Oscillator

Oscillator

An Oscillator may be described as a source of Alternating voltage. It is different than Amplifier.

The output signal from an Amplifier has a Waveform similar to the input signal but is stronger in power. The DC power source used to bias the active device provides the extra power present in the output signal.

Since the Amplifier accepts energy from the DC power supply. And Transforms it into energy at the signal Frequency, it can be thought of as an energy Converter. The input signal controls the energy Conversion process,. So if there is no input signal, there will be no energy Conversion and no output signal.

The Oscillator, on the other hand, requires no External signal to Initiate or maintain the energy Conversion process. Instead an output signals is produced as long as source of DC power is connected. Fig. 1, shows the block diagram of an Amplifier and an Oscillator.

Oscillators may be Classified in terms of their output Waveform, Frequency range Components, or circuit Configuration.

It is referred to as a Harmonic Oscillator if the output Waveform is Sinusoidal;. Otherwise, it is referred to as a Relaxation Oscillator, which can produce Waveforms with square, Triangular, and Saw-tooth shapes.

Oscillators employ both active and passive Components. The active Components provide energy Conversion Mechanism. Typical active devices are Transistor, FET etc.

The Frequency of Oscillation is Typically determined by passive Components. Additionally, they affect Stability, which measures how output Frequency (drift) changes with time, temperature, and other Variables. Resistors, Inductors, Capacitors, Transformers, and Resonant crystals are examples of passive devices.

Capacitors used in Oscillators Circuits should be of high quality. Because of low losses.

Damped Oscillation

The inductance and capacitance values in the LC tank circuit determine how frequently the oscillatory voltage occurs. We now understand that in order for resonance to take place in the tank circuit,. There must exist a frequency point. Where the capacitive reactance, XC, and the inductive reactance, XL, are equal to one another (XL = XC),. Cancelling one another out and leaving only the DC resistance in the circuit to oppose the flow of current.

If we now place the curve for inductive reactance on top of the curve for capacitive reactance. So that both curves are on the same axes,. The point of intersection will give us the resonance frequency point, ( ƒr or ωr ) as shown below.

Resonance Frequency

where: ƒr is in Hertz, L is in Henries and C is in Farads. Then the frequency at which this will happen is given as:

Then by simplifying the above equation. We get the final equation for  Resonant Frequency,ƒr in a tuned LC circuit as:

Resonant Frequency of a LC Oscillator

Where:

L is the Inductance in Henries C is the Capacitance in Farads ƒr is the Output Frequency in Hertz

This equation shows that if either L or C are decreased, the frequency increases. This output frequency is commonly given the abbreviation of ( ƒr ) to identify it as the “resonant frequency”. To keep the oscillations going in an LC tank circuit,. We have to replace all the energy lost in each oscillation. And also maintain the amplitude of these oscillations at a constant level.

As a result, the amount of energy replaced must match the energy lost during each cycle. The amplitude would rise if the energy replaced was too much, leading to supply rail clipping. As an alternative, if insufficient energy is replaced, the oscillations would cease as the amplitude eventually decreased to zero.

The simplest way of replacing this lost energy is to take part of the output from the LC tank circuit,. Amplify it and then feed it back into the LC circuit again. This process can be achieved using a voltage amplifier using an op-amp, FET or bi-polar transistor as its active device.

The desired oscillation will, however, decay to zero if the loop gain of the feedback amplifier is too small,. And the waveform will be distorted if it is too large. The level of energy fed back to the LC network needs to be precisely controlled to create a steady oscillation.

Then there must be some form of automatic amplitude or gain control. When the amplitude tries to vary from a reference voltage either up or down. To maintain a stable oscillation the overall gain of the circuit must be equal to one or unity. Any less and the oscillations will not start or die away to zero, any more the oscillations will occur. But the amplitude will become clipped by the supply rails causing distortion. Consider the circuit below.

Basic Transistor LC Oscillator Circuit

A Bi-polar Transistor is used as the LC oscillators amplifier with the tuned LC tank circuit acts as the collector load. Another coil L2 is connected between the base and the emitter of the transistor. Whose electromagnetic field is “mutually” coupled with that of coil L. Mutual inductance exists between the two circuits.

The changing current flowing in one coil circuit induces, by electromagnetic induction, a potential voltage in the other (transformer effect) so as the oscillations occur in the tuned circuit, electromagnetic energy is transferred from coil L to coil L2 and a voltage of the same frequency as that in the tuned circuit is applied between the base and emitter of the transistor.

