Communication Systems Diagrams

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Unit I: Linear Modulation Square Law Modulator Circuit Input $m(t)$ Non-linear Device Bandpass Filter AM Output Ring Modulator (Balanced Modulator) Circuit $m(t)$ 4 Diodes $c(t)$ BPF DSB-SC Carrier Input AM Diode Detector Circuit AM Input R C LPF Demodulated $m(t)$ AM Waveform & Spectrum (Time & Frequency Domain) Time Domain ($s_{AM}(t)$): t Amplitude Carrier $A_c \cos(2\pi f_c t)$ modulated by $m(t)$ Frequency Domain ($S_{AM}(f)$): $f_c - W$ $f_c + W$ $f_c$ f Magnitude Unit II: Angle Modulation (FM) Armstrong Indirect FM Transmitter Block Diagram $m(t)$ Integrator Narrowband FM Frequency Multiplier Mixer Frequency Multiplier Wideband FM Out Crystal Oscillator Local Oscillator Direct FM Transmitter Block Diagram $m(t)$ Varactor Diode Modulator FM Signal Frequency Multiplier Output FM Varactor Diode Modulator Circuit (Direct FM) $m(t)$ L Oscillator FM Output Varactor Diode PLL FM Demodulator Block Diagram FM Input Phase Detector Loop Filter (LPF) VCO Demodulated $m(t)$ Pre-emphasis and De-emphasis Circuits Pre-emphasis Input $m(t)$ R C Pre-emphasized $m'(t)$ De-emphasis Input $m'(t)$ R C Demodulated $m(t)$ Unit III: Noise Receiver for Noise Measurement Block Diagram (Y-Factor Method) Noise Source Device Under Test (DUT) Amplifier Power Meter Output Power Hot/Cold State Unit IV: Transmitters & Receivers Superheterodyne AM Receiver Block Diagram Antenna RF Amp Mixer IF Amp Detector Audio Amp Speaker Local Oscillator Superheterodyne FM Receiver Block Diagram Antenna RF Amp Mixer IF Amp Limiter Demodulator Speaker Local Oscillator SSB Radio Telephone Transmitter Block Diagram Mic Audio Amp Balanced Modulator Sideband Filter Mixer Power Amp Antenna Carrier Osc Local Osc Ratio Detector Circuit FM Input Limiter Phase Shift Network Discriminator Demodulated $m(t)$ Includes Diodes and Transformers Simple AGC Circuit Input Signal Variable Gain Amplifier Output Rectifier/LPF Delayed AGC Circuit Input Signal Variable Gain Amplifier Output Rectifier/LPF Delay Circuit Unit V: Pulse Modulation PWM Generation Block Diagram $m(t)$ Comparator PWM Output Sawtooth/Triangle Wave PPM Generation Block Diagram (from PWM) PWM Input Monostable Multivibrator PPM Output PWM and PPM Waveforms (for Sinusoidal Input) Modulating Signal $m(t)$ (Sinusoidal): Carrier (Sawtooth/Triangle Wave): PWM Output: PPM Output: TDM System Block Diagram (Commutator) $m_1(t)$ $m_2(t)$ $m_N(t)$ Commutator TDM Output TDM Input Decommutator $m_1(t)$ $m_2(t)$ $m_N(t)$ Foster-Seeley Discriminator Circuit FM In L1 L2 L3 C1 C2 R1 R2 Output $m(t)$ Quadrature Detector Circuit FM Input Limiter Phase Shift Network 90 deg Multiplier LPF Demodulated $m(t)$ ⭐ TOPIC 1 — AM RECEIVER / SUPERHETERODYNE RECEIVER A superheterodyne receiver is a type of radio receiver that converts a received radio frequency (RF) signal to a fixed intermediate frequency (IF) before further processing. This architecture provides superior selectivity and sensitivity compared to earlier designs. Block Diagram (describe for drawing) Draw blocks in this order, ensuring clear connections: Antenna (receives RF signal) $\rightarrow$ RF Amplifier (amplifies and pre-selects) $\rightarrow$ Mixer (combines RF with LO) $\rightarrow$ Local Oscillator (LO) (generates a stable tunable frequency) $\rightarrow$ IF Filter & Amplifier (fixed frequency amplification and filtering) $\rightarrow$ Detector (Envelope Detector) (extracts the baseband message) $\rightarrow$ AF Amplifier (amplifies audio) $\rightarrow$ Speaker (converts electrical signal to sound). Additionally, draw an Automatic Gain Control (AGC) line originating from the Detector and feeding back to control the gain of the RF Amplifier and IF Amplifier stages. Antenna RF Amp Mixer IF Amp Detector Audio Amp Speaker Local Oscillator AGC Working RF Amplifier: This stage tunes to the desired radio frequency (RF) channel and provides an initial amplification of the weak incoming signal. It also helps in improving the overall signal-to-noise ratio (SNR) of the receiver and rejects unwanted signals, including the image frequency. Mixer: The mixer is a non-linear device that combines the amplified RF signal with a stable, locally generated signal from the Local Oscillator. This process, known as heterodyning, produces sum and difference frequencies. Local Oscillator (LO): The LO generates a continuously tunable frequency, $f_{LO}$. It is tuned such that the difference frequency between $f_{LO}$ and the desired RF signal ($f_{RF}$) is always equal to a constant Intermediate Frequency (IF). A common tuning scheme is high-side injection, where $f_{LO} = f_{RF} + f_{IF}$. This ensures that as the RF frequency changes, the IF remains constant. IF Amplifier: This stage operates at a fixed, relatively low IF (e.g., 455 kHz for AM broadcast). Since the IF is constant, highly selective and stable filters can be designed for this stage, providing the bulk of the receiver's gain (typically 40–60 dB) and excellent selectivity to reject adjacent channels. Detector (Envelope Detector): For AM signals, an envelope detector (often a simple diode detector) is used to extract the original audio (modulating) signal from the modulated IF carrier. It rectifies the AM signal and then uses a low-pass filter to smooth out the carrier component, leaving the audio envelope. AF Amplifier: The relatively weak audio signal recovered by the detector is amplified by the audio frequency (AF) amplifier to a level sufficient to drive a loudspeaker or headphones. AGC (Automatic Gain Control): The AGC circuit monitors the output level of the detector. If the received signal is strong, the AGC generates a control voltage that reduces the gain of the RF and/or IF amplifier stages. Conversely, for weak signals, it increases the gain. This prevents receiver overload from strong stations, maintains a relatively constant audio output level regardless of signal strength, and improves listening comfort and receiver stability. Advantages High Sensitivity: The multiple stages of amplification, especially at IF, allow reception of very weak signals. High Selectivity: The fixed IF allows for the design of highly selective filters (e.g., crystal or ceramic filters) that can effectively reject adjacent channel interference. Stable Operation: Most of the amplification occurs at a fixed frequency (IF), making the amplifier design more stable and predictable. Constant IF: Since all RF signals are converted to the same IF, a single, high-performance IF amplifier and filter stage can be used for all stations, simplifying design and improving performance. ⭐ TOPIC 2 — FM RECEIVER & DETECTION (PLL, Ratio Detector, Foster–Seeley) An FM receiver is designed to demodulate frequency-modulated signals. Similar to AM, superheterodyne architecture is commonly used. FM Receiver Block Diagram Antenna $\rightarrow$ RF Amplifier $\rightarrow$ Mixer $\rightarrow$ Local Oscillator (LO) $\rightarrow$ IF Amplifier $\rightarrow$ Limiter $\rightarrow$ FM Detector $\rightarrow$ Audio Amplifier $\rightarrow$ Speaker Antenna RF Amp Mixer IF Amp Limiter FM Detector Speaker Local Oscillator Key Sections IF Amplifier: For FM, the IF amplifier typically has a wider bandwidth (e.g., $\approx 180$ kHz for broadcast FM) than AM IF stages to accommodate the wider bandwidth of FM signals. It provides significant gain and improves selectivity. Limiter: This is a crucial stage unique to FM receivers. It removes any amplitude variations (noise, interference) from the FM signal, ensuring that only frequency changes are passed to the detector. This makes FM inherently immune to amplitude noise. FM Detector Methods: The FM detector (demodulator) converts frequency variations into voltage variations. Common types include: Foster–Seeley Discriminator: A phase-shift network that converts frequency deviation into corresponding phase shifts, which are then detected as voltage changes. It requires a limiter for good performance. Ratio Detector: Similar to the Foster–Seeley, but uses back-to-back diodes and a tertiary winding to provide inherent amplitude limiting, making it less sensitive to amplitude variations. Phase-Locked Loop (PLL) Detector: Offers excellent linearity, sensitivity, and noise immunity. It's widely used in modern FM receivers. PLL Detector Explanation A Phase-Locked Loop (PLL) is a feedback control system that generates an output signal whose phase is related to the phase of an input signal. For FM detection, a PLL consists of: Phase Detector (PD): Compares the phase of the incoming FM signal with the phase of the Voltage-Controlled Oscillator (VCO) output. It produces an error voltage proportional to the phase difference. Low Pass Filter (LPF): Filters out high-frequency components from the phase detector output, leaving a slowly varying control voltage. Voltage-Controlled Oscillator (VCO): Generates an output frequency that is directly proportional to the DC control voltage applied to its input. Feedback Loop: The output of the LPF controls