## Introduction

Simply put, an oscillator is a device that can convert DC power into AC power without external signal excitation. The so-called "oscillation" implies alternating current. This article will mainly explain the circuits of different sine wave oscillators, including their working principles, how to realize their functions, circuit composition and comparison of advantages and disadvantages of different forms of circuits. This article uses a large number of circuit diagrams and formulas to explain in detail, which can help you understand in a better way.

Basics of oscillators and their different types

## Catalog

## I The Principle of Feedback Oscillator

### 1.1 How Does the Feedback Oscillator Work?

The feedback oscillator is when the power is turned on, the various electrical disturbance signals in the loop are selected by the frequency selection network, and the signal of a certain frequency is fed back to the input terminal, and then the cycle of amplification → feedback → amplification → feedback , The amplitude of the signal increases continuously, and the oscillation is established from small to large. As the signal amplitude increases, the amplifier will enter a non-linear state, and the gain will decrease. When the feedback voltage is exactly equal to the input voltage, the oscillation amplitude will no longer increase and enter a balanced state.

As can be seen from the figure below, the feedback oscillator is a closed loop composed of an amplifier and a feedback network. The amplifier is usually a tuned amplifier with an oscillation circuit as a load. The feedback network is generally a linear network composed of passive components.

Figure1. Block Diagram of Feedback Oscillator

In order to generate **self-oscillation**, there must be **positive feedback**, that is, the signal fed back to the input terminal and the signal at the input terminal of the amplifier have the same phase.

For the above figure, suppose the voltage amplification factor of the amplifier is K(s), the voltage feedback coefficient of the feedback network is F(s), and the closed-loop voltage amplification factor is Ku(s), then

by

We can write

If a certain frequency ω1=ω, then T(jω1) is equal to 1. From the above formula, we can see that Ku(jω) will tend to infinity. This shows that there is no external signal, and self-excited to produce signal output, namely self-oscillation. Therefore, the condition of self-oscillation is that the loop gain is 1.

Definition:

### 1.2 Equilibrium Conditions

The equilibrium condition of the oscillator is

this can also be expressed as

If a certain frequency ω1=ω, then T(jω1) is equal to 1. From the above formula, we can see that Ku(jω) will tend to infinity. This shows that there is no external signal, and self-excited to produce signal output, namely self-oscillation. Therefore, the condition of self-oscillation is that the loop gain is 1.

The above two formulas are the amplitude and the phase equilibrium conditions respectively.

Equilibrium conditions are also called "two conditions for maintaining self-oscillation". The amplitude balance condition determines the amplitude of the oscillator output signal, and the phase equilibrium condition determines the frequency of the oscillator output signal. But it must be pointed out that the loop can only meet the phase equilibrium condition at a certain frequency (f), which is the resonant frequency (f0) of the loop.

### 1.3 Starting Conditions of the Oscillator

When the oscillator is in actual application, there should be no external signal Us(s) shown in Figure 1. The initial source of oscillation is electrical signals such as electrical shock and various thermal noises that inevitably exist when the oscillator is switched on.

It can be seen from the establishment process of the oscillation that in order to make the oscillator start-up, the feedback voltage Uf and the input voltage Ui should be in phase at the beginning of the oscillation (that is, positive feedback); Uf>Ui should be required in amplitude, that is:

Vibration conditions: φA+φF=2nπ(n=0,1,2,•••)

AF>1

Simply put, as we know, the condition of unity gain must be met to make the oscillation continue. But to start the oscillation, the voltage gain of the positive feedback loop must be greater than 1, so that the amplitude of the output voltage can reach the required potential. Then the gain must be reduced to 1, so that the output voltage can be maintained at the required potential and the oscillation phenomenon can continue.

Transition from |T(jω)|>1 to |T(jω)|=1 when the oscillator is working

The amplifier must work in the linear amplification region of the transistor when amplifying small signals.

When the oscillation is started, the amplifier works in the linear region. At this time, the output of the amplifier increases linearly with the increase of the input signal; as the amplitude of the input signal increases, the amplifier gradually enters the saturation or cut-off region from the amplification region, and enters a nonlinear state. The closed-loop gain of will decrease with the increase of the input signal, as shown in the figure below:

Figure2. Graphical Representation of Amplitude Conditions

When the loop gain drops to |T(jω)|=1, the growth process of the amplitude will stop, and the oscillator will reach a balanced state and perform constant amplitude oscillation. It can be seen that the transition of the oscillator from amplified oscillation to steady amplitude oscillation is realized by the non-linear characteristics of the amplifier.

