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6.3.4 Frequency Stability
The stability of an oscillation frequency often plays a very important role in applications such as electronic clocks (clock), the generator frequency and timing circuits. This stability depends on three factors. O first factor is the temperature, because the elements of the oscillator is a function of temperature. O second factor is the effect of varying the dc voltage and the third factor is the effect of "loading" of the oscillator, the oscillator receives in his exit.
The effect of temperature is important in oscillators LC. The value of inductance increases with temperature, whereas, the capacitance decreases. Thus, circuits have been devised by which these effects to be mutually exclusive. Accurate, however, balance is impossible to realize. We also note that the effect of temperature is less if the resonant circuit has a high quality factor Q.
Changes or fluctuations in voltage affect mainly the parameters of active components (transistors, etc), thus have an indirect effect and the frequency of oscillation. The problem is addressed by applying a very good electronic stabilization in the supply voltage. The effect of loading frequency stability is important, since it degrades the Q of the parallel resonant circuit. In practice it is preferable to use a buffer (buffer), because this circuit has high input impedance and low output impedance, thus leaving almost unaffected the Q of the resonant circuit.
6.3.5 Crystal oscillators
As mentioned above, a circuit with high Q ensures very good stability in the frequency of oscillation. The quartz crystal (quartz) is an element that behaves like a resonant circuit high Q. The function of the crystal based on piezoelectric effect, which is: If in a crystal contained between two electrodes apply mechanical vibrations generated in the surface electrical charges that develop ac voltages. Conversely, if the electrodes of the crystal apply ac voltage, the Coulomb forces develop internal stresses and crystal oscillate mechanically.
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The resonant frequency and quality factor Q of the crystal depends on the size, from the intersection and by the way of support. O quartz crystal found in hexagonal form. The Sch.6.9 shows the electrical equivalent circuit of the crystal and the change in impedance of Z, the frequency (response curve).
Figure 6.9. Crystal (quartz). equivalent circuit and complex characteristic
The resistance of the ohmic resistance R, inductance L and capacity of the CS series equivalent circuit (Sch.6.9 b) represents the electrical equivalent sizes of mechanical vibration characteristics of the crystal. The parallel capacity CP represents the electrostatic capacity between electrodes of the crystal.
As seen from the response curve of the crystal c Sch.6.9 has two resonant frequencies, a series of fos, where the impedance is small and a parallel, where the impedance is high. In both cases, the Q of the circuit is large. For most crystals, the difference in fop - fos between the two resonant frequencies are very small. The crystal we can coordinate on one or other of the two resonant frequencies.
It turns out that the above two frequencies equivalent to the size of the crystal given by the equations:
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and
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(6.3.22)
(6.3.23)
Figure 6.10. Crystal oscillator with a BJT
The quartz crystals are available for frequencies from 10 kHz to 330 MHz. We find it easier crystals at frequencies 100 kHz, 1 MHz, 2 MHz, 4 MHz, 5 MHz, 10 MHz and 25 MHz. Also, we find easily 3.579545 MHz crystal frequency used in oscillators colour burst of TV. In the market there are also crystals frequency 32.768 kHz (divide by 215 gives 1 Hz) used in digital watches. Finally, there are ready crystal oscillator within a "furnace" constant temperature and therefore high frequency stability, such as 10544 of Hewlett Packard (10 MHz).
From the equivalent circuit is crystal clear that we can use the crystal as a coordinate branch of the oscillator type Clapp. This gives the crystal oscillator with a BJT the Sch.6.10.
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Similarly, the Sch.6.11 shows a crystal oscillator with TE. This circuit uses a great aid so that we have to exit the square waveform. The pair of Zener diodes provide the output pulse width equal to the Zener voltage Vz of them.
6.4 Non-resonant vibrators
Conducting an oscillator does not necessarily require the use of a Resonant circuit with L and C in the lattice anasyzefxis. Can be used as any other net, which only contain data combined R and C, so non-resonant, but the evidence to satisfy the requirements anasyzefxis and phase transition criteria Barkhausen, Eq. (6.2.6) and Eq. (6.2 .7).
These non-resonant oscillators with netting RC, will be discussed in the following paragraphs.