the VCO frequency, forming a closed-loop system. Working: When an FM signal enters the PLL, the phase detector and LPF generate a voltage that forces the VCO to track the instantaneous frequency of the input FM signal. The control voltage applied to the VCO, which varies in proportion to the input frequency deviation, represents the demodulated audio signal. FM Input Phase Detector Loop Filter (LPF) VCO Demodulated $m(t)$ Advantages of PLL Detector Best Linearity: Offers highly linear frequency-to-voltage conversion. High Noise Immunity: Excellent rejection of noise, especially when the PLL is locked. Automatic Amplitude Rejection: Inherently ignores amplitude variations in the input signal. Integrated Solution: Can be easily implemented in integrated circuits. ⭐ TOPIC 3 — DSB–SC / BALANCED MODULATOR (GENERATION & DETECTION) Double Sideband Suppressed Carrier (DSB-SC) modulation is an amplitude modulation technique where the carrier wave is suppressed, leaving only the two sidebands (upper and lower) which carry the information. Generation using Balanced Modulator A balanced modulator is a circuit designed to produce a DSB-SC signal. It typically uses two identical non-linear devices (such as diodes, transistors, or FETs) configured in a balanced bridge or differential arrangement. It takes two inputs: the message signal $m(t)$ and the carrier signal $c(t) = A_c \cos(\omega_c t)$. Principle: The carrier signal is applied to the two non-linear devices in a way that causes their non-linear characteristics to cancel out the carrier component in the output. The message signal is applied to modulate the carrier before this cancellation. The output signal is primarily composed of the product term $m(t) \cdot \cos(\omega_c t)$, which represents the DSB-SC signal. Circuit Explanation (Ring Modulator Example) A common type of balanced modulator is the Ring Modulator (also known as a Lattice Modulator), often implemented with four diodes and two transformers: Two identical diode branches: The circuit consists of two pairs of diodes (e.g., $D_1-D_2$ and $D_3-D_4$) arranged in a ring or bridge configuration. Carrier fed 180° out of phase: The carrier signal is applied across the center taps of two transformers, effectively feeding it $180^\circ$ out of phase to opposite sides of the diode bridge. When the carrier is strong, it drives the diodes into conduction or cutoff, effectively switching the circuit. Modulating signal fed in phase: The message signal is applied to the other input of the transformers, feeding it in phase to the diode pairs. Carrier components cancel: Due to the symmetrical arrangement of the diodes and transformers, when no modulating signal is present, the carrier signal components cancel out at the output port. Sidebands add: When the modulating signal is present, it unbalances the circuit, allowing the product terms (the upper and lower sidebands) to appear at the output, while the carrier remains suppressed. A Bandpass Filter (BPF) at the output ensures only the desired sidebands are passed. $m(t)$ 4 Diodes $c(t)$ BPF DSB-SC Carrier Input Coherent Detection / Synchronous Detection To recover the original message signal from a DSB-SC wave, coherent detection is necessary because the carrier is suppressed. This method involves: Multiplication: The received DSB-SC signal is multiplied by a locally generated carrier signal that is perfectly synchronized in both frequency and phase with the original carrier used at the transmitter. If the received signal is $s_{DSB}(t) = A_c m(t) \cos(\omega_c t)$ and the local carrier is $2\cos(\omega_c t)$, the product is $2 A_c m(t) \cos^2(\omega_c t) = A_c m(t) (1 + \cos(2\omega_c t))$. Low-Pass Filtering: This product signal is then passed through a low-pass filter (LPF). The LPF removes the high-frequency $2\omega_c t$ component, leaving only the term proportional to $A_c m(t)$, which is the original message signal. The main challenge with coherent detection is maintaining perfect synchronization of the local carrier, which requires complex circuitry (e.g., a Phase-Locked Loop - PLL). ⭐ TOPIC 4 — SSB GENERATION / FILTER & PHASE SHIFT METHODS Single Sideband (SSB) modulation is an amplitude modulation technique where only one of the two sidebands is transmitted, and the carrier is suppressed. This saves significant bandwidth and power compared to AM and DSB-SC. Two Major Methods for SSB Generation 1. Filter Method This is the most common and straightforward method for generating SSB signals. DSB-SC Generation: First, a Double Sideband Suppressed Carrier (DSB-SC) signal is generated using a balanced modulator (as described in Topic 3). The output of the balanced modulator contains both the upper sideband (USB) and the lower sideband (LSB), but no carrier. Sideband Filtering: The DSB-SC signal is then passed through a highly selective and narrow bandpass filter (e.g., a crystal filter or ceramic filter). This filter is designed to pass either the USB or the LSB, while sharply rejecting the other sideband. The filter needs to have a very steep skirt selectivity to effectively separate the sidebands, which are often very close in frequency. Typical bandwidths for these filters are 2–3 kHz. Amplification: The selected single sideband signal is then amplified to the desired transmission power. Advantages: Provides very high spectral purity and good suppression of the unwanted sideband and carrier. Disadvantages: Requires complex and expensive crystal or mechanical filters, especially for high frequencies, and is less flexible for changing operating frequencies. $m(t)$ Balanced Modulator DSB-SC Sideband Filter SSB Output Carrier $c(t)$ 2. Phase Shift Method (Weaver Method / Phasing Method) This method generates SSB without the need for sharp filters, relying instead on phase manipulation. Phase Shift Networks: It uses two 90° phase shift networks. One network shifts the phase of the message signal $m(t)$ by $90^\circ$ to produce $m_q(t)$ (Hilbert transform). The other shifts the phase of the carrier $c(t)$ by $90^\circ$ to produce $c_q(t)$. Two Balanced Modulators: The original message $m(t)$ is modulated with the original carrier $c(t)$ in the first balanced modulator, producing $s_1(t) = m(t)c(t)$. The phase-shifted message $m_q(t)$ is modulated with the phase-shifted carrier $c_q(t)$ in the second balanced modulator, producing $s_2(t) = m_q(t)c_q(t)$. Combination: The outputs of the two balanced modulators are then either added or subtracted. Adding $s_1(t) + s_2(t)$ produces one sideband (e.g., USB). Subtracting $s_1(t) - s_2(t)$ produces the other sideband (e.g., LSB). Advantages: No critical filters are needed, making it suitable for integrated circuits and allowing easier frequency changes. Disadvantages: Requires precise 90° phase shifts over a wide range of audio frequencies, which is difficult to achieve perfectly, leading to some suppression of the unwanted sideband. Advantages of SSB Reduced Bandwidth: Occupies only half the bandwidth of AM or DSB-SC, allowing more channels in the same spectrum. (e.g., 3 kHz for voice, compared to 6 kHz for AM). Power Efficient: All transmitted power is concentrated in the information-carrying sideband(s), as the carrier and one sideband are suppressed. This leads to higher power efficiency and greater range for a given transmitter power. No Carrier: Since the carrier is suppressed, no power is wasted on transmitting it, and interference from the carrier itself is eliminated. Long-Distance HF Communication: Due to its efficiency and reduced bandwidth, SSB is widely used for long-distance high-frequency (HF) radio communication. ⭐ TOPIC 5 — NOISE (Thermal, Shot, AM, FM, DSB–SC) Noise is any unwanted electrical energy that interferes with the transmitted signal and degrades its quality. Understanding different types of noise and their effects on various modulation schemes is crucial in communication systems. Thermal Noise (Johnson-Nyquist Noise) Generation: This noise is generated by the random thermal agitation of charge carriers (electrons) within an electrical conductor, even when no current is flowing. It is inherent in all electronic components that have electrical resistance (e.g., resistors, conductors, semiconductor junctions). Characteristics: Power: The noise power is given by the formula $N = kTB$, where $k$ is Boltzmann's constant ($1.38 \times 10^{-23}$ J/K), $T$ is the absolute temperature in Kelvin, and $B$ is the bandwidth in Hertz over which the noise is measured. White Noise: It has a uniform power spectral density across all frequencies of interest, meaning its power is evenly distributed. Hence, it is also known as "white noise." Gaussian Distribution: The amplitude of thermal noise follows a Gaussian probability distribution. Shot Noise Generation: Shot noise arises from the discrete nature of charge carriers (electrons or holes) and their random fluctuations as they cross a potential barrier in semiconductor devices (diodes, transistors, vacuum tubes). It occurs due to the random arrival