When the oscillating circuit is powered on, the current of the transistor increases abruptly from zero, and the sudden change current contains a wide spectrum component.

The start-up process of the circuit is very short! As long as the circuit satisfies the starting conditions, after the oscillator is powered on, there will be an output signal with stable amplitude at the output.

Figure3. Circuit Start-up Process

### 1.4 Stable Conditions of the Oscillator

If the loop gain characteristic has two equilibrium points A and B, among them, point A is stable and point B is unstable.

Figure4. Stable Conditions of the Oscillator

It can be seen from the above discussion that in order to stabilize the equilibrium point, |T(ω0)| must have a negative slope change near UiA.

Stable conditions are divided into amplitude stable conditions and phase stable conditions

To make the amplitude stable, the oscillator must have the ability to prevent amplitude changes at its equilibrium point. Then the amplitude stability condition should be

Since the feedback network is a linear network, which means the size of the feedback coefficient does not change with the input signal, so the amplitude stability condition can be written as

The phase stability depends on the increase of ω, and the decrease of , meaning that the phase characteristic of the parallel oscillator circuit ensures the phase stability.

Therefore, the phase stability condition is. The higher the Q value of the loop, the larger of the value of , and the better phase stability.

### 1.5 General Composition of Sine Wave Oscillator

(1) Amplifying circuit-realize energy control.

(2) Positive feedback network-meets the conditions for starting vibration.

(3) Frequency selection network-only one frequency satisfies the oscillation condition to obtain a sine wave output of a single frequency. Commonly used frequency selection networks include RC frequency selection and LC frequency selection

(4) Amplitude stabilization link-makes the circuit easy to start and oscillate stably, with little waveform distortion.

**Examples of oscillation circuits:**

High frequency resonant amplifier and sine wave oscillator

Figure5. High Frequency Small Signal Resonant Amplifier

Figure6. Mutual Inductance Coupled Oscillator

## II LC Oscillator Circuit

LC oscillators can be divided into three types: mutual inductance coupled oscillators, inductive feedback oscillators and capacitive feedback oscillators according to their different feedback networks.

This section focuses on different types of feedback LC oscillators and three-point oscillators.

### 2.1 The Composition Principle of the Oscillator

Figure7. General Form of Three-terminal Oscillator

The basic circuit is the so-called three-terminal (also called three-point) oscillator, which means the circuit formed by connecting the three terminals of the LC loop and the three electrodes of the transistor respectively, as shown in the figure.

The three-terminal LC oscillator is a feedback type LC oscillator. In order to obtain positive feedback, the feedback circuit must make the instantaneous polarity of the transistor's AC voltage meet a certain phase relationship: when Vbe is negative, Vce should be positive, namely, Vbe and Vce are in reverse phase, and Veb and Vce are in phase. Only when the reactance Xce and Xeb have the same properties can they be guaranteed to be in phase.

When the resistance of the loop element is very small, its influence can be ignored, and the influence of the input impedance and output impedance of the transistor can also be ignored. To maintain oscillation, the circuit must meet the requirements. Otherwise, the loop resonance condition cannot be met.

- The criteria for the three-terminal oscillator circuit to meet the phase equilibrium condition is as follows:

(1) The reactance properties of Xce and Xeb are the same, but the reactance properties of Xcb are opposite. That is, ce and be are the same resisting piece, and cb resisting piece.

(2) The oscillation frequency should satisfy 1Xo+Xcl-Xol

Based on this criterion, it can be quickly judged whether the oscillating circuit composition is reasonable or not.

- Three-terminal LC oscillator

The three-terminal LC oscillation circuit is often used, and its operating frequency is about a few MHz to a few hundred MHz. The frequency stability is also higher than that of the transformer coupled oscillation circuit, which is about 10-3~10-4. After some frequency stabilization measures, it can be higher.

There are many types of three-terminal LC oscillators, mainly:

Inductance three-terminal type, also known as Hartley oscillator; capacitor three-terminal type, also known as Colpitts oscillator; series type improved capacitor three-terminal type, also known as Clapp parallel type improved capacitor three-terminal type , Also known as Sellier oscillator.

The three-terminal oscillator has two basic circuits, as shown in the figure below.

