Types of Oscillators MCQ Quiz - Objective Question with Answer for Types of Oscillators - Download Free PDF

Explanation:

Relaxation Oscillator

Definition: A relaxation oscillator is an electronic oscillator that generates a non-sinusoidal repetitive waveform, such as a square wave or a triangle wave. It operates based on the charging and discharging of a capacitor through a resistor or other nonlinear device, leading to the periodic switching of the circuit between two states.

Working Principle: In a relaxation oscillator, a capacitor is charged through a resistor until the voltage across the capacitor reaches a certain threshold. At this point, a nonlinear device, such as a Unijunction Transistor (UJT) or other switching element, rapidly discharges the capacitor. This cycle of charging and discharging generates the desired oscillatory waveform.

Advantages:

• Simple design and easy to construct.
• Can generate various waveforms such as square, triangle, and sawtooth waves.
• Useful in timing and waveform generation applications.

Disadvantages:

• Less frequency stability compared to other types of oscillators.
• May produce more harmonic distortion in the output waveform.

Applications: Relaxation oscillators are commonly used in applications such as flashing lights, clock generation, waveform generation, and time delay circuits.

Correct Option Analysis:

The correct option is:

Option 3: UJT (Unijunction Transistor)

This option is correct because the Unijunction Transistor (UJT) is a well-known component used in the construction of relaxation oscillators. The UJT's unique characteristic of having a negative resistance region allows it to effectively switch between high and low resistance states, facilitating the rapid charging and discharging cycles needed for oscillation.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: JFET (Junction Field-Effect Transistor)

While JFETs are versatile components used in various electronic circuits, they are not typically used as the primary switching element in relaxation oscillators. JFETs are more commonly employed in amplification and switching applications where linear characteristics are desired.

Option 2: BJT (Bipolar Junction Transistor)

BJTs can be used in oscillator circuits, but they are not as commonly used in relaxation oscillators as UJTs. BJTs are more suitable for linear amplification and switching applications, and while they can be used to create oscillations, they lack the specific characteristics that make UJTs ideal for relaxation oscillators.

Option 4: Diode

Diodes are primarily used for rectification, voltage regulation, and signal modulation. While they can be part of oscillator circuits, they are not typically used as the main switching component in relaxation oscillators. Diodes lack the necessary negative resistance region that UJTs have, which is crucial for the operation of relaxation oscillators.

Conclusion:

Understanding the specific characteristics and applications of electronic components is crucial for identifying their roles in various circuits. The Unijunction Transistor (UJT) is particularly suited for use in relaxation oscillators due to its unique switching properties, making it the correct choice for generating non-sinusoidal waveforms in timing and waveform generation applications.

Explanation:

Correct Option Analysis:

The correct option is:

Option 3: Colpitts oscillator and Hartley oscillator.

This option correctly identifies a pair of LC oscillators. Both Colpitts and Hartley oscillators are types of LC oscillators, which means they use inductors (L) and capacitors (C) to generate oscillations. Let's delve into the details of these oscillators to understand why this is the correct pair.

Colpitts Oscillator:

The Colpitts oscillator is a type of LC oscillator that generates sinusoidal oscillations. It was invented by American engineer Edwin H. Colpitts in 1918. In this oscillator, the feedback network consists of a voltage divider made of two capacitors in series and an inductor connected in parallel with them. The key elements in a Colpitts oscillator are:

• A tank circuit consisting of a parallel LC network, where the inductor (L) and the capacitors (C1 and C2) are used to determine the oscillation frequency.
• A transistor or an operational amplifier to provide the necessary gain to sustain the oscillations.
• A feedback network that ensures a positive feedback loop, which is essential for maintaining the oscillations.

The oscillation frequency of a Colpitts oscillator is given by the formula:

f = 1 / (2π√(L * (C1 * C2) / (C1 + C2)))

Where:

• f is the frequency of oscillation.
• L is the inductance of the inductor.
• C1 and C2 are the capacitances of the capacitors in the feedback network.

The Colpitts oscillator is widely used in radio frequency (RF) applications due to its simplicity and stability. It is known for producing a stable and pure sine wave output, making it suitable for high-frequency applications.

Hartley Oscillator:

The Hartley oscillator, named after its inventor Ralph Hartley, is another type of LC oscillator that generates sinusoidal oscillations. The feedback network in a Hartley oscillator consists of a tapped inductor and a capacitor. The key elements in a Hartley oscillator are:

• A tank circuit consisting of a tapped inductor (with two inductive sections, L1 and L2) and a capacitor (C) that together determine the oscillation frequency.
• A transistor or an operational amplifier to provide the necessary gain to sustain the oscillations.
• A feedback network that ensures a positive feedback loop, essential for maintaining the oscillations.

