Oscillators and Feedback Amplifier MCQ Quiz - Objective Question with Answer for Oscillators and Feedback Amplifier - Download Free PDF

Three-Stage Cascade Amplifier and Overall Noise Figure Calculation

Problem Statement: In a three-stage cascade amplifier, each stage has a gain of 10 dB and a noise figure of 10 dB. We are tasked with calculating the overall noise figure of this cascade system.

Solution:

To calculate the overall noise figure (F_overall) of a cascade amplifier, we use Friis's formula for noise figure in cascaded systems:

Friis's Formula:

F_overall = F₁ + ^{(F₂ - 1)}/_G1 + ^{(F₃ - 1)}/_{G1 × G2} + ...

Where:

• F_n = Noise figure of the nth stage (in linear scale).
• G_n = Gain of the nth stage (in linear scale).

Step 1: Convert Gains and Noise Figures from dB to Linear Scale

The given gain (G) and noise figure (F) for each stage are 10 dB:

• G = 10 dB → G (linear) = 10^G(dB)/10 = 10^10/10 = 10.
• F = 10 dB → F (linear) = 10^F(dB)/10 = 10^10/10 = 10.

Step 2: Apply Friis's Formula

Since there are three stages, Friis's formula for the overall noise figure becomes:

F_overall = F₁ + ^{(F₂ - 1)}/_G1 + ^{(F₃ - 1)}/_{G1 × G2}

Substitute the values for F₁, F₂, F₃, G₁, and G₂:

• F₁ = 10 (linear).
• F₂ = 10 (linear).
• F₃ = 10 (linear).
• G₁ = G₂ = 10 (linear).

Thus:

F_overall = 10 + ^{(10 - 1)}/₁₀ + ^{(10 - 1)}/_{10 × 10}

F_overall = 10 + 0.9 + 0.09

F_overall = 10.99

Final Answer: The overall noise figure of the three-stage cascade amplifier is 10.99 (linear scale).

Explanation:

• An amplifier can be converted into an oscillator by doing some change in the amplifier circuit as:
• Connect the output of the amplifier to the input by a positive feedback circuit.
• The phase-shifted the output by 180° and feed this phase shift output to the input via a feedback circuit.
• An arrangement of the RC tuned circuit is connected as a load to the amplifier.
• Oscillator circuit block diagram.

The correct answer is: 2) A circuit that generates a non-sinusoidal wave without any input is called a linear oscillator.

Explanation:

1. Linear Oscillators (Option 1 - TRUE)

   • Generate sinusoidal waveforms (e.g., sine waves).

   • Examples: LC oscillators (Hartley, Colpitts), RC oscillators (Wien Bridge, Phase Shift).

2. Non-Linear Oscillators (Option 2 - FALSE)

   • Generate non-sinusoidal waveforms (e.g., square, triangle, sawtooth waves).

   • Not called linear oscillators—they are called relaxation oscillators or multivibrators.

3. Frequency Determination (Option 3 - TRUE)

   • Oscillator frequency depends on RC (resistor-capacitor) or LC (inductor-capacitor) networks.

4. Multivibrators (Option 4 - TRUE)

   • Used to generate square waves, pulses, or other non-sinusoidal signals.

   • Examples: Astable, Monostable, and Bistable multivibrators.

Concept:

The Colpitts oscillator is a type of LC oscillator used to generate high-frequency sinusoidal oscillations, especially in RF applications.

It works based on the principle of LC parallel resonance and uses a combination of capacitors and inductors to determine its frequency of oscillation.

Explanation:

The formula provided in statement 3 is incorrect in the way it's expressed.

The correct frequency of oscillation is given by:

$\omega =\frac{1}{\sqrt{L\cdot C_{eq}}}$, where $C_{eq}=\frac{C_1{C}_2}{C_1+C_2}$

This is the equivalent capacitance of two capacitors in series.

