Oscillating circuit generators are irreplaceable as sources of sinusoidal high-frequency oscillations. To generate oscillations with frequencies less than 15 ... 20 kHz, they are inconvenient, since the oscillatory circuit is too cumbersome.
Another disadvantage of low-frequency LC - generators is the difficulty of tuning them in the frequency range. All this has led to the widespread use of RC generators at the above frequencies, in which frequency electric RC filters are used instead of an oscillatory circuit. Generators of this type can generate fairly stable sinusoidal oscillations over a relatively wide frequency range from fractions of a hertz to hundreds of kilohertz. They are small and lightweight, and these advantages of RC generators are most fully manifested in the low frequency region.
4.2 Block diagram of the rc-generator
This circuit is shown in Fig. No. 7.
Fig. No. 7. Structural scheme RC autogenerator.
The circuit contains an amplifier 1, loaded with a resistor and receiving power from a constant voltage source 3. For self-excitation of the amplifier, i. E. to obtain sustained oscillations, it is necessary to supply to its input a part of the output voltage that exceeds the input voltage (or equal to it) and coincides with it in phase. In other words, the amplifier must be covered with positive feedback, and the four-pole feedback 2 must have a sufficient transmission coefficient. This problem is solved in the case when the two-pole device 2 contains a phase-shifting circuit consisting of resistors and capacitors, the phase shift between the input and output voltages is 180 0.
4.3 The principle of operation of the phase-shifting circuit
The diagram of which is shown in Fig. No. 8a, illustrated using the vector diagram in Fig. No. 8b.
Fig. 8. Phase-shifting circuits: a - schematic diagram; b - vector diagram; c, d - three-link chains
Let the voltage U1 be applied to the input of this RC circuit. It causes a current I in the circuit, creating a voltage drop across the capacitor
(where ω is the frequency of the voltage U1) and across the resistor U R = IR, which is simultaneously the output voltage U2. In this case, the phase shift angle between the current I and the voltage Uc is equal to 90 0, and between the current I and the voltage U R - zero. The voltage vector U1 is equal to the geometric sum of the vectors U C and U R and makes an angle φ with the vector U2. The smaller the capacitance of the capacitor C, the closer the angle φ to 90 0.
4.4 Conditions for self-excitation of rc - oscillator
The largest angle φ, which can be obtained by changing the values of the elements of the RC-circuit, is close to 90 0. In practice, circuit elements R and C are selected as follows. So that the angle φ = 60 0. Therefore, to obtain the phase angle φ = 180 0, which is necessary to fulfill the phase balance condition. It is required to connect three RC links in series.
In fig. No. 8 c, d shows two variants of three-link phase-shifting circuits. The phase shift between the output and input voltages by an angle of 180 0 at R1 = R2 = R3 = R and C1 = C2 = C3 = C is provided at frequencies: f 01 ≈ (in the circuit in Fig. 8c) and f 02 ≈ (in the circuit 8d), where R is expressed in ohms, C- in farads, and f 0 - in hertz. The values of f 01 and f 02 are simultaneously the frequency of self-oscillations.
To ensure the balance of the amplitudes, the gain of the amplifier K us should not be less than the transmission coefficient of the feedback circuit K o.s. =. Calculations show that for the given schemes K o.c =. Thus, self-oscillations in RC-generators containing three-link phase-shifting circuits with the same links are possible only if the conditions
f auto = f 01 (or f auto = f 02); K mustache ≥29.
Sinusoidal oscillators are performed with an oscillating LC circuit and frequency-dependent RC circuits. LC-generators are designed to generate high-frequency signals (over several tens of kilohertz), and RC-generators are used on low frequencies(up to units of hertz).
