RRB JE CBT2 : EXPERT
03 Jun

Analog-to-Digital and Digital-to-Analog Conversion

DAC Resolution

The resolution of a Digital-to-Analog Converter (DAC) determines the smallest change in analog output voltage that can be produced for a one-bit change in the digital input.

Significance of Higher Resolution

A higher DAC resolution provides:

  • More output levels
  • Smaller output step size
  • Better analog signal reproduction
  • Improved precision and accuracy

Resolution Does Not Directly Determine

  • Power consumption
  • Maximum conversion speed
  • Maximum input voltage

Open-Loop Differential Amplifier

An open-loop differential amplifier amplifies the difference between two input voltages without using feedback.

Characteristics

  • Inputs applied to both terminals
  • High gain
  • Output depends upon voltage difference
  • No feedback path

Important Points

Input is not applied only to the inverting terminal.Input is not applied only to the non-inverting terminal.Output is not always zero.The output is determined by the differential input voltage.


High-Frequency Response of CE Amplifier

The high-frequency gain of a Common Emitter amplifier is mainly affected by:

  • Collector-Base Junction Capacitance (Ccb)
  • Emitter-Base Junction Capacitance (Ceb)

Collector-Base Junction Capacitance

Also known as Miller capacitance.Effects:

  • Produces feedback path
  • Reduces gain at high frequencies

Emitter-Base Junction Capacitance

Effects:

  • Influences input impedance
  • Reduces input signal amplitude at high frequencies

Overall Effect

These capacitances create a low-pass filtering effect which reduces amplifier gain at high frequencies.


FeatureCollector–Base Junction Capacitance (Ccb)Emitter–Base Junction Capacitance (Ceb)
Other NameMiller CapacitanceInput Junction Capacitance
LocationBetween Collector and BaseBetween Emitter and Base
NatureReverse-biased junction capacitanceForward-biased junction capacitance
Main EffectCreates a feedback path between output and inputAffects the input circuit
Impact on GainReduces gain at high frequenciesIndirectly affects signal amplification
Impact on Input SignalMinor direct effectReduces input signal amplitude at high frequencies
Impact on Input ImpedanceLittle direct effectInfluences input impedance
Frequency ResponseLimits high-frequency performance due to Miller effectLimits high-frequency response at input
Role in TransistorCauses feedback from collector to baseStores charge in emitter-base junction
Practical ConcernMiller effect increases effective input capacitanceSlows response to high-frequency input signals

Oscillators

Hartley Oscillator

A Hartley oscillator is an LC oscillator employing inductive feedback.

Construction

  • Two inductors (or tapped inductor)
  • One capacitor

These components form a resonant tank circuit.

Principle of Operation

Works on the principle of parallel resonance.

Features

  • Inductive feedback
  • Variable frequency oscillator
  • Produces sinusoidal waveform
  • Frequency determined by tank circuit

RC Phase Shift Oscillator

An RC Phase Shift Oscillator uses an amplifier and RC network to generate sinusoidal oscillations.

Barkhausen Criterion

For sustained oscillations:

  • Total phase shift around loop = 360° or 0°
  • Loop gain ≥ 1

RC Network

Three RC sections provide:180° phase shiftAmplifier provides:180° phase shiftTotal:360° phase shift

Amplifier Gain Requirement

Minimum amplifier gain:29

Oscillation Frequency

f = 1 / (2πRC√6)


Feedback Amplifiers

Voltage-Series Feedback Amplifier

A voltage-series feedback amplifier samples output voltage and feeds it back in series with the input.

Characteristics

  • Increased input impedance
  • Decreased output impedance
  • Improved gain stability

Equivalent Nature

Acts as a:Voltage-Controlled Voltage Source (VCVS)

Example

Non-inverting OP-AMP

Not Correct

It is not known as a transconductance amplifier.


Operational Amplifiers

Non-Inverting OP-AMP

In a non-inverting OP-AMP:

  • Input is applied at non-inverting terminal
  • Output remains in phase with input

Characteristics

  • No phase inversion
  • Positive input produces positive output
  • Negative input produces negative output

Voltage Regulators

IC 7905

The IC 7905 belongs to the 79XX negative voltage regulator family.

Output Voltage

7905 → -5 VSimilarly:

  • 7912 → -12 V
  • 7915 → -15 V

IC 723 Voltage Regulator

The IC 723 is a versatile voltage regulator used for positive and negative voltage regulation.

Specifications

Output Voltage Range

2 V to 37 V

Output Current

Up to 150 mA

Features

  • Internal reference source
  • Error amplifier
  • Series pass transistor
  • Current limiting circuit
  • Thermal protection

Rectifiers

Bridge Rectifier

A bridge rectifier is a full-wave rectifier using four diodes arranged in bridge configuration.

Characteristics

  • Full-wave rectification
  • No center-tapped transformer required
  • Better transformer utilization
  • Improved efficiency

Peak Inverse Voltage (PIV)

PIV is the maximum reverse voltage a diode can withstand.

Bridge Rectifier

For a bridge rectifier:PIV per diode = Peak input voltage


Ripple Factor

Ripple factor indicates the amount of AC content present in the rectified output.

