Q10 (i): Schmitt Trigger
A Schmitt Trigger is a comparator circuit with hysteresis, implemented using positive feedback. It is
used to convert an analog input signal into a digital output signal. Unlike a normal comparator, the
Schmitt Trigger provides two threshold voltages: Upper Threshold Point (UTP) and Lower
Threshold Point (LTP). The hysteresis provided by these thresholds helps eliminate noise and
provides a clear, stable output transition. When the input signal exceeds UTP, the output switches
from LOW to HIGH. When it drops below LTP, the output switches from HIGH to LOW. This makes
it ideal for waveform shaping and debouncing applications.
Applications include: signal conditioning, square wave generation, noise immunity, and digital logic
input stabilization.
Q10 (ii): Differential Amplifier Design (V0 = 2V1 –
3V2)
To achieve V0 = 2V1 – 3V2, we use a combination of inverting and non-inverting op-amp circuits:
Step 1: Create a non-inverting amplifier to generate 2V1. This uses an op-amp with gain 2 using
resistor values R1 and Rf such that Gain = 1 + (Rf/R1).
Step 2: Use an inverting amplifier to produce –3V2 using gain = –Rf/R1 = –3.
Step 3: Sum these using a summing amplifier. The resulting output is:
V0 = 2V1 – 3V2.
This modular approach using op-amps is standard in analog computation and signal processing
applications.
Q11 (i): Non-Inverting Amplifier Analysis
Given: R1 = 10kΩ, Rf = 100kΩ, V1 = 1V, RL = 10kΩ.
(a) Output Voltage:
V0 = V1 * (1 + Rf/R1) = 1V * (1 + 100k/10k) = 11V
(b) Closed-loop Gain (Af): Af = 11
(c) Loop Gain:
β = R1 / (R1 + Rf) = 10 / 110 = 0.0909
Assuming A_OL = 10^5, Loop Gain = A_OL * β = 10^5 * 0.0909 ≈ 9090
(d) Load Current:
I_L = V0 / RL = 11V / 10kΩ = 1.1 mA
(e) Output Current ≈ Load Current = 1.1 mA
These calculations help in analyzing real-world amplifier performance with resistive loads.
Q11 (ii): Integrator
The op-amp integrator uses a capacitor in the feedback path instead of a resistor. The basic
configuration uses an inverting op-amp, where the output voltage is:
V0(t) = – (1/RC) ∫ Vin(t) dt
This circuit outputs a voltage proportional to the time integral of the input signal. The frequency
response shows decreasing gain with increasing frequency, making it ideal for signal integration or
low-pass filtering.
At low frequencies, gain is high; at high frequencies, it attenuates the signal. The gain magnitude is:
|A(f)| = 1 / (2πfRC)
Applications: waveform generation, analog computers, and signal processing.
Q12 (i): Block Diagram of Op-Amp
Block Diagram:
1. Differential Input Stage: Accepts two inputs (inverting and non-inverting) and amplifies the
difference.
2. Gain Stage: Provides high voltage gain and includes compensation circuitry.
3. Output Stage: Typically a push-pull amplifier providing low output impedance.
Each block serves a critical purpose:
- Input Stage: Sets input impedance and bias conditions.
- Gain Stage: Provides necessary amplification.
- Output Stage: Drives load, ensuring sufficient current and voltage swing.
The op-amp behaves ideally with infinite input impedance, zero output impedance, and infinite gain.
Practical designs approximate these conditions.
Q12 (ii): Instrumentation Amplifier (Gain 1 to 1000)
Instrumentation amplifiers are precision differential amplifiers with high input impedance and
adjustable gain. A typical design uses three op-amps:
- The first two act as buffers.
- The third provides differential amplification.
Gain is set by:
G = 1 + (2R/RG)
Where RG is the gain resistor. For example:
- For Gain = 1000: RG ≈ 20Ω (if R = 10kΩ)
- For Gain = 1: RG → ∞
Applications: ECG, sensor interfacing, strain gauges, and industrial measurement systems due to
excellent CMRR and stability.
Q13 (i): Second Order Low-Pass Butterworth Filter
(fc = 1 kHz)
Butterworth filters offer a maximally flat passband response. For a second-order low-pass design:
Sallen-Key topology is used with:
fc = 1 / (2πRC)
Choose:
- R = 15.9kΩ
- C = 0.01µF
This ensures fc = 1 kHz.
The filter provides –40 dB/decade roll-off after cutoff frequency. Butterworth design is preferred for
audio and instrumentation applications due to flat response near fc.
Q13 (ii): Types of Filters
(a) Low-Pass Filter:
- Passes signals below fc
- Attenuates above fc
- Used in audio, anti-aliasing
(b) High-Pass Filter:
- Passes above fc
- Blocks low frequencies
- Used in speaker systems, coupling circuits
(c) Band-Pass Filter:
- Allows a range between two cutoff frequencies
- Used in RF and audio equalizers
(d) Band-Stop (Notch) Filter:
- Rejects narrow frequency band
- Used to eliminate 50/60 Hz noise
Each filter type has a unique frequency response and application depending on the signal
requirements.