LC-type oscillators are based on the use of selective LC amplifiers with narrow bandwidth. The conditions for generating sinusoidal oscillations (8.1) and (8.2) are created for the tuning frequency f 0 an oscillatory circuit when its resistance is purely active. The prerequisite for the fulfillment of relation (8.1) for the frequency f 0 serves to change the phase shift j at introduced by the amplifier when the frequency deviates from the resonant frequency, since the resistance resonant circuit ceases to be active and acquires a reactive (inductive or capacitive) character. The validity of relation (38) for the resonant frequency is due to the maximum value of the gain at the frequency f 0.
The circuit implementation of LC generators is quite diverse. They may differ in the way they are connected to an oscillatory LC circuit in the amplifier and create positive feedback. One of the circuits of LC-generators is shown in Fig. 8.2.
The amplifier stage is made on a transistor VT included according to the OE scheme. The elements R1, R2, R e, C e are designed to set the rest mode and temperature stabilization. The output signal is taken from the collector of the transistor through a blocking capacitor C p2.
The parameters of the oscillating circuit are the capacitance of the capacitor WITH and primary inductance w 1 transformer. The feedback signal is removed from the secondary winding w 2 inductively coupled to the winding w 1, and through a decoupling capacitor С р1 is fed to the input of the transistor. The required phasing of the feedback voltage is achieved by appropriately connecting the ends of the secondary winding. The ratio of the number of turns of the primary and secondary windings w 1 /w 2 >1.
If we take the inductive coupling of M windings w 1 and w 2 is ideal, then to ensure the balance of amplitudes, it is necessary that the current transfer coefficient of the transistor β at the rest point satisfies the relation β ≥ w 1 /w 2 .
Frequency f generated oscillations is close to resonant frequency oscillatory circuit
Parameter dependency L and WITH and the parameters of the transistor on temperature leads to a temperature dependence of the frequency f... In conditions of constant temperature, frequency instability is caused by a change in the differential parameters of the transistor from a change in the position of the quiescent point of the amplifier stage.
Frequency instability of generators is estimated by the coefficient of relative instability d f= D f / f * 100%, where D f- absolute frequency deviation from the nominal value f... The coefficient of relative frequency instability of transistor LC-generators without taking special additional stabilization measures is a few percent. Highest frequency stability with coefficient d f= (10 -3 ¸ 10 -5)% is achieved when using a quartz resonator in oscillators.
LC-type generators are implemented in the form of hybrid integrated circuits in which the reactive elements L and C used as hinged.
Generators for frequencies below several tens of kilohertz are built using frequency-dependent RC circuits. Operational amplifiers in an integrated design are usually used as an amplifying link. OU generator circuits are shown in Fig. 8.3.
The principle of operation of the simplest RC generator of sinusoidal oscillations (Fig. 8.3, a) is that at a certain frequency, the phase shift of the three links of the RC circuit is j w = 180 °.
If such a circuit is connected between the output and the inverting input of the op-amp, then the total phase shift will be equal to 360 °, i.e. positive feedback is generated. Frequency f 0, at which the angle j w = 180°, is called quasi-resonant. With parameters R and C (R1 = R2 = R3 || R 0 = R, C1 = C2 = C3 = C) it is related by the relation
Such a chain attenuates the signal by a factor of 29, therefore, to create stable oscillations, it is necessary that the amplifier has a gain TO≥ 29. Then the condition amplitude balance |Ќ || ẁ | ≥ 1... This problem is solved by choosing the resistances of the resistors. R 0 and R os (K = R os / R 0 ≥ 29).
Of the RC circuits that do not phase shift the transmitted signal at a quasi-resonant frequency, the Wien bridge circuit is most widespread. The schematic of a sinusoidal oscillator based on an op amp with a Wien bridge is shown in Fig. 8.3, b. Frequency-dependent feedback link C1, R1, C2, R2(Wine bridge) is connected between the output and the direct input of the op-amp. The elements R 0 and R os are designed to obtain the required gain of the amplifying link.
At the generation frequency f 0 Wien bridge transmission ratio w= 1/3, therefore, self-excitation of the generator is possible when TO> 3. For the non-inverting amplifier used in this circuit, this corresponds to the choice R os/ R 0 ≥ 3.