The oscillation frequency of a Hartley oscillator is given by the formula:

f = 1 / (2π√(L * C))

Where:

• f is the frequency of oscillation.
• L is the total inductance of the tapped inductor (L = L1 + L2).
• C is the capacitance of the capacitor in the tank circuit.

The Hartley oscillator is also widely used in RF applications. It is known for its simplicity and ease of tuning, as the frequency can be adjusted by varying the tapping point on the inductor. This makes it a popular choice for variable frequency oscillators.

Both Colpitts and Hartley oscillators are LC oscillators that utilize inductors and capacitors to generate oscillations. They are fundamental building blocks in RF and communication systems, providing stable and reliable oscillations for various applications.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Crystal oscillator and Phase-shift oscillator.

This option is incorrect because a crystal oscillator is not an LC oscillator. A crystal oscillator uses the mechanical resonance of a vibrating crystal (typically quartz) to create an electrical signal with a precise frequency. On the other hand, a phase-shift oscillator is an RC oscillator that uses resistors (R) and capacitors (C) to generate oscillations. Therefore, this pair does not fit the category of LC oscillators.

Option 2: Wien bridge oscillator and Phase-shift oscillator.

This option is incorrect because both the Wien bridge oscillator and the phase-shift oscillator are RC oscillators, not LC oscillators. The Wien bridge oscillator uses resistors and capacitors in a specific bridge configuration to generate oscillations, while the phase-shift oscillator uses a network of resistors and capacitors to produce the required phase shift for oscillation. Therefore, this pair does not fit the category of LC oscillators.

Option 4: Wien bridge oscillator and Colpitts oscillator.

This option is incorrect because the Wien bridge oscillator is an RC oscillator, while the Colpitts oscillator is an LC oscillator. As the question specifically asks for a pair of LC oscillators, this combination does not satisfy the requirement.

Conclusion:

Understanding the differences between various types of oscillators is crucial for correctly identifying their operational characteristics and applications. LC oscillators, such as Colpitts and Hartley oscillators, use inductors and capacitors to generate oscillations and are widely used in RF applications for their stability and simplicity. On the other hand, RC oscillators, like the Wien bridge and phase-shift oscillators, use resistors and capacitors and are typically used in audio frequency applications. Crystal oscillators, which use the mechanical resonance of crystals, provide highly precise frequencies and are commonly used in time-keeping and communication systems. Recognizing these differences helps in selecting the appropriate oscillator for a given application.

The correct option is 4

Concept:

• RC Coupling Capacitor: The coupling capacitor acts as a high-pass filter, allowing AC signals to pass while blocking DC. As frequency decreases, the capacitor's impedance increases, causing it to block more of the signal.
• Phase Shift due to Capacitor: This high-pass filtering introduces a -90° phase shift for signals at the lower 3-dB frequency (where the amplitude is reduced by 3 dB).
• CE Amplifier Phase Shift: The common-emitter amplifier itself introduces an additional -180° phase shift.
• Total Phase Shift: Therefore, the total phase shift at the lower 3-dB frequency is the sum of these individual shifts: -90° (capacitor) + (-180°) (CE amplifier) = -270°.
• Correction: However, it's important to note that due to the finite gain of the amplifier at the 3-dB frequency, the actual phase shift is slightly less negative than -270°. This results in a corrected phase shift of approximately -225°.

Therefore, the correct answer is 4)  225°.

Concept:

Colpitts Oscillator:

• The Colpitts Oscillator consists of a parallel LC resonator tank circuit whose feedback is achieved by way of a capacitive divider
• The center tapping of the tank sub-circuit is made at the junction of a “capacitive voltage divider” network to feed a fraction of the output signal back to the emitter of the transistor
• The two capacitors in series produce a 180° phase shift which is inverted by another 180° to produce the required positive feedback
• The oscillating frequency which is a pure sine-wave voltage is determined by the resonance frequency of the tank circuit

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

\({f_r} = \frac{1}{{2\pi \sqrt {L{C_T}} }}\)

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

Note:

Colpitt's Oscillator works in Class C mode.

Additional Information 

Hartley Oscillator:

In a Hartley oscillator, the positive output freed-back is inductively coupled by a tank circuit consisting inductor coil with a center tap.

The tank circuit of the Hartley Oscillator is shown:

RC phase shift oscillator:

In an RC phase shift oscillator, the phase of the feedback voltage is shifted by 180 degrees with a three-stage RC phase shift network

Concept:

UJT relaxation oscillation:

• The uni-junction transistor (UJT) has two doped regions with three external leads. It has one emitter and two bases.
• The emitter is heavily doped having many holes.
• The UJT is used to trigger the SCR. 
• The trigger voltage is equal to the capacitor voltage since the capacitor is connected between the anode and the ground.
• When the capacitor charges to the trigger voltage, UJT turns ON, discharging the capacitor through R4, thus turning ON the SCR.