In this way the necessary automatic feedback voltage is applied to the amplifying transistor. The amount of feedback can be increased or decreased by altering the coupling between the two coils L and L2. When the circuit is oscillating its impedance is resistive and the collector and base voltages are 180 out of phase. In order to maintain oscillations (called frequency stability) the voltage applied to the tuned circuit must be “in-phase” with the oscillations occurring in the tuned circuit.

The feedback path between the collector and the base must therefore be given an additional 180 phase shift. This is accomplished by either connecting a phase shift network between the output and input of the amplifier or by winding the coil of L2 in the proper direction relative to coil L, giving us the correct amplitude and phase relationships for the oscillators circuit.

The LC Oscillator is therefore a “Sinusoidal Oscillator” or a “Harmonic Oscillator” as it is more commonly called. LC oscillators can generate high frequency sine waves for use in radio frequency (RF) type applications with the transistor amplifier being of a Bi-polar Transistor or FET.

The Hartley LC Oscillator, Colpitts LC Oscillator, Armstrong Oscillator, and Clapp Oscillator, to name a few, are the most popular harmonic oscillators. There are many different ways to build an LC filter network and amplifier.

The Hartley Oscillator

The main drawbacks of the simple LC oscillator circuit. We examined in the previous tutorial include the lack of a mechanism for regulating the oscillations’ amplitude and the difficulty of tuning the oscillator to the required frequency.

If L1 and L2’s total electromagnetic coupling is too low,. There won’t be enough feedback, and the oscillations will eventually stop and become zero. Similarly, if the feedback was too strong, the oscillations would keep getting louder until the circuit’s limitations caused signal distortion. As a result, “tuning” the oscillator becomes extremely challenging.

However, it is possible to feedback exactly the right amount of voltage for constant amplitude oscillations. If we feed back more than is necessary the amplitude of the oscillations can be controlled by biasing the amplifier in such a way that if the oscillations increase in amplitude, the bias is increased and the gain of the amplifier is reduced.

If the amplitude of the oscillations decreases the bias decreases and the gain of the amplifier increases, thus increasing the feedback. In this way the amplitude of the oscillations are kept constant using a process known as Automatic Base Bias.

One significant benefit of automatic base bias in a voltage controlled oscillator is that it allows for the provision of a Class-B or even Class-C bias condition of the transistor,. Which can increase the oscillator’s efficiency. The benefit of this is that the quiescent collector current is very low. Because it only flows for a small portion of the oscillation cycle.

Then this “self-tuning” base oscillator circuit forms one of the most common types of LC parallel resonant feedback oscillator configurations called the Hartley Oscillator circuit.

Hartley Oscillator Tuned Circuit

In the Hartley Oscillator the tuned LC circuit is connected between the collector and the base of the transistor amplifier. As far as the oscillatory voltage is concerned, the emitter is connected to a tapping point on the tuned circuit coil.

The feedback    of   the     tuned  tank  circuit is taken  from the centre tap of the inductor coil or even two separate coils in series which are in parallel with a variable capacitor, C as shown.

The Hartley circuit is often referred to as a split-inductance oscillator because coil L is centre-tapped. In effect, inductance L acts like two separate coils in very close proximity with the current flowing through coil section XY induces a signal into coil section YZ below.

An Hartley Oscillator circuit can be made from any configuration that uses either a single tapped coil (similar to an autotransformer) or a pair of series connected coils in parallel with a single capacitor as shown below.

Basic Hartley Oscillator Circuit

When the circuit is oscillating, the voltage at point X (collector), relative to point Y (emitter), is 180o out-of-phase with the voltage at point Z (base) relative to point Y. At the frequency of oscillation, the impedance of the Collector load is resistive and an increase in Base voltage causes a decrease in the Collector voltage.

Then there is a 180 phase change in the voltage between the Base and Collector and this along with the original 180 phase shift in the feedback loop provides the correct phase relationship of positive feedback for oscillations to be maintained.

The amount of feedback depends upon the position of the “tapping point” of the inductor. If this is moved nearer to the collector the amount of feedback is increased, but the output taken between the Collector and earth is reduced and vice versa.

Resistors, R1 and R2 provide the usual stabilizing DC bias for the transistor in the normal manner while the capacitors act as DC-blocking capacitors.

In this Hartley Oscillator circuit, the DC Collector current flows through part of the coil and for this reason the circuit is said to be “Series-fed” with the frequency of oscillation of the Hartley Oscillator being given as.