RC-generator is called a generator of harmonic oscillations, in which instead of an oscillatory system containing elements L and WITH, a resistive-capacitive circuit is used ( RC-chain) with frequency selectivity.
The exclusion of inductors from the circuit makes it possible to significantly reduce the dimensions and weight of the generator, especially at low frequencies, since the dimensions of the inductors sharply increase with decreasing frequency. An important advantage RC-generators compared to LC- generators are the ability to manufacture them using integral technology. but RC- generators have a low stability of the frequency of the generated oscillations, due to the low quality factor RC- circuits, as well as a bad form of oscillations due to poor filtering of higher harmonics in the spectrum of the output oscillation.
RC- generators can operate in a wide frequency range (from fractions of a hertz to tens of megahertz), however, they have found application in communication equipment and measuring equipment mainly at low frequencies.
Fundamentals of Theory RC-generators were developed by Soviet scientists V.P. Aseev, K.F. Teodorchik, E.O.Saakov, V.G. Kriksunov, and others.
RC- the generator usually includes a broadband amplifier made on a lamp, transistor or integrated circuit, and RC- a feedback loop with selective properties and determining the frequency of oscillations. The amplifier compensates for energy losses in passive elements and ensures the fulfillment of the amplitude self-excitation condition. The feedback loop ensures that the self-excitation phase condition is fulfilled only at one frequency. By the type of feedback circuit RC-generators are divided into two groups:
with zero phase shift in the feedback loop;
with a phase shift in the feedback loop by 180.
To improve the shape of the generated vibrations in RC-generators use elements with nonlinearity, which limit the increase in the amplitude of the oscillations. The parameters of such an element change depending on the amplitude of the oscillations, and not on their instantaneous values (a thermistor, the resistance of which depends on the degree of heating by the current passing through it). With such a limitation, the form of oscillations does not change; they remain harmonic even in a stationary mode.
Consider both types RC- autogenerators.
Oscillator with 180 phase shift in the feedback circuit.
Such an autogenerator is also called an autogenerator with a three-link chain. RC.
In the schemes RC- generators with a phase shift in the feedback circuit by 180, amplifiers are used that invert the phase of the input voltage. Such an amplifier can, for example, be an inverting-input operational amplifier, a single-stage amplifier, or a multi-stage amplifier with an odd number of inverting stages.
In order for the phase balance equation to be fulfilled, the feedback circuit must provide a phase shift of OC = 180.
To substantiate the structure of the feedback loop, let us reproduce the phase-frequency characteristics of the simplest RC-links (Fig. 3.4).
Rice. Option 3 RC-link and its phase response
Rice. Option 4 RC-link and its phase response
It can be seen from the graphs that one simplest RC-link introduces a phase shift not exceeding 90. Therefore, a phase shift of 180 can be carried out by cascading three elementary RC-links (fig. 5).
Rice. 5 Schemes and phase characteristics of three-link RC-chains
The elements RC-circuits are calculated so as to obtain a phase shift of 180 at the generation frequency. One of the variants of the generator with a three-link circuit RC shown in Figure 6
Rice. 6 Generator with three-link chain RC
The generator consists of a resistive transistor amplifier and a feedback circuit. A single-stage amplifier with a common emitter carries out a phase shift between the voltage on the collector and the base K = 180. Therefore, to perform the phase balance, the feedback circuit must provide an OC = 180 frequency of the generated oscillations.
Let's analyze the feedback loop, for which we will compose a system of equations using the loop current method.
Solving the resulting system with respect to the feedback coefficient, we obtain the expression
It follows from the expression that the phase shift of 180 is obtained in the case when it will be a real and negative value, i.e.
therefore, generation is possible at a frequency
At this frequency, the module of the feedback coefficient
This means that in order to excite self-oscillations, the amplifier coefficient must be greater than 29.