Comparison

RectifierRipple Factor
Half-Wave RectifierHigher
Full-Wave RectifierLower

Important Observation

A Half-Wave Rectifier has more than twice the ripple factor of a Full-Wave Rectifier.


Diodes

Forward Biased PN Junction

When a diode is forward biased:

  • Depletion region decreases
  • Potential barrier decreases
  • Majority carrier flow increases

Important Point

Current conduction occurs primarily due to majority carriers.The statement that heavy current flow occurs because of minority carriers is incorrect.


Zener Diode

A Zener diode operates in reverse breakdown region and maintains nearly constant voltage.

Temperature Effect

The breakdown voltage changes according to the temperature coefficient.


Special Diode with Different Forward and Reverse Resistance

Characteristics

  • Forward resistance = 0 Ω
  • Reverse resistance = 1 kΩ

Forward bias behaves like a short circuit.Reverse bias behaves like a resistor.


Phase-Locked Loop (PLL)

A PLL is an electronic control system that synchronizes an oscillator with an input signal.

Components

  • Phase Detector
  • Low Pass Filter
  • Voltage Controlled Oscillator (VCO)
  • Feedback Network

Function of Low Pass Filter

Removes high-frequency noise from phase detector output.

Capture Range

Controlled by PLL filter characteristics.

Lock Range

Primarily determined by:

  • VCO
  • Loop gain

Therefore:

  • Filter controls capture range.
  • Filter does not control lock range.

Communication Systems

Raised Cosine Filter

A Raised Cosine Filter is used to reduce Inter-Symbol Interference (ISI).

Roll-Off Factor

β lies between:0 ≤ β ≤ 1

Interpretation

β = 0Ideal brick-wall responseβ = 1Maximum excess bandwidth

Bandwidth Formula

BW = Rs(1 + β)/2where Rs is the symbol rate.


Sinc Pulse Shaping

Sinc pulse shaping is used for ideal Nyquist transmission.

Important Property

A sinc function is obtained as the inverse Fourier transform of a rectangular frequency response.Therefore:Sinc pulse shaping is derived from a rectangular function.


Oscilloscope and CRT

CRT Oscilloscope

A Cathode Ray Tube Oscilloscope displays electrical signals as voltage versus time waveforms.

Major Components

  • CRT
  • Vertical deflection system
  • Horizontal deflection system
  • Time base circuit

Vertical Deflection

Vertical deflection is proportional to:Amplitude of the input signalA higher input amplitude produces greater vertical movement of the electron beam.


Primary Function of CRT

The CRT visually displays electrical waveforms.It achieves this through:

  • Electron gun
  • Deflection system
  • Phosphor screen

Graticule

The graticule provides a reference scale for waveform measurements.

Applications

  • Amplitude measurement
  • Time measurement
  • Frequency calculation
  • Waveform comparison

Time Delay Measurement in CRO

Time delay is measured by:

  • Using the time-base control
  • Measuring horizontal displacement

Protective Relays

Sensitivity

Sensitivity refers to the ability of a relay to detect and respond to very small fault currents.A highly sensitive relay can operate even for minor fault conditions.


Solved Examples

Example 1: Zener Breakdown Voltage Variation

Question

A Zener diode has a breakdown voltage of 7 V at 300 K and a temperature coefficient of 2.3 mV/°C. Determine the breakdown voltage at 400 K.

Solution

Temperature rise:ΔT = 400 − 300 = 100°CVoltage change:ΔVz = 2.3 × 100 = 230 mVΔVz = 0.230 VNew breakdown voltage:Vz = 7 + 0.230Vz = 7.23 V

Answer

Vz = 7.23 V


Example 2: Voltage-Series Feedback Amplifier Impedances

Question

Input impedance without feedback = 5 kΩOutput impedance without feedback = 10 kΩFeedback factor:Aβ = 19Find input and output impedance with feedback.

Solution

Input impedance:Rif = Ri(1 + Aβ)Rif = 5 × 20Rif = 100 kΩOutput impedance:Rof = Ro/(1 + Aβ)Rof = 10/20Rof = 0.5 kΩ

Answer

Input impedance = 100 kΩOutput impedance = 0.5 kΩ


Example 3: Special Diode Circuit

Question

A special diode has:

  • Forward resistance = 0 Ω
  • Reverse resistance = 1 kΩ

Load resistance = 1 kΩInput square wave:+4 V and −4 VFind output voltage during reverse bias.

Solution

Total resistance:1 kΩ + 1 kΩ = 2 kΩUsing voltage division:Output voltage:Vo = (-4) × (1/2)Vo = -2 V

Answer

Vo = -2 V


Example 4: Bridge Rectifier PIV

Question

A bridge rectifier is supplied by:24 sin(ωt) VFind PIV of each diode.

Solution

Peak voltage:Vp = 24 VFor bridge rectifier:PIV = Vp

Answer

PIV = 24 V


Example 5: Open-Loop OP-AMP Output

Question

Open-loop gain:AOL = 10⁵Input voltage:Vin = 100 mVSupply:±15 VFind output voltage.

Solution

Theoretical output:Vo = AOL × VinVo = 10⁵ × 0.1Vo = 10000 VSince output cannot exceed supply limits,Vo = +15 V

Answer

Output voltage = +15 V

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