80C51 MCU s. Application Note. Analyzing the Behavior of an Oscillator and Ensuring Good Start-up. Oscillator Fundamentals

Transcription

1 Analyzing the Behavior o an Oscillator and Ensuring Good Start-up This application note explains how an oscillator unctions and which methods can be used to check i 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. 8C5 MCU s Application Note Figure. Basic Oscillator Architecture Noise Xtal Ampliier G() Feed-back Loop H() The basic architecture o an oscillator (regardless o its structure) is shown in Figure and built around an ampliier, a eed-back and noise applied on Xtal input. The role o each elements is explained hereater: Ampliier: Used to ampliy the signal applied on Xtal and to lock the oscillations exhibit. 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 ilter the output signal and to send it to the Xtal input. The oscillator stability is linked to the bandwidth o the loop. The narrower the ilter, the more stable the oscillator. Crystals or ceramic resonators are generally used because they have the narrowest bandwidth and eiciency or the stability o the requency. Rev.

2 Noise: Thanks to the noise an oscillator is able to startup. This noise has dierent 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 o the chip and in particular on Xtal input o the ampliier. The noise origin can be industrial, astronomic, semiconductor,... transient noise during the power-up. The noise is coupled to the ampliier rom the inside and outside o the chip through the package, the internal power rails,... Figure 2 shows the typical oscillator structure used in most microcontroller chips. An onchip ampliier connected to an external eed-back consists in a crystal or a resonator and two capacitors (a). Sometimes a resistor is inserted (b) between the ampliier output and the crystal in order to limit the power applied, avoiding the destruction o the crystal. Figure 2. Typical Oscillator Structures Xtal Xtal a) b) 2

3 Typical Oscillator Operation The process involved in start-up and locking o oscillator is explained hereater (see Figure 3): Biasing process. The power-up is applied and the ampliier output ollows the power until it reaches its biasing level where it can ampliy the noise signal on its input. Oscillation. The ampliied noise on the output () is iltered by the eed-back loop which has a pass-band requency corresponding to the nominal oscillator requency. The iltered output noise is ampliied 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 ound where the closed-loop gain is maintained with the unity. Figure 3. Process Needed to Reach a Stable Oscillation VDD Bias Level Vxtal2 t Biasing Start Oscillation Lock Steady State 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 transorm voltage energy to mechanical vibrations and vice-versa. At certain vibrational requencies, there is a mechanical resonance. Main resonances are called: undamental, third, ith,... overtones. Overtones are not harmonics but dierent mechanical vibrational modes. This crystal is an eicient pass-band ilter which exhibits a good requency stability. The equivalent model, shown in Figure 4, consists o two resonant circuits: C, L and R is a series resonant circuit (s), In addition the series circuit, C in parallel orms a parallel circuit which has a parallel resonance requency (a). 3

4 Figure 4. Crystal Models. C Q R L C Q2 Figure 5 plots the module and phase o the impedance crystal and shows both the series and parallel resonance requencies. Figure 5. Phase and Module Versus the Frequency Z() db ( ) ) φ() 9 degree C s := 6.28 C L s R Series. 7 L := Parallel a Rp a s C C C 36 )) The behavior o the crystal depends on the requency and is summarized in Table. Table. Nature o the Impedance Versus the Frequency Frequency < s =s s < < a =a >a Z() Capacitive C Resistance R Inductive L Resistance Rp Capacitive C Phase( )

5 The impedance phase is related to the requency and each elements o the model plays a role in speciic requency ranges. The main electrical characteristics o these elements are summarized hereater. Series resonance requency s := Quality actor Qs := 6.28 C L L 6.28 s R Parallel resonance requency := a s C C Quality actor Qp := C 6.28 p R With External Load, CL requency p := s C 2( C CL) ESR := ESR R C CL 2 Quality actor Qp := CL 6.28 p ESR Table 2 gives some typical crystal characteristics. Table 2. Examples o Crystal Characteristics Frequency R L C C s p Qs Qp MHz ohms mh F pf MHz MHz k 3. 3 (2) k () k k k k k k K 98 Note:. 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 oscillate the crystal close to the s or between s and a resonance requencies. The irst 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 a requency. This is due to the high quality actor at a and the diiculty to stabilize an oscillator at this requency. 5