The generator output voltage is usually taken from the collector of the transistor. To obtain harmonic oscillations, a thermistor is included in the emitter circuit R T with a positive temperature coefficient of resistance. With an increase in the amplitude of oscillations, the resistance R T increases and the depth of negative feedback in the AC amplifier increases, respectively, the gain decreases. When a stationary oscillation mode occurs ( TO= 1), the amplifier remains linear and there is no distortion of the collector current waveform.
Oscillator with zero phase shift in the feedback circuit.
A characteristic feature of the circuits RC- generators with zero phase shift in the feedback circuit is the use of amplifiers in them that do not phase inverting input signal... Such an amplifier can be, for example, an operational amplifier with a non-inverting input or a multistage amplifier with an even number of inverting stages. Let's consider some possible variants of feedback circuits providing zero phase shift (Fig. 7).
Rice. 7 Variants of feedback circuits providing zero phase shift
They consist of two links, one of which represents RС- a link with a positive phase shift, and the second - with a negative phase shift. As a result of the addition of the phase response at a certain frequency (generation frequency), a phase shift of zero can be obtained.
In practice, the most often used as a selective circuit with a zero phase shift is a phase-balanced bridge, or, in another way, a Wien bridge (Fig. 7 c), the application of which is shown in the diagram RC-generator with zero phase shift, made on the operational amplifier (Fig. 8).
Rice. eight RC- generator with zero phase shift in the OS circuit
In this circuit, the voltage from the output of the amplifier is applied to its non-inverting input through the feedback circuit formed by the elements of the Wien bridge R 1 C 1 and R 2 C 2. Resistive chain RR T forms another feedback- negative, which is designed to limit the increase in the amplitude of oscillations and preserve their harmonic form. The negative feedback voltage is applied to the inverting input of the operational amplifier. Thermistor R T must have a negative temperature coefficient of resistance.
Feedback Loop Gain
must be real and positive, and this is possible when the equality
From here the frequency of the generated oscillations is determined. If R 1 = R 2 =R, C 1 = C 2 = C, then
The amplitude condition of self-excitation at frequency 0 requires the fulfillment of the inequality
With equality R 1 = R 2 = R and C 1 = C 2 = C gain TO > 3.
The vibration frequency can be changed by changing the resistances R or capacitor capacitors WITH, which are part of the Wien bridge, and the amplitude of the oscillations is regulated by the resistance R.
Main advantage RC-generators before LC-generators is that the former are easier to implement for low frequencies. For example, if in a generator circuit with zero phase shift in the feedback circuit (Fig. 8) R 1 = R 2 = 1 MOhm, C 1 = C 2 = 1 μF, then the generated frequency
.
To get the same frequency in LC-generator, inductance would be required L= 10 16 H at WITH= 1 μF, which is difficult to implement.
V RC-generators it is possible by simultaneously changing the values of the capacities WITH 1 and WITH 2, obtain a wider frequency tuning range than is the case in LC-generators. For LC-generators
while for RC-generators, at WITH 1 = WITH 2
To the disadvantages RC-generators should be attributed to the fact that at relatively high frequencies they are more difficult to implement than LC-generators. Indeed, the value of the capacitance cannot be reduced to less than the mounting capacitance, and a decrease in the resistances of the resistors leads to a drop in the gain, which makes it difficult to fulfill the amplitude condition for self-excitation.
The listed advantages and disadvantages RC-generators caused their use in the low-frequency range with a large frequency overlap coefficient.
In this article, we will consider an RC oscillator and its principle of operation, consider in detail its circuits, including an operational amplifier.
Description and working principle
We have seen in the amplifier manuals that the single stage transistor amplifier can generate 180 o phase shift between its output and input signals when connected in a class A type configuration.
In order for the oscillator to withstand indefinitely, there must be sufficient feedback of the correct phase, that is, "positive feedback", and the transistor amplifier is used as an inverting stage to achieve this.
V RC generator circuits the input is biased 180 o through the amplifier stage and 180 o again through the second inverting stage, which gives us a "180 o + 180 o = 360 o" phase shift, which is effectively 0 o, thereby giving us the required positive feedback... In other words, the phase shift of the feedback loop should be "0".
