Unit 4: Amplifiers and Oscillators - Subjective Questions

RC Coupled CE Amplifier:

The circuit uses a transistor in Common Emitter configuration with RC coupling between stages.

Components and their functions:

• and (Voltage divider): Provide proper DC base bias and stabilize the operating point (Q-point).
• (Collector resistor): Acts as the load and converts collector current variations into output voltage.
• (Emitter resistor): Provides thermal stability through negative DC feedback.
• (Bypass capacitor): Bypasses AC signal around to prevent AC negative feedback and maintain high gain.
• and (Coupling capacitors): Block DC while allowing AC signal to pass between stages, isolating DC bias of adjacent stages.

Working:

• When an AC signal is applied at the base, it causes variation in base current.
• This variation is amplified as a larger collector current.
• The amplified signal appears across with a phase shift.
• The coupling capacitor transfers this amplified AC to the next stage.

The name "RC coupled" comes from using Resistors (R) and Capacitors (C) for coupling between stages.

Frequency Response Curve:

The frequency response is a plot of voltage gain versus frequency (on a log scale). It is divided into three regions:

1. Low Frequency Region (Gain falls):

• At low frequencies, the reactance of coupling capacitors becomes high.
• This causes a significant voltage drop across coupling and bypass capacitors, reducing the signal reaching the load.
• Also, the bypass capacitor fails to bypass effectively, introducing negative feedback.

2. Mid Frequency Region (Constant gain):

• The gain remains constant and maximum.
• Reactance of coupling capacitors is negligible ().
• Shunt (stray) capacitance reactance is very high, so it has no effect.

3. High Frequency Region (Gain falls):

• At high frequencies, the reactance of shunt/junction capacitances becomes low.
• These capacitances shunt the input/output signals to ground, reducing gain.
• Also affected by transistor's inherent inter-electrode capacitances.

Bandwidth: , where and are the lower and upper cutoff frequencies (points where gain falls to of maximum, i.e., dB points).

Feedback: Feedback is the process of returning a portion of the output signal back to the input of an amplifier.

Positive Feedback (Regenerative):

• The feedback signal is in phase with the input signal.
• The net input increases, hence gain increases.
• Feedback factor makes denominator :
• Used in oscillators.
• Decreases stability, increases distortion and noise.

Negative Feedback (Degenerative):

• The feedback signal is out of phase (opposite) to the input signal.
• The net input decreases, hence gain decreases.
• Gain equation:
• Used in amplifiers.
• Increases stability, bandwidth; reduces distortion and noise.

Key Distinction Table:

Derivation of Feedback Gain:

Let:

• = gain without feedback (open loop gain)
• = feedback factor
• = input signal, = output signal, = feedback signal

For negative feedback, the net input to the amplifier:

The output is:

Solving:

Stability of Gain:

Differentiating with respect to :

Thus:

Conclusion: The fractional change in gain with feedback is reduced by a factor of . Hence negative feedback makes the gain more stable against variations in transistor parameters, temperature, and supply.

Effect of Negative Feedback on Bandwidth:

Negative feedback increases the bandwidth of an amplifier.

Explanation:

• Without feedback, let the gain be with lower cutoff and upper cutoff .
• With negative feedback, the gain reduces to .

New cutoff frequencies:

• Lower cutoff frequency decreases:
  

• Upper cutoff frequency increases:
  

Bandwidth relationship:

Gain-Bandwidth Product:

• The product of gain and bandwidth remains constant.
  

Conclusion: Negative feedback reduces gain by a factor but increases bandwidth by the same factor, keeping the gain-bandwidth product constant.

Effect of Negative Feedback on Noise and Distortion:

Noise Reduction:

• Let be the noise generated within the amplifier.
• With negative feedback, the noise at the output is reduced by a factor :
  
• The noise is reduced only if it is generated inside the feedback loop.

Distortion Reduction:

• Nonlinear distortion produced by the amplifier is also reduced:
  

Working principle:

• The distorted/noise component appearing at output is fed back out of phase to the input.
• This partly cancels the distortion generated in the amplifier.

Important Notes:

• Noise reduction applies only to noise generated within the amplifier, not noise present at the input signal itself.
• Since gain also reduces by the same factor, the signal-to-noise ratio may not always improve unless additional gain is provided by a preamplifier.

Conclusion: Negative feedback improves the quality (fidelity) of amplification by reducing internally generated noise and harmonic distortion by a factor .

Effect of Negative Feedback on Impedances:

The effect depends on the type of feedback connection (sampling and mixing).

