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Explanation using a specific oscillator circuit - Colpitts oscillator circuit

Page views: 14 Date:Dec 02,2022
     Taking the Colpitts oscillator circuit shown in Figure 4.8-1 as an example, we will investigate the oscillation frequency, load resistance, and frequency variability.
 
     (a) Oscillation Frequency
 
     If the nominal frequency of the crystal oscillator is 10MHz and the load capacitance is 16pF, the crystal oscillator's parameters are as shown in the table below.
Here, C3 is used to adjust the oscillation frequency. The relationship between the circuit's load capacitance CL and each capacitance constant is given by the following formula, from which C3 is derived. (I am collecting the image from Sichuan)
 
     Due to CL=16pF, C1=100pF, and C2=300pF, C3 is calculated to be 20.3pF. However, due to the base capacitance of Tr and stray capacitance on the circuit, the actual oscillation frequency is slightly lower than 10MHz. A tunable capacitor can be used to fine-tune C3.
 
     The variability of the oscillation frequency is calculated from each load capacitance using formula 4.6(1). For example, if C3 is between 10pF and 30pF, and the parameters of the small crystal oscillator in Table 4.8-1 are C0=1.9pF and r=250, then CL can vary from 8.8pF to 21.4pF. At these two extremes, the change in resonant frequency fr is △fL/fr=355×10-6 and 163×10-6, respectively. The difference of 192×10-6 is the frequency variability.
 
     In addition, Figure 4.8-2 shows that the smaller the load capacitance, the greater the frequency variability due to changes in capacitance, while the larger the load capacitance, the less sensitive the frequency is to capacitance changes. The pulling range must be determined by the load capacitance CL. The variability of the old crystal oscillator is 402×10-6, which means that even for the same circuit, the old model has a much larger adjustment range.
 
     Table 4.8-1 Comparison of parameters and characteristics of small and 

project

old model resonators

Item Small Model Old Model (HC-49/U)

Nominal frequency (MHz) 

10

10

R1(Ω)

25

13

C1(pF)

7.6×10-3

22.7×10-3

C0(pF)

1.9

4.8

C0 / C1

250

211

Ts

11.9ppm

26.2ppm

Frequency Modulation Range 

192ppm

402ppm


     (b) Negative resistance
The negative resistance of the oscillation circuit shown in Figure 4.8-1 can be calculated using equation (4.5) if the transconductance (gm) of Tr is assumed to be 50mS. The calculated value is -422Ω. However, due to the influence of the parallel resistor unit on the reactance of capacitors C1 and C2, the actual negative resistance is smaller than this value. The simulated result for the negative resistance at the frequency of this resistor is shown as curve A in Figure 4.8-3. The negative resistance at 10MHz is -320Ω. The compensation frequency mentioned earlier is about 3MHz. (The figure is collected in Sichuan.)
 
     In addition, when a small resonator (R1=25Ω, C0=1.9pF) with a load capacitance of 16PF is used, the equivalent resistance RL can be calculated as 31.3Ω from equation (4.4). The negative resistance is about 10 times larger, which provides sufficient margin for oscillation.
 
     Curves B and C show the negative resistance when the capacitance of C1 and C2 is changed. As the capacitance decreases, the negative resistance increases at 10MHz. However, changing the load capacitance can easily alter the oscillation frequency, so caution is necessary.
 
     The actual measurement method for negative resistance follows the procedure described in section 4.5.
 