Concept of Virtual Ground:

• The differential input voltage Vid between the noninverting and inverting input terminals is essentially zero.
• This is because even if the output voltage is few volts, due to a large open-loop gain of the op-amp, the difference voltage Vid at the input terminals is almost zero.

Where Vid is differential voltage, Vin1 is noninverting voltage, Vin2 is inverting voltage.

If the output voltage is 10 V and A i.e., the open-loop gain is 104 then, 

V out = A Vid

Vid = V out / A

= 10 / 104

= 1 mV.

Hence Vid is very small, for analyzing the circuit assumed to be zero.

Vid = Vin1 - Vin2

(Vin1 - Vin2) = V out / A

= V out / ∞ = 0

Calculation:

Circuit diagram:

Two terminals of Op-Amp i.e.; Inverting Terminal and Non-Inverting Terminal are at equipotential.

Apply KCL at node 1V_pp,

\(\frac{{1{V_{pp}} - 0}}{{10\;k}} + \frac{{1{V_{pp}} - {V_0}}}{{100k}} = 0\)

\(\frac{{10{V_{pp}} + 1{V_{pp}} - {V_0}}}{{100K}} = 0\)

\(11{V_{pp}} - {V_0} = 0\)

Closed-loop gain is given by the ratio of output to the input.

so the Closed-loop voltage gain is given by,

\(\frac{{{V_0}}}{{{V_{pp}}}} = 11\)

RC phase shift oscillator:

• It consists of three pairs of RC combinations, each providing a 60° phase shift, thus a total of 180° phase shift.
• RC oscillators are used to generate low or audio-frequency signals. Hence they are also known as audio-frequency oscillators.

The frequency of oscillation is given by:

\(f = {1\over 2\pi RC\sqrt{6}}\space Hz\) 

Calculation:

Given, f = 1000 kHz

\(C = \frac{1}{\sqrt{6}\pi} \space pF\)

\(10^6 = {1\over 2\pi R\times{1\over\sqrt{6}\pi}\times 10^{-12}\times\sqrt{6}}\)

\(R = {1\over 2\times 10^{-12}\times10^6}\)

R = 500 kΩ 

Colpitts oscillator:

• The Colpitts oscillator consists of one inductor and one split capacitor in the tank circuit.
• A capacitor with a center tap is used in the feedback system of the Colpitts oscillator
• It is used for the generation of sinusoidal output signals with very high frequencies

RC phase shift oscillator:

The circuit diagram of the RC phase shift oscillator is shown below:

The frequency produced by the above phase shift oscillator is given by:

\(f = \frac{1}{{2\pi RC\sqrt 6 }}\)

Wein bridge oscillator:

The circuit diagram of the Wein bridge oscillator is shown below:

The frequency of oscillation is given by:

\({\omega _o} = \frac{1}{{RC}}\)

\({f_o} = \frac{{1}}{{2\pi RC}}\)

Explanation:

OP-AMP

Operational amplifiers are linear devices that have all the properties required for nearly ideal DC amplification and are therefore used extensively in signal conditioning, filtering, or to perform mathematical operations such as add, subtract, integration and differentiation.

• It is a high voltage gain direct coupled amplifier.
• It can be used to perform mathematical operations on analog signals, hence it is called an operational amplifier.
• Op-amp is available as IC 741.
• The open-loop voltage gain of an ideal Op-amp is infinite.
• Op-amp consists of two terminals inverting(-ve) and non-inverting(+ve).

Maximum gain is limited to the open-loop gain of the op-amp but, for a linear amplifier, we need to add resistive elements in feedback known as inverting operational amplifiers.

At a frequency that is somewhat less than 10 Hz, the gain is flat down to DC and very high (10⁵).

The typical open-loop gain of an op-amp can be drawn as:

Hence the gain of an operational amplifier will be maximum at 1 Hz

So option (1) is the correct answer.

RC phase shift oscillator:

• RC phase shift oscillator as shown in the figure is used to invert the input for a 180° phase difference. Hence, the gain of the RC phase shift oscillator is negative. 
• The single R-C network gives the 60° phase shift. Hence the total phase shift provided by the feedback network is 1800. 
• In the RC phase shift oscillator, the inverting amplifier produces a 180° phase shift.
• The RC Phase shift oscillator has a fixed frequency and is used at lower frequencies.
• The circuit is simple to design.
• It can produce output over the audio frequency range.

