Table of Contents

**INTRODUCTION TO OSCILLATORS**

Oscillators are observed everywhere in the universe on all levels. Oscillators are defined as subsystems of the universe which exhibit an oscillating behavior. In connection with an oscillator there is an energy field which goes from the center to infinite. Oscillators couple by means of exchange of energy. All kinds of oscillators may couple. The coupling may take place over enormous relative distances.

Galaxies are oscillators. They are composed of solar systems which couple. Solar systems are oscillators composed of stars and planets. Stars and planets are oscillators. Gravity is the field mechanism for exchange of energy between oscillators of this kind. Other fields for exchange of energy are electromagnetism, the strong and the weak nuclear forces. Apparently the coupling of oscillators is the basic principle of the universe.

Electrical circuits are man-made systems for handling and transport of energy. The electrical world may be coupled to the mechanical world by means of flux (generators, motors). The electrical world may be coupled to the chemical world by means of charge (batteries). Electrical circuits are nonlinear systems

Very often design of electrical circuits is based on the assumption of linear lumped models for the elements in order to be able to setup analytic expressions for the behavior. An electrical circuit is a fractal pattern of coupled oscillators e.g. a resistor may be modeled as a linear damped oscillator if the parasitic components are taken into account.

Electronic circuits are electrical circuits for handling of information. Oscillators are kernel components of electronic circuits. Oscillators create sine waves as carriers of signals (Radio, TV) or square waves as clock control in digital systems. Steady state oscillators are considered nonlinear circuits having a time-varying DC bias point. They may be investigated as time-varying linear systems. Apparently the steady state chaotic behavior is more common than the steady state limit cycle behavior wanted in electrical oscillators.

**To Simulate the Hartley Oscillator and obtain the transient Response**

**Objectives for Hartley Oscillator:-**

- To Simulate the Transistor Hartley Oscillator and obtain the transient response.

**Material Required for Hartley Oscillator****:-**

- Multisim Software
- Input Power Source
- Power supply
- Inductor
- Transistors
- Resistors
- Capacitors
- Connecting Wires
- Ground

**Summary of Hartley Oscillator****:-**

In a Hartley oscillator the oscillation frequency is determined by a tank circuit comprising of two inductors and one capacitor. The inductors are connected in series and the capacitor is connected across them in parallel. Hartley oscillators are commonly used in radio frequency (RF) oscillator applications and the recommended frequency range is from 20 KHz to 30MHz. Hartley oscillators can be operated at frequencies lower than 20 KHz, but for lower frequencies the inductor value need to be high and it has a practical limit.

The Hartley Oscillator is a particularly useful circuit for producing good quality sine wave signals in the RF range, (30kHz to 30MHz) although at the higher limits of this range and above, The Colpitt’s oscillator is usually preferred. Although both these oscillators oscillator use an LC tuned (tank) circuit to control the oscillator frequency,

The frequency of oscillation can be calculated in the same way as any parallel resonant circuit, using:

**Where L = L1 + L2**

This basic formula is adequate where the mutual inductance between L1 and L2 is negligible, but needs to be modified when the mutual inductance between L1 and L2 is considerable

**The operation for ****Hartley Oscillator**

When the collector supply is given, a transient current is produced in the oscillatory or tank circuit. The oscillatory current in the tank circuit produces a.c. voltage across L1.

The auto-transformer made by the inductive coupling of L1 and L2 helps in determining the frequency and establishes the feedback. As the CE configured transistor provides 180o phase shift, another 180o phase shift is provided by the transformer, which makes 360o phase shift between the input and output voltages.

This makes the feedback positive which is essential for the condition of oscillations. When the loop gain |βA| of the amplifier is greater than one, oscillations are sustained in the circuit.