 
     Non-adjustable harmonic oscillation circuit
     Regarding the harmonic oscillation circuit shown in Figure 4.8-1, which is suitable for Colpitts-type oscillators, assuming the oscillation frequency is 30MHz, we try to discuss the circuit constants. At 30MHz, the negative resistance characteristic of curve A in Figure 4.8-3 is only 30Ω, and the fundamental frequency at 30MHz has already started oscillating at 10MHz due to the compensating frequency below 10MHz.
     Since the compensating frequency fc is set to be above 10MHz, considering the parallel resistance mentioned earlier, the various resistor units and capacitors are determined to obtain the negative resistance (as shown in Figure 4.8-5). With fc set at 15MHz, the negative resistance is -200Ω, and there is a possibility of full oscillation if the equivalent resistance RL when loaded with the crystal oscillator's third harmonic is below 200Ω.
     3. CMOS Oscillation Circuit
     (a) Oscillation Frequency
     Figure 4.8-6 shows the oscillation circuit of a commonly used CMOS inverter circuit. In this circuit, a crystal oscillator with a nominal frequency of 10MHz and a load capacitance of 12pF is used. The capacitance coefficients in this case are discussed below.
     The gate-side capacitance Cg and the drain-side capacitance Cd of the CMOS inverter have parasitic and stray capacitances. If the capacitance values on both sides are set to 6pF, then the synthesized capacitance is 3pF. Since the load capacitance of the crystal oscillator CL is 12pF, the synthesized capacitance of Cg and Cd after subtracting 3pF is set to 9pF. As a result, Cg=Cd=18pF. The load capacitance of the crystal oscillator is the sum of the capacitance capacity and the parasitic and stray capacitances, and the load capacitance determines the oscillation frequency. Typically, Cg (along with a parallel capacitance) is set as the tuning capacitor for adjusting the frequency.
     The resistance Rd in the circuit is used to limit the crystal current, taking into account the size of the inverter sequence and the effect on the reactive resistance of Cd.
     (b) Negative Resistance
     In the CMOS inverter circuit, if the resistor unit Rd is not installed, the negative resistance will be too high. Therefore, Rd must be inserted before adjusting the negative resistance. For example, if the negative resistance is set to 10 times, then Rd is approximately 2kΩ.
 
     (c) Crystal Current
     When designing a CMOS inverter circuit with a small oscillator, special attention must be paid to the crystal current. If there is no resistor Rd, there will be excessive crystal current, which can easily excite the parasitic effects of the crystal oscillator and make the oscillation unstable.
     The circuit current in Figure 4.8-6 is measured with a high-frequency current detector to be approximately 0.5mV (60uW). To suppress the crystal current, simply reducing the capacitance Cg and Cd will suffice. However, since the load capacitance has changed, the oscillation frequency will also change accordingly.
     In addition, the best way to reduce the crystal current is to increase the resistance Rd, but because the negative resistance is easy to decrease, attention must be paid to confirmation.
     To obtain the load capacitance CL of the circuit simply, if the input capacitance of the IC and the capacitance of the substrate solder joint are set to Cs, then the following formula can be used to represent it.
     In summary, in order to use the resonator with peace of mind, the oscillation circuit must use a MOS-IC with high input impedance, and the negative resistance R1 of the oscillation circuit must be designed to be at least 5 times the equivalent resistance RL when the resonator is loaded. Compared with the standard value, the series resistance R1 of the resonator must be strictly required, but if the manufacturing cost of the crystal oscillator is increased, then it cannot be said that a good solution for unstable oscillation has been found.

     5.Precautions for Implementation
     1.Regarding Use Environment
     (1) Climate Resistance
     (a) Maximum and minimum temperature and humidity during use and storage.
     (b) Environment with toxic gases, water, saltwater, or oil contamination.
     (c) Environment exposed to ozone, ultraviolet light, and radiation.
     (2) Electrical and Mechanical Environment
     (a) Environment with static electricity or prone to static electricity.
     (b) Environment subjected to vibration.
     (c) Environment subjected to shock.
     (d) Environment subjected to tensile and bending forces.
     Using the product beyond the specified range may lead to fatal defects such as frequency changes, impedance changes, product detachment, leakage, oscillation stoppage, and static damage. Therefore, it is recommended to confirm the performance before using the product.
 