Input Impedance:

• Series mixing (voltage subtracted at input) increases input impedance:
  
• Shunt mixing (current subtracted at input) decreases input impedance:
  

Output Impedance:

• Voltage sampling (output voltage sampled) decreases output impedance:
  
• Current sampling (output current sampled) increases output impedance:
  

Summary Table (Four Topologies):

Conclusion: Series mixing raises input impedance, shunt mixing lowers it; voltage sampling lowers output impedance, current sampling raises it.

Barkhausen Criterion:

For an oscillator to produce sustained (undamped) oscillations, the feedback must be positive and two conditions must be satisfied:

Condition 1 (Magnitude):
The magnitude of the loop gain must be equal to (or greater than) unity:

where = amplifier gain, = feedback factor.

Condition 2 (Phase):
The total phase shift around the loop must be or an integer multiple of :

Explanation:

• If : oscillations have constant amplitude (sustained).
• If : oscillations grow in amplitude (build-up phase).
• If : oscillations die out (damped).

Practical operation:

• Initially is kept slightly greater than 1 to start oscillations from noise.
• Amplitude stabilizing mechanisms then bring it back to for sustained output.

Conclusion: Barkhausen criterion is the fundamental requirement for any feedback oscillator to sustain oscillations without an external input signal.

RC Phase Shift Oscillator:

Circuit: Consists of a CE amplifier (providing phase shift) followed by a feedback network of three RC sections. Each RC section provides phase shift, giving a total of in the feedback network.

Working:

• The transistor amplifier provides a phase shift of .
• The three-section RC network provides an additional .
• Total phase shift = (or ), satisfying the Barkhausen phase condition.
• Positive feedback with sustains oscillations.

Frequency of Oscillation:

For identical RC sections, the frequency is:

Gain condition:
The amplifier must provide a minimum gain to overcome feedback network attenuation:

Advantages:

• Simple circuit, good frequency stability.
• Suitable for low and audio frequencies.

Disadvantages:

• Difficult to change frequency (need to vary 3 elements simultaneously).
• Not suitable for high frequencies.
• Poor frequency stability compared to LC oscillators at high frequencies.

Hartley Oscillator:

Circuit: An LC oscillator where the tank circuit consists of two inductors ( and ) and a single capacitor (). It uses inductive feedback through a tapped inductor.

Working:

• The tank circuit (, , ) determines the oscillation frequency.
• The transistor amplifier provides phase shift.
• The tapped inductor provides an additional , giving total (satisfying Barkhausen phase condition).
• Energy oscillates between the inductors and capacitor to sustain oscillations.

Frequency of Oscillation:

where the effective inductance (with mutual inductance ):

If mutual inductance is neglected: .

Condition for sustained oscillation:

Advantages:

• Easy frequency variation using a single variable capacitor.
• Wide frequency range (RF).

Disadvantages:

• Harmonic content is high.
• Poor frequency stability compared to crystal oscillators.

Colpitts Oscillator:

Circuit: An LC oscillator where the tank circuit uses two capacitors ( and ) and a single inductor (). It uses capacitive feedback through a tapped capacitor arrangement.

Working:

• The tank circuit (, , ) sets the frequency of oscillation.
• The transistor amplifier provides phase shift.
• The tapped capacitor network provides an additional , giving total .
• The Barkhausen criterion is satisfied, producing sustained oscillations.

Frequency of Oscillation:

where the equivalent (series) capacitance:

Condition for sustained oscillation:

Advantages:

• Better frequency stability than Hartley oscillator.
• Suitable for high frequencies (RF) because capacitors work well at high frequency.
• Simpler construction (no tapped inductor needed).

Disadvantages:

• Difficult to adjust frequency (both capacitors must be varied).

Comparison with Hartley: Colpitts uses two capacitors and one inductor, whereas Hartley uses two inductors and one capacitor.

Wien Bridge Oscillator:

Circuit: Uses a Wien bridge network as the frequency-determining feedback element along with a two-stage amplifier (or op-amp). The bridge has a series RC arm and a parallel RC arm.

Working:

• The amplifier provides (or ) phase shift (typically two stages/non-inverting).
• The Wien bridge network provides phase shift at the resonant frequency.
• The lead-lag network selects a single frequency where the phase shift is zero and feedback is maximum.

Frequency of Oscillation:

For a balanced bridge with and :

Condition for oscillation:
At this frequency, the feedback factor , so the amplifier gain must be:

Advantages:

• Excellent frequency stability.
• Low distortion (pure sine wave).
• Easy frequency variation using ganged variable resistors/capacitors.
• Wide frequency range (audio frequencies).

Disadvantages:

• Requires two amplifier stages for the needed phase shift.
• Cannot generate very high frequencies.

Applications: Widely used in audio signal generators and function generators.

Negative Resistance Oscillator:

Definition: A negative resistance oscillator uses a device that exhibits a negative resistance region in its V-I characteristic, where an increase in voltage causes a decrease in current (i.e., ).