Conclusion:

Statement 3 is incorrect due to the incorrect formula for the oscillation frequency in a Colpitts oscillator.

Concept of Negative Feedback Amplifier:

Negative feedback is a technique where a portion of the output signal is fed back to the input with opposite phase to improve amplifier performance. Key effects include:

• Stabilization of gain

• Reduction of distortion and noise

• Control of input/output impedances​

Additional Information

1) Reduces nonlinear distortion in the output

• True: Negative feedback linearizes the amplifier's response, reducing harmonic and intermodulation distortion.

2) Reduces the effect of temperature on the output

• True: By stabilizing the gain, negative feedback makes the amplifier less sensitive to temperature variations in components (e.g., transistor β shifts).

3) Reduces unwanted electrical signals (noise) generated in the circuit

• True: Feedback suppresses internally generated noise (e.g., thermal noise, hum) by the same factor as distortion.

4) Reduces the bandwidth of the amplifier

• False (Correct Answer):

  • Negative feedback increases bandwidth by trading gain for frequency response.

  • The gain-bandwidth product (GBW) remains constant: Lower midband gain → Higher cutoff frequency.

• The transistor amplifier in which collector current flows for the entire cycle of input AC signal is called class A amplifier.
• The transistor amplifier in which collector current flows for the half-cycle of an AC signal is called a class B amplifier.
• The transistor amplifier in which collector current flows for less than half the cycle of an AC signal is called a class C amplifier

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,

$\frac{1V_{pp}-0}{10k}+\frac{1V_{pp}-V_0}{100k}=0$

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

$11V_{pp}-V_0=0$

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

so the Closed-loop voltage gain is given by,

$\frac{V_0}{V_{pp}}=11$

Barkhausen stability criteria

The Barkhausen stability criteria is a mathematical requirement used in electronics to predict whether a linear electronic circuit may oscillate.

It is commonly utilized in the design of electronic oscillators as well as general negative feedback circuits such as op-amps to keep them from oscillating.

Barkhausen's criteria is a necessary but not sufficient condition for oscillation:

Barkhausen Conditions For Oscillation:

It states that if 'A' is the gain of the amplifying element in the circuit and β(s) is the feedback path transfer function, so βA is the loop gain around the circuit's feedback loop, the circuit will maintain steady-state oscillations only at frequencies for which:

1. The loop gain is equal to one in absolute magnitude, which means that |βA| = 1
2. The phase shift through the loop is either zero or an integer multiple of 2π or 360⁰.

Important Points

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:

$f=\frac{1}{2\pi RC\sqrt{6}}Hz$ 

Calculation:

Given, f = 1000 kHz

$C=\frac{1}{\sqrt{6}\pi }pF$

${10}^6=\frac{1}{2\pi R\times \frac{1}{\sqrt{6}\pi }\times {10}^{-12}\times \sqrt{6}}$

$R=\frac{1}{2\times {10}^{-12}\times {10}^6}$

R = 500 kΩ 

Phase shift oscillator:

• The phase shift oscillator is a linear electronic circuit that produces a sine wave output.
• It consists of an inverting amplifier element such as a transistor or op-amp with its output feedback to its input through a phase shift network consisting of resistors and capacitors in a ladder network.
• The feedback network shifts the phase of the amplifier output by 1800 at the oscillation frequency to give positive feedback. 

Wein bridge oscillator :

• The Wein bridge oscillator uses two RC networks connected together to produce a sinusoidal oscillator.
• The Wein bridge oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay or phase advance depending upon the circuit frequency
• At the resonant frequency, the phase shift is 00.

Clapp oscillator:

• The Clapp oscillator is an LC oscillator that uses a particular combination of an inductor and three capacitors to set the oscillator frequency.
• The Clapp is often drawn as a Colpitts oscillator that has an additional capacitor placed in series with the inductor.
• This comes under linear or harmonic oscillators, which produces a sine wave output.
• Clapp oscillator is also one kind of phase shift oscillator containing L, C elements, and a transistor or op-amp along with feedback, so it provides phase shift.

