5 5 -175 9.2 Yes
000
R1 C1L1
Cxtal1
5p
Cxtal2
8p
Cxtal3 5p
C0 5p
Cp2
Cp1
Xtal1
Crystal
Xtal2
Amplifier
gm
0.01A/V

Printed on recycledpaper.
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4363A–80C51–07/04 xM
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