Exam Notes

Op-Amp Characteristics

Input Bias Current

  • Input bias current I<em>BI<em>B is defined as the average of the base currents entering the input terminals of the op-amp. I</em>B=(I<em>B++I</em>B−)/2I</em>B = (I<em>{B+} + I</em>{B-})/2

Input Offset Current

  • The difference between the bias currents at the input terminals of an op-amp is called the input offset current.
    I<em>OS=∣I</em>B+−IB−∣I<em>{OS} = |I</em>{B+} - I_{B-}|

Ideal Characteristics of Op-Amp

  • Bandwidth: Infinity
  • Input impedance: Infinity
  • Output impedance: Zero
  • Common Mode Rejection Ratio (CMRR): Infinity
  • Open loop gain: Infinity

Current Mirror Circuit

  • A circuit in which the output current is equal to the input current is called a current mirror.
  • In a current mirror circuit, the output current is the mirror image of the input current.

Slew Rate

  • The slew rate is defined as the maximum rate of change of output voltage caused by a step input voltage.

  • It is specified in volts per second (V/s).

  • Formula: dvdt\frac{dv}{dt}

Hysteresis in Comparator

  • The difference between the upper and lower threshold voltages is called hysteresis.

Purpose of Hysteresis in Comparator

  • Prevents noise from causing fake triggering when the input voltage is near the threshold.
  • Provides a stable and clean output even with slowly changing or noisy input signals.

Frequency Synthesizer

  • A frequency synthesizer generates a range of frequencies from a single reference frequency using techniques such as phase-locked loops (PLL).

Phase-Locked Loop (PLL) Circuit for FM Demodulation

  • The basic PLL circuit for FM demodulation consists of:
    • Phase detector (PD)
    • Low Pass Filter (LPF)
    • Voltage-Controlled Oscillator (VCO)

Analog-to-Digital Converter (ADC)

  • To determine the digital output for an input voltage of 8V, with a signal range of 0 to 12V and an 8-bit ADC:

    • An 8-bit ADC has 28=2562^8 = 256 levels.
    • V<em>OFS=V</em>Full Scale2n−1V<em>{OFS} = \frac{V</em>{\text{Full Scale}}}{2^n - 1}

  • Resolution:
    12 V255=0.04706 V\frac{12 \text{ V}}{255} = 0.04706 \text{ V}

  • Digital Output Calculation:
    Digital Output=Input VoltageResolution=8 V0.04706 V=170\text{Digital Output} = \frac{\text{Input Voltage}}{\text{Resolution}} = \frac{8 \text{ V}}{0.04706 \text{ V}} = 170

Classification of A/D Converters

  • Flash ADC
  • SAR ADC (Successive Approximation Register ADC)
  • Dual slope ADC
  • Sigma Delta ADC
  • Pipelined ADC

ADC Specifications

  • Resolution: Number of bits used to represent the analog input.
  • Conversion Time: Time taken to convert an analog signal to digital.

Op-Amp Output Voltage Calculation

  • Non-inverting input voltage:
    V<em>+=V</em>2=2R3RV<em>i=23V</em>iV<em>+ = V</em>2 = \frac{2R}{3R} V<em>i = \frac{2}{3} V</em>i
  • Voltage divider at inverting input:
    V<em>−=RR+RV</em>o=Vo2V<em>- = \frac{R}{R + R} V</em>o = \frac{V_o}{2}
  • Equating V<em>+V<em>+ and V</em>−V</em>-, we get:
    23V<em>i=V</em>o2\frac{2}{3} V<em>i = \frac{V</em>o}{2}
    V<em>o=43V</em>iV<em>o = \frac{4}{3} V</em>i

Precision Rectifier vs. Conventional Rectifier

Precision Rectifier

  • Uses op-amp for zero threshold.
  • Accurate for small voltages.
  • High precision output.

Conventional Rectifier

  • Uses diodes with a 0.7V threshold loss.
  • Not suitable for low voltage signals.
  • Output distorted for low signals.

Applications of Comparator

  • Zero-crossing detector
  • Oscillator units
  • Analog-to-Digital converters
  • Voltage level detector
  • Window detector

Multiplier Circuits

Basic Multiplier

  • Produces output V<em>o=kV</em>1V2V<em>o = k V</em>1 V_2 (analog).

Squaring Circuit

  • Both inputs are the same, so Vo=kV2V_o = k V^2

Square Root Circuit

  • Output, Vo=VV_o = \sqrt{V}, obtained by configuring feedback & divide-connected transistor (in op-amp configuration).

Multiplier Terminology

  • Linearity: The output follows V<em>1×V</em>2V<em>1 \times V</em>2.
  • Bandwidth: Frequency range where multiplier operates accurately.
  • Input Offset Voltage: Small voltage difference needed to take output to zero.
  • Temperature Sensitivity: Sensitivity to temperature changes.

ADC Calculation

  • Given: 8-bit ADC, Voltage range = 2V
  • Steps: 28=2562^8 = 256
  • Step size: Voltage range2n−1=228−1=2255=0.00784\frac{\text{Voltage range}}{2^n - 1} = \frac{2}{2^8 - 1} = \frac{2}{255} = 0.00784

ADC Error Calculation

  • Given: 12-bit ADC, Voltage range = 5V

  • Steps: 212=40962^{12} = 4096

  • Step size: 5212−1=0.00122\frac{5}{2^{12} - 1} = 0.00122

  • Digital Output:
    10.00122=819\frac{1}{0.00122} = 819

  • Digital output = Input Voltage / Resolution

  • Digital output=840.0941=85.02\text{Digital output} = \frac{84}{0.0941} = 85.02

  • Output in Binary, Decimal 85 = 01010101

ADC Specifications (Repeated)

  1. Resolution
  2. Quantization error
  3. Conversion time

Limitations

  1. Limited Efficiency
  2. Fixed output Voltage
  3. Limited current output

Isolation Amplifier

  • An isolation amplifier is an amplifier that offers an ohmic or electrical isolation between its input and output terminals.

Applications of Isolation Amplifier

  1. Power drivers
  2. Power test equipments.

Barkhausen Criteria for Oscillation

  • The Barkhausen criteria for oscillation require two conditions to be met:
    • The loop gain must be unity or greater (∣AB∣=1|AB| = 1).
    • The total phase shift around the loop must be zero or a multiple of 360 degrees.

Optocoupler

  • The combined package of an LED and a photodiode is called an optocoupler.

Applications of Optocoupler

  • Used to provide isolation in high voltage applications.
  • Used to transmit data in the megahertz range.
  • Used in wideband signal transmission.