6 Overtone or Fundamental Mode Vibrational mode is used to reduce the crystal cost. Above 2MHz it is costly to produce such crystals tuned on the undamental mode. To avoid that, an overtone mode is used to tune the oscillation requency. To work properly, this vibrational mode needs a speciic schematic where a requency trap is installed on the oscillator output to short-circuit the undamental mode and orce the overtone mode. The trap is an LC ilter installed between the and the ground. The requency on this ilter is calculated on the undamental mode using the Thomson equation (see Figure 6). Figure 6. A LC trap is Used or an Overtone Oscillator Xtal C X C2 Ltrap Ctrap Ftrap = π Ltrap Ctrap Drive Level The characteristics o quartz crystals are inluenced by the drive level. In particular, when the drive level increases, the requency and the resistance change through nonlinear eects. In extreme cases an inharmonic mode may replace the main mode as the selective element and cause the requency o the oscillator jump to a dierent requency. With an overdrive level, the crystal substrate itsel may be damaged. Typical characteristic o requency vs. drive levels is shown in Figure 7. Figure 7. Frequency Shit vs. Drive Level Drive level is a measurement o the total power dissipated through the crystal operating in the circuit. Typical drive levels are between 5 uw and uw ( mw). Drive levels should be kept at the minimum level that will initiate and maintain oscillation. It should be less than hal o the maximum drive level. Excessive drive may cause correlation diiculties, requency drit, spurious emissions, "ringing" wave orms, excessive ageing, and/or atal structural damage to the crystal. 6

7 The maximum drive, PMax, is speciied by the crystal manuacturer. The maximum RMS current which can low in the crystal and it is given by the ollowing expression: PMrms := 2 ESR IMrms IMrms := PMrms ESR where ESR is equivalent resistance at the parallel requency, p. For example,. Watt Maximum power with an ESR o 32 ohms gives a 56mA maximum RMS current. The RMS voltage across the crystal can be evaluated in the same manner: UMrms := PMrmsESR where UMrms is the maximum RMSvalue. For example, i PMrms is.watt and ESR =32Ohms, the maximum RMS voltage accross the crystal is.8v. In case o overdrive power, a resistor must be connected between the ampliier output and the crystal as shown in Table 2. Class-A Ampliier Figure 8 gives an example o a class-a ampliier. Resistance R is used to bias the output stage to VDD/2. Cxtal and Cxtal2 are the parasitic capacitors due to input and output ampliier pads plus the parasitic capacitances o the package. Rout is the equivalent output resistance o the ampliier. The equivalent schematic is true only or the linear area o the gain and or small signal conditions. This linear operation occurs during the startup when the power is applied. The transer unction is oten irst order and low-pass ilter type. Xtal R VDD Xtal vin G Rout G() G vout Cxtal Cxtal2 VSS a) b) VSS c) Figure 8. (a) Typical structure o a class-a ampliier. (b) Equivalent schematic. (c) Gain response. Next section explains the two speciic ampliier areas needed to startup and lock an oscillator. 7

8 The Two Operating Areas Figure 9 illustrates the transer unction o a CMOS ampliier. An ampliier 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: vout() = G() vin( ) ) The dynamic range o this linear region is typically /- 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 ampliication is automatically reduced while the output oscillation increases until a stabilization point is ound (amplitude limitation). Figure 9. Gain Curve and the Two Ampliication Region vs B Non-Linear region VDD/2 A VDD/2 Linear region B Non-Linear Region ve The oscillations start gradually. The noise on its input is ampliied until the level reaches VDD. I conditions (gain and phase) as speciied above are ulilled, startup is normally guaranteed at circuit power-on time. Indeed, during power-on, noise over a large spectrum appears and is suicient to start-up the system. Only a ew microvolts or millivolts are needed but the startup time is inversely proportional to this level. Typical waveorm o an oscillation is shown in Figure. Figure. Start and Lock o a Feedback Oscillator Vxtal2 Start and lock Steady State 8