The frequency of oscillations can be adjusted by varying the “tuning” capacitor, C or by varying the position of the iron-dust core inside the coil (inductive tuning) giving an output over a wide range of frequencies making it very easy to tune. Also the Hartley Oscillator produces an output amplitude which is constant over the entire frequency range.

As well as the Series-fed Hartley Oscillator above, it is also possible to connect the tuned tank circuit across the amplifier as a shunt-fed oscillator as shown below.

Shunt-fed Hartley Oscillator Circuit

Both the AC and DC Components of the Collector current follow separate circuit paths in the Shunt-fed Hartley Oscillator. Less power is lost in the tuned circuit because the Capacitor, C2, blocks the DC Component from flowing through the Inductive coil, L.

The Radio Frequency Coil (RFC), L2, is an RF choke with a high Reactance at the Frequency of Oscillations, Allowing the DC Component to pass through L2 to the power supply while the Majority of the RF current is applied to the LC tuning tank circuit via Capacitor, C2. The RFC coil, L2, could be swapped out for a Resistor, but the Efficiency would suffer.

Colpitts Oscillator

Another LC Oscillator design is the Colpitts Oscillator, which bears the name of its creator, Edwin Colpitts. The Hartley Oscillator we looked at on the previous page is very similar to the Colpitts Oscillator in many ways. The tuned tank circuit, like the Hartley Oscillator, is made up of an LC Resonance Sub-circuit connected between the base and collector of a single stage Transistor Amplifier, which results in a sinusoidal output waveform.

The Colpitts Oscillator’s basic design is similar to the Hartley Oscillator’s, with the Exception that the tank Sub-center Circuit’s tap is now made at the Intersection of a “Capacitive voltage divider” network rather than an Inductor of the Autotransformer type as in the Hartley Oscillator.

Colpitts Oscillator Circuit

The Colpitts oscillator uses a capacitor voltage divider as its feedback source.

The two capacitors, C1 and C2 are placed across a common inductor, L as shown so that C1, C2 and L forms the tuned tank circuit the same as for the Hartley oscillator circuit.

The advantage of this type of tank circuit configuration is that with less self and mutual inductance in the tank circuit, frequency stability is improved along with a more simple design. As with the Hartley oscillator, the Colpitts oscillator uses a single stage bi-polar transistor amplifier as the gain element which produces a sinusoidal output. Consider the circuit below.

Basic Colpitts Oscillator Circuit 

The junction of capacitors C1 and C2, which are connected in series and function as a straightforward voltage divider, is connected to the emitter of the transistor amplifier. Capacitors C1 and C2 charge up and then discharge through the coil L when the power supply is first turned on. The base-emitter junction receives the oscillations applied across the capacitors, which are then amplified at the collector output. The C1 and C2 values determine how much feedback there will be; the higher the feedback, the lower the C1 and C2 values.

Similar to the Hartley oscillator circuit,. The required positive feedback is obtained for long-lasting undamped oscillations in order to achieve the necessary external phase shift. The ratio of C1 to C2, which are typically “ganged” together to provide a constant amount of feedback so that as one is adjusted, the other does too, determines the amount of feedback.

The frequency of oscillations for a Colpitts oscillator is determined by the resonant frequency of the LC tank circuit and is given as:

where CT is the capacitance of C1 and C2 connected in series and is given as:.

The configuration of the transistor amplifier is of a Common Emitter Amplifier with the output signal 180o out of phase with regards to the input signal. The additional 180o phase shift require for oscillation is achieved by the fact that the two capacitors are connected together in series but in parallel with the inductive coil resulting in overall phase shift of the circuit being zero or 360o .

Resistors, R1 and R2 provide the usual stabilizing DC bias for the transistor in the normal manner while the capacitor acts as a DC-blocking capacitors. The radio-frequency choke (RFC) is used to provide a high reactance (ideally open circuit) at the frequency of oscillation, ( ƒr ) and a low resistance at DC.

Colpitts Oscillator using an Op-amp

We can also use either a field effect transistor (FET) or an operational amplifier in place of a bi-polar junction transistor (BJT) as the amplifier’s active stage of the Colpitts oscillator (op- amp). An Op-amp Colpitts Oscillator operates in the exact same way as the transistorised version, with the same method of calculating the operating frequency. Take a look at the circuit below.

Colpitts Oscillator Op-amp Circuit

The advantages of the Colpitts Oscillator over the Hartley oscillators are that the Colpitts oscillator produces a more purer sinusoidal waveform due to the low impedance paths of the capacitors at high frequencies. Also due to these capacitive reactance properties the Colpitts oscillator can operate at very high frequencies into the microwave region.