Figure8. Capacitive Feedback Oscillator and Inductive Feedback Oscillator

### 2.2 Capacitive Feedback Oscillator

Capacitive feedback three-terminal oscillator is an electronic component, also called Colpitts oscillator, which is a kind of self-excited oscillator. It is composed of a series capacitor, an inductance circuit and a positive feedback amplifier. It is named because the three end points of the two series capacitors of the oscillating circuit are connected to the three pins of the oscillating tube respectively.

Figure9. Capacitive Feedback Oscillator

As shown in the figure, use C2 to feed back part of the voltage of the resonant tank to the base. The three end points of the LC resonant tank are respectively connected to the three electrodes of the transistor, so it is called a capacitive feedback three-terminal oscillator, or Colpitts oscillator.

The vector analysis method can be used to prove that the circuit meets the phase balance condition. As long as the ratio of C1 and C2 is appropriately selected and the amplifier has enough amplification, the circuit can oscillate.

Figure10. Capacitive Feedback Oscillator

- Advantages of Colpitts circuit:

(1) Good oscillation waveform;

(2) The frequency stability of the circuit is high. If the capacitance of the circuit is increased appropriately, the influence of unstable factors on the oscillation frequency can be reduced;

(3) The operating frequency of the three-terminal circuit of the capacitor can be made higher. The output and input capacitors of the oscillator tube can be directly used as the oscillation capacitor of the loop, and the operating frequency can reach a very high frequency range of tens of MHz to hundreds of МHz. .

Disadvantages of Colpitts circuit:

When adjusting C1 and C2 to change the oscillation frequency, the feedback coefficient will also change, which will affect the starting conditions and working status. But as long as a variable capacitor is connected to both ends of L and C1 and C2 are fixed capacitors, the feedback coefficient will not be affected when the frequency is adjusted.

### 2.3 Inductive feedback oscillator

(1) Circuit composition

In order to overcome the shortcomings that the transformer primary coil and the secondary coil in the transformer feedback oscillation circuit are not tightly coupled, the N1 and N2 of the transformer feedback oscillation circuit can be combined into one coil. As shown in the figure below, in order to strengthen the resonance effect, the capacitor C is connected across the entire coil. This is the inductive feedback oscillator circuit, or Harley oscillator.

Figure11. Inductive Feedback Oscillator Circuit

(2) Working principle

★The circuit includes four parts: amplifier circuit, frequency selection network, feedback network and non-linear element (transistor), and the amplifier circuit can work normally.

★Use the instantaneous polarity method to judge whether the circuit meets the phase condition of sine wave oscillation: disconnect the feedback, add the input voltage with frequency f0, give its polarity, and judge that the polarity of the feedback voltage obtained from N2 is the same as the input voltage , So the circuit satisfies the phase condition of sine wave oscillation.

★As long as the circuit parameters are selected properly, the circuit can meet the amplitude condition and produce sine wave oscillation.

The following figure shows the AC path of the inductive feedback oscillation circuit. The three ends of the primary coil are connected to the three poles of the transistor, so the inductive feedback oscillation circuit is called an inductive three-point circuit.

Figure12. AC Path of Inductive Feedback Oscillator Circuit

(3) Advantages and disadvantages

The coupling between N2 and N1 in the inductance feedback oscillation circuit is tight, the amplitude is large, and it is easy to oscillate; when C uses a variable capacitor, a wide adjustment range of oscillation frequency can be obtained, and the highest oscillation frequency can reach tens of MHz. Since the feedback voltage is taken from inductance, it has greater reactance to high-frequency signals, and the feedback signal contains more high-order harmonic components, and the output voltage waveform is not good.

The following introduces two improved capacitor three-terminal oscillation circuits:

**Clap oscillator:**

The following figure (a) is the principle circuit of the Krapper oscillator, and (b) is its AC equivalent circuit. Its characteristic is that a capacitor C3 is added to the inductance branch of the aforementioned capacitive three-point oscillating resonant tank. Its value is relatively small, requiring C3<< C1, C3<< C2.

Figure13. Clapp Oscillator

Regardless of the influence of the capacitance between the poles, the total capacitance CΣ of the resonant circuit is the series connection of C1, C2 and C3, namely. Thus, the oscillation frequency is .

The condition for the above formula to be true is that C1 and C2 must be selected relatively large. It can be seen that the influence of C1 and C2 on the oscillation frequency is significantly reduced, so the influence of the capacitance between the transistors connected in parallel with C1 and C2 is also very large. It is smaller, and the stability of the oscillation frequency is improved.

