Op-Amp Characteristics and Data Converter Principles (DAC/ADC)
Ideal and Practical Operational Amplifier with Characteristics
Operational Amplifier
An operational amplifier (Op-Amp) is a high gain, DC-coupled electronic amplifier with two inputs (inverting and non-inverting) and one output, used to perform mathematical operations such as addition, subtraction, integration and differentiation.
Ideal Operational Amplifier
An ideal Op-Amp is a hypothetical amplifier having perfect characteristics and is used only for theoretical analysis.
Characteristics of Ideal Op-Amp
Infinite open-loop voltage gain
Infinite input impedance
Zero output impedance
Infinite bandwidth
Infinite slew rate
Zero input offset voltage
Infinite Common Mode Rejection Ratio (CMRR)
Infinite Power Supply Rejection Ratio (PSRR)
No noise and distortion
Practical Operational Amplifier
A practical Op-Amp is a real device (example:
IC 741
Whose characteristics are close to, but not exactly same as, an ideal Op-Amp.
Characteristics of Practical Op-Amp
Very high but finite open-loop gain
High but finite input impedance
Low but non-zero output impedance
Limited bandwidth
Finite slew rate
Small input offset voltage
High but finite CMRR
High but finite PSRR
Presence of noise and distortion
Typical values for IC 741
Open-loop gain ≈ 2 × 10⁵
Input impedance ≈ 2 MΩ
Output impedance ≈ 75 Ω
Bandwidth ≈ 1 MHz
Slew rate ≈ 0.5 V/µs
DC and AC Characteristics of Operational Amplifier
The characteristics of an Op-Amp describe its performance under DC (static) and AC (dynamic) operating conditions.
1. DC Characteristics of Op-Amp
DC characteristics indicate the behavior of an Op-Amp for constant or slowly varying signals.
1. Input Offset Voltage (V_OS)
It is the small DC voltage required between input terminals to make output zero.
Ideally zero, but practically a few millivolts.
2. Input Bias Current (I_B)
The average of currents flowing into the inverting and non-inverting terminals.
Ideally zero, but practically in nanoampere range.
3. Input Offset Current (I_OS)
Difference between the input bias currents.
Ideally zero.
4. Input Impedance (R_in)
Resistance offered by the input terminals.
Ideally infinite, practically very high.
5. Output Impedance (R_out)
Resistance seen at the output terminal.
Ideally zero, practically low.
6. Common Mode Rejection Ratio (CMRR)
Ability of Op-Amp to reject common mode signals.
CMRR = \frac{A_d}{A_c}
Ideally infinite.
7. Power Supply Rejection Ratio (PSRR)
Ability to reject variations in power supply voltage.
Ideally infinite.
2. AC Characteristics of Op-Amp
AC characteristics describe the behavior of Op-Amp for time–
Varying signals.
1. Open Loop Voltage Gain (A_v)
Ratio of output voltage to input voltage without feedback.
Very high at low frequencies and decreases with frequency.
2. Bandwidth
Frequency range over which the Op-Amp operates effectively.
Practical Op-Amp has limited bandwidth.
3. Gain Bandwidth Product (GBW)
Product of gain and bandwidth.
Constant for a given Op-Amp.
GBW = A_v \times BW
4. Slew Rate (SR)
Maximum rate of change of output voltage.
SR = \frac{dV_o}{dt} ; (V/\mu s)
Limits high-frequency performance.
5. Frequency Response
Gain decreases at –20 dB/decade beyond cut-off frequency.
6. Noise
Undesired electrical disturbances at output.
Practically present.
3 unit
Weighted Resistor Digital-to-Analog Converter (DAC)
Definition
A Weighted Resistor DAC is a digital–
To-
analog converter in which each digital input bit is connected through a resistor weighted according to its binary significance. The circuit converts a binary digital input into a proportional analog output voltage.
Circuit of Weighted Resistor DAC
Op-Amp Based Weighted Resistor DAC (4-bit example)
Copy code
b3 (MSB) ──S3──R─────┐
b2 ──S2──2R───┼──► (−) Op-Amp ──► Vo
b1 ──S1──4R───┤
b0 (LSB) ──S0──8R───┘
(+)
GND
S3 to S0 → switches controlled by digital bits
R, 2R, 4R, 8R → weighted resistors
Op-Amp is in inverting summing configuration
Working Principle
Each digital bit controls a switch.