V resistance-capacitance generator or just in the generator RC we exploit the fact that a phase shift occurs between the input to the RC network and the output from the same network, for example using RC elements in the feedback branch.
RC phase circuit
The diagram on the left shows one resistor-capacitor network whose output voltage “leads” the input voltage by less than 90 degrees. An ideal single pole RC circuit will produce a phase shift of exactly 90 o, and since the oscillation requires 180 o phase shift, the design RC oscillator you must use at least two single-pole.
However, in reality it is difficult to obtain exactly 90 ° phase shift, so more stages are used. The magnitude of the actual phase shift in the circuit depends on the values of the resistor and capacitor, and the selected oscillation frequency with a phase angle (Φ) is given as:
Where: X C is the capacitance of the capacitor, R is the resistance of the resistor, and ƒ is the frequency.
In our simple example above, the values of R and C were chosen so that at the required frequency, the output voltage ahead of the input voltage at an angle of about 60 o. Then, the phase angle between each successive RC section is increased by an additional 60 °, giving a phase difference between the input and output of 180 ° (3 x 60 °), as shown in the following vector diagram.
Then, by connecting three such RC networks together in series, we can produce a full 180 o phase shift in the circuit at the selected frequency, and this forms the basis of the "phase shift generator", otherwise called RC generator .
We know that in an amplifier circuit using a bipolar transistor or op amp, it will produce a 180 ° phase shift between its input and output. If a three-stage RC network with a phase shift is connected between this input and the output of the amplifier, the total phase shift required for regenerative feedback is 3 x 60 o + 180 o = 360 o, as shown below.
Three RC stages are cascaded to obtain the required slope for a stable oscillation frequency. The phase shift of the feedback loop is -180 o when the phase shift of each stage is -60 o. This happens when ω = 2πƒ = 1.732 / RC(tan 60 o = 1.732). Then, in order to achieve the required phase shift in the RC oscillator circuit, it is necessary to use several RC phase-shifting networks, such as the circuit below.
Basic RC oscillator circuit
Base RC generator, also known as phase shift generator, generates a sine wave output using regenerative feedback derived from a resistor-capacitor combination. This regenerative feedback from the RC network is due to the capacitor's ability to store electric charge(similar to the LC-tank circuit).
This resistor-capacitor feedback network can be connected as shown above to create an initial phase shift (phase change network) or interchangeably to create a lagged phase shift (phase lag network), the result remains the same as sinusoidal oscillations. which occur only at a frequency at which the total phase shift is 360 o.
By changing one or more resistors or capacitors in a phase-shifted network, the frequency can be changed, and this is usually done by keeping the same resistors and using a 3-digit variable capacitor.
If all resistors R and capacitors C in the phase shift network are equal in magnitude, then the frequency of the oscillations created by the RC generator is determined as:
Where:
ƒ r - output frequency in hertz
R - resistance in ohms
C - capacitance in Farads
N - number of RC stages, (N = 3)
Since the resistor-capacitor combination is RC generator circuits also acts as an attenuator, creating complete attenuation -1 / 29th (Vo / Vi = β) in all three stages, the amplifier voltage gain must be high enough to overcome these RC losses. Therefore, in our three-stage RC network above, the amplifier gain must also be equal to or greater than 29.
The influence of the amplifier load on the feedback network affects the oscillation frequency and can cause the generator frequency to be 25% higher than the calculated one. The feedback network must then be driven from a high impedance output source and fed into a low impedance load such as a common emitter transistor amplifier, but it is better to use an op amp as it fully meets these conditions.
Operational amplifier RC oscillator
When used as RC generators, RC generators with operational amplifier are more common than their bipolar transistor counterparts. The oscillator circuit consists of a negative gain op-amp and a three-section RC network that generates a 180 ° phase shift. The phase-shifted network is connected from the output of the op-amp back to its "inverting" input, as shown below.