times of electrons at the anode in a vacuum tube or the random passage of carriers across a PN junction in a semiconductor. Characteristics: Power: The mean square current of shot noise is proportional to the average DC current flowing through the device. White Noise: Like thermal noise, shot noise is generally considered white noise because its power spectral density is uniform over a wide frequency range. Frequency Dependence: It is more significant at higher frequencies and in active devices. Noise in AM (Amplitude Modulation) Effect: In AM systems, noise primarily adds to the amplitude of both the carrier and the sidebands. This means that noise directly interferes with the information-carrying amplitude variations. SNR Degradation: The signal-to-noise ratio (SNR) in AM is significantly degraded because noise directly modulates the envelope. When the signal level is low (e.g., during quiet passages in speech or music), the noise can become very noticeable, leading to poor quality reception. Threshold Effect: AM systems do not exhibit a distinct threshold effect in the same way FM does; noise degradation is more gradual as signal strength decreases. Noise in FM (Frequency Modulation) Effect: FM is inherently more robust to noise than AM. Since information is encoded in frequency variations, and the amplitude of the FM signal is kept constant, a limiter circuit can remove most amplitude noise components. Noise Affects Phase: Noise primarily affects the phase of the FM signal, which translates into frequency variations, but these are generally less noticeable than amplitude variations. Threshold Effect: FM systems exhibit a distinct "threshold effect" . Below threshold: If the input SNR falls below a certain threshold level (typically around 10-12 dB), the noise suddenly becomes very prominent, and the demodulated signal quality degrades rapidly. Above threshold: Above this threshold, FM provides excellent noise immunity. The process of frequency demodulation itself provides a "noise quieting" effect, where the output SNR can be significantly higher than the input SNR, especially for wideband FM. This is a major advantage of FM. Noise in DSB–SC and SSB (Suppressed Carrier Systems) DSB–SC: While DSB-SC saves power by suppressing the carrier, its SNR performance is actually poorer than standard AM for the same transmitted power. This is because the coherent detector needs a clean, synchronized carrier for demodulation. Any phase noise or frequency offset in the locally generated carrier adds significantly to the output noise. Without the carrier, the envelope detector cannot be used, and coherent detection is more susceptible to noise if synchronization is imperfect. SSB: SSB systems, by transmitting only one sideband, occupy the minimum possible bandwidth for a modulated signal. This reduced bandwidth means less noise power is admitted into the receiver ($N = kTB$, so smaller $B$ means smaller $N$). Consequently, SSB has a better SNR performance than AM or DSB-SC for the same transmitted power. It still requires coherent detection, so local oscillator stability is crucial. ⭐ TOPIC 6 — FM GENERATION (Direct, Indirect, Armstrong) Frequency Modulation (FM) generation involves varying the instantaneous frequency of a carrier signal in proportion to the instantaneous amplitude of the message signal. There are two primary categories of FM generation: Direct FM and Indirect FM. Direct FM Generation Direct FM involves directly changing the frequency of a high-frequency oscillator in response to the modulating signal. Principle: The frequency-determining components (usually capacitance or inductance) of an LC oscillator or an RC oscillator are varied directly by the modulating signal. Method: Varactor Diode Modulator: A common direct FM method uses a varactor diode (also known as a varicap diode). A varactor diode is a PN junction diode whose capacitance varies with the reverse-bias voltage applied across it. The varactor diode is placed in parallel with the tank circuit (LC circuit) of a high-frequency oscillator. The modulating signal $m(t)$ is applied across the varactor diode, varying its reverse bias. This in turn changes its capacitance. As the varactor's capacitance changes, the resonant frequency of the oscillator ($f_0 = \frac{1}{2\pi\sqrt{LC_{total}}}$) changes accordingly, producing an FM signal. Advantages: Simple to implement and can produce wideband FM (WBFM) directly. Disadvantages: Instability: The direct variation of the oscillator's frequency-determining components often leads to poor frequency stability. Any changes in temperature, power supply, or component aging can cause the center frequency to drift significantly. Non-linearity: The relationship between the modulating voltage and the capacitance (and thus frequency) of the varactor diode can be non-linear, leading to harmonic distortion if not properly compensated. $m(t)$ L Oscillator FM Output Varactor Diode Indirect FM Generation (Armstrong Method) The Armstrong method (Indirect FM) generates a stable, wideband FM signal by first creating a narrow-band Phase-Modulated (PM) signal and then converting it to FM using an integrator and frequency multipliers. Principle: Phase modulation (PM) and frequency modulation (FM) are related. An FM signal can be obtained from a PM signal if the modulating signal is first integrated. That is, if $m(t)$ is integrated to get $\int m(t) dt$, and this integrated signal phase modulates a carrier, the result is an FM signal. Steps: Integrator: The message signal $m(t)$ is first passed through an integrator circuit. This converts the message signal into a form suitable for phase modulation that will eventually result in frequency modulation. Narrowband PM Generator: The integrated message signal is then used to phase modulate a crystal-controlled oscillator, which is highly stable. This creates a Narrowband Phase Modulated (NBPM) signal. Since PM is closely related to FM, this NBPM signal is essentially a Narrowband FM (NBFM) signal with a small frequency deviation. Frequency Multipliers: To achieve the desired wideband FM (WBFM) signal, the NBFM signal's frequency deviation needs to be increased. This is done by passing the signal through one or more frequency multiplier stages. A frequency multiplier multiplies both the carrier frequency and the frequency deviation by the same factor. Mixer (Frequency Translation): If the final carrier frequency is not the desired one after multiplication, a mixer stage is used. The multiplied NBFM signal is mixed with a signal from another local oscillator. The output of the mixer is then filtered to select the desired sum or difference frequency, which will have the correct carrier frequency and the desired wide frequency deviation. Additional Frequency Multipliers: Further frequency multiplication stages may be used after the mixer to reach the final desired carrier frequency and frequency deviation. Advantages: High Frequency Stability: The use of a crystal oscillator for the initial carrier generation ensures excellent frequency stability for the final FM signal, overcoming the main drawback of direct FM. Can generate WBFM with high linearity. Disadvantages: More complex circuitry due to the need for integrators, frequency multipliers, and mixers. $m(t)$ Integrator Narrowband FM Frequency Multiplier Mixer Frequency Multiplier Wideband FM Out Crystal Oscillator Local Oscillator ⭐ TOPIC 7 — ANGLE MODULATION BASICS (FM + PM) Angle modulation is a category of modulation techniques where the phase angle of the carrier wave is varied in accordance with the message signal. This contrasts with amplitude modulation (AM), where the amplitude of the carrier is varied. The two main types of angle modulation are Frequency Modulation (FM) and Phase Modulation (PM). Frequency Modulation (FM) Definition: In FM, the instantaneous frequency of the carrier wave is varied proportionally to the instantaneous amplitude of the modulating (message) signal, while the amplitude of the carrier remains constant. Mathematical Representation: If the carrier is $A_c \cos(\omega_c t + \phi_0)$ and the message is $m(t)$, the instantaneous frequency $f_i(t) = f_c + k_f m(t)$, where $k_f$ is the frequency sensitivity. The FM signal is then $s_{FM}(t) = A_c \cos(\omega_c t + 2\pi k_f \int m(\tau) d\tau)$. Characteristics: Constant amplitude, making it robust against amplitude noise. Bandwidth is generally wider than AM, especially for wideband FM. Exhibits a threshold effect for noise immunity (see Topic 5). Phase Modulation (PM) Definition: In PM, the instantaneous phase of the carrier wave is varied proportionally to the instantaneous amplitude of the modulating (message) signal, while the amplitude and carrier frequency remain constant. Mathematical Representation: The instantaneous phase $\phi_i(t) = \omega_c t + k_p m(t) + \phi_0$, where $k_p$ is the phase sensitivity. The PM signal is then $s_{PM}(t) = A_c \cos(\omega_c t + k_p m(t))$. Characteristics: Also has constant amplitude, offering