Introduction to LC Oscillators

LC Oscillators are electronic circuits that form a continuous periodic waveform at a precise frequency.

Oscillators convert a DC input (feed voltage) into an AC output (waveform). This output waveform can have a wide variety of different shapes and frequencies, and depending on the application, it can be complex in shape or a simple pure sine wave.

Oscillators are used in many test equipment that produce sinusoidal sinus waves, square, saw tooth or triangular shaped waveforms, or only a series of repetitive pulses of varying or constant width. LC Oscillators are widely used in radio frequency circuits due to their good phase noise properties and ease of application.

An Oscillator is basically an amplifier with "Positive Feedback" or regenerative feedback (in-phase), and one of the many problems in electronic circuit design is to stop the release of amplifiers when trying to ensure the release of oscillators.

Oscillators work by applying DC energy to this resonator circuit at the required frequency, eliminating the losses of the feedback resonator circuit in the form of either capacitor, inductor or both in the same circuit. In other words, an oscillator is an amplifier that uses positive feedback, which produces an output frequency without using an input signal.

Therefore, oscillators are self-sustaining circuits that produce a periodic output waveform at a certain frequency, and any electronic circuit must have the following three features for it to function as an oscillator.

  • Any type of amplification
  • Positive feedback (regeneration)
  • Frequency determination feedback network

An oscillator has a small signal feedback booster with an open loop gain of more than one or slightly larger for oscillations to begin, but the average cycle gain must continue to maintain oscillations. In addition to these reactive components, an amplifier device such as OPAMP or Bipolar Transistor is required.

Unlike an amplifier, external AC input is not required to ensure the operation of the oscillator, since dc feed energy is converted by the oscillator to AC energy at the required frequency.

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Basic Oscillator Feedback Circuit

Here: β is the feedback coefficient.

Non-Feedback Oscillator Gain

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Here: A is open circuit voltage gain.

Feedback Oscillator Gain

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Here: β is the feedback coefficient. Aβ is cycle gain. 1+Aβ is the feedback factor. Gv is a closed loop gain.

Oscillators are circuits that produce a frequency-selective LC resonance tank circuit and a continuous voltage output waveform at the required frequency with inductor, capacitor or resistance values forming a feedback network. This feedback network is <1) kazancı="" olan="" ve="" aβ="">a slimming network that initiates oscillations when it is suddenly (β 1 and returns to Aβ=1 when oscillations begin.</1)>

The frequency of LC oscillators is controlled using the adjusted or resonant inductive/capacitive (LC) circuit, and the resulting output frequency is known as the Oscillation Frequency. By making oscillators a reactive network feedback, the phase angle of the feedback will change to a function of the frequency, and this is called Phase shift.

Basically, there are types of oscillators:

  1. Sinusoidal Oscillators – these are known as Harmonic Oscillators and are type Oscillators of the type "LC Adjusted-feedback" or "RC-set feedback", which usually produce a completely sinusoidal waveform with constant amplitude and frequency.
  2. Non-Sinusoidal Oscillators – these are known as Relaxation Oscillators and produce complex non-sinusoidal waveforms that change very quickly from one stability condition such as "Square-wave", "Triangular-wave" or "Saw-tooth-wave" to another.

Oscillator Resonance

When a constant voltage is applied to a circuit consisting of an inductor, capacitor and resistance, but at a changing frequency, the reactor of both capacitor/resistance and inductor/resistance circuits is to change both the amplitude and phase of the output signal compared to the previous circuit.

At high frequencies, the colorance of a capacitor is very low as a short circuit, while the coloring of the inductor acts as an open circuit. At low frequencies, the opposite is true, the shutter of the capacitor acts as an open circuit and the inductor's coloring acts as a short circuit.

Between these two ends, the combination of inductor and capacitor produces a "Resonance" circuit with a Resonance Frequency (εr) in which capacitive and inductive reactance are equal and destroy each other, leaving only resistance, and prevents the flow of the current. This means that there is no phase shift as the current is in the same phase as the voltage.

Basic LC Oscillator Tank Circuit

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The circuit consists of an inductive coil, L and a capacitor, C. The capacitor stores energy in the form of an electrostatic field and stores inductive coil energy in the form of an electromagnetic field, while producing a potential (static voltage) along its plates. The capacitor is charged up to DC supply voltage (V) by switching to position A. When the capacitor is fully charged, the switch switch switches to position B.

The loaded capacitor is now connected parallel to the inductive coil so that the capacitor begins to empty itself from the coil. When the current passing through the coil begins to rise, the voltage on the C begins to decrease.

This rising current creates an electromagnetic field around the coil that resists this current flow. When the capacitor completely drains the energy stored in the capacitor at startup C, C is now stored as an electromagnetic field in the inductive coil, around the L coil windings.

Since there is no external voltage to maintain the current inside the coil, the electromagnetic field begins to fall. In the coil (e = -Ldi/dt) a back impetus is induced and the current flows in the original direction.

This current charges the capacitor, C, with the opposite polarity of its original load. C continues to charge until the current drops to zero and the electromagnetic field of the coil completely collapses.

The energy initially activated through the switch is returned to the capacitor, which, although now at the opposite pole, still has the potential for an electrostatic voltage on it. The capacitor now begins to drain again through the coil, and the whole process is repeated. The polarity of the voltage changes as the energy is transmitted back and forth between the capacitor and the inductor that produces ac-type sinusoidal voltage and current waveform.

This process then forms the basis of the tank circuit of LC oscillators, and theoretically this back-and-forth cycle will continue indefinitely. However, when the energy is transferred from the capacitor, inductor and inductor to the capacitor, some energy losses occur, which reduces the oscillations to zero over time.