**Sellier oscillator:**

Figure14. Sellier Oscillator

so the oscillation frequency:

L is the inductance of the inductance coil of the resonant amplifier circuit; C is the total capacitance of the resonant circuit. In the LC resonance circuit, the inductance L(H)/capacitance C(F)=10^{5}~10^{6}, which can achieve better results.

## III RC Oscillator Circuit

### 3.1 Brief Introduction of RC Oscillator and its Circuit

● What is an RC oscillator?

(1) The sine wave oscillator has no input signal and is a positive feedback amplifier with a frequency selection network. If resistors and capacitors are used to form a frequency selection network, it is called an RC oscillator, which is generally used to generate 1Hz-1MHz low-frequency signals. The frequency selection effect of the RC frequency selection network is not as good as that of the LC resonant circuit, so the waveform and stability of the RC oscillator are worse than that of the LC oscillator.

(2) RC oscillator can be divided into sine wave oscillator and non-sine wave oscillator according to whether the output wave type is sine wave.

(3) There are many kinds of RC oscillation circuits: bridge type, phase shift type, double T type, the most commonly used is bridge type oscillation circuit, namely RC series-parallel frequency selection network.

● Features of RC oscillator

(1) RC phase-shift oscillator features: simple, poor frequency selection, unstable amplitude, inconvenient frequency adjustment, generally used in occasions with fixed frequency and low stability requirements. Frequency range: several hertz-tens of kilohertz

(2) RC series-parallel network oscillator features: it can easily and continuously change the oscillation frequency, it is convenient to add negative feedback to stabilize the amplitude, and it is easy to get a good oscillation waveform.

(3) Double T frequency selective network oscillator characteristics: good frequency selection characteristics, difficult frequency modulation, suitable for generating single frequency oscillation.

● RC oscillator circuit

The oscillating circuit composed of RC frequency selection network is called RC oscillating circuit, which is suitable for low-frequency oscillation, and is generally used to generate low-frequency signals of 1Hz~1MHz. The circuit is composed of four parts: amplifier circuit, frequency selection network, positive feedback network, and amplitude stabilization link. The main advantage is simple structure, economic and convenient. According to the different forms of the RC frequency selection network, the RC oscillator circuit can be divided into an RC lead (or lag) phase shift oscillator circuit and a Wien circuit oscillator circuit.

For RC oscillator circuits, increasing the resistance R can reduce the oscillation frequency, and increasing the resistance does not need to increase the cost. The frequency of the sine wave generated by the commonly used LC oscillator circuit is relatively high. If a sine wave with a lower frequency is to be generated, the oscillation circuit must have a larger inductance and capacitance. This will not only cause the components to be bulky, heavy and inconvenient to install, but also difficult to manufacture. high cost. Therefore, the sinusoidal oscillation circuit below 200kHz generally adopts an RC oscillation circuit with a lower oscillation frequency.

### 3.2 RC Phase Shift Oscillator

The phase shift oscillator is an oscillator composed of an advanced phase shift or a lag phase shift circuit as a frequency selection network and an inverting amplifier. It has the advantages of simple circuit, economy and convenience, but the effect of frequency selection is poor, the amplitude is not stable enough, and the frequency adjustment is inconvenient. Therefore, it is generally used for occasions with fixed frequency and low stability requirements. Its oscillation frequency is:

Figure15. RC Phase Shift Oscillator Schematic Diagram

### 3.3 Wien Bridge Oscillator

The RC series-parallel frequency selection network and amplifier can be combined to form an RC oscillator circuit, and the amplifier part can be an integrated operational amplifier.

As shown in the figure, the RC series-parallel frequency selection network is connected between the output of the operational amplifier and the non-inverting input to form positive feedback. Rt and R1 are connected between the output of the operational amplifier and the inverting input to form negative feedback. . The positive feedback circuit and the negative feedback circuit constitute a Wien bridge circuit, and the input and output ends of the operational amplifier are respectively connected across the diagonal of the bridge. Therefore, this kind of oscillation circuit is called a Wien bridge oscillation circuit.

Figure16. Wien Bridge Oscillator

The oscillating signal is input from the non-inverting terminal, so a non-inverting amplifier is formed. The output voltage is in phase with the input voltage, and the closed-loop voltage amplification factor is equal to:

When the RC series-parallel frequency selection network is ω=ω0=1/RC, Fu=1/3, εf=0, so as long as |Au|=1+(Rt/R1)>3, that is, Rt>2R1, oscillation The circuit can meet the self-excited oscillation amplitude and phase start-up conditions to produce self-excited oscillation, the oscillation frequency f0=1/2πRC.