noise immunity. The frequency deviation in PM is proportional to the derivative of the message signal, $f_i(t) = f_c + \frac{k_p}{2\pi} \frac{dm(t)}{dt}$. Relation Between FM and PM FM and PM are closely related and can be derived from each other: PM $\rightarrow$ FM: If a message signal $m(t)$ is first integrated to produce $\int m(t) dt$, and this integrated signal is used to phase modulate a carrier, the resulting modulated wave will be an FM signal. $s_{FM}(t) = A_c \cos(\omega_c t + k_p \int m(\tau) d\tau)$ where $k_p$ effectively becomes the frequency deviation constant. FM $\rightarrow$ PM: Conversely, if a message signal $m(t)$ is first differentiated to produce $\frac{dm(t)}{dt}$, and this differentiated signal is used to frequency modulate a carrier, the resulting modulated wave will be a PM signal. $s_{PM}(t) = A_c \cos(\omega_c t + k_f \int \frac{dm(\tau)}{d\tau} d\tau) = A_c \cos(\omega_c t + k_f m(t))$ where $k_f$ effectively becomes the phase deviation constant. This relationship is fundamental and is exploited in the Armstrong (indirect) method of FM generation, where a PM signal is generated and then converted to FM. ⭐ TOPIC 8 — AUTOMATIC GAIN CONTROL (AGC) Automatic Gain Control (AGC) is a feedback control system used in radio receivers and other electronic systems to maintain a relatively constant output signal level despite variations in the input signal strength. It automatically adjusts the gain of the amplifier stages to prevent signal overloading and ensure comfortable listening. Purpose of AGC Maintain Constant Output: Ensures that the audio output level remains relatively steady, even when the receiver tunes between strong and weak stations, or when signal strength fluctuates due to fading. Prevent Distortion: High-amplitude input signals can drive amplifier stages into saturation, causing severe distortion. AGC reduces the gain for strong signals, preventing this overload. Protect IF Amplifier: Prevents the IF amplifier (and subsequent stages) from being overdriven by strong signals, which can lead to non-linear operation and intermodulation distortion. Improve Listening Comfort: Eliminates the need for manual volume adjustment by the user when changing channels or experiencing signal fading. Types of AGC Systems The basic principle of AGC involves rectifying a portion of the receiver's output (usually from the IF amplifier or detector) to generate a DC control voltage. This DC voltage is then fed back to earlier amplifier stages (RF and/or IF) to control their gain. 1. Simple AGC (Undelayed AGC) Mechanism: In a simple AGC system, the control voltage is generated as soon as a signal is detected. This voltage is continuously applied to reduce the gain of the controlled amplifier stages. Operation: As the input signal strength increases, the detector output voltage rises. This voltage is rectified and filtered to produce a DC AGC voltage, which is then fed back to the RF and IF amplifier stages. The AGC voltage biases the controlled amplifier transistors/tubes in such a way that their gain is reduced. Conversely, for weaker signals, the AGC voltage decreases, increasing amplifier gain. Disadvantages: Even for very weak signals, the AGC circuit will attempt to reduce gain slightly, which can slightly reduce the receiver's sensitivity for the weakest signals. Input Signal Variable Gain Amplifier Output Rectifier/LPF 2. Delayed AGC Mechanism: Delayed AGC introduces a threshold voltage. The AGC action (gain reduction) only begins when the input signal strength exceeds a predetermined level. For signals below this threshold, the receiver operates at its maximum gain. Operation: A diode or other threshold device is incorporated into the AGC circuit. This diode is reverse-biased by a fixed voltage. The AGC voltage generated by the detector must overcome this reverse bias before it can affect the gain of the amplifier stages. This ensures that weak signals receive full amplification. Advantages: Maximizes sensitivity for weak signals, as the gain is not reduced until the signal is strong enough. This is particularly useful for distant stations. Input Signal Variable Gain Amplifier Output Rectifier/LPF Delay Circuit 3. Amplified AGC Mechanism: In situations where a stronger and faster-acting AGC voltage is required, an additional transistor or amplifier stage is used to amplify the rectified AGC voltage before it is applied to control the gain. Advantages: Provides a more effective and responsive AGC action, suitable for receivers operating in environments with rapidly changing signal strengths. ⭐ TOPIC 9 — AM TRANSMITTER / HIGH LEVEL MODULATION An AM (Amplitude Modulation) transmitter is an electronic system that modulates a high-frequency carrier wave with an audio frequency (AF) message signal, amplifies the modulated signal, and then transmits it via an antenna. High-level modulation refers to performing the modulation process at a high power level, typically in the final RF amplifier stage. Block Diagram Microphone $\rightarrow$ AF amplifier $\rightarrow$ Modulator $\rightarrow$ RF Oscillator $\rightarrow$ Buffer Amplifier $\rightarrow$ Driver Amplifier $\rightarrow$ Power Amplifier (modulated by AF) $\rightarrow$ Antenna Microphone AF Amplifier Modulator RF Oscillator Power Amplifier Antenna High-Level Modulation (Collector/Drain Modulation) In high-level modulation, the modulation process occurs at the high-power output stage of the RF amplifier chain. This means that both the carrier and the modulating signal are amplified to their final power levels before modulation takes place. Specifically, for a Class C RF power amplifier, the modulating signal is applied to vary the supply voltage (e.g., collector voltage for BJT, drain voltage for FET) of the final RF power amplifier. Modulator Action: The AF amplifier output is fed to the modulator, which then controls the DC supply voltage of the final RF power amplifier. As the amplitude of the modulating signal changes, it effectively changes the supply voltage available to the RF power amplifier. This causes the amplitude of the RF carrier wave, which is being amplified by this stage, to vary in accordance with the modulating signal. High Efficiency: Class C amplifiers, commonly used in the final RF power stage, are highly efficient (up to 70-80%). By modulating at this high power level, the overall efficiency of the transmitter is maintained, as only one high-power modulation stage is needed. Applications: High-level modulation is typically used in high-power AM broadcast transmitters (e.g., hundreds of kilowatts) where maximizing efficiency is critical. Contrast with Low-Level Modulation: In low-level modulation, the modulation occurs at a low power level (e.g., in a buffer or driver stage), and the modulated signal is then amplified by linear power amplifiers. While low-level modulation is simpler, linear amplifiers are less efficient than Class C, making high-level modulation preferable for high-power applications. Working of a High-Level AM Transmitter Microphone: Converts sound waves into electrical audio signals. AF Amplifier: Amplifies the weak audio signal from the microphone to a sufficient power level to drive the modulator. RF Oscillator: Generates a stable, high-frequency carrier wave ($f_c$). This signal is typically crystal-controlled for frequency stability. Buffer Amplifier/Driver Amplifier: These stages amplify the RF carrier signal to an intermediate power level, isolating the oscillator from load variations. Modulator (High Level): The output of the AF amplifier (modulating signal) is fed to the modulator. This modulator then varies the DC supply voltage of the final RF Power Amplifier. Power Amplifier (Class C): This is the final RF stage, typically operating as a Class C amplifier for high efficiency. Its output amplitude is directly controlled by the varying supply voltage from the modulator. Thus, the RF carrier is amplitude-modulated at this high power level. Antenna: The high-power AM modulated signal is converted into electromagnetic waves and radiated into space by the antenna. ⭐ TOPIC 10 — SAMPLING / PAM / PWM / PPM Pulse modulation techniques involve representing an analog message signal by a series of discrete pulses. Instead of modulating a continuous carrier, these methods change a characteristic of a pulse train (amplitude, width, or position) according to the message signal. Sampling Theorem The sampling theorem, also known as the Nyquist-Shannon sampling theorem, states that to perfectly reconstruct an analog signal from its sampled version, the sampling frequency ($f_s$) must be at least twice the highest frequency component ($f_{m(max)}$) present in the analog message signal. Condition: $f_s \geq 2 f_{m(max)}$ If $f_s The minimum sampling rate, $2 f_{m(max)}$, is called the Nyquist rate. Pulse Amplitude Modulation (PAM) Principle: In PAM, the amplitude of each pulse in a periodic pulse train is varied linearly with the instantaneous amplitude of the message signal at the sampling instant. Generation: The message signal is sampled at regular intervals. The amplitude of each pulse is made proportional to the amplitude of the message signal at that sampling time. Characteristics: The duration (width) and position of the pulses remain constant. PAM is susceptible to noise, similar to AM, because noise can easily alter the amplitude of the pulses. It is often an intermediate step in other pulse modulation techniques like PCM. Pulse Width Modulation (PWM) / Pulse Duration Modulation (PDM) Principle: In PWM, the width (duration) of each pulse in a periodic pulse train is varied proportionally to the instantaneous amplitude of the message signal at the sampling instant. Generation: This is typically achieved by comparing the message signal with a high-frequency sawtooth or triangular wave (carrier). The points where the message signal crosses the sawtooth/triangular wave determine the edges of the pulses, thus varying their width. $m(t)$ Comparator PWM Output Sawtooth/Triangle Wave Characteristics: The amplitude and position of the pulses remain constant. Less susceptible to noise than PAM because information is not in amplitude. Requires more power than PAM due to varying pulse width. Pulse Position Modulation (PPM) Principle: In PPM, the position (timing) of each pulse, relative to a fixed reference point (e.g., the position of the previous pulse or a synchronization pulse), is varied proportionally to the instantaneous amplitude of the message signal at the sampling instant. Generation: PPM is often generated by modifying PWM pulses. A common method is to use a monostable multivibrator triggered by the trailing (or leading) edge of a PWM signal. Since the position of the trailing edge of a PWM pulse varies with the message signal, the output pulse of the monostable multivibrator will have its position varied accordingly, creating a PPM signal. PWM Input Monostable Multivibrator PPM Output Characteristics: The amplitude and width of the pulses remain constant. Highly immune to noise, as noise typically affects amplitude or width, not precise timing, making it more robust than PAM or PWM. Requires synchronization between transmitter and receiver to establish the reference position. PWM and PPM Waveforms (for Sinusoidal Input) Modulating Signal $m(t)$ (Sinusoidal): Represents the original analog information. Carrier (Sawtooth/Triangle Wave): A high-frequency reference signal used for modulation. PWM Output: The pulse width varies with the modulating signal's amplitude. When $m(t)$ is high, pulse width is wide; when $m(t)$ is low, pulse width is narrow. PPM Output: The position of the pulses varies with the modulating signal's amplitude. The pulses themselves have constant amplitude and width. ⭐ Topic 11 — FM Spectrum / Modulation Index / Carson Rule The spectrum of an FM signal is more complex than that of an AM signal. Unlike AM, where the bandwidth is simply twice the message bandwidth, FM's bandwidth depends on both the modulating frequency and the frequency deviation, characterized by the modulation index. Modulation Index ($\beta$) The FM modulation index ($\beta$) is a dimensionless quantity that defines the extent of frequency variation relative to the modulating frequency. Formula: $\beta = \frac{\Delta f}{f_m}$ $\Delta f$ (Frequency Deviation): The maximum change in the instantaneous carrier frequency from its unmodulated center frequency, caused by the peak amplitude of the modulating signal. $f_m$ (Modulating Frequency): The highest frequency component of the modulating signal (baseband signal). The modulation index determines the number of significant sidebands in the FM spectrum. A larger $\beta$ implies a wider range of frequency variation for a given modulating frequency, leading to more sideband components. Narrowband FM (NBFM): When $\beta \ll 1$ (typically $\beta Wideband FM (WBFM): When $\beta \ge 1$ (or $\beta > 0.5$), the FM spectrum contains many significant sideband pairs, and its bandwidth is much wider. FM Spectrum The exact spectrum of an FM signal with a single sinusoidal modulating tone can be represented using Bessel functions. It consists of a carrier component and an infinite number of sideband pairs spaced at multiples of the modulating frequency ($f_m$) around the carrier frequency ($f_c$). The amplitude of each sideband component is given by Bessel functions of the first kind, $J_n(\beta)$. The amplitudes of the carrier and sidebands depend on the modulation index $\beta$. As $\beta$ increases, power shifts from the carrier into the sidebands. For certain values of $\beta$, the carrier component can even drop to zero. Carson's Rule for Bandwidth While the theoretical FM spectrum extends infinitely, most of the signal power is contained within a finite bandwidth. Carson's rule provides a practical approximation for the effective bandwidth of an FM signal, especially for wideband FM. Formula: $BW_{FM} \approx 2(\Delta f + f_m) = 2 f_m (\beta + 1)$ This rule states that the bandwidth is approximately twice the sum of the maximum frequency deviation ($\Delta f$) and the highest modulating frequency ($f_m$). For NBFM ($\beta \ll 1$), Carson's rule simplifies to $BW_{FM} \approx 2f_m$, similar to AM. For WBFM ($\beta \gg 1$), Carson's rule approximates $BW_{FM} \approx 2\Delta f$. Significance: Carson's rule is widely used in system design to determine the required channel bandwidth for FM transmissions, balancing spectral efficiency with signal fidelity. ⭐ Topic 12 — AM Power / Modulation Index / Time & Frequency Domain Amplitude Modulation (AM) involves varying the amplitude of a high-frequency carrier wave in direct proportion to the instantaneous amplitude of the modulating (message) signal. Understanding its power distribution, modulation index, and representation in time and frequency domains is fundamental. AM Signal Representation Time Domain: An AM signal $s_{AM}(t)$ for a single-tone modulating signal $m(t) = A_m \cos(\omega_m t)$ and carrier $c(t) = A_c \cos(\omega_c t)$ is given by: $s_{AM}(t) = A_c [1 + m \cos(\omega_m t)] \cos(\omega_c t)$ where $m = \frac{A_m}{A_c}$ is the modulation index. Time Domain ($s_{AM}(t)$): The envelope of the AM signal mirrors the shape of the modulating signal. The carrier frequency is much higher than the modulating frequency. t Amplitude Carrier $A_c \cos(2\pi f_c t)$ modulated by $m(t)$ Frequency Domain: Using trigonometric identities, the AM signal can be expanded as: $s_{AM}(t) = A_c \cos(\omega_c t) + \frac{m A_c}{2} \cos((\omega_c + \omega_m)t) + \frac{m A_c}{2} \cos((\omega_c - \omega_m)t)$ This shows three distinct frequency components: the carrier at $\omega_c$, the upper sideband (USB) at $\omega_c + \omega_m$, and the lower sideband (LSB) at $\omega_c - \omega_m$. Frequency Domain ($S_{AM}(f)$): A spectral plot shows three impulses at $f_c$, $f_c+f_m$, and $f_c-f_m$. For a complex message signal, the sidebands become continuous spectra around $f_c$. $f_c - W$ $f_c + W$ $f_c$ f Magnitude Modulation Index ($m$) Definition: The modulation index, also known as the modulation depth, indicates the extent of amplitude variation of the carrier relative to its unmodulated level. For sinusoidal modulation, $m = \frac{A_m}{A_c}$, where $A_m$ is the peak amplitude of the modulating signal and $A_c$ is the peak amplitude of the unmodulated carrier. Significance: $m $m = 1$ (Critical modulation / 100% modulation): The carrier amplitude momentarily drops to zero during the negative peak of the modulating signal. This is the ideal case for maximum efficiency without distortion. $m > 1$ (Over-modulation): The carrier amplitude attempts to go negative, causing the envelope to be clipped and leading to severe distortion of the demodulated signal. This also generates unwanted sidebands (splatter) that cause interference. AM Power Distribution The total power ($P_t$) of an AM signal is distributed among the carrier and the two sidebands. For a single-tone modulating signal: Carrier Power ($P_c$): The power in the unmodulated carrier. If the carrier amplitude is $A_c$ and resistance is $R$, $P_c = \frac{A_c^2}{2R}$. Sideband Power ($P_{SB}$): Each sideband (USB and LSB) carries power. The total sideband power is $P_{SB} = P_{USB} + P_{LSB} = \frac{m^2 P_c}{2}$. Total Power ($P_t$): The sum of carrier power and total sideband power. $P_t = P_c + P_{USB} + P_{LSB} = P_c + \frac{m^2 P_c}{2} = P_c (1 + \frac{m^2}{2})$ Efficiency: The transmission efficiency ($\eta$) of AM is the ratio of useful power (sideband power) to total transmitted power: $\eta = \frac{P_{SB}}{P_t} = \frac{m^2/2}{1 + m^2/2} = \frac{m^2}{2+m^2}$ For 100% modulation ($m=1$), the maximum efficiency is $\eta = \frac{1}{2+1} = \frac{1}{3}$, or approximately 33.3%. This means that in standard AM, at most one-third of the total transmitted power carries information, while two-thirds is wasted on the carrier. This low efficiency is a major drawback of AM. ⭐ Topic 13 — Mixer / Image Frequency / Local Oscillator In superheterodyne receivers (both AM and FM), the mixer