9 Series and Parallel Oscillators series resonant oscillator Some oscillator architectures orce the crystal to operate around the series requency and some others to work around the parallel requency. This section gives inormation about these working modes. This structure used a non inverted ampliier to orce oscillation at its the natural series resonant requency s. The crystal phase is zero, the resistance is minimum (R) and the current low is maximum. Figure. Series Resonant Structure Q Xtal Xtal Q2 Q R Q2 X The eedback (X) ilters the oscillation requency and send this signal in phase to Q input. Parallel Resonant Oscillator This structure used an inverted ampliier to orce oscillation between s and a resonance requencies where the crystal impedance appears inductive (L). This structure is called Pierce. To have this requency resonant, p, the imaginary part o the crystal impedance must be zero. So only capacitive reactance can cancel the inductive one. This is why the C and C2 capacitors are added on Xtal and (see Figure 2). Figure 2. Parallel Resonant Structure Q Xtal Q2 Q Xtal L CL Q2 C X C2 ESR The resonance requency is given hereater: p := s C 2( C CL) where CL is the capacitive load equivalent to the C in parallel to C2. The equivalent series resistance (ESR) is a little higher than or s and is given with the next expression: ESR R C 2 = , CL CL C C C C2 Considering the expression o p, CL plays an important role to have the required oscillation requency. CL is the loading capacitor used during the crystal calibration by the crystal manuacturer to tune the oscillator requency. I an accurate requency is = 9

10 required CL must be respected. Here are some standard values are 3, 2, 24,3, and 32 pf. Analysis Method Open-loop Gain and Phase Two methods o oscillator analysis are considered in this application note. One method involves the open-loop gain and phase response versus requency. A second method considers the ampliier as a one-port with negative real impedance to which the ilter is attached. The second one will be preerred or very low requency (32KHz). The next sections explains the basics o these two methods and how to use them. This irst method analyzes the product o the gain o the ampliier and the eed-back loop. Figure 3. Basic Oscillator Architecture Noise vn() vin() Ampliier G() Feed-back Loop H() vout() The general equation to start-up the oscillation process is shown hereater. Let s express vout(): vout() = G() H() vout() G() vn() the transer unction between vout() and vn() is: vout() vn() = G() G() H() the start-up condition can now be evaluated with the Barkhausen criteria: G() H() > Φ( G() H() ) = and lock condition can be expressed: G() H() = This start-up condition depends on the product o the gain and eed-back but also on the requency. The lock condition is controlled by the non-linear area o the ampliier output. The gain is automatically reduced while the output oscillation increased until a stabilization point is ound.

11 To analyze the oscillation conditions, it is useul to use a Spice simulator. Some reeware are available on the Web and only the basic unctions o Spice are required. Figure 4 shows a typical oscillator Spice circuit use to demonstrate the AC small signal analysis. Figure 4. Typical crystal oscillator structure. As seen previously, the open-loop gain is analyzed to check the oscillation conditions. To do that the eed-back loop is broken. The crystal has to be loaded with the same impedance than the input impedance o the ampliier. Figure 5 shows the Spice circuit used to analyses the oscillation conditions. A 6MHz crystal is used or this analysis and CP and CP2 are tuned to have the oscillation conditions (G> db, Phase=). Figure 5. Spice Circuit Used to Analyze the Oscillation Conditions Xtal 38pF Figure 6 plots the gain and the phase o the open-loop circuit. At 6.MHZ the gain is greater than unity (38dB) and the phase is zero. The oscillation conditions are met ensuring a good oscillator startup.

