Voltage Controlled Oscillator

Voltage Controlled Oscillator What is an oscillator? An oscillator is an electronic circuit that produces an output waveform without an external signal source. The key to oscillator operation is a positive feedback. There is an amplifier where sufficient energy is coupled back from its output to its input. A positive feedback can be obtained in two ways:  If the output of the amplifier is 1800 phase shifted from the input, then the feedback has to produce a 1800 phase shift as shown below; or

Fig-1: Positive feedback, 1800 phase shift in feedback  If the output of the amplifier is in-phase with the input, then the feedback has to make no phase shift.

Fig-2: Positive feedback, no phase shift in feedback In any case, the output from the feedback network is in phase with the input of the amplifier.

Therefore, depending on the product of the gains of the feedback network and the amplifier, the amplitude of the output signal is determined. The frequency of the output signal depends upon the frequency determining circuit in the feedback network. The switch in the above figure illustrates the basic principle of how the oscillator produces an output waveform without any input signal. In Figure 1, the switch S is momentarily closed, applying an input signal to the circuit. This results in a signal at the output from the amplifier, a portion of which is fed back to the input by the feedback network. Then the switch is open, but the circuit continues to oscillate because the feedback network is supplying the input to the amplifier. The feedback network delivers an input to the amplifier, which in turn generates an input for the feedback network. This circuit action is referred to as regenerative feedback and is the basis for all oscillators. An oscillator needs a brief trigger signal to start the oscillations. Most oscillators provide their own trigger simply by turning the circuit on. Requirements of Oscillation  The circuit must have regenerative feedback; that is, feedback that results in a combined 360°(or 0°) voltage phase shift around the circuit loop.  The circuit must receive some trigger signal to start the oscillations. In addition to the conditions stated above, the circuit must fulfill the Barkhausen criterion. This condition states that for an oscillator to work properly, the product of the gain of the amplifier and the attenuation of the feedback network must be equal to one.

If the criterion is not met, one of the following occurs: 1. If 2. If

, the oscillations die out after a few cycles. , the oscillator drives itself into saturation and cutoff clipping.

These principles are illustrated in the following figures:

Fig-3: The effects of

on oscillator operation.

If , each oscillation results in a lower-amplitude signal being fed back to the input (as shown in Fig-3a). After a few cycles, the signal fades out. This loss of signal amplitude is called damping. If , each oscillation results in a larger and larger signal being fed back to the input (as shown in Fig-3b). In this case, the amplifier is quickly driven into clipping. When , each oscillation results in a consistently equal signal being fed back to the input (as shown in Fig-3c). One final point: Since there is always some power loss in the resistive components, in practice must always be just slightly greater than 1. There are many types of oscillator. The main difference in these oscillators is the type of circuit used in the feedback network. An RC or an LC circuit can be used. Some of the most common RC oscillators are Phase-shift, Wien-Bridge. Some common LC resonant oscillators are Colpitts, Clapp, Hartley and Armstrong. If stable frequency is required, a crystal-controlled oscillator is used. A crystal-controlled oscillator uses a quartz crystal to control the operating frequency. The key to the operation of a crystal-controlled oscillator is the piezoelectric effect. Because the topic of interest is a voltage-controlled oscillator, a crystal oscillator will not

be discussed here. The design analysis of the VCO will be done depending on clapp oscillator. So the remaining oscillator types are not explained here. The Colpitts Oscillator The Colpitts oscillator is a discrete LC oscillator that uses a pair of tapped capacitors and an inductor to produce regenerative feedback.

Fig-4: Colpitts oscillator The key to understanding this circuit is knowing how the feedback circuit produces its 180° phase shift (the other 180° is from the inverting action of the CE amplifier). The feedback circuit produces a 180° voltage phase shift as follows: 1. The amplifier output voltage is developed across . 2. The feedback voltage is developed across . 3. As each capacitor causes a 90° phase shift, the voltage at the top of (the output voltage) must be 180° out of phase with the voltage at the bottom of (the feedback voltage). The first two points are fairly easy to see. is between the collector and ground. This is where the output is measured. is between the transistor base and ground, or in other words, where the input is measured. Point three is explained using the circuit in Figure 5.

