**
SINE WAVE GENERATION**

Producing and manipulating the sine wave function is a common problem encountered by circuit designers. Sine wave circuits pose a significant design challenge because they represent a constantly controlled linear oscillator. Sine wave circuitry is required in a number of diverse areas, including audio testing, calibration equipment, transducer drives, power conditioning and automatic test equipment (ATE). Control of frequency, amplitude or distortion level is often required and all three parameters must be simultaneously controlled in many applications.

A number of techniques utilizing both analog and digital approaches are available for a variety of applications. Each individual circuit approach has inherent strengths and weaknesses which must be matched against any given application.

__PHASE SHIFT OSCILLATOR __

A **phase-shift oscillator** is a simple electronic oscillator. It
contains an inverting amplifier and a feedback filter which
'shifts' the phase of the amplifier output by 180 degrees at
a specific oscillation frequency.

The filter produces a phase shift that increases with frequency. It must have a maximum phase shift of considerably greater than 180° at high frequencies, so that the phase shift at the desired oscillation frequency is 180°.

The most common way of achieving this kind of filter is using three identical cascaded resistor-capacitor filters, which together produce a phase shift of zero at low frequencies, and 270 degrees at high frequencies. At the oscillation frequency each filter produces a phase shift of 60 degrees and the whole filter circuit produces a phase shift of 180 degrees.

The circuit consists of a
common source FET amplifier followed by a three section R-C phase shift network.
The amplifier stage is self-biased with a capacitor bypassed source resistor R_{s} and
a drain bias resistance R_{D}. The output of the last section is
supplied back to the gate. If the loading of the phase-shift network on the
amplifier can be assumed to be negligible, a phase shift of 180° between the
amplified output voltage V_{out} and the input voltage V_{in} at
the gate is produced by the amplifier itself. The three-section R-C phase shift
network produces an additional phase shift, which is a function of frequency
and equals 180° at some frequency of operation. At this frequency the total
phase shift from the gate around the circuit and back to gate will be exactly
zero. This particular frequency will be the one at which the circuit will
oscillate provided that the magnitude of the amplification is sufficiently
large. In a FET phase-shift oscillator voltage series feedback [that is,
feedback voltage proportional to the output voltage V_{out} and
supplied in series with the input signal at the gate is used.

The frequency of the oscillator output depends upon the values of capacitors C and resistors R used in the phase shift network. Using basic RC circuit analysis technique, it can be shown that the network phase shift is 180° when

**X _{c} =
√6 R or 1 / 2∏fc =
√6 R or f = 1 / / 2∏ R c √6**

The frequency can be
adjusted over a wide range if variable capacitors are used.As well as phase
shifting, the R-C network attenuates the amplifier output. Network
analysis shows that when the necessary phase shift of 180° is obtained,
this network attenuates the output voltage by a factor of 1/29. This means
that the amplifier must have a voltage gain of 29 or more. When the
amplifier voltage gain is 29 and feedback factor of R-C network, β= 1/29
then the loop gain is **β **A = 1, the amplifier phase
shift of – 180° combined with the network phase shift of + 180° gives a loop
phase shift of zero. Both of these conditions are necessary to satisfy the** Barkhausen
criteria**. If the amplifier gain is much greater than 29, the oscillator
output waveform is likely to be distorted. When the gain is slightly greater
than 29, the output is usually a reasonably pure sinusoidal.

The advantages and disadvantages of phase shift oscillators are given below :

**Advantages:**

§ It is cheap and simple circuit as it contains resistors and capacitors (not bulky and expensive high-value inductors).

§ It provides good frequency stability.

§ The phase shift oscillator circuit is much simpler than the Wien bridge oscillator circuit because it does not need negative feedback and the stabilization arrangements.

§ The output is sinusoidal that is quite distortion free.

§ They have a wide frequency range (from a few Hz to several hundred kHz).

§ They are particularly suitable for low frequencies, say of the order of 1 Hz, as these frequencies can be easily obtained by using R and C of large values.

**Disadvantages**

§ The output is small. It is due to smaller feedback.

§ It is difficult for the circuit to start oscillations as the feedback is usually small.

§ The frequency stability is not as good as that of Wien bridge oscillator.

§ It needs high voltage (12 V) battery so as to develop sufficiently large feedback voltage.

**Applications**

FET phase-shift oscillator is used for generating signals over a wide frequency range. The frequency may be varied from a few Hz to 200 Hz by employing one set of resistors with three capacitors ganged together to vary over a capacitance range in the 1 : 10 ratio. Similarly the frequency ranges of 200 Hz to 2 kHz, 2 kHz to 20 kHz and 20 kHz to 200 kHz can be obtained by using other sets of resistors.

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