Atmel 80C51 Montage- und Bedienungsanleitung

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

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

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

Phase(°) -90 0 +90 0-90

Q2Q1 R1 L1 C1

9.998

9.999

1.0001

1.0002

1.0003

1.0004

1.0005

100

6.034

f()

)

9.998 10

⋅

6 6 7 7 7 7 7 7

−

)) 360

6.28

⋅

Parallel

Z(f)

φ(f)

egree

Rp C0

Series

fs 1

6.28 C1 L1

⋅⋅

fa fs 1 C1

+⋅:=

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

⋅

Parallel resonance

frequency Quality factor

ESR

Qp 1

C0 6.28

⋅

fa fs 1 C1

+⋅:=

ESR R1 1 C0











⋅:=

fp fs 1 C1

2C0 CL

()

⋅











⋅:=

Qp 1

CL 6.28

⋅

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

2π×

Ltrap Ctrap

××

-----------------------------------------------------------=

C1 C2 Ctrap

Ltrap

Xtal1 Xtal2

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

⋅:=

UMrms PMrms ES

⋅:=

VDD

VSS

G(f)

VSS

Cxtal1 Cxtal2

Rout

vin vout

a) b) c)

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

()

vin f

)()×

VDD/2

Linear region

Non-Linear region

Non-Linear Region

Vxtal2

Start and lock Steady State

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

Q1 R1

Xtal1 Xtal2 Xtal2

Xtal1

Q2Q1 CL

ESR

Q2Q1

C1 C2

Xtal1 Xtal2

fp fs 1 C1

2C0 CL

()

⋅











⋅:=

ESR R

-------+





×2

CL 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

()

Hf f

()×

vout f

()×

()

vn f

()×

vout f

()

vn f

()

------------------

()

()×

–

--------------------------------------=

()

()×1>

()

()×()0

()

()×1

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