What is the minimum gain needed for the oscillator to oscillate?

The voltage gain of the amplifier circuit MUST be equal too or greater than three “Gain = 3” for oscillations to start because as we have seen above, the input is 1/3 of the output.

What is Q in Colpitts oscillator?

In general, oscillator PN depends on Q (quality factor) of the energy storing device frequently called resonator tank circuit and the applied DC-bias (voltage/current) condition. Colpitts oscillator topology is known for high frequency low phase noise signal sources, it comes in 3-flavors.

How does Colpitts oscillator work?

Oscillator is an amplifier with the positive feedback and it converts DC input signal into AC output waveform with certain variable frequency drive and certain shape of output waveform (like sine wave or square wave, etc) by using the positive feedback instead of input signal.

What is the loop gain of an oscillator?

In oscillators using positive feedback it is important that amplitude of the oscillator output remains stable. Therefore the closed loop gain must be 1 (unity). In other words, the gain within the loop (provided by the amplifier) should exactly match the losses (caused by the feedback circuit) within the loop.

What is the voltage gain condition for oscillator to start up?

For oscillation to begin, the voltage gain around the positive feedback loop must be greater than 1 so that the amplitude of the output can build up to a desired level. The gain must then decrease to 1 so that the output stays at the desired level and oscillation is sustained.

Which is the formula for the frequency of oscillation of Colpitts oscillator?

The frequency of the oscillator can be from around 500 KHz to 2 MHz depending on the values chosen for C1, C2 and L1. Start with L1 = 100 uH and C1 = 4.7 nF and C2 = 1 nF. This oscillator circuit can produce a sine wave output in excess of 10 Vpp at an approximate frequency set by the value chosen for L1.

How is positive feedback supplied in a Colpitts oscillator?

In a Colpitts oscillator (shown below), positive feedback is supplied through a capacitive divider.

What is Q factor of crystal?

Q is the short form of Quality. This Q factor determines Crystal’s frequency stability. In general, the Q factor of a crystal has a range from 20, 000 to more than 100,000. Sometimes, the Q factor of a crystal is more than 200,000 also observable.

How do you find the frequency of oscillation in Colpitts oscillator?

What feedback method is used in the Colpitts oscillator?

Voltage series feedback is used in Colpitts oscillator. In voltage series feedback a part of output voltage is fed back to input.

What is loop gain formula?

The loop gain is calculated by imagining the feedback loop is broken at some point, and calculating the net gain if a signal is applied. In the diagram shown, the loop gain is the product of the gains of the amplifier and the feedback network, −Aβ.

What is gain of oscillator?

How do you calculate frequency in Hartley oscillator?

In this circuit, we calculate a hartley oscillator frequency based on the formula, frequency= 1/2π√ LtC , where C is the value of the capacitor and LT is the equivalent inductance of the inductors in series. The equivalent inductance in series is equal to the sum of both inductors together.

How the feedback is obtained in a Colpitts oscillator?

Then to summarise, the Colpitts Oscillator consists of a parallel LC resonator tank circuit whose feedback is achieved by way of a capacitive divider. Like most oscillator circuits, the Colpitts oscillator exists in several forms, with the most common form being similar to the transistor circuit above.

Why positive feedback is necessary for oscillation?

Positive feedback is used in oscillator to satisfy Barkhausen’s Criteria in order to produce sustain oscillations. Oscillator produces sinusoidal waveform without any input signal hence starting voltage is noise signal which may be due to resistor’s, power supply.

How is positive feedback correlated with oscillation?

These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity.

How to realize a Colpitts oscillator?

Apart from the BJT -based Colpitts Oscillator shown, they are also realizable using valves or FET (Field Effect Transistor) or Op-Amp. Figure 2 shows such a Colpitts oscillator which uses an Op-Amp in inverting configuration in its amplifier section.

What is the antiresonant frequency of a Colpitts oscillator?

This means that for the oscillator to start, the voltage gain A v must satisfy the above condition in terms of capacitance ratios. The antiresonant frequency of the Colpitts oscillator occurs when the reactance presented by the inductance, and total capacitance, are equal.

What is the gain of an op-amp based oscillator?

The gain of the opamp based oscillator can be individually set using the components Rf and R1 and it is a great advantage. The gain of an inverting op-amp amplifer is given by the equation; A = -Rf/R1.

What is the gain of an inverting op-amp?

The opamp is arranged in the inverting mode where R1 is the input resistor and Rf is the feedback resistor. The gain of the opamp based oscillator can be individually set using the components Rf and R1 and it is a great advantage. The gain of an inverting op-amp amplifer is given by the equation; A = -Rf/R1.