​Relaxation oscillator:

• A relaxation oscillator is a nonlinear electronic oscillator circuit that produces nonsinusoidal repetitive output signals such as a triangle wave or square wave.
• Relaxation oscillators are generally used to produce low-frequency signals.
• These oscillators will not provide any phase shift in their output
• Examples of Relaxation oscillators are Astable multivibrator, flyback or sweep oscillator, etc.

The feedback amplification factor is given by $A_f=\frac{A}{1+A\beta }$

where A is open-loop gain and βA is loop gain.

As feedback increases the gain decreases thereby bandwidth increases.

The negative feedback in amplifiers causes

1. reduced the voltage gain and increases the stability in gain

2. increases the bandwidth by the factor (1+Aβ) to maintain constant gain-bandwidth product

3. Reduces the distortion and noise in the amplifier

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:

${\omega }_o=\frac{1}{RC}$

$f_o=\frac{1}{2\pi RC}$

The correct option is 4

Concept:

A. Hartley oscillator - II. LC tuned circuit

Explanation: The Hartley oscillator is an electronic oscillator circuit in which the oscillation frequency is determined by an LC (inductor-capacitor) tank circuit. The frequency can be adjusted based on the values of the inductors and capacitors used.

B. Crystal oscillator - III. Greater stability

Explanation: A Crystal oscillator uses a quartz crystal for frequency control and offers excellent frequency stability due to the quartz crystal's high Q-factor. This makes a crystal oscillator more stable compared to the other oscillator circuits.

C. Wien bridge oscillator - I. Two-stage RC coupled amplifier

Explanation: The Wien Bridge Oscillator employs a feedback circuit with an RC (resistor-capacitor) network to produce sinusoidal oscillations. Its design can involve a two-stage RC coupled amplifier and it's often used for generating audio frequencies.

Concept:

Negative feedback circuit:

The feedback amplification factor is given by:

 A_f = $\frac{A_o}{1+A_o\beta }$

Where,

A_o is open-loop gain

A_oβ is the loop gain.

Explanation:

The negative feedback in amplifiers causes:

• Reduced the gain and increases the stability in G.
• Increases the bandwidth to maintain constant gain-bandwidth product
• Reduces the distortion and noise in the amplifier
• The signal-to-noise ratio is not affected.
• The voltage gain (A_v) of an amplifier is defined as the ratio of output voltage to the input voltage.

Av = V_o/V_in

Here, V_o is the output voltage of an amplifier and V_in is the input voltage of an amplifier.

• In a negative feedback amplifier, closed-loop voltage gain is given 

            A_v = V_o / V_in = 1/(1+A_oβ)

Here, β = feedback factor,

A_o = open-loop gain of the amplifier.

• This expression clearly shows that closed-loop voltage gain has reduced by introducing negative feedback. 
• We know that a product of gain and bandwidth is inversely proportional so here bandwidth of amplifier will increase ;

            (gain × bandwidth = 0.35)

• A negative feedback amplifier decreases the current gain.

• One of the most important features of the crystal oscillator is its frequency stability as it has the ability to provide a constant frequency output under varying load conditions.
• The stability of the crystal oscillator is closely related to its quality factor or Q.
• High-Q crystal oscillator will oscillate at constant frequency because it produces oscillation only when it is nearer to its resonance frequency.
• A typical Q for a crystal oscillator ranges from 104 to 106.

Important Points:

• The crystal of crystal oscillator is usually made of the quartz material and provides a high degree of frequency stability and accuracy.
• It uses a piezoelectric crystal and when an ac voltage is applied across a crystal it starts vibrating at the frequency of supply voltage this effect is known as piezoelectric effect and the crystal which exhibits this effect is known as piezoelectric crystals.
• Conversely, when these crystals are placed under mechanical strain to vibrate, they produce an ac voltage