and local oscillator are critical components that work together to convert the incoming radio frequency (RF) signal to a fixed Intermediate Frequency (IF). This conversion is essential for achieving high selectivity and sensitivity. Mixer (Frequency Converter) Function: The mixer is a non-linear circuit that takes two input signals—the received RF signal ($f_{RF}$) and a locally generated signal from the Local Oscillator ($f_{LO}$)—and produces an output that contains their sum and difference frequencies, as well as harmonics. Principle: Due to its non-linear characteristic (e.g., a diode or transistor operating in a non-linear region), the mixer multiplies the two input signals. If the inputs are $\cos(2\pi f_{RF} t)$ and $\cos(2\pi f_{LO} t)$, the output will contain terms like $\cos(2\pi (f_{LO} + f_{RF}) t)$ and $\cos(2\pi (f_{LO} - f_{RF}) t)$, or $\cos(2\pi (f_{RF} - f_{LO}) t)$. Output: The desired output of the mixer is the Intermediate Frequency (IF), which is typically selected to be the difference frequency: $f_{IF} = |f_{LO} - f_{RF}|$ Types: Mixers can be passive (e.g., diode mixers) or active (e.g., transistor mixers, balanced mixers). Active mixers provide gain, while passive mixers usually introduce some loss. Local Oscillator (LO) Function: The LO is a tunable oscillator that generates a stable, unmodulated sine wave whose frequency ($f_{LO}$) is chosen such that when mixed with the desired RF signal ($f_{RF}$), it produces the fixed IF. Tuning: As the receiver is tuned to different RF stations, the LO frequency must change proportionally to maintain a constant IF. This is typically achieved by ganging the tuning capacitor of the LO with that of the RF amplifier stage. High-side vs. Low-side Injection: High-side Injection: $f_{LO} = f_{RF} + f_{IF}$. The LO frequency is higher than the RF frequency. This is common in AM broadcast receivers (e.g., $f_{IF} = 455$ kHz). Low-side Injection: $f_{LO} = f_{RF} - f_{IF}$. The LO frequency is lower than the RF frequency. Stability: The frequency stability of the LO is crucial. Any drift in $f_{LO}$ directly translates into a shift in the IF, which can cause the signal to fall outside the IF filter's passband, leading to poor reception or loss of signal. Image Frequency ($f_{image}$) Definition: The image frequency is an unwanted input RF signal that, when mixed with the local oscillator frequency, also produces a signal at the IF. It is a potential source of interference in superheterodyne receivers. Calculation: The image frequency is related to the desired RF frequency ($f_{RF}$) and the IF ($f_{IF}$) as follows: For high-side injection ($f_{LO} = f_{RF} + f_{IF}$): $f_{image} = f_{LO} + f_{IF} = (f_{RF} + f_{IF}) + f_{IF} = f_{RF} + 2f_{IF}$ For low-side injection ($f_{LO} = f_{RF} - f_{IF}$): $f_{image} = f_{LO} - f_{IF} = (f_{RF} - f_{IF}) - f_{IF} = f_{RF} - 2f_{IF}$ Interference: If a strong signal exists at the image frequency, it will be converted to the IF along with the desired signal, causing interference. Since the image frequency is typically $2f_{IF}$ away from the desired RF frequency, it can be difficult for the RF amplifier's pre-selector filter to completely reject it, especially if the IF is low. Rejection: To minimize image frequency interference, the RF amplifier stage often includes a tunable bandpass filter that provides sufficient selectivity to attenuate signals at the image frequency before they reach the mixer. A higher IF generally provides better image frequency rejection because the image frequency is further away from the desired RF, making it easier to filter. ⭐ Topic 14 — Pre-Emphasis / De-Emphasis / Squelch These techniques are primarily used in FM systems to improve signal-to-noise ratio (SNR) and enhance listening quality, especially in the presence of high-frequency noise components. Pre-Emphasis Problem: In FM systems, noise has a triangular power spectral density, meaning its power increases with frequency. This causes higher frequency components of the message signal to be more susceptible to noise during transmission. Moreover, speech and music signals typically have lower power content at higher frequencies. Principle: Pre-emphasis is a process applied at the transmitting end (before modulation) to artificially boost the amplitude of the higher frequency components of the modulating (message) signal. This is usually done using a simple RC high-pass filter. Purpose: By increasing the amplitude of high-frequency components before adding noise, these components become more prominent relative to the noise during transmission. This effectively improves the SNR of the high-frequency components. Time Constant: The degree of pre-emphasis is determined by a standard time constant ($\tau$). In many regions, including India, a time constant of $\tau = 75 \mu s$ is used for broadcast FM. This corresponds to a corner frequency of $f_c = \frac{1}{2\pi\tau} \approx 2.12$ kHz. Pre-emphasis Circuit (RC High-Pass Filter) Input $m(t)$ R C Pre-emphasized $m'(t)$ De-Emphasis Principle: De-emphasis is the complementary process to pre-emphasis, applied at the receiving end (after demodulation) to restore the original frequency response of the message signal. It is usually implemented using an RC low-pass filter with the exact same time constant as the pre-emphasis circuit. Purpose: While restoring the original signal's frequency balance, the de-emphasis filter also attenuates the high-frequency noise components that were amplified by the pre-emphasis (and have increased in power due to the FM noise spectrum). This results in a significant improvement in the overall SNR of the demodulated signal. Benefit: The combined effect of pre-emphasis and de-emphasis is to improve the overall SNR of the high-frequency message components without affecting the low-frequency components, leading to a clearer and less noisy audio output. De-emphasis Circuit (RC Low-Pass Filter) Input $m'(t)$ R C Demodulated $m(t)$ Squelch (Noise Gate) Problem: In FM receivers, when no signal is present or the signal is very weak (below the FM threshold), the output of the demodulator is predominantly static or hiss (noise). This can be annoying to the listener. Principle: Squelch is a circuit that mutes the receiver's audio output when the received signal strength falls below a predetermined threshold or when the noise level exceeds a certain limit. It acts as an automatic noise gate. Operation: The squelch circuit continuously monitors either the signal strength (often from the AGC line or IF output) or the noise level (by filtering out high-frequency components from the demodulator output, which are mostly noise when no signal is present). When the signal is too weak or the noise is too high, the squelch circuit activates, cutting off the audio path to the speaker. When a sufficiently strong and clean signal is detected, the squelch opens, allowing the audio to pass. Purpose: Improves listening comfort by eliminating annoying background noise (static) when no desired signal is being received. ⭐ Topic 15 — QAM Transmitter & Receiver Quadrature Amplitude Modulation (QAM) is a digital modulation scheme that conveys data by changing (modulating) the amplitude of two carrier waves. These two carrier waves are 90 degrees out of phase with each other (i.e., in quadrature). QAM effectively combines both amplitude and phase modulation to transmit more bits per symbol, thereby increasing spectral efficiency. QAM Transmitter (Generation) A QAM transmitter processes an incoming digital data stream and maps groups of bits into symbols. Each symbol corresponds to a unique combination of amplitude and phase. To achieve this, the data stream is split into two components: Serial-to-Parallel Converter: The incoming binary data stream is divided into two parallel streams: the In-phase (I) channel data and the Quadrature (Q) channel data. For example, in 16-QAM, 4 bits are grouped per symbol. The first 2 bits might map to the I channel amplitude, and the next 2 bits to the Q channel amplitude. Level Converters / Digital-to-Analog Converters (DACs): The digital I and Q data streams are converted into analog voltage levels. These levels represent the desired amplitudes for the respective in-phase and quadrature carriers. Carrier Generation: A stable local oscillator generates a carrier wave, $A_c \cos(\omega_c t)$. Phase Shifter: A $90^\circ$ phase shifter creates a quadrature carrier, $A_c \sin(\omega_c t)$. Multipliers (Modulators): The I-channel analog voltage (representing $I(t)$) is multiplied with the in-phase carrier $\cos(\omega_c t)$. This produces $I(t) \cos(\omega_c t)$. The Q-channel analog voltage (representing $Q(t)$) is multiplied with the quadrature carrier $\sin(\omega_c t)$. This produces $Q(t) \sin(\omega_c t)$. Combiner (Summing Amplifier): The outputs of the two multipliers are added together to form the final QAM signal: $s_{QAM}(t) = I(t) \cos(\omega_c t) + Q(t) \sin(\omega_c t)$ Bandpass Filter and Power Amplifier: The QAM signal is then filtered to