Since the feedback is connected to the inverting input, the op-amp is therefore connected in its "inverting amplifier" configuration, which produces the required 180 o phase shift, while the RC network produces another 180 o phase shift at the desired frequency (180 o + 180 O).
Although it is possible to cascade only two single pole RC stages to achieve the required 180 ° (90 ° + 90 °) phase shift, the oscillator stability at low frequencies is generally poor.
One of the most important features RC oscillator is its frequency stability, which is its ability to provide a constant frequency sine wave output under various load conditions. By cascading three or even four RC stages (4 x 45 o), the stability of the oscillator can be greatly improved.
Commonly used RC generators with four stages, because commonly available op-amps come in four-layer integrated circuits, so designing a four-stage generator with a phase shift of 45 o relative to each other is relatively easy.
RC generators stable and provide a well-formed sinusoidal output with a frequency proportional to 1 / RC, and therefore a wider frequency range is possible with a variable capacitor. However, RC oscillators are limited to frequency applications due to bandwidth limitations to obtain the desired phase shift at high frequencies.
In the next lesson on Oscillators, we will look at another type RC generator, called bridge oscillators Wien, which uses resistors and capacitors as a circuit to create a low frequency sine wave.
The use of generators with oscillatory circuits (type LC) to generate oscillations with frequencies less than 15-20 kHz is difficult and inconvenient due to the bulkiness of the circuits. Currently, for these purposes, generators of the type RC, in which, instead of an oscillatory circuit, selective RC filters are used. Generators type RC can generate very stable sinusoidal oscillations in a relatively wide frequency range from fractions of a hertz to hundreds of kilohertz. In addition, they are small in size and weight. The most complete advantages of type generators RC appear in the low frequency range.
Block diagram of a sinusoidal oscillator type RC is shown in Fig. 1.5.
Rice. 1.5
The amplifier is built in a conventional resistive circuit. For self-excitation of the amplifier, that is, for the transformation of the initially arisen oscillations into continuous ones, it is necessary to supply a part of the output voltage to the input of the amplifier, which exceeds the input voltage or is equal to it in magnitude and coincides with it in phase, in other words, to cover the amplifier with positive feedback of sufficient depth ... When the output of the amplifier is directly connected to its input, self-excitation occurs, however, the form of the generated oscillations will sharply differ from the sinusoidal, since the conditions for self-excitation will be simultaneously fulfilled for oscillations of many frequencies. To obtain sinusoidal oscillations, it is necessary that these conditions are fulfilled only at one certain frequency and are sharply violated at all other frequencies.
Rice. 1.6
This task is solved using phase-shifting chain, which has several links RC and serves to rotate the phase of the output voltage of the amplifier by 180 °. The phase change depends on the number of links NS and equal
Due to the fact that one link RC changes phase by an angle< 90°, минимальное число звеньев фазовращающей цепочки NS -- 3. In practical generator circuits, three-link phase-shifting chains are usually used.
In fig. 1.6 shows two variants of such chains, which are called "R-parallel" and "C-parallel", respectively. The frequency of the generated sinusoidal oscillations for these circuits under the condition R1 = R 2 = R 3 = R and C t = C 2 = C3 = C is calculated by the following formulas: for the circuit in Fig. 1.6, a:
for the circuit in Fig. 4.6, b:
To ensure the balance of amplitudes, the gain of the amplifier must be equal to or exceed the attenuation introduced by the phase-shifting circuit through which the voltage from the output enters the input of the amplifier.
Calculations show that for the above schemes the attenuation
Consequently, circuits using three-link phase-shifting chains having the same links can generate sinusoidal oscillations with a frequency f 0 only if the amplifier gain exceeds 29.
In a phase-shifting chain with the same links, each subsequent link has a shunting effect on the previous one. To reduce the shunting action of the links and reduce the attenuation in the phase-shifting feedback circuit, the so-called progressive chains. In this case, the resistance of the resistor of each subsequent link is selected in tn times greater than the resistance of the previous link, and the capacitances of the subsequent links decrease by the same amount:
Usually the value T does not exceed 4-5.