**Procedure for ****Hartley Oscillator****:-**

- Open Multisim
- Place the Resistor on the Circuit and double click to place it.
- Place the Transistor on the Circuit and double click to place it.
- Similarly for other components i.e. Source, Inductor Ground etc.
- After Mounting the required components wire them up.
- Multisim will place the wire between the components selected..
- The circuit is ready for analyses
- Set the timings Save it
- Run simulation.

**Circuit diagram of ****Hartley Oscillator****:-**

**Simulation of ****Hartley Oscillator****:-**

**Formulas of ****Hartley Oscillator****:–**

To find the frequency, we know that

F = 1/ (2*pi*√LC)

Where LT = L1 + L2

**Results of ****Hartley Oscillator****:-**

S.NO | C | LT(mH) | F |

1 | 1 µF | 2 | 3.56 kHz |

2 | 8200pF | 51 | 7.78kHz |

** **

**Observations for ****Hartley Oscillator****:-**

I have observed and learned various things like

- The frequency may be adjusted using a single variable capacitor, one side of which can be earthed.
- The output amplitude remains constant over the frequency range.
- Either a tapped coil or two fixed inductors are needed, and very few other components.

**To simulate the Colpitt’s Oscillator and obtain the transient response**

**Objectives of Colpitt’s Oscillator:-**

- To simulate the Colpitt’s Oscillator and obtain the transient response.

**Material Required for Colpitt’s**** Oscillator****:-**

- Multisim Software
- Input Power Source
- Power supply
- Inductor
- Transistors
- Resistors
- Capacitors
- Connecting Wires
- Ground

**Summary for Colpitt’s Oscillator:-**

A Colpitt’s oscillator looks just like the Hartley oscillator but the inductors and capacitors are replaced with each other in the tank circuit.

The resistors R1, R2 and Re provide necessary bias condition for the circuit. The capacitor Ce provides a.c. ground thereby providing any signal degeneration. This also provides temperature stabilization.

The capacitors Cc and Cb are employed to block d.c. and to provide an a.c. path. The radio frequency choke (R.F.C) offers very high impedance to high frequency currents which means it shorts for d.c. and opens for a.c. Hence it provides d.c. load for collector and keeps a.c. currents out of d.c. supply source. Tank Circuit The frequency determining network is a parallel resonant circuit which consists of variable capacitors C1 and C2 along with an inductor L. The junction of C1 and C2 are earthed. The capacitor C1 has its one end connected to base via Cc and the other to emitter via Ce. The voltage developed across C1 provides the regenerative feedback required for the sustained oscillations Operation.

When the collector supply is given, a transient current is produced in the oscillatory or tank circuit. The oscillatory current in the tank circuit produces a.c. voltage across C1 which are applied to the base emitter junction and appear in the amplified form in the collector circuit and supply losses to the tank circuit. If terminal 1 is at positive potential with respect to terminal 3 at any instant, then terminal 2 will be at negative potential with respect to 3 at that instant because terminal 3 is grounded. Therefore, points 1 and 2 are out of phase by 180.

As the CE configured transistor provides 180o phase shift, it makes 360o phase shift between the input and output voltages. Hence, feedback is properly phased to produce continuous Undamped oscillations. When the loop gain |βA| of the amplifier is greater than one, oscillations are sustained in the circuit.

The equation for frequency of Colpitt’s oscillator is given as

**f=12πLCT−−−−√f=12πLCT**

CT is the total capacitance of C1 and C2 connected in series.

**1CT=1C1+1C21CT=1C1+1C2**

**CT=C1×C2C1+C2**

**Procedure for ****Colpitt’s Oscillator****:-**

- Open Multisim
- Place the Resistor on the Circuit and double click to place it.
- Place the Transistor on the Circuit and double click to place it.
- Similarly for other components i.e. Source, Inductor Ground etc.
- After Mounting the required components wire them up.
- Multisim will place the wire between the components selected..
- The circuit is ready for analyses
- Set the timings Save it
- Run simulation.