remove unwanted harmonics and amplified to the necessary power level for transmission. The resulting QAM signal's envelope and phase will vary depending on the instantaneous values of $I(t)$ and $Q(t)$, effectively representing multiple bits per symbol. Digital Data In S/P Conv. & Level Map I(t) Q(t) Multiplier (I) Multiplier (Q) Combiner QAM Out LO cos($\omega_c$t) 90° Phase Shift sin($\omega_c$t) QAM Receiver (Demodulation) A QAM receiver synchronously demodulates the incoming QAM signal to recover the original I and Q data streams. Bandpass Filter and Amplifier: The received QAM signal is filtered and amplified. Carrier Recovery: A crucial step is to recover the exact carrier frequency and phase used at the transmitter. This is typically done using a Phase-Locked Loop (PLL) or other carrier recovery circuits. This recovered carrier provides both $\cos(\omega_c t)$ and $\sin(\omega_c t)$ references. Two Multipliers (Demodulators): The received QAM signal is multiplied by the recovered in-phase carrier $\cos(\omega_c t)$. This isolates the I-channel component. The received QAM signal is multiplied by the recovered quadrature carrier $\sin(\omega_c t)$. This isolates the Q-channel component. Low-Pass Filters (LPFs): The outputs of the multipliers are passed through LPFs to remove the high-frequency $2\omega_c t$ components, leaving only the baseband $I(t)$ and $Q(t)$ signals. Analog-to-Digital Converters (ADCs) / Level Detectors: The analog $I(t)$ and $Q(t)$ signals are converted back into digital data by comparing their amplitude levels against thresholds. Parallel-to-Serial Converter: The parallel I and Q digital data streams are combined to reconstruct the original serial digital data stream. Key Challenge: Accurate carrier recovery is vital for proper QAM demodulation, as any phase error will cause crosstalk between the I and Q channels. ⭐ Topic 16 — Radio Telephone / Telegraph Transmitter Radio transmitters are systems that convert information (voice, data, etc.) into an electromagnetic wave suitable for propagation through space. The design varies depending on the type of information and modulation scheme. Radio Telegraph Transmitter (CW - Continuous Wave) A radio telegraph transmitter is used for transmitting Morse code or other on/off keying (OOK) digital data. It typically uses Continuous Wave (CW) modulation, where the carrier is simply turned on and off. Block Diagram: RF Oscillator $\rightarrow$ Buffer Amplifier $\rightarrow$ Driver Amplifier $\rightarrow$ Keying Circuit $\rightarrow$ RF Power Amplifier $\rightarrow$ Antenna RF Oscillator Buffer Amplifier Driver Amplifier Keying Circuit RF Power Amplifier Antenna RF Oscillator: Generates a stable, unmodulated high-frequency carrier wave. Buffer Amplifier: Isolates the oscillator from subsequent stages to prevent frequency pulling and ensures frequency stability. Driver Amplifier: Amplifies the carrier to a level sufficient to drive the final power amplifier. Keying Circuit: This is where the Morse code (or digital data) is applied. It switches the RF carrier ON and OFF according to the keying sequence. Keying can be done in various stages (e.g., oscillator, buffer, or final amplifier) but is often applied to a low-power stage for cleaner keying. RF Power Amplifier: Amplifies the keyed (modulated) RF signal to the desired transmission power. Antenna: Radiates the electromagnetic waves into space. Radio Telephone Transmitter (Voice Communication) A radio telephone transmitter is designed for voice communication. It typically uses AM, FM, or SSB modulation, with SSB being highly efficient for long-distance communication. Block Diagram (General for SSB Radio Telephone): Microphone $\rightarrow$ Audio Amplifier $\rightarrow$ Balanced Modulator $\rightarrow$ Carrier Oscillator $\rightarrow$ Sideband Filter $\rightarrow$ Mixer $\rightarrow$ Local Oscillator $\rightarrow$ RF Amplifier (Driver/Power) $\rightarrow$ Antenna Mic Audio Amp Balanced Modulator Sideband Filter Mixer Power Amp Antenna Carrier Osc Local Osc Microphone: Converts speech into electrical audio signals. Audio Amplifier: Amplifies the audio signal to a suitable level for modulation. Balanced Modulator: Generates a DSB-SC signal by mixing the audio signal with an intermediate carrier frequency from the Carrier Oscillator. Sideband Filter: Selects either the Upper Sideband (USB) or Lower Sideband (LSB) from the DSB-SC signal, creating an SSB signal. Mixer: Translates the SSB signal from the intermediate frequency to the desired final RF transmission frequency by mixing it with a signal from a Local Oscillator. RF Power Amplifier: Amplifies the SSB signal to the required transmission power. Antenna: Radiates the SSB signal. ⭐ Topic 17 — Multiplexing Multiplexing is a technique that allows multiple analog or digital signals to be combined and transmitted simultaneously over a single shared communication medium (channel). The primary goal is to efficiently utilize available bandwidth and reduce transmission costs by sharing resources. The two most common types of multiplexing in analog communication systems are Frequency Division Multiplexing (FDM) and Time Division Multiplexing (TDM). Frequency Division Multiplexing (FDM) Principle: FDM assigns a unique frequency band to each individual message signal within the total bandwidth of the communication channel. Each signal is modulated onto a different carrier frequency, and these modulated signals are then combined for transmission. Process: Each message signal modulates a separate sub-carrier frequency. These sub-carriers are spaced sufficiently far apart in the frequency spectrum to prevent overlap (using guard bands). The modulated signals (each occupying its own frequency slot) are then summed up and transmitted over the common channel. At the receiver, a bank of bandpass filters is used to separate the individual modulated signals. Each separated signal is then demodulated to recover the original message. Applications: Analog radio and television broadcasting, traditional telephone systems (where multiple voice calls are carried over a single trunk line), early cellular systems, and cable TV systems. Advantages: Relatively simple to implement for analog signals, less susceptible to timing synchronization issues. Disadvantages: Requires guard bands to prevent inter-channel interference, which wastes bandwidth. All channels are continuously active, leading to inefficient power usage if some channels are idle. Time Division Multiplexing (TDM) Principle: TDM divides the available time on a single communication channel into successive, non-overlapping time slots. Each message signal is assigned a recurring time slot for transmission. Instead of sharing frequency, signals share access to the channel over time. Process: Each analog message signal is first sampled (converted into discrete pulses, e.g., PAM). A commutator (electronic switch) sequentially connects each sampled signal to the transmission line for a brief, fixed duration (its assigned time slot). These interleaved samples from multiple channels form a composite pulse train, which is then transmitted. At the receiver, a synchronized de-commutator (another electronic switch) separates the samples belonging to each channel based on their timing. Each channel's samples are then passed through a low-pass filter to reconstruct the original analog message signal. Synchronization: Precise synchronization between the transmitter's commutator and the receiver's de-commutator is essential to ensure that samples are correctly assigned to their respective channels. Applications: Digital telephony (e.g., PCM systems), digital cellular systems (e.g., GSM), satellite communication, and optical fiber communication. Advantages: No guard bands are required in the frequency domain, leading to more efficient use of bandwidth. Can be more robust to certain types of noise than FDM. Suitable for digital signals. Disadvantages: Requires precise timing synchronization. More complex circuitry for sampling and synchronization. TDM System Block Diagram (Commutator) $m_1(t)$ $m_2(t)$ $m_N(t)$ Commutator TDM Output TDM Input Decommutator $m_1(t)$ $m_2(t)$ $m_N(t)$ ⭐ Topic 18 — VSB Modulation Steps Vestigial Sideband (VSB) modulation is a compromise between Double Sideband Suppressed Carrier (DSB-SC) and Single Sideband (SSB) modulation. It transmits one full sideband and a "vestige" (a small part) of the other sideband, along with a reduced or full carrier. This technique is primarily used in television broadcasting. Motivation for VSB SSB Disadvantages: While SSB is bandwidth-efficient, generating and demodulating true SSB for wideband signals (like video) is very difficult due to the need for ideal filters with infinitely sharp cutoff characteristics and perfect phase synchronization. DSB/AM Disadvantages: DSB and standard AM require twice the message bandwidth, which is inefficient for wideband signals. Video Signal Characteristics: Video signals contain significant low-frequency (DC) components. Full