The non-resonant oscillators using mesh netting for RC anasyzefxis is especially useful at low frequencies and integrated circuits where there may or reliance on use of coils.
Typical representatives of this class of oscillators is phase shifting the oscillator, the oscillator and Wien bridge oscillator with a double T.
741/351
R3 O-V:
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6-4.1 Transfer Oscillator Phase
The Sch.6.12 shows a type of oscillator phase shifting with TE. As observed, consists of a TE for aid and rank one lattice anasyzefxis composed of three RC elements in series. The netting anasyzefxis provides the necessary anasyzefxi voltage from the output to the input of the amplifier. O TE used in connection with reverse amplifier, therefore, the output of the input signal is amplified and displayed with phase difference 180 °. The additional phase difference of 180 ° required during the second criterion Barkhausen, we have to sway, should be provided by the feedback network. Only then, the total loop phase is 360 ° <0 °. The circuit will oscillate at a fixed frequency f0 where the phase transition through the lattice is exactly 180 ° and the strengthening of the amplifier Ln is large enough to satisfy the Barkhausen criterion and the oscillating circuit.
Amplifier
1N 4735 VZ = 6,2 V VD1 = VD2 = 0,7 V
Figure 6.12. Oscillator phase shifting with TE
Based on the Barkhausen criteria is demonstrated that the oscillation frequency of the oscillator phase transfer given by the equation:
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aid to the corresponding frequency, must be:
so the RC network degrades the signal -29 times. (The minus indicates that the resonance frequency of the lattice phase difference creates exactly 180 °).
Therefore,
R2> 29 R1 (6.4.3)
To calculate this oscillator, first start by choosing an appropriate value of C, and then compute the R.
Example 6-7
We calculate oscillator phase shifting oscillation frequency 500 Hz.
Solution
We accept in principle the value C = 100 nF. Therefore, solving for R
Eq. (6.4.1), we
2W6C / 2 pi x N6 x 100 x 500 x 10-9
use the E12 series of resistors and in practice we take R = 1.5 kQ.
In order not to load the amplifier due to the lattice, we choose R1> 10R. Therefore, marginally, R1 = 10 R = 15 KW
Based on Eq. (6.4.3), the resistance of the TE ansyzefxis will be.
R2> 29 x R1 = 29 x 15 KW = 435 KW
In practice we use R2 = 1 MO (potentiometer).
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We choose the 741 for the low frequencies the LM318 or LF351 for high frequencies, because they have higher SR.
The Sch.6.13 shows the oscillator phase shifting BJT. The transistor is a common syndesmologimeno emitter (CE), which means that generates 180 ° phase difference between input and output and 180 °, which creates a lattice we anasyzefxis 360 ° (the 0 °), which requires the second criterion Barkhausen.
O parallel combination of R1 and R2 gives a fairly large equivalent resistance R = 12k / / 47k 10 KW. Thus, the amplifier uses a pair Darligton, so we can ignore the high impedance input. The resistor R3 (100 O) is used to suppress unwanted vibrations at high frequencies. In the Handbook, the type of oscillation frequency f0 is the same as that which applies in the case of TE, Eq. (6.4.1). The type, however, the threshold payment Eq. (6.4.2) is valid only if we replace the ratio R2 / R1 to the expression of A than for amplifier
transistors, Eq. (06/03/19)
To find the oscillation frequency of the oscillator above and if we maintain the oscillations. Given and hfe = 200 hie = 1 KW.
Solution
The oscillation frequency is:
while, according to Eq. (6.3.19), the gain of the amplifier is:
| A h / eRC = 200x0.47 = 94
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So, the | If | is much greater than 29 and therefore comfortably satisfied Eq.
(6.4.2). Therefore we maintain the oscillations.