If the bit = 1, the switch connects the resistor to reference voltage (Vref).
If the bit = 0, the switch connects the resistor to ground.
Each resistor produces a current proportional to its weight.
The Op-Amp sums all currents and converts them into an analog output voltage.
Output Voltage Expression (4-bit DAC)
Where:
� = digital inputs (0 or 1)
MSB has highest weight
Negative sign due to inverting Op-Amp
Example
For digital input 1011:
Advantages
Simple and easy to understand
High conversion speed
Good accuracy for small number of bits
Disadvantages
Requires precise resistor values
Difficult to design for higher resolution
Sensitive to resistor mismatch
Not suitable for large bit DACs
Applications
Audio signal processing
Digital voltmeters
Data acquisition systems
Function generators
Comparison of DAC and ADC Specifications
Digital-to-Analog Converter (DAC) and Analog-to-Digital Converter (ADC) are essential data conversion devices. Their specifications define the accuracy, resolution, and speed of conversion.
1. Resolution
DAC:
Smallest change in analog output corresponding to a 1-LSB change in digital input.
ADC:
Smallest change in analog input that produces a change in digital output.
2. Accuracy
DAC:
Difference between actual analog output and ideal output.
ADC:
Difference between actual digital output and true analog input value.
3. Linearity (INL)
DAC:
Measures deviation of the output staircase from an ideal straight line.
ADC:
Measures uniformity of step sizes across the input range.
4. Differential Non-Linearity (DNL)
DAC:
Deviation in step size between adjacent output levels.
ADC:
Deviation in code width between successive digital codes.
DNL > 1 LSB may result in missing codes.
5. Offset Error
DAC:
Output voltage when digital input is all zeros.
ADC:
Input voltage required to produce the first non-zero digital output.
6. Gain Error
DAC:
Difference between actual and ideal slope of output characteristic.
ADC:
Error in full-scale range after offset error is removed.
7. Conversion Speed
DAC:
Time required to update the analog output.
ADC:
Time required to convert analog input into digital form.
8. Settling Time / Conversion Time
DAC:
Settling time is the time taken for output to reach within ±½ LSB of final value.
ADC:
Conversion time is the time required to complete one full conversion
Dual Slope Analog to Digital Converter (ADC)
Definition
A Dual Slope ADC is an integrating type analog-to-digital converter that converts an analog input voltage into a digital output by using two integration phases:
Integration of input voltage
De-integration using a reference voltage
Block Diagram of Dual Slope ADC
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Vin ──►┐
│
Vref ──►┼──► Analog Switch ─► Integrator ─► Comparator ─► Counter ─► Digital Output
│
Clock ────────────────────────────────────────────────►
(Draw neat block diagram in exam)
Working / Operation
The operation of Dual Slope ADC is divided into three steps:
1. Integration Phase
The analog input voltage Vin is applied to the integrator for a fixed time T₁.
The integrator output increases linearly with slope proportional to Vin.
At the end of this phase, the integrator output reaches a value proportional to Vin × T₁.
2. De-integration Phase
The input voltage is disconnected.
A known reference voltage (Vref) of opposite polarity is applied.
The integrator output now ramps back towards zero.
The time taken to reach zero is T₂, which depends on the magnitude of Vin.
3. Counting Phase
During de-integration, a counter counts clock pulses.
The number of pulses counted is proportional to T₂.
Since T₂ ∝ Vin, the digital count represents the input voltage.
Key Relationship
Digital Output ∝ Input Voltage
Advantages of Dual Slope ADC
High accuracy
Excellent noise rejection
Insensitive to component variations
No need for precise resistor values
Good linearity
Low offset and drift errors
Ideal for low-speed, high-precision measurements
Disadvantages (Optional – write if asked)
Slow conversion speed
Not suitable for high-speed applications
Applications
Digital voltmeters (DVM)
Digital multimeters
Industrial instrumentation
Precision measurement systems