• The frequency produced by the above phase shift oscillator is given by:

  \(f = \frac{1}{{2\pi RC\sqrt 6 }}\)

Note:

• To obtain a phase shift of 180^o at a frequency f, a minimum of 3 highpass RC circuits are needed.
• Hence identical RC elements are used to simplify analysis and design.
• Also, it is not viable to change circuit elements to get the desired frequency.

Hence changing the value of R and C to get the desired frequency is not the advantage of the R-C phase shift oscillator.

Crystal Oscillator:

• Crystal oscillators are fixed frequency oscillators with a high Q-factor.
• It operates on the principle of the inverse piezoelectric effect in which alternating voltage applied across the crystal surfaces causes it to vibrate at its natural frequency.
• It is these vibrations that eventually get converted into oscillations.
• These oscillators are made of Quartz crystal Rochelle salt and Tourmaline.
• Quartz is inexpensive, naturally available, and mechanically strong when compared to others.

In a crystal oscillator, the crystal is suitably cut and mounted between two metallic plates as shown in the figure.

      ​

Hartley Oscillator:

In a Hartley oscillator, the positive output feed-back is inductively coupled by a tank circuit consisting of an inductor coil with a center tap.

The tank circuit of Hartley Oscillator is shown:

Colpitts oscillator:

• The Colpitts oscillator consists of two capacitors and one inductor
• A capacitor with a center tap is used in the feedback system of the Colpitts oscillator
• It is used for the generation of sinusoidal output signals with very high frequencies

Phase Shift Oscillators:

• Phase Shift and Wein-bridge oscillators are used to generate audio frequencies, i.e. frequencies in AF Range.
• Commonly used phase shift oscillator using three lag circuit is as shown:

Hartley Oscillator:

In a Hartley oscillator, the positive output freed-back is inductively coupled by a tank circuit consisting inductor coil with a center tap.

The tank circuit of the Hartley Oscillator is shown:

Applications

• The Hartley oscillator is to produce a sine wave with the desired frequency
• Hartley oscillators are mainly used as radio receivers
• The Hartley oscillator is Suitable for oscillations in RF (Radio-Frequency) range, up to 30 MHz. Hence they are used as a high-frequency oscillator.

Concept:

• An oscillator consists of an amplifier with gain A & a feedback network with gain β.
• The feedback network is used for phase shifting.
• The amplifier receives the output of the phase-shifting network.
• The amplifier then amplifies it and adds a 180° phase shift. This phase-shifted output of the amplifier is applied to the input of feedback.
• Feedback networks shift the amplifier output to 180°.
• Thus, due to the total 360° phase shift, the feedback becomes positive feedback.
• This gives rise to the oscillation if the Barkhausen criteria is satisfied.

Explanation:

• Three RC sections are used which are called ladder networks.
• The phase shift provided by three RC networks is 180°.
• Thus the total phase shift in the circuit is 360°. 

→ The gain of the amplifier must be sufficient so that,

|Aβ| ≥ 1

Then, the Barkhausen criterion is satisfied and Barkhausen oscillation are produced.

Calculation:

The frequency of oscillation is given by

\(\rm f_0 = \frac{1}{2 \pi RC \sqrt 6}\)

Given, C = 5 pF, f₀ = 800 kHz

\(\rm R = \frac{1}{2 \pi f_0 C \sqrt 6}\)

\(R = \frac{1}{2 \pi \times 800 \times 10^3 \times 5 \times 10^{-12} \times \sqrt 6}\)

∴ R = 16.2 kΩ

Hence, correct option is (3)

Crystal Oscillator:

A crystal oscillator is the most stable frequency oscillator.

Advantages:

• The crystal oscillator is possible to obtain a very high precise and stable frequency of oscillators
• It has very-low-frequency drift due to change in temperature and other parameters
• The Q is very high
• It has automatic amplitude control

Disadvantages:

• These are suitable for high-frequency application
• Crystals of low fundamental frequencies are not easily available

• Hartley and Colpitts's oscillators are LC oscillators.
• LC oscillators are unstable oscillators.
• Phase shift oscillator is suitable for oscillations in AF range up to 1 kHz
• Crystals like quartz have high-quality factors, Q (range: 104 - 106). The high-quality factor will result in high-frequency stability.

Colpitts oscillator:

• The Colpitts oscillator consists of one inductor and two capacitors.
• A capacitor with a center tap is used in the feedback system of the Colpitts oscillator
• It is used for the generation of sinusoidal output signals with very high frequencies

The frequency of oscillations of Colpitt’s oscillator is given by,

\(f = \frac{1}{{2\pi \sqrt {L{C_{eq}}} }}\)

\({C_{eq}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}\)

Similarly, the frequency of oscillation of Hartley oscillator is given as,