carrier (AM) or a vestigial carrier in VSB is needed to preserve these DC components during demodulation. VSB Modulation Steps The generation of a VSB signal involves a standard AM modulation process followed by specialized filtering: AM Signal Generation: The wideband message signal (e.g., video signal) is first used to amplitude modulate a high-frequency carrier. This results in a standard AM signal (or a DSB-LC signal if the carrier is not suppressed). Vestigial Sideband Filter: The AM signal is then passed through a special type of filter called a vestigial sideband filter. This filter has a carefully designed frequency response: It passes one complete sideband (e.g., the Upper Sideband for TV). It passes only a small portion (a vestige) of the other sideband (e.g., the Lower Sideband). It often passes the carrier component at exactly half its original amplitude (or a significant portion of it). The filter's response is typically complementary around the carrier frequency. Transmission: The filtered VSB signal is then amplified and transmitted. Example (NTSC TV Broadcasting): In NTSC television, the video signal modulates a carrier. The resulting signal passes through a VSB filter that transmits the entire upper sideband, the carrier, and a vestige of the lower sideband (about 0.75 MHz out of a 4 MHz baseband). This allows the total transmitted bandwidth for video to be reduced from 8 MHz (for DSB) to approximately 6 MHz. Advantages of VSB Bandwidth Efficiency: Reduces the required bandwidth compared to DSB or AM, getting closer to SSB efficiency without its complexity. Simpler Filtering: Less stringent filter requirements compared to SSB, as an ideal brick-wall filter is not needed. The filter only needs to have a gradual cutoff around the carrier. Preservation of DC Component: The presence of a carrier component (even reduced) in VSB allows for simpler envelope detection at the receiver and accurate preservation of the DC component of the modulating signal (crucial for video signals, which contain brightness information). Flexibility: Can be used for both analog and digital transmission where bandwidth is a concern and low-frequency components must be preserved. ⭐ Topic 19 — FM Figure of Merit The "Figure of Merit" (FOM) is a performance metric used to compare the noise performance of different modulation systems. It quantifies how much a modulation scheme improves the signal-to-noise ratio (SNR) at the output of the demodulator, relative to the SNR at the input of the receiver (or the baseband SNR if unmodulated). For angle modulation, the FOM often compares FM to AM. Definition The figure of merit ($F$) for a modulation system is typically defined as the ratio of the output SNR (SNR at the demodulator output) to the input SNR (SNR at the receiver input, typically measured at the detector input before demodulation): $F = \frac{(SNR)_O}{(SNR)_I}$ However, when comparing different modulation schemes, it's often more insightful to compare their output SNRs under similar input noise conditions. For FM, the figure of merit is often expressed as the ratio of the output SNR of an FM system to the output SNR of an AM system, assuming the same input noise power and message signal parameters. $F = \frac{SNR_{FM}}{SNR_{AM}}$ FM Figure of Merit Calculation (for Wideband FM with sinusoidal modulation) For a wideband FM system with peak frequency deviation $\Delta f$ and highest modulating frequency $f_m$, the output SNR can be shown to be: $SNR_{FM,O} = \frac{3}{2} \beta^2 \frac{P_c}{N_0 B_{FM}}$ where $\beta$ is the modulation index, $P_c$ is carrier power, $N_0$ is noise power spectral density, and $B_{FM}$ is FM bandwidth. For an AM system with modulation index $m$ and message bandwidth $B_m$, the output SNR is: $SNR_{AM,O} = \frac{m^2}{2} \frac{P_c}{N_0 B_m}$ Assuming $B_{FM} \approx 2(\Delta f + f_m)$ and $B_m = f_m$, and considering $\beta = \Delta f / f_m$, the figure of merit for FM over AM (for comparable conditions) is approximately: $F_{FM/AM} \approx 3 \beta^2$ Significance of FM Figure of Merit Noise Suppression: The fact that FM has a higher figure of merit (i.e., $F > 1$) indicates its superior noise performance compared to AM. This improvement is primarily due to two factors: Limiting: The use of a limiter in FM receivers removes amplitude variations caused by noise, which directly improves SNR. Frequency Deviation: A larger frequency deviation ($\Delta f$, leading to a larger $\beta$) means the information is spread over a wider bandwidth. While this increases the input noise power, the demodulation process effectively translates this wider deviation into a higher output signal power relative to the noise, providing a processing gain. Threshold Effect: The high figure of merit for FM is valid above the FM threshold. Below the threshold, the noise performance of FM degrades rapidly, and its figure of merit drops sharply. Bandwidth vs. SNR Trade-off: FM allows for a trade-off between bandwidth and SNR. By increasing the modulation index (and thus bandwidth), a significant improvement in output SNR can be achieved. In essence, FM provides a significant advantage in noise immunity, which is quantified by its figure of merit, making it suitable for high-fidelity audio broadcasting where noise reduction is paramount. ⭐ Topic 20 — AM & FM SNR Derivations The Signal-to-Noise Ratio (SNR) is a critical performance metric in communication systems, indicating the quality of a received signal. Derivations of SNR for AM and FM provide insights into their inherent noise performance characteristics. AM SNR Derivation For a standard AM system with a single-tone modulating signal $m(t) = A_m \cos(\omega_m t)$, the modulated signal is $s_{AM}(t) = A_c [1 + m \cos(\omega_m t)] \cos(\omega_c t)$, where $m = A_m/A_c$ is the modulation index. Input Noise Power ($N_I$): Assuming additive white Gaussian noise (AWGN) with power spectral density $N_0/2$, and a receiver bandwidth $B_{AM} = 2f_m$ (where $f_m$ is the message bandwidth), the input noise power is $N_I = N_0 B_{AM} = 2 N_0 f_m$. Input Signal Power ($S_I$): The total transmitted power for AM is $P_t = P_c (1 + \frac{m^2}{2})$. This represents the input signal power to the detector. Input SNR ($SNR_I$): $SNR_I = \frac{P_t}{N_I} = \frac{P_c (1 + m^2/2)}{2 N_0 f_m}$ Output Signal Power ($S_O$): After envelope detection, the recovered message signal power is proportional to $A_m^2$, which relates to the sideband power. $S_O = \frac{m^2 P_c}{2}$. Output Noise Power ($N_O$): In an ideal envelope detector, the output noise power is $N_O = N_0 f_m$. Output SNR ($SNR_O$): $SNR_{AM,O} = \frac{S_O}{N_O} = \frac{m^2 P_c / 2}{N_0 f_m} = \frac{m^2 P_c}{2 N_0 f_m}$ Conclusion for AM SNR: The output SNR of AM is directly proportional to the square of the modulation index ($m^2$). This means that for under-modulated signals ($m The presence of the carrier component in AM helps in simple envelope detection, but it consumes significant power without carrying information, contributing to the relatively poor power efficiency and output SNR compared to suppressed carrier systems or FM at higher SNRs. FM SNR Derivation For a Wideband FM (WBFM) system with a single-tone sinusoidal modulating signal $m(t) = A_m \cos(\omega_m t)$, peak frequency deviation $\Delta f$, and modulation index $\beta = \Delta f / f_m$. Input Noise Power ($N_I$): Assuming AWGN with power spectral density $N_0/2$ and using Carson's rule for FM bandwidth $B_{FM} \approx 2(\Delta f + f_m)$, the input noise power is $N_I = N_0 B_{FM} = 2 N_0 (\Delta f + f_m)$. Input Signal Power ($S_I$): The transmitted power of an FM signal is constant and equal to the carrier power $P_c$. Input SNR ($SNR_I$): $SNR_I = \frac{P_c}{N_I} = \frac{P_c}{2 N_0 (\Delta f + f_m)}$ Output Signal Power ($S_O$): After ideal FM demodulation, the output signal power is proportional to the square of the frequency deviation, $S_O = k (\Delta f)^2$. Specifically, $S_O = \frac{3 P_c \beta^2}{2}$. Output Noise Power ($N_O$): Due to the triangular noise spectrum in FM and the effect of the limiter, the output noise power after demodulation and a baseband low-pass filter (bandwidth $f_m$) is $N_O = \frac{N_0 f_m^3}{3}$. Output SNR ($SNR_O$): $SNR_{FM,O} = \frac{S_O}{N_O} = \frac{3 P_c \beta^2 / 2}{N_0 f_m^3 / 3} = \frac{3}{2} \beta^2 \frac{P_c}{N_0 f_m}$ Conclusion for FM SNR: The output SNR of FM is proportional to the square of the modulation index ($\beta^2$) and thus proportional to $(\Delta f)^2$. This means that increasing the frequency deviation (and consequently the bandwidth) significantly improves the output SNR. This is a fundamental trade-off in FM: increased bandwidth for improved noise performance. Wideband FM has best SNR: For WBFM, where $\beta \gg 1$, the output SNR can be significantly higher than the input SNR, demonstrating the "noise quieting" or "processing gain" characteristic of FM. This makes FM highly suitable for applications requiring high-fidelity audio, as long as the input signal is above the FM threshold.