12 Figure 6. Gain and Phase response or the open-loop gain. Gain(dB) Phase( ) Phase = 3 44 Gain = 38dB Phase 2 8 Gain MHz 6.7MHz This method allows to check the maximum capacitive loads and the maximum electrical characteristics o the crystal. Figure 7 (a) plots the gain and phase when Cp and CP2 are too big. The gain is now too small to guarantee a proper startup. The phase begins to shit and is no longer zero. Figure 7 (b) plots the gain and phase when the equivalent resistance o the crystal (R) 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 7. Gain and phase or two conditions. 8.3 Phase > G=-3dB G=.3dB MHz a) 6.88MHz MHz b) 6.796MHz V(VXtal)/V(VXtal)) DB(V(VXtal)/V(VXtal)) a) Cp and Cp2 are too big (56pF), b) R is too big = 4ohms. Table 3 resumes the case studies analyze with the spice model and tool. 2

13 Table 3. Oscillation Conditions versus Cp, Cp2 and R Cp(pF) Cp2(pF) R(ohms) Oscillation Conditions Yes No No CP and CP2 are generally chosen to be equal maintaining a gain in closed loop equal to the unity. Negative eed-back resistance The second method analyzes the real part on the input impedance o the ampliier and compares it with the real part o the pass-band ilter. The impedance seen on the input ampliier is negative under certain conditions and cancelled the crystal resistance. In that case there is no more lost o energy and oscillations are stabilized. Figure 8 shows the equivalent model o an oscillator. The crystal is equivalent to a RLC ilter corresponding to the motional arm. Z3 in the equivalent impedance accross Xtal and pins including the C crystal capacitor and Cx3. Z and Z2 are the input and output impedances including the two external capacitors Cp and Cp2 used to adjust the oscillator operating point. Figure 8. a) Oscillator Equivalent model b) Equivalent model around the resonance. a) b) Crystal R L C R Crystal L C Xtal Z3 Rin Ampliier Cin Z Z2 Ampliier Figure 8 shows in what conditions the oscillator will oscillate. To have an oscillation stable in steady condition, the lost o energy in the crystal has to be cancelled. This condition occurs when: Rin = R 3

14 and at the requency: = C Cin 6, 28 L C Cin Cin is the equivalent capacitor seen between Xtal and and is equal to: Cin = C Cx3 Cx Cx Cx Cx2 where Cx and Cx2 are the global capacitors seen on the input and output pins. Cx3 is the capacitor seen between Xtal and pins. To ensure a good startup o the oscillator, Cx and Cx2 have to be correctly adjusted. In order to deine them, the ampliier impedance must respect the conditions on Rin and Cin parameters: Rin: Cx and Cx2 has to be adjusted to have Rin > R: Rin( Zc) = ( Cx Cx2) gm ( gm Cx3) 2 ω 2 ( Cx Cx2 Cx2 Cx3 Cx Cx3) 2 Cin: Cx and Cx2 have to be adjusted to obtain a negative imaginary part and inally a input capacitor. Im( Zc) = gm 2 Cx3 ω 2 ( Cx Cx2) ( Cx Cx2 Cx Cx3 Cx2 Cx3) 2 ω (( gm Cx3) 2 ω 2 ( xc Cx2 Cx2 Cx3 Cx Cx3) 2 ) C = Im( Zc) , 28 gm is the ampliier gain. An example is given hereater. The main characteristics o this case study is: Ampliier: gm=.a/v, Cxtal=5p, Cxtal2=8pF, Cxtal3=5p Crystal: R=8, L=.64mH, C=8.5F, C=5pF 4

15 Figure 9. Oscillator Example Crystal R L C C 5p Xtal Cxtal3 5p Cp Cxtal 5p gm.a/v Cxtal2 8p Cp2 Ampliier Table 4 shows two cases: irst, there is no external additional capacitors and second two capacitors are adjusted to the oscillation requency. When there is no capacitor Rin is less than R (8 ohms) and no oscillation occurs. With Cp=Cp2=5p, Rin is -75 ohms and is greater than R and the condition to have oscillations is met. As with the previous method, Cp and Cp2 can be tuned and the electrical characteristics can be checked. Table 4 resumes the case studies. Table 4. Cp and Cp2 capacitors with R=8ohms. Cp(pF) Cp2(pF) Rin(ohms) Cin(pF) Oscillation Condition No Yes Conclusions Two methods have been presented to analyze and to check the oscillation conditions.they have shown the possibility to predict the added capacitors in versus the electrical characteristics o the crystal or resonator devices. It will help to speciy the margin o the crystal and resonator devices. 5

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