Principle:

• Normally, a resistance dissipates energy.
• A device with negative resistance supplies energy to the circuit.
• When connected to an LC tank circuit, the negative resistance cancels the positive resistance (losses) of the tank.
• This compensates for energy losses and sustains oscillations.

Devices used:

• Tunnel diode (Esaki diode)
• UJT (Unijunction transistor)
• Gunn diode

Working:

• The device is biased in its negative resistance region.
• The effective circuit resistance becomes zero or negative.
• Barkhausen criterion is effectively satisfied, producing sustained oscillations.

Frequency of Oscillation:

Advantages:

• Can operate at very high frequencies (microwave range).
• Simple circuit with few components.

Applications:

• Microwave oscillators, high-frequency signal generation.

Comparison of Hartley and Colpitts Oscillators:

Conclusion: Both are LC oscillators for RF generation. The main difference is the type of feedback (inductive vs capacitive) and the arrangement of reactive elements. Colpitts is generally preferred at higher frequencies due to better stability.

Negative Feedback in Amplifiers:

Amplifiers require faithful and stable reproduction of the input signal. Negative feedback provides:

• Gain stability: Gain becomes independent of transistor parameter variations.
• Increased bandwidth: .
• Reduced distortion: Harmonic distortion reduced by .
• Reduced noise: Internal noise reduced by .
• Controllable impedances: Input/output impedances can be adjusted as required.

The trade-off is reduced gain, which is acceptable since gain can be increased by adding stages.

Positive Feedback in Oscillators:

Oscillators must generate a signal without any external input. This requires:

• Self-sustaining oscillations: Positive feedback () allows the output to feed the input in phase.
• Barkhausen criterion: Total phase shift and loop gain .
• The signal builds up from circuit noise and sustains itself.

Conclusion:

• Negative feedback stabilizes and improves amplification (needs an input).
• Positive feedback generates a continuous waveform (no input needed).
• Their opposite objectives dictate the choice of feedback type.

Given:

• Open loop gain
• Feedback factor (5%)

Step 1: Gain with feedback

Step 2: When open loop gain drops to

Step 3: Percentage change in gain

Without feedback, gain changed from 200 to 100:

With feedback, gain changed from 18.18 to 16.67:

Conclusion: A 50% drop in open loop gain results in only about 8.3% change in closed loop gain. This demonstrates the gain stabilization provided by negative feedback.

Lower Cutoff Frequency ():

At low frequencies, the coupling capacitor and its associated resistance form a high-pass filter. The lower cutoff frequency occurs when the capacitive reactance equals the resistance:

At this frequency, the gain falls to of the mid-band gain ( dB point).

Upper Cutoff Frequency ():

At high frequencies, the shunt (stray/junction) capacitance with the effective resistance forms a low-pass filter:

Significance:

• At both and , the output power drops to half of its maximum value (hence dB points).
• Voltage gain at these points .
• Bandwidth is defined as: .
• These frequencies define the useful frequency range over which the amplifier maintains nearly constant gain.

Conclusion: The 3-dB frequencies mark the boundaries of the amplifier's operating bandwidth.

Four Topologies of Negative Feedback:

Feedback is classified based on how the output is sampled and how it is mixed at the input.

1. Voltage-Series Feedback (Series-Shunt):

• Samples output voltage, mixes in series at input.
• Increases input impedance, decreases output impedance.
• Also called a voltage amplifier feedback; stabilizes voltage gain.

2. Current-Series Feedback (Series-Series):

• Samples output current, mixes in series at input.
• Increases both input and output impedance.
• Called transconductance amplifier feedback.

3. Voltage-Shunt Feedback (Shunt-Shunt):

• Samples output voltage, mixes in shunt (parallel) at input.
• Decreases both input and output impedance.
• Called transresistance amplifier feedback.

4. Current-Shunt Feedback (Shunt-Series):

• Samples output current, mixes in shunt at input.
• Decreases input impedance, increases output impedance.
• Called current amplifier feedback.

Summary:

Conclusion: The choice of topology depends on the desired input/output impedance and the type of quantity to be stabilized.

Given:

Step 1: Equivalent Capacitance

Step 2: Frequency of Oscillation

Conclusion: The Colpitts oscillator oscillates at approximately 74.6 kHz.

Distinction between LC and RC Oscillators:

Applications of LC Oscillators:

• Radio transmitters and receivers
• RF signal generation
• Local oscillators in communication systems

Applications of RC Oscillators:

• Audio frequency signal generators
• Function generators
• Low frequency testing equipment

Conclusion: LC oscillators are preferred for high frequencies because required inductor/capacitor values are practical, while RC oscillators are ideal for low/audio frequencies where inductors would be impractically large.