**Circuit diagram for Colpitt’s Oscillator:-**

**Simulation of ****Colpitt’s Oscillator****:-**

**Formulas of ****Colpitt’s Oscillator****:-**

Design the CE Amplifier for the given Gain.

- Choose C1
- Calculate C2 from AV > C1/C2
- Calculate C from f=1/(2П (L1C)1/2), where C= C1C2 /(C1+C2)

**Results of ****Colpitt’s Oscillator****:-**

S.NO |
CT (µF) |
L(mH) |
Fr |

1 | 5 | 1 | 2.25 kHz |

2 | 0.427 | 1 | 7.7 MHz |

**Observations of ****Colpitt’s Oscillator****:-**

W have observed and learned various things like

The Colpitt’s Oscillator can be used in high frequency to produce pure sinusoidal waveform because of low impedance paths of the capacitors at high frequencies. It has wide operation range from 1 to 60 MHz

The advantages of the Colpitt’s Oscillator over the Hartley oscillators are that the Colpitt’s oscillator produces a more pure sinusoidal waveform due to the low impedance paths of the capacitors at high frequencies.

**To simulate the Wein Bridge Oscillator and obtain the transient response**

**Objectives of Wein Bridge Oscillator:-**

- To simulate the Wein Bridge Oscillator
- Obtain the Transient response.
- Observe the results.

**Material Required for Wein Bridge Oscillator:-**

- Multisim Software
- Input Power Source
- Power supply
- Inductor
- Transistors (BC 107)
- Resistors (1, 2.2,10 33 , 6.8) K Ω
- Capacitors (10,100,0.01) µf
- RPS (0 – 30 V)
- Potentiometer
- CRO
- Connecting Wires
- Ground

**Summary for Wein Bridge Oscillator:-**

The Wein bridge oscillator is a standard circuit for generating low frequencies in the range of 10Hz to about 1MHz.The method used for getting +ve feedback in wein bridge oscillator is to use two stages of an RC-coupled amplifier. Since one stage of the RC-coupled amplifier

introduces a phase shift of 180 deg, two stages will introduces a phase shift of 360 deg. At the

frequency of oscillations f the +ve feedback network shown in fig makes the input & output in the phase. The frequency of oscillations is given as

f =1/2π√R1C1R2C2

In addition to the positive feedback

**The operation for ****Wein Bridge Oscillator**

When the circuit is switched ON, the bridge circuit produces oscillations of the frequency stated above. The two transistors produce a total phase shift of 360 so that proper positive feedback is ensured. The negative feedback in the circuit ensures constant output. This is achieved by temperature sensitive tungsten lamp Lp. Its resistance increases with current.

If the amplitude of the output increases, more current is produced and more negative feedback is achieved. Due to this, the output would return to the original value. Whereas, if the output tends to decrease, reverse action would take place.

**Advantages of Wein Bridge Oscillator**

The advantages of Wien bridge oscillator are as follows −

- The circuit provides good frequency stability.
- It provides constant output.
- The operation of circuit is quite easy.
- The overall gain is high because of two transistors.

**Procedure for ****Wein Bridge Oscillator****:-**

- Open Multisim
- Place the Resistor on the Circuit and double click to place it.
- Place the Transistor on the Circuit and double click to place it.
- Similarly for other components i.e. Source, Inductor Ground etc.
- After Mounting the required components wire them up.
- Multisim will place the wire between the components selected..
- The circuit is ready for analyses
- Set the timings Save it
- Run simulation.