6.4.2 Oscillator Wien Bridge
One of the most commonly used audio frequency oscillators, due to its stability and simplicity, is the oscillator bridge Wien, depicting the Sch.6.14 with TE. As seen from the Sch.6.14a, netting anasyzefxis the oscillator is the pass band filter (FZD), with R and C, which is inserted in the field of anasyzefxis positive (+ input) of the TE. O street anasyzefxis negative (- input) created by the two resistors R1 and R2, in which the TE as an inverting terminal
Figure 6.14. Wien bridge oscillator with TE (a) Equivalent
circuit schematic showing the bridge Wien (b)
amplifier. The netting of the Wien bridge is connected between the input and output terminals of the amplifier, while the fourth side of the bridge grounded. The Wien bridge is composed of a series RC network in one of the industry and a parallel R / / C next to the field. In
other two branches are connected ohmic resistors R1 and R2, which determine the voltage gain of the inverter amplifier AO.
Based on the criteria Barkhausen, proved that the oscillation frequency of the oscillator with a Wien bridge is given by:
(6A4)
O demotion created the panel in this frequency band is:
(6.4.5)
while the phase transition caused the frequency is 0 °. Therefore, to sway the TE we should create different hour ¬ phase 0 °. In addition, to satisfy the Barkhausen condition vans> 1 and Eq. (6.4.5), the amplifier should have at least 3 support. Because TE is syndesmologimenos without inversion (non-inverting amplifier), the aid will be:
So R2> 2R1 (6.4.6)
Example 6-9
We compute Wien bridge oscillator with oscillation frequency 5 kHz.
Solution
We accept an appropriate value of the capacitor, eg C = 10 nF, and calculate R from the
Eq. (6.4.4), ie
R = 1 = 1 9 = 3.2 kO
(A) (b)
Figure 6.15. Lattice double T (filter tooth) and the response curve
The netting or double T filter is a narrowband filter cutoff (FSZA) or filter tooth (see Section 5.2.6) and a filter combination of a low and high frequency filter. O Demotion filter at the resonance frequency can also be below 60 dB. It turns out that the resonance frequency is given by:
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Finally, we accept
R1 - 10 kO and Eq. (6.4.6), we find
R2> 2R1> 2 x 10 KW> 20 KW (use pot. KW 50)
6.4.3 Oscillator Dual T
As we saw, the Wien bridge oscillator uses a filter in the pass band
street anasyzefxis positive (+ input) of the TE. Equally well we can create an audio frequency oscillator with a suitable setting TE
passive filter in the way anasyzefxis negative (- input) of the TE. Such a filter is the dual lattice T, shown in Sch.6.15.
(6.4.7)
The phase transition through the netting at the frequency is -90 °. To have maintained the oscillations the amplifier should have very large (theoretically infinite) support, in practice 40 to
5.6K 2C = 10 nF 5.6 K CCR / 2 20 nF0 KR2
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60 dB (100 έως 1000), to cover losses due to high water down the panel.
O oscillator with double T TE using the above mesh / filter as shown in Sch.6.16.
Figure 6.16. TE oscillator and dual lattice T
Example 6-10
We calculate oscillator with double T 3 kHz resonant frequency and enhancing 100 (40 dB).
Solution
We accept in principle the logical value C = 10 nF. Then, from Eq. (6.4.6), we
So, we get
R = 5.6 kQ (E12 series)
We accept R1 = 10 kQ (potentiometer). So, from the known type of aid reversed amplifier we find:
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R2 = KR1 = 100 x 10 kO = 1 MO
The Zener diodes provide adaptive anasyzefxi negative. That is, the position coordinate, f0 when the voltage applied to the Zener is small, the Zener are put off (ie outside the region Zener). This gives a very small negative anasyzefxi which creates greater support, thus leading to oscillations in f0.
The frequency f0 than the Zener voltage increases to the point where they begin to agoun and their resistance drops, allowing more negative anasyzefxi decreasing aid ¬ aid amplifier. Thus, the oscillation frequency are excluded completely. The minimum output voltage is approximately Vminp Vz As the oscillator Wien, the minimum distortion occurs at this minimum width of the output voltage.
The oscillator double T has many advantages in oscillator Wien. The oscillations of the oscillator double T adjusted by varying a single resistor, while the Wien oscillator must also configure two resistors.
The double T filter is more selective than the filter Wien, resulting in a double T oscillator is more stable and less sensitive to fortoma.Epipleon, the oscillator is double T anasyzefxis exact level is not as critical as the Wien, so is easier to create oscillations. The only advantage is that Wien oscillator circuit has fewer components and is therefore simpler.