     2 Regarding Handling and Storage
     (1) Handling
     Avoid handling methods that subject the product to external pressure such as impact, prolonged vibration, and packaging deformation.
     (2) Storage
     Do not store in high temperature and high humidity conditions. Do not store in environments filled with water, salt water, oil, and toxic gases (alkaline water, sulfurous acid, nitrous acid, alkali, ammonia, etc.). Do not store in situations that may result in poor appearance (discoloration, rusting of the casing, lead wires, etc.) and poor characteristics (frequency deviation). Do not store in situations that can cause oxidation of lead wire solder and deterioration of welding characteristics.
     Regarding the taping of surface-mounted products, the separation strength of the cover tape increases with time, and the cover tape is prone to breakage during use.



     3 Placement of Crystal Devices
When mounting a leaded crystal device on a printed circuit board, the spacing of the holes in the substrate must match the spacing of the device's leads. If the leads are forcibly inserted into mismatched holes, the glass portion of the base may crack, damaging the seal and causing performance degradation.
 
     4 Usage after Soldering
After soldering the crystal resonator onto the printed circuit board, avoid subjecting it to unexpected shocks or stress. In particular, if a leaded crystal resonator is dropped or twisted and then forcefully bent back into place, the glass base may develop cracks, leading to poor sealing. Additionally, performance degradation can occur if the leads of an SMD-type crystal resonator become detached or if the casing develops cracks. Depending on the type of crystal resonator, some may not be suitable for ultrasonic cleaning. If ultrasonic cleaning is planned, please consult with the manufacturer. Depending on the frequency and output power of the ultrasonic waves, there is a possibility that resonance of the crystal chip could cause damage, so be careful. Furthermore, small crystal devices may experience packaging damage and cracking due to stress from bending of the circuit board, so pay attention to this issue.
5 Regarding the impact of rapid temperature changes on SMD components mounted on printed circuit boards
When using surface-mount crystal oscillators with ceramic casings, the solder joints may crack due to the difference in thermal expansion coefficients between the mounting circuit board and the ceramic casing when operating in a large temperature difference environment for a long time. It is best to confirm this in advance if such environmental conditions are expected.
 
     6 Regarding the design of circuit board pads
     When designing the solder pads for crystal oscillators, their length should be limited as much as possible to prevent signal interference and abnormal vibration. The stray capacitance between the large solder pads should also be designed to be small. Additionally, it is important to avoid the crystal oscillator circuit pads intersecting with other circuit pads.
     7 About performance testing
To obtain accurate data, perform performance measurements after determining the surrounding environment, measuring instruments, and measurement sequence.
 
     Surrounding environment during measurement:
     Due to the significant impact of the surrounding environment on measurement results, pay attention to the following points:
     (a) The room temperature should be maintained at 25±2℃, and the relative humidity should be below 55%.
     (b) When measuring the temperature characteristics of the crystal oscillator, use a calibrated thermometer to confirm the temperature of the constant temperature bath.
(c) For crystal oscillators sensitive to electrostatic discharge, take electrostatic countermeasures when in use.
 
     Measurement molds and mounting circuits during inspection:
Due to the different stray capacitance and impedance between the inspection mold and the mounted circuit, even if the original product was good, it may become defective when mounted on a printed circuit board and checked with the inspection mold.
 
     Pay attention to measurement timing and placement time:
     (a) Before measuring the frequency of the crystal oscillator, set an appropriate preheating time from turning on the power to stabilization.
(b) When testing temperature characteristics, wait until all performance parameters are completely stable after heating before testing.
 
     About excitation level:
     Use the excitation level according to the individual specifications of the sample, and set the circuit conditions accordingly. If the excitation level exceeds the specification value by a large margin, the oscillation frequency may shift to the positive or negative pole depending on the shape of the oscillator. Pay attention to this point.
8 Reliability Testing
There are various methods for reliability testing, and it is important to implement them within the specified range of stress to prevent degradation and damage.
 
     (1) Heating
Common methods include temperature cycling and high-temperature aging. Other methods such as thermal shock should be discussed with the manufacturer beforehand, as they may induce greater stress.
 