In fig. 1.7 shows one of the possible schemes of an oscillator type RC with a phase-shifting chain.
From the point of view of ensuring the condition of phase balance, such a generator could be built on one transistor (T2) with a common emitter. However, in this case, the feedback loop shunts the resistor R K amplifying transistor and reduces its gain, and the low input resistance of the transistor dramatically increases the attenuation in the feedback circuit. Therefore, it is advisable to separate the output of the phase-shifting circuit and the input of the amplifier using an emitter follower assembled on a transistor T1.
The autogenerator starts at the moment the power source is turned on. The resulting collector current pulse contains a wide and continuous frequency spectrum, which necessarily includes the required generation frequency. Due to the fulfillment of the self-excitation conditions, the oscillations of this frequency become undamped, while the oscillations of all other frequencies, for which the phase balance condition is not satisfied, rapidly decay.
Self-oscillators with phase-shifting circuits are usually used to generate sinusoidal oscillations of a fixed frequency. This is due to the difficulty of tuning the frequency over a wide range. Range autogenerators type RC are built in a slightly different way. Let's consider this issue in more detail.
If the amplifier turns the phase of the input signal to 2? (for example, an amplifier with an even number of stages), then when covered with positive feedback of sufficient depth, it can generate electrical oscillations without turning on a special phase-shifting chain. To isolate the required frequency of sinusoidal oscillations from the entire spectrum of frequencies generated by such a circuit, it is necessary to ensure that the self-excitation conditions are satisfied for only one frequency. For this purpose, a series-parallel selective circuit can be included in the feedback circuit, the diagram of which is shown in Fig. 1.8.
Rice. 1.7
Let's define the properties of this chain, considering it as a voltage divider.
There is an obvious relationship between the output and input voltages.
The voltage transfer ratio of this circuit
At a quasi-resonant frequency w 0, the voltage transfer coefficient must be equal to a real number. This is possible only if the resistances expressed by the corresponding mathematical notation in the numerator and denominator of the last formula will have the same character. This condition is satisfied only if the real part of the denominator is zero, i.e.
Hence the quasi-resonance frequency
As for the voltage transfer coefficient, at the quasi-resonant frequency it is equal to
Substituting into this formula the value
Considering R1 = R 2 = R and C 1 = С 2 = С, we find the final values of f 0
The attenuation introduced by the considered electoral chain at the quasi-resonant frequency is
This means that the minimum gain at which the amplitude balance condition is satisfied must also be 3. Obviously, this requirement is quite easy to fulfill. A real transistor amplifier having two stages (the smallest even number) allows a voltage gain much greater than TO O = 3. Therefore, it is advisable, along with positive feedback, to introduce negative feedback into the amplifier, which, while reducing the gain, at the same time, significantly reduces the possible nonlinear distortions of the generated oscillations. Schematic diagram such a generator is shown in Fig. 1.9.
Frequency hopping transistor RC oscillator circuit
The thermistor in the emitter circuit of the transistor T1 is designed to stabilize the amplitude of the output voltage when the temperature changes. Frequency adjustment is carried out using a paired potentiometer R1R2.
Currently, discrete elements (transistors) are rarely used to power generators. Most often used for these purposes Various types integrated circuits. Circuits based on op amps, multipliers, comparators and timers are distinguished by their simplicity, stability of parameters, and versatility. The flexibility and versatility of the op-amp allows with a minimum number of external components to create simple, but at the same time, convenient for tuning and adjustment generators of almost all types with satisfactory parameters.
The principle of operation of such generators is based on the use of phase-shifting or resonant elements in the OS circuits: a Wien bridge, a double T-shaped bridge, and shifting RC circuits.
There are other ways to generate sinusoidal oscillations, for example by filtering triangular pulses or extracting the first harmonic component of rectangular pulses.