Using double adjustable potentiometer or double adjustable capacitor can easily adjust the oscillation frequency. In the commonly used RC oscillator circuit, the high stability capacitor is generally used to switch the frequency band (coarse frequency adjustment), and then the double variable potentiometer is used to fine-tune the frequency.

## IV Quartz Crystal Oscillator Circuit

### 4.1 What is a Quartz Crystal Oscillator?

Quartz crystal oscillator refers to a device made on the principle that the crystal resonates due to the piezoelectric effect when the frequency of the electrical signal is equal to the natural frequency of the quartz crystal. It is a key component of crystal oscillators and narrow-band filters.

Although the appearance, size and frequency of the quartz crystal oscillator are different, the structure principle is basically the same. In order to improve the stable and reliable operation of the quartz crystal, the shell components of the quartz crystal oscillator will be sealed and evacuated. Or fill with nitrogen.

### 4.2 Quartz Crystal

(1) Structure

Figure17. Structure of the Quartz Crystal

(2) Basic characteristics

Applying an electric field between the plates→mechanical deformation of the crystal

Mechanical force is applied between the plates → the crystal generates an electric field

Piezoelectric effect: alternating voltage → mechanical vibration → alternating voltage

When the alternating voltage frequency = natural frequency, the amplitude is the largest → piezoelectric resonance

The natural frequency of mechanical vibration is related to the size of the wafer, and the stability is high.

### 4.3 Quartz Crystal Oscillator Circuit

The high quality factor of quartz crystal is used to form an LC oscillator circuit.

(1) Parallel Type quartz crystal oscillator

Figure18. Parallel Type Quartz Crystal Oscillator

Quartz crystal works between fs and fp, which is quite a large inductance, and forms a capacitive three-point oscillator with C1 and C2. Because the Q value of the quartz crystal is very high, which can reach more than several thousand, the circuit can obtain high oscillation frequency stability.

Figure19. Frequency Characteristics of Parallel Quartz Crystal Oscillator

(2) Series type quartz crystal oscillator

Figure20. Series Type Quartz Crystal Oscillator Circuit

The quartz crystal works at fs, which is resistive, and has the smallest impedance, the strongest positive feedback, and zero phase shift, which meets the phase balance condition of oscillation.

For frequencies other than fs, the impedance of the quartz crystal increases, and the phase shift is not zero, then the oscillation condition is not met, and the circuit does not oscillate.

Figure21. Frequency Characteristics of Series Quartz Crystal Oscillator

## V Non-sine Wave Generating Circuit

### 5.1 What is a Non-sine Wave Generating Circuit?

It is composed of an integrating circuit and a hysteresis comparator circuit. The role of the integrator circuit is to produce a transient process. The hysteresis comparator acts as a switch, that is, the steady state is destroyed by the continuous closing of the switch, and a transient process is generated.

Commonly used non-sine wave generating circuits include rectangular wave generating circuits, triangular wave generating circuits and sawtooth wave generating circuits, etc. They are often used as signal sources in pulse and digital systems.

### 5.2 Rectangular Wave Generator

It is composed of hysteresis comparison circuit and RC timing circuit. The output has no steady state and there are two transient states; if the output is high level, it is defined as the first transient state, and the output is low level as the second transient state.

Basic components:

(1) Switching circuit: The output has only two situations of high level and low level, called two states; therefore, a voltage comparator is used.

(2) Feedback network: self-control, when the output is in a certain state, it breeds the condition of turning into another state. Feedback should be introduced.

(3) Delay link: Make the two states maintain a certain period of time and determine the oscillation frequency. Use RC circuit to achieve.

Circuit composition:

Figure22. Rectangular Wave Generating Circuit

### 5.3 Triangle Wave and Sawtooth Wave Signal Generator

The circuit structure of the triangle wave generator: hysteresis comparator + inverting integrator

working principle:

Figure23. Circuit of Triangle Wave Generator

Sawtooth wave generator: change the forward and reverse charging time constant of the integrator, thereby changing the duty cycle.

Figure24. Circuit Diagram of Sawtooth Generator

uo1=+UZ, D is cut off, charging time constant: R4C.

uo1=-UZ, D is on, charging time constant: (R6∥R4)C≈R6C.

Figure25. The Waveform of the Sawtooth Generator

## VI Quiz

LC resonant circuits are used in:

a) RF and ultrasonic oscillators.

b) AF and ultrasonic oscillators.

c) LF sweep oscillators.

d) Variable frequency crystal oscillators.

Answer: a

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