     (2) Vibration
When applying vibration, the crystal oscillator has its own mechanical resonance frequency. If the vibration frequency matches it, larger vibration can be applied. Scanning sine waves can be used to apply vibration at any frequency.
 
     (3) Drop impact
     Drop impact can cause deterioration (accumulation of stress) in the crystal oscillator, but there is also a possibility of mixed shipment of experimental products with good products. Therefore, control is necessary.

     9 Reflow soldering
     Reflow soldering conditions (preheating, maximum temperature, time, number of passes, etc.) should be within the range specified in the instruction manual or individual sample book.
     In addition, when using an infrared heater, the absorption rate of the infrared rays by the crystal unit varies depending on the color and material of the unit, so the heating level must be confirmed.
     When using reflow soldering for crystal units, follow the furnace temperature curve specified in the individual sample book. See example of soldering with leaded solder (Sn-37Pb) in Fig. 5.1-1 and example of soldering with lead-free solder (Sn-     3.0Ag-0.5Cu) in Fig. 5.1-2.
     The reflow oven temperature is shown in Fig. 5.1-3 and temperature measurement should be performed next to the crystal unit. When using lead-free solder, the temperature curve varies depending on the composition of each solder, so sufficient consultation with the manufacturer is necessary.
     2 Crystal Oscillator
     2.1 Lead-Type Crystal Oscillator
     Regarding the design of printed circuit boards, if a crystal oscillator mounted on the board is higher than other components, it may be hit by some object, exerting an abnormal external force on the base. As a result, the glass bead at the bottom of the base will be damaged. Therefore, install the crystal oscillator as close as possible to other components with similar heights.
     (2) Fixation of the crystal oscillator
     When a crystal oscillator is mounted vertically on a printed circuit board, to prevent lead fatigue due to mechanical resonance, it is recommended to closely attach the oscillator to the board during soldering. When the crystal oscillator is mounted horizontally as shown in Figure 5.2-2, do not bend the leads directly from the glass part of the oscillator to prevent the glass part of the base from cracking. To avoid the state shown by the dotted line in the figure, perform lead bending and shaping in advance before mounting, and fix the oscillator to the substrate using tape and adhesive.
     (3) Soldering
     Regarding the soldering temperature conditions for the crystal oscillator, the conditions must be limited based on the type of product and ensure compatibility with common electronic components during the design stage. Furthermore, when performing reflow soldering after mounting a lead-type crystal oscillator horizontally, it is necessary to fully consult with the manufacturer regarding temperature conditions and the performance of the oscillator after soldering.
     2.2 SMD Crystal Oscillator
     (1) Frequency variation according to mounting direction on the substrate
On small SMD oscillators that use metal leads, the length of the conductor (two in total) from the electrode on the crystal chip to the base joint varies depending on the structure. Due to the different stray capacitances of each solder pad, changing the mounting direction of the crystal oscillator based on the oscillation circuit configuration and grounding of the metal leads will also change the oscillation frequency. This is due to the influence of the stray capacitance between the metal leads and the conductors. (Refer to Figure 5.2-3)
     If there is a large capacitance connected to both ends of the resonator in the oscillation circuit, there will not be an extreme frequency change even if the mounting direction is changed 180 degrees. However, when one end of the resonator is grounded, there will be a significant frequency change, which must be noted. (Refer to Figure 5.2-4)
     2 Crystal Oscillator
     3.1 Electrostatic Damage
When using a crystal oscillator with a C-MOS IC, the IC may be damaged by static electricity. Therefore, attention must be paid to packaging, mounting, and soldering to avoid electrostatic damage similar to that of the C-MOS IC.
 
     3.2 Variable Capacitor
When using a variable capacitor to adjust the frequency of the oscillator, use a screwdriver that matches the size of the variable capacitor. If the variable capacitor is forced too much, it may be damaged.

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