Fig-5: Colpitts oscillator frequency determining circuit. Figure 5 is the equivalent representation of the tank circuit in the Colpitts oscillator. Let’s assume that the inductor is the voltage source and it induces a current in the circuit. With the polarity shown across the inductor, the current causes potentials to be developed across the capacitors with the polarities shown in the figure. Note that the capacitor voltages are 180° out of phase with each other. When the polarity of the inductor voltage reverses, the current reverses, as does the resulting polarity of the voltage across each capacitor (keeping the capacitor voltages 180° out of phase). The value of the feedback voltage is determined (in part) by the of the circuit. For the Colpitts oscillator, is defined by the ratio of . By formula:

or As with any oscillator, the product of must be slightly greater than 1. As mentioned earlier and . Therefore:

As with any tank circuit, this one will be affected by a load. To avoid loading effects (the circuit loses some efficiency), the output from a Colpitts oscillator is usually transformercoupled to the load. Capacitive coupling is also acceptable so long as:

where

is the total capacitance in the feedback network

The following is an interpretation to calculate the conditions necessary for oscillation. It is based on the fact that an ideal tuned circuit (infinite Q), once excited, will oscillate infinitely because there is no resistance element present to dissipate the energy. In the actual case (where the inductor Q is finite), the oscillations die out because energy is dissipated in the resistance. It is the function of the amplifier to maintain oscillations by supplying an amount of energy equal to that dissipated. This source of energy can be

interpreted as a negative resistor in series with the tuned circuit. If the total resistance is positive, the oscillations will die out, while the oscillation amplitude will increase if the total resistance is negative. To maintain oscillations, the two resistors must be of equal magnitude. To see how a negative resistance is realized, the input impedance of the circuit in Figure 5a will be derived. Figure 5b shows an equivalent small signal circuit of Figure 5a.

The steady state loop equations are:

After Ib is eliminated from these two equations, Zin is obtained as follows:

If

, the input impedance is approximately equal to:

That is the input impedance of the circuit in fig-4a is a negative resistor,

in series with a capacitor,

which is the series combination of two capacitors. With an inductor L (with the series resistance Rs) connected across the input, it is clear that the condition for sustained oscillation is

This interpretation of the oscillator readily provides several guidelines, which can be used in the design. First, C1 should be as large as possible so that and C2 is to be large so that

when these two capacitors are large, the transistor base-to-emitter and collector-to-emitter capacitances will have a negligible effect on the circuit’s performance. However, Eq. (8) limits the maximum value of the capacitances since

where G is the maximum value of gm. For a given product of C1 and C2, the series capacitances is a maximum when C1 = C2 = Cm. Thus Eq. (10) can be written

This equation is important in that it shows that for oscillations to be maintained, the minimum permissible reactance (1/ωCm) is a function of the resistance of the inductor and the transistor’s mutual conductance gm. When an inductor is connected across the input, the oscillator becomes a Colpitts oscillator. The total input impedance when an inductor is connected becomes

The frequency of oscillation is obtained by equating the imaginary part to zero. Which gives:

An oscillator circuit known as the Clapp circuit or Clapp-Gouriet circuit is shown in Figure 5. This oscillator is equivalent to the one just discussed, but it has the practical advantage of being able to provide another degree of design freedom by making Co much smaller than C1 and C2. It is possible to use C1 and C2 to satisfy the condition of Eq. (10) and then adjust Co for the desired frequency of oscillation , which is determined from

Co is to reduce the effects of junction capacitance of the transistor on the operating frequency. Referring to the high frequency equivalent of the transistor, it can be seen that  C1 is in parallel with the Miller input capacitance,

.

 is in parallel with the Miller output capacitance, . These types of oscillators can be made voltage controlled oscillators by changing capacitor Co from a fixed value to a voltage dependent capacitor, commonly referred to as tuning diode or varactor. The use of just a single diode is typically discouraged. For small DC voltages, the tuning diode becomes conductive in the positive half of the sine wave,

and this reduces the Q and deteriorates the phase noise performance. As a minimum, a high-performance oscillator requires one set of anti-parallel diodes. For approximate design, the effect of C1 and C2 and the junction capacitance can be ignored and the frequency can be estimated using the following formula:

k Fig-7: Clapp Oscillator