Wien Bridge Oscillator

One of the simplest sine wave oscillators which uses a RC network in place of the conventional LC tuned tank circuit to produce a sinusoidal output waveform, is the Wien Bridge Oscillator.

The reason the circuit is based on a frequency-selective version of the Whetstone bridge circuit is how the Wien Bridge Oscillator got its name. A common circuit used as an audio frequency oscillator is the Wien Bridge oscillator,. A two-stage RC coupled amplifier with good stability at its resonant frequency, low distortion, and ease of tuning.

Wien Bridge Oscillator circuit

The output of the operational amplifier is fed back to both the inputs of the amplifier. One part of the feedback signal is connected to the inverting input terminal (negative feedback) via the resistor divider network of R1 and R2 which allows the amplifiers voltage gain to be adjusted within narrow limits.

The other part is fed back to the non-inverting input terminal (positive feedback) via the RC Wien Bridge network. The RC network is connected in the positive feedback path of the amplifier and has zero phase shift a just one frequency. Then at the selected resonant frequency, ( ƒr ) the voltages applied to the inverting and non-inverting inputs will be equal and “in-phase” so the positive feedback will cancel out the negative feedback signal causing the circuit to oscillate.

Also the voltage gain of the amplifier circuit MUST be equal to three “Gain =3” for oscillations to start. This value is set by the feedback resistor network, R1 and R2 for an inverting amplifier and is given as the ratio -R1/R2.

Also, due to the open-loop gain limitations of operational amplifiers, frequencies above 1MHz are unachievable without the use of special high frequency op-amps. Then for oscillations to occur in a Wien Bridge Oscillator circuit the following conditions must apply.

1. With no input signal the Wien Bridge Oscillator produces output oscillations.

2. The Wien Bridge Oscillator can produce a large range of frequencies.

3. The Voltage gain of the amplifier must be at least 3.

4. The network can be used with a Non-inverting amplifier.

5. The input resistance of the amplifier must be high compared to R so that the RC network is not overloaded and alter the required conditions.

6. The output resistance of the amplifier must be low so that the effect of external loading is minimised.

7.  If the voltage gain of the amplifier is too small, the desired oscillation will decay and stop, and if it is too large, the output amplitude rises to the value of the supply rails, saturating the op-amp and resulting in a distorted output waveform. Therefore, some method of stabilising the oscillation amplitude must be provided.

8. With amplitude stabilisation in the form of feedback diodes, oscillations from the oscillator can go on indefinitely.

Quartz Crystal Oscillator

Any oscillator’s frequency stability, or more specifically, its capacity to deliver a constant frequency output under a variety of load conditions, is one of its most crucial characteristics. Temperature, variations in the load, and adjustments in the DC power supply are a few of the variables that have an impact on an oscillator’s frequency stability.

Frequency stability of the output signal can be improved by the proper selection of the components used for the resonant feedback circuit including the amplifier but there is a limit to the stability that can be obtained from normal LC and RC tank circuits.

To obtain a very high level of oscillator stability a Quartz Crystal is generally used as the frequency

When a voltage source is applied to a small thin piece of quartz crystal,. It begins to change shape producing a Characteristic known as the Piezo-electric effect.

This Piezo-electric effect is the property of a crystal by which an Electrical charge produces a Mechanical force by changing the shape of the crystal and vice versa, a Mechanical force applied to the crystal produces an Electrical charge.

Then, Piezo-electric devices can be classed as Transducers. As they convert energy of one kind into energy of another (Electrical to Mechanical or Mechanical to Electrical).

This Piezo-electric effect produces Mechanical Vibrations or Oscillations. Which are used to replace the LC tank circuit in the previous Oscillators.

There are many different types of crystal Substances. Which can be used as Oscillators with the most important of these for electronic Circuits being the quartz Minerals. Because of their greater Mechanical strength.

A very small, thin wafer of cut quartz is used as the quartz crystal in a quartz crystal Oscillator, and the two parallel surfaces have been Metallized to create the necessary Electrical connections. A quartz Crystal’s physical Dimensions, or “Characteristic Frequency,” are carefully Regulated. Because they have an impact on the Oscillations’ final Frequency. The crystal cannot be used at any other Frequency after it has been cut and shaped. In other words, its Frequency is determined by its size and shape.

