Lc oscillators pdf

The first practical oscillators were based on electric arcs, which were used for lighting in the 19th century. The current through an arc light is unstable due to its negative resistance, and often breaks into spontaneous oscillations, causing the arc to make hissing, humming or howling sounds [9] which had been noticed by Humphry Davy in , Benjamin Silliman in , [10] Auguste Arthur de la Rive in , [11] and David Edward Hughes in Independently, in the same year, George Francis FitzGerald realized that if the damping resistance in a resonant circuit could be made zero or negative, the circuit would produce oscillations, and, unsuccessfully, tried to build a negative resistance oscillator with a dynamo, what would now be called a parametric oscillator.

He attached an LC circuit tuned circuit to the electrodes of an arc lamp, and the negative resistance of the arc excited oscillation in the tuned circuit. Duddell demonstrated his oscillator before the London Institute of Electrical Engineers by sequentially connecting different tuned circuits across the arc to play the national anthem 'God Save the Queen'. In Danish physicists Valdemar Poulsen and P.

Pederson were able to increase the frequency produced into the radio range by operating the arc in a hydrogen atmosphere with a magnetic field, inventing the Poulsen arcradio transmitter, the first continuous wave radio transmitter, which was used through the s. The vacuum-tube feedback oscillator was invented around , when it was discovered that feedback 'regeneration' in the recently invented audionvacuum tube could produce oscillations.

At least six researchers independently made this discovery, although not all of them can be said to have a role in the invention of the oscillator. Round patented amplifying and oscillating circuits in The first and most widely used relaxation oscillator circuit, the astable multivibrator, was invented in by French engineers Henri Abraham and Eugene Bloch. Vacuum-tube feedback oscillators became the basis of radio transmission by However, the triode vacuum tube oscillator performed poorly above MHz because of interelectrode capacitance.

The first of these was the Barkhausen—Kurz oscillator , the first tube to produce power in the UHF range. The most important and widely used were the klystron R. Varian, and the cavity magnetron J. Randall and H. Boot, Mathematical conditions for feedback oscillations, now called the Barkhausen criterion, were derived by Heinrich Georg Barkhausen in The first analysis of a nonlinear electronic oscillator model, the Van der Pol oscillator, was done by Balthasar van der Pol in He originated the term 'relaxation oscillation' and was first to distinguish between linear and relaxation oscillators.

The leading edge of this square wave is used to derive a reset pulse to discharge the capacitor in the oscillator's ramp core. This ensures that the ramp waveform produced is of the same frequency as the counter output. For a given capacitor charging current, the amplitude of the output waveform will decrease linearly with frequency.

In musical terms, this means a waveform an octave higher in pitch is of half the amplitude. In order to produce a constant amplitude over the full range of the oscillator, some compensation scheme must be employed. This is often done by controlling the charging current from the same microprocessor that controls the counter reset value. Sometimes we need a timed signal to use as a clock but alsofor other things. General theory A very popular local oscillator circuit that is mostly used in radio receivers is the Hartley Oscillator circuit.

The Barkhausen stability criterionsays that the loop gain exceeds unity at the resonant frequency the fase shift around the loop is where bad enough seems that the Barkhausen Stability Criterion is simple, intuitive, and wrong. Confusion over terminology [ edit ] The term 'digitally controlled oscillator' has been used [ citation needed ] to describe the combination of a voltage-controlled oscillator driven by a control signal from a digital-to-analog converter, and is also sometimes used to describe numerically controlled oscillators.

Relation to earlier VCO designs [ edit ] Many voltage-controlled oscillators for electronic music are based on a capacitor charging linearly in an op-amp integrator configuration. Historical context [ edit ] In the early s, many manufacturers were beginning to produce polyphonic synthesizers. Problems with the design [ edit ] For a given capacitor charging current, the amplitude of the output waveform will decrease linearly with frequency. Musical Applications of Microprocessors.

Sound Synthesis and Sampling. Motorola Manuals User Manuals. The tuned circuit is a resonator consisting of an inductor L and a capacitor C connected together.

Charge flows back and forth between the capacitor's plates through the inductor, so the tuned circuit can store electrical energy oscillating at its resonant frequency. There are small losses in the tank circuit, but the amplifier compensates for those losses and supplies the power for the output signal. LC oscillators are often used at radio frequencies, when a tunable frequency source is necessary, such as in signal generators, tunable radio transmitters and the local oscillators in radio receivers.

In an LC oscillator, the feedback network is mainly composed of three impedances see figure 1. All three impedances Z1, Z2 and Z3 are pure reactance elements, implying that they can be either capacitive or inductive, depending on our design needs.

In figure 1, for convenience, we have shown the amplifying element as an operational amp, but other devices could be also used. For example, if Z1 and Z2 were capacitors, then Z3 would be an inductor; if Z1 and Z2 were inductors, then Z3 would be a capacitor.

At this point, it is a good idea to remind that the necessary conditions for oscillation are:. In general, both the amplifier and the feedback network will alter the magnitude and the phase of the signal. So, both A and B are complex values, and each value has magnitude and argument phase.

The Colpitts oscillator was invented in by the American engineer Edwin H. The Colpitts circuit, like other LC oscillators, consists of a gain device such as a bipolar junction transistor, field effect transistor, operational amplifier, or vacuum tube with its output connected to its input in a feedback loop containing a parallel LC circuit tuned circuit which functions as a bandpass filter to set the frequency of oscillation.

The frequency of oscillation is actually the resonance frequency. At resonance, total capacitive and total inductive reactances, are canceled out:. The term C, is equivalent to the series combination of C1 and C2 in the standard manner:. Thus, the mathematical expression for B fo is given by:. By using an inverting amplifier which also provides o of phase shift , there is no doubt that the condition stated by equation 3 , is well satisfied.

In our example, the amplifier is an inverting amplifier, based on an op-amp. So, its voltage gain is given by:. By choosing the minimum gain, the total loop gain will be equal to 1 and the amplitude of the oscillations will remain constant. However, there are inevitable tolerances. So, in practice, we must choose a much greater gain, to ensure that oscillations will always start-up. At a much greater gain, the amplitude of the oscillations will rapidly grow up with time, until the amplifier will be saturated and it will start clipping.

The Hartley oscillator was invented in by American engineer Ralph Hartley. The distinguishing feature of the Hartley oscillator is that the tuned circuit consists of a single capacitor in parallel with two inductors in series or a single tapped inductor , and the feedback signal needed for oscillation is taken from the center connection of the two inductors.

The classic Hartley oscillator is shown in Figure 3.