JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II ANALOG COMMUNICATIONS Previous Question Paper (August/September - 2022 - R16)

Frequency Division Multiplexing (FDM) is a technique where the available bandwidth of a communication channel is divided into several non-overlapping frequency slots. Each slot is assigned to a different signal, allowing multiple signals to be transmitted simultaneously over a single physical medium.

The process involves modulating each baseband signal onto a distinct carrier frequency. These modulated signals are then combined using a summer circuit and transmitted. At the receiver, bandpass filters are used to separate the signals, followed by individual demodulators to recover the original baseband information.

Block Diagram Description: The transmitter consists of multiple signal sources (m1, m2, ..., mn) connected to individual modulators (MOD1, MOD2, ..., MODn) driven by different carrier frequencies (f1, f2, ..., fn). The outputs are combined in a summer and sent through a channel. The receiver uses a bank of bandpass filters (BPF1, BPF2, ..., BPFn) tuned to the respective carrier frequencies to extract the signals, which are then passed through demodulators to retrieve the original messages.

An envelope detector is a simple and efficient circuit used to recover the message signal from an Amplitude Modulated (AM) wave. It consists of a diode, a resistor, and a capacitor connected in parallel.

Operation Principle: When the AM signal is applied to the diode, it acts as a half-wave rectifier, allowing only the positive half-cycles to pass. The capacitor charges rapidly to the peak value of the input signal through the low forward resistance of the diode. When the input voltage falls below the capacitor voltage, the diode becomes reverse-biased and stops conducting. The capacitor then discharges slowly through the resistor R. If the time constant (RC) is chosen correctly, the discharge rate follows the envelope of the AM signal.

Mathematical Representation: An AM signal is given by:

Where A is the carrier amplitude, k_a is the sensitivity, and m(t) is the message signal. The envelope detector extracts the envelope:

To ensure accurate detection, the RC time constant must satisfy the condition:

where f_c is the carrier frequency and W is the highest frequency component of the message signal. This ensures the capacitor tracks the carrier peaks without following the rapid carrier oscillations, while also being able to discharge fast enough to follow the variations of the message signal.