Quartz Crystal Oscillator circuit

An RLC series circuit, which represents the Mechanical Vibrations of the quartz crystal,. Is shown in parallel with a Capacitance, Cp,. Which represents the Electrical connections to the crystal in the Equivalent circuit. The Equivalent Impedance of quartz crystals has two Resonances:. A series Resonance where Cs Resonates with the Inductance L. And a parallel Resonance where L Resonates with the series combination of Cs and Cp as shown.

Crystal Reactance

The slope of the Reactance against Frequency above, shows that the Series Reactance at Frequency ƒs is Inversely Proportional to Cs because below ƒs and above ƒp the crystal appears Capacitive, i.e. dX/dƒ, where X is the Reactance.

The slope of the Reactance against Frequency above,. Shows that the series Reactance at Frequency fs is Inversely Proportional to Cs. Because below fs and above fp the crystal appears Capacitive,. I.e. dX/d f, where X is the Reactance. Between Frequencies ƒs and ƒp, the crystal appears Inductive as the two parallel Capacitances cancel out. The point where the Reactance values of the Capacitances and Inductance cancel each other out Xc = XL is the Fundamental Frequency of the crystal.

A quartz crystal has a Resonant Frequency similar to that of a Electrically tuned tank circuit. But with a much higher Q factor due to its low resistance, with typical Frequencies ranging from 4kHz to 10MHz.

Since some crystals vibrate at more than one Frequency, the cut of the crystal also affects how it will act. The crystal also has two or more Resonant Frequencies with both a Fundamental Frequency and Harmonics like the second or third Harmonic if its Thickness is not parallel or uniform. However, the Fundamental Frequency is Typically used because it is stronger or more Pronounced than the others. Three Reactive Components make up the Equivalent circuit above, and there are two Resonant Frequencies—the highest is a Parallel-type Resonant Frequency and the lowest is a Series-type Frequency.

An Amplifier circuit will Oscillate. If it has a loop gain greater than or equal to one and positive Feedback, as we saw in the previous Tutorials. Because a quartz crystal always seeks to Oscillate when a voltage source is applied to it,. The Oscillator in a quartz crystal Oscillator circuit will Oscillate at the Crystal’s Fundamental parallel Resonant Frequency.

Colpitts Crystal Oscillator

The design of a Crystal Oscillator is very similar to the design of the Colpitts Oscillator we looked at in the previous Tutorial, except that the LC tank circuit has been replaced by a quartz crystal as shown below.

These types of Crystal Oscillators are designed around the common emitter Amplifier stage of a Colpitts Oscillator. The input signal to the base of the Transistor is Inverted at the Transistors output.

The output signal at the Collector is then taken through a 180o phase Shifting network. Which includes the crystal operating in a series Resonant mode. The output is also fed back to the input which is “In-phase”

with the input Providing the necessary positive Feedback. Resistors, R1 and R2 bias the Resistor in a Class A type operation while Resistor Re is chosen. So that the loop gain is slightly greater than unity.

Capacitors, C1 and C2 are made as large as possible in order that the Frequency of Oscillations can Approximate to the series Resonant mode of the crystal and is not Dependant upon the values of these Capacitors.

The circuit diagram above of the Colpitts Crystal Oscillator circuit shows that Capacitors, C1 and C2. Shunt the output of the Transistor which reduces the Feedback signal.

Therefore, the gain of the Transistor limits the maximum values of C1 and C2.

The output Amplitude should be kept low in order to avoid Excessive power Dissipation in the crystal. Otherwise could destroy itself by Excessive Vibration.

Pierce Crystal Oscillator

The Pierce Oscillator is a crystal Oscillator that does not have a Resonant tank circuit. Because it Incorporates the crystal into its Feedback path. Because the Pierce Oscillator has a very high input Impedance. And connects the crystal between the output Drain Terminal and the input Gate Terminal. As shown below, it uses a JFET as its Amplifier.

Pierce Crystal Oscillator circuit

In this simple circuit, the crystal determines the Frequency of Oscillations. And operates on its series Resonant Frequency giving a low Impedance path between output and input.

There is a 180° phase shift at Resonance, making the Feedback positive. The Amplitude of the output sine wave is limited to the maximum voltage range at the Drain Terminal.

The voltage across the radio Frequency choke, RFC,. Reverses during each cycle while the resistance, R1, controls the amount of Feedback and crystal drive. Because a Pierce Oscillator can be Implemented with the fewest Components possible,. It is used in some form in the Majority of digital clocks, watches, and timers.