This oscillation movement between the capacitor (C) regarding the back and forth transition of energy to the inductor (L) would have continued indefinitely if not for energy losses in the circuit. Electrical energy is lost in DC or at the actual resistance of the inductor coil, insulating the capacitor and in the radiation from the circuit, thereby continuously reducing the oscillation until it is completely finished and the process stops.

Then, in a practical LC circuit, the amplitude of the oscillation voltage decreases with each half cycle of oscillation and eventually drops to zero. Oscillations are then said to be "dampened" by the quality of the circuit or the amount of damping determined by the Q factor.

Dampened Oscillations

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The frequency of the oscillation voltage depends on the inductans and capacitance value in the LC tank circuit. Now we know that in order for resonance to occur in the tank circuit, there must be a frequency point of XC, capacitive reacqueence is the same as XL, inductive reacquence (XL = XC ) and therefore they remove each other only by leaving DC resistance in the circuit to counter the flow of the current that will cancel.

Now if we place the inductive reacquer curve of the inductor above the capacitor's capacitive reactance curve, so that both curves are on the same frequency axes, the intersection gives us the resonant frequency point, ( εr or ωr ) As shown below:

Resonance Frequency

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Where: εr is in Hertz, L is in Henry, and C is in Farad.

Then the calculated frequency of this is given as follows:

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Then, by simplifying the equation above, we get the final equation for Resonance Frequency, εr in an adjusted LC circuit as follows:

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Where: εr is in Hertz, L is in Henry, and C is in Farad.

In this equation, if L or C decreases, it indicates that the frequency increases. This output frequency is usually abbreviated to (εr) to define it as "resonance frequency".

To maintain oscillations in an LC tank circuit, we need to replace all the energy lost in each oscillation, as well as keep the amplitude of these oscillations at a constant level. Therefore, the amount of energy changed should be equal to the energy lost during each cycle.

If the altered energy is too large, the amplitude will increase until the supply rails are cut off. Alternatively, if the amount of energy changed is too small, the amplitude will gradually decrease to zero and the oscillations will stop.

The simplest way to replace this lost energy is to take some of the output from the LC tank circuit, upgrade it and then feed it back to the LC circuit. This can be performed using a voltage amplifier that uses an OPAMP, FET or bipolar transistor as its active device. However, if the cycle gain of the feedback amplifier is too small, the desired oscillation drops to zero, and if it is too large, the waveform is disturbed.

To produce a constant oscillation, the level of energy fed back into the LC network must be accurately controlled. Then, when amplitude tries to change up or down from a reference voltage, there should be some kind of automatic amplitude or gain control.

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Basic Transistor LC Oscillator Circuit

A Bipolar Transistor is used as an LC oscillator amplifier and the tuned LC tank circuit serves as collector load. Another coil L2connects the electromagnetic field between the base and the emitor of the transistor, which is "mutually" connected by that of the coil L.

There is a "mutual inductace" between the two circuits, and the changing current flowing in one coil circuit induces a potential voltage in the other with electromagnetic induction (transformer effect) so that electromagnetic energy is transferred from the coil as oscillations occur in the tuned circuit. A voltage is applied from L to L2 coil and at the same frequency as in the circuit set between the base and the transmittor. In this way, the amplifier applies the required automatic feedback voltage to the transistor.

The amount of feedback can be increased or reduced by changing the coupling between the two coils L and L2. The impedance is resistant when the circuit oscillates and the collector and base voltages are 180o out of phase. To maintain oscillations (called frequency stability), the voltage applied to the adjusted circuit must be "in the same phase" as the oscillations occurring in the tuned circuit.

Therefore, we must add an additional 180 o phase shifts to the feedback path between the collector andthe base. This is achieved by wrapping the L2 coil in the right direction according to the coil L, which gives us the correct amplitude and phase relationships for the oscillator circuit, or by connecting a phase shift network between the output and input of the amplifier.

The LC Oscillator is therefore a "Sinusoidal Oscillator" or a "Harmonic Oscillator", as it is more commonly called. LC oscillators can produce high frequency sinus waves for use in radio frequency (RF) type applications with a Bipolar Transistor or transistor amplifier with FET.

Harmonic Oscillators come in many different forms because there are many different ways to create an LC filter network and amplifier, the most common of which are Hartley LC Oscillator, Colpitts LC Oscillator, Armstrong Oscillator and Clapp Oscillator.

LC Oscillator Question Sample 1

A 200mH inducing and a 10pF capacitor are connected in parallel to form an LC oscillator tank circuit. Calculate the oscillation frequency.

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Then from the example above, we can see that by reducing the value of capacitance, C or inductancy, L will have the effect of increasing the oscillation frequency of the LC tank circuit.


The basic conditions for an LC oscillator resonance tank circuit are given below.

  • For oscillations to exist, an oscillator circuit must include a DC power supply, as well as an "Inductor", (L) or a "Capacitor", (C) reactive (frequency-dependent) component.
  • In the LC circuit, which is a simple inductor-capacitor, oscillations are dampened over time due to component and circuit losses.
  • Voltage amplification is required to overcome these circuit losses and achieve positive gain.
  • The amplifier's total gain must be greater than one.
  • Oscillations can be maintained by feeding back into the circuit, which is set at the correct amplitude and in the same phase (0o)as part of the output voltage.
  • Oscillations can occur only when feedback is "Positive" (self-renewal).
  • The overall phase shift of the circuit should be zero or 360o, so that the output signal from the feedback network will be "in the same phase" as the input signal.
  • In the next tutorial about oscillators, we will examine the work of one of the most common LC oscillator circuits, which uses two inducent coils to create a central stage induct in the resonance tank circuit. This type of LC oscillator circuit is commonly known as the Hartley Oscillator.