In the field of high-frequency electronic circuits, LC sine wave oscillators are widely used and come in several types, including the inductive feedback three-terminal oscillator, capacitive feedback three-terminal oscillator, and improved versions such as the Clapp oscillator and the Colpitts oscillator. Each type has its own advantages and disadvantages. The inductive feedback oscillator is easy to start due to mutual inductance between the coils, but it suffers from poor stability and is typically suited for low-frequency applications. On the other hand, the capacitive feedback oscillator offers better stability, produces a cleaner output waveform, and can operate at higher frequencies. This discussion will focus primarily on the LC three-terminal oscillator.
**First, the Inductive Feedback Three-Terminal Oscillator**
The inductive feedback oscillator, as shown in Figure 1, is characterized by its ease of starting because of the mutual inductance between L1 and L2. Another advantage is that when adjusting the frequency by changing the loop capacitance, the feedback coefficient remains largely unaffected, making it more convenient for tuning.
**Second, the Capacitive Feedback Three-Terminal Oscillator**
Also known as the Colpitts oscillator, this circuit is depicted in Figure 2. The feedback coefficient (F) is determined by the series combination of C1 and C2, resulting in an effective total capacitance given by:
$$ C = \frac{C_1 \cdot C_2}{C_1 + C_2} $$
The approximate oscillation frequency is calculated using:
$$ f = \frac{1}{2\pi\sqrt{LC}} $$
One of the main benefits of the capacitive feedback oscillator is its superior output waveform quality. The collector and base currents can return to the emitter through a low-impedance capacitor branch, which helps suppress harmonic components, leading to a more sinusoidal output. Additionally, unstable capacitances like distributed or junction capacitances are connected in parallel with the circuit, so increasing the circuit capacitance can reduce their impact, improving frequency stability. This makes the capacitive feedback oscillator ideal for high-frequency applications.
**Third, the General Expression of Oscillation Equilibrium Condition**
For an oscillator to function, it must satisfy the condition:
$$ AF = 1 $$
This includes both amplitude balance ($|AF| = 1$) and phase balance conditions.
**Fourth, the Starting Condition and Steady Amplitude Principle**
At startup, the system requires $|AF| \geq 1$ to overcome internal losses. As the amplitude increases, the nonlinear characteristics of the active device help limit the growth, preventing distortion. The frequency selection network plays a key role in selecting the fundamental frequency from the harmonics, ensuring a clean sine wave output. Additional nonlinear stabilization elements can also be added to the feedback network to maintain stable amplitude.
**Fifth, the Basic Working Principle of the LC Oscillator**
An oscillator is a device that converts DC power into AC power without external input. The LC oscillator consists of active components like transistors and passive networks with frequency-selective feedback. It can produce either sinusoidal or non-sinusoidal waveforms. Sinusoidal oscillators are used in communication systems, control devices, and signal generation, while non-sinusoidal ones are used in digital systems and measurement equipment. The block diagram of a basic LC oscillator is shown in Figure 3.
To form an oscillator, three essential conditions must be met:
1. A circuit containing two or more energy storage components, such as inductors and capacitors.
2. A power source to compensate for energy loss in the circuit.
3. A control mechanism, often implemented via positive feedback, to maintain stable oscillations.
**Sixth, the Circuit**
Figure 6 shows the general circuit design of an LC sine wave oscillator. The startup process and waveform are illustrated in Figures 8 and 9, respectively. During testing, components can be shorted or removed to observe how they affect the oscillator’s performance. Researchers also study the frequency range, static operating point, feedback coefficient, load effects, and the impact of temperature and power supply variations on frequency stability. These tests ensure the oscillator operates reliably under different conditions.
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