**Circuit diagram for ****Wein Bridge Oscillator****:-**

**Simulation for ****Wein Bridge Oscillator****:-**

**Formulas for ****Wein Bridge Oscillator****:–**

Given R=10kΩ, C=0.01μF

FT = 1/ 2πRC

**Results of ****Wein Bridge Oscillator****:-**

S.NO |
CT (µF) |
L(mH) |
Fr |

1 | 5 | 1 | 2.25 kHz |

2 | 0.427 | 1 | 7.7 MHz |

**Observations of ****Wein Bridge Oscillator****:-**

We have observed that in Wein Bridge

- We have a lead and lag network. When capacitor and resistor are in series are lead network and if these elements are in parallel with respect to v the network is called lag network.
- It is the type of RC oscillator
- The maximum power is transferred when the overall circuit oscillates

**To simulate the RC Phase Oscillator using Transistor and obtain the transient response**

**Objectives of RC Phase Oscillator:-**

- To simulate the RC Phase Oscillator using Transistor

**Material Required for RC Phase Oscillator:-**

- Multisim
- Input Power Source
- Transistors (BC 107BP)
- Resistors (2.4, 3.3,6.2,10,10,33,600) K Ω
- Capacitors (330) pf
- Connecting Wires
- Multimeter
- Ground

**Summary of RC Phase Oscillator:-**

RC phase-shift oscillators use resistor-capacitor (RC) network to provide the phase-shift required by the feedback signal. They have excellent frequency stability and can yield a pure sine wave for a wide range of loads.

Ideally a simple RC network is expected to have an output which leads the input by 90o.

However, in reality, the phase-difference will be less than this as the capacitor used in the circuit cannot be ideal. Mathematically the phase angle of the RC network is expressed as

Where, XC = 1/ (2πfC) is the reactance of the capacitor C and R is the resistor. In oscillators, these kind of RC phase-shift networks, each offering a definite phase-shift can be cascaded so as to satisfy the phase-shift condition led by the Barkhausen Criterion.

Here the collector resistor RC limits the collector current of the transistor, resistors R1 and R (nearest to the transistor) form the voltage divider network while the emitter resistor RE improves the stability. Next, the capacitors CE and Co are the emitter by-pass capacitor and the output DC decoupling capacitor, respectively. Further, the circuit also shows three RC networks employed in the feedback path.

This arrangement causes the output waveform to shift by 180 during its course of travel from output terminal to the base of the transistor. Next, this signal will be shifted again by 180 by the transistor in the circuit due to the fact that the phase-difference between the input and the output will be 180 in the case of common emitter configuration. This makes the net phase-difference to be 360 satisfying the phase-difference condition.

Hence it can be concluded that the RC phase-shift oscillators can be designed in many ways as the number of RC networks in them is not fixed. However it is to be noted that, although an increase in the number of stages increases the frequency stability of the circuit, it also adversely affects the output frequency of the oscillator due to the loading effect.

The generalized expression for the frequency of oscillations produced by a RC phase-shift oscillator is given by

Where, N is the number of RC stages formed by the resistors R and the capacitors C.

**Procedure for ****RC Phase Oscillator****:-**

- Open Multisim
- Place the Resistor on the Circuit and double click to place it.
- Place the Transistor on the Circuit and double click to place it.
- Similarly for other components i.e. Source, Inductor Ground etc.
- After Mounting the required components wire them up.
- Multisim will place the wire between the components selected..
- The circuit is ready for analyses
- Set the timings Save it
- Run simulation.

**Circuit diagram of ****RC Phase Oscillator****:-**

**Simulation of ****RC Phase Oscillator****:-**

**Formulas for ****RC Phase Oscillator****:–**

To find the frequency,

Ft=1/2ΠRC (6+4K) 1/2, where K= Rc /R, R=Ra=Rb

**Results for o ****RC Phase Oscillator****:-**

S.NO |
K |
R kOhm |
Ft (KHz) |

1 | 0.24 | 10 | 6.096 |

2 | 0.12 | 1 | 3.021 |

**Observations of ****RC Phase Oscillator****:-**

We observed that this circuit is not expensive and gives excellent frequency stability. This circuit is simpler compared with a Wein bridge oscillator because it doesn’t require the stabilization planning & negative feedback. The circuit output is sinusoidal that is somewhat distortion-free.