Draw and explain the working of following digital circuits. (a) A/D Converter (b) Bistable multivibrator c) Schmitt trigger

(a) A/D Converter (Analog to Digital Converter)

An A/D converter is a device that converts an analog signal, such as a voltage, into a digital representation that can be used by digital circuits and microprocessors. The conversion process involves several steps, including sampling, quantization, and encoding.

Working of an A/D Converter:

1. Sampling: The analog signal is sampled at regular intervals, determined by the sampling frequency. The Nyquist-Shannon sampling theorem states that the sampling frequency must be at least twice the highest frequency component of the analog signal to accurately reconstruct the signal.

2. Quantization: Each sampled value is then quantized, which means it is approximated by a finite number of levels. The difference between the actual analog value and the quantized digital value is known as quantization error.

3. Encoding: Finally, the quantized values are encoded into a binary format that can be processed by digital systems.

Here is a simplified block diagram of an A/D converter:

Analog Input ---> Sample and Hold Circuit ---> Quantizer ---> Digital Encoder ---> Digital Output

Types of A/D Converters:

There are several types of A/D converters, including:

1. Successive Approximation Register (SAR) A/D Converter: Uses a binary search algorithm to find the closest digital value to the analog input.

2. Flash A/D Converter: Uses a bank of comparators to convert the entire analog signal to a digital output in one step, making it the fastest type.

3. Sigma-Delta A/D Converter: Uses oversampling and noise shaping to achieve high resolution.

4. Dual Slope A/D Converter: Integrates the input signal over a fixed period and then measures the time it takes to return to zero, which is proportional to the input.

Example:

Consider a simple 3-bit A/D converter with a reference voltage of 5V. The input voltage range is 0 to 5V, and with 3 bits, we have (2^3 = 8) quantization levels. The voltage resolution is (5V / 8 = 0.625V) per level. If the analog input is 2.5V, the digital output would be the binary representation of the quantized level closest to 2.5V.

(b) Bistable Multivibrator

A bistable multivibrator, also known as a flip-flop, is a digital circuit that has two stable states and can be used to store one bit of information. The circuit can be set to one state or reset to another state by applying appropriate signals.

Working of a Bistable Multivibrator:

1. Set State: When a set signal is applied, the flip-flop transitions to and remains in the set state until a reset signal is received.

2. Reset State: When a reset signal is applied, the flip-flop transitions to and remains in the reset state until a set signal is received.

3. Output: The output of the flip-flop remains constant until the state is changed by a set or reset signal.

Here is a simplified block diagram of a bistable multivibrator:

Set Input ---> Flip-Flop ---> Q (Output)
Reset Input -----------------> /Q (Inverted Output)

Types of Bistable Multivibrators:

1. SR Flip-Flop: Set-Reset flip-flop, which can be set or reset based on the input signals.

2. D Flip-Flop: Data or Delay flip-flop, which captures the value of the data input at a particular edge of the clock signal.

3. JK Flip-Flop: A more versatile flip-flop that can be used as an SR flip-flop, a D flip-flop, or a T flip-flop (Toggle flip-flop).

4. T Flip-Flop: Toggles its output on every clock cycle when the T input is high.

Example:

Consider an SR flip-flop with the following truth table:

S	R	Q (next state)	/Q (next state)
0	0	No Change	No Change
0	1	0	1
1	0	1	0
1	1	Invalid	Invalid

If the current state is Q=0 and /Q=1, applying a set signal (S=1, R=0) will change the state to Q=1 and /Q=0.

(c) Schmitt Trigger

A Schmitt trigger is a comparator circuit with hysteresis, meaning it has two different threshold voltage levels for switching from high to low and from low to high. This feature makes it useful for cleaning up noisy signals and creating a stable digital output from an analog input.

Working of a Schmitt Trigger:

1. Non-Inverting Schmitt Trigger: When the input voltage exceeds the upper threshold, the output switches to a high state. When the input voltage falls below the lower threshold, the output switches to a low state.

2. Inverting Schmitt Trigger: When the input voltage falls below the lower threshold, the output switches to a high state. When the input voltage exceeds the upper threshold, the output switches to a low state.

3. Hysteresis: The difference between the upper and lower threshold is known as hysteresis, which helps prevent false triggering due to noise.

Here is a simplified block diagram of a Schmitt trigger:

Analog Input ---> Schmitt Trigger ---> Digital Output

Example:

Consider a non-inverting Schmitt trigger with an upper threshold of 3V and a lower threshold of 2V. If the input voltage rises above 3V, the output becomes high. If the input voltage then drops below 2V, the output becomes low. If the input voltage fluctuates between 2V and 3V, the output remains unchanged, demonstrating the hysteresis effect.