Understanding Radio Wave Propagation and Signal Processing

In ground wave propagation, radio waves travel along the surface of the Earth, following the curvature of the planet. Freq Range: 30 kHz to 300 kHz (Low Freq). Key Points: Travels along the ground. Strongly attenuated by terrain, trees, buildings, etc. Limited to short distances (few hundred km). APPS: AM radio (MW band). Navigation systems & military communication.In sky wave propagation, radio waves R transmitted towards the ionosphere, which reflects or refracts them back to Earth. Freq Range: 3 MHz to 30 MHz (High Freq). Key Points: Enables long-distance communication, even intercontinental. Depends on time of day, solar activity, & ionospheric conditions. Reflected by ionospheric layers (F-layer, E-layer, etc.). APPS: International broadcasting. HAM radio, military communication, aviation (HF band). In space wave propagation, waves travel in straight lines directly between transmitting & receiving antennas. Freq Range: Above 30 MHz (VHF, UHF, SHF, etc.). Key Points: Requires line-of-sight. Blocked by hills & obstacles. Effective 4 short to medium distances, or via satellite. APPS: TV broadcast ,Mobile phones, Satellite communication, Microwave links, WiFi, Bluetooth

What R the limitations of TRF receivers? How does super-heterodyne fix them? Poor Selectivity: TRF receivers use tuned circuits at RF frequencies, which makes it difficult to isolate a single station clearly. The filters aren't sharp, so nearby stations can interfere. 2. Low Sensitivity:: High-frequency signals R weak, & TRF circuits cannot amplify them effectively. This leads to poor performance in receiving distant or low-power stations. 3. Uneven Gain: The gain of TRF amplifiers varies with frequency. As a result, some stations sound louder while others R barely audible. This causes an unstable listening experience. 4. Difficult Tuning: TRF receivers require multiple tuned circuits to be manually aligned to the same frequency. This makes tuning complex & prone to mismatch. 5. Limited Frequency Coverage: The TRF receiver works well only 4 a narrow band of frequencies. It cannot handle wide tuning ranges without performance issues. How Super-Heterodyne Fixes These: 1. Improved Selectivity: By converting the signal to a fixed intermediate frequency (IF), super-heterodyne receivers use sharp & high-Q filters that isolate a single station very effectively. 2. Higher Sensitivity: At the intermediate frequency, amplifiers work better & provide higher gain. This allows the receiver to detect & process weaker signals. 3. Constant Gain :Since all amplification happens at a fixed frequency (IF), the gain remains consistent across all channels & stations. This ensures uniform volume & clarity. 4. Easy Tuning : Only the local oscillator needs to be tuned. The mixer automatically converts the desired station to IF, simplifying the entire tuning process. 5. Wide Frequency Coverage : The local oscillator can shift any RF frequency into the IF range. This allows the receiver to cover a broad spectrum efficiently without compromising quality.

A Super-Heterodyne Receiver is a radio receiver that converts all incoming RF signals to a fixed Intermediate Frequency (IF) using a process called frequency mixing. This simplifies filtering, improves selectivity, and allows for better signal amplification and detection. Working : 1. Antenna: The antenna captures incoming radio frequency (RF) signals from various broadcasting stations. 2. RF Amplifier: It amplifies the weak RF signals picked up by the antenna to a suitable level. Helps improve sensitivity and reduce noise. 3. Mixer: The heart of the super-heterodyne system. Takes the amplified RF signal and mixes it with a signal from the local oscillator. This process produces new frequencies: 𝑓_𝑠𝑢𝑚=𝑓_𝑐+𝑓_{𝐿𝑂 ,,,,,,,,} 𝑓_{𝑑𝑖𝑓𝑓}=∣𝑓_𝑐−𝑓_𝐿𝑂∣. The difference frequency is selected as the Intermediate Frequency (IF) — usually 455 kHz for AM receivers. 4. Local Oscillator: Generates a signal with a frequency slightly different from the incoming RF. This makes frequency translation possible for every station to the same IF. It is tuned along with RF stage, so the difference always remains constant. 5. IF Amplifier: Amplifies the intermediate frequency signal. Most of the gain and selectivity is provided here, because it's easier to design sharp filters at a fixed frequency. Helps remove adjacent channel interference. 6. Detector / Demodulator: Extracts the original audio signal (baseband) from the modulated IF signal. For AM, this is usually done using envelope detection. 7. Audio Amplifier and Output: Amplifies the audio signal and sends it to speakers or headphones for output. Final stage of the receiver. Advantages: High selectivity and sensitivity. Stable gain over wide frequency ranges. Simplified filtering and amplification due to fixed IF. ||||||||||||||||||| Time scaling is a transformation where the time axis of a signal is compressed or expanded by a factor. It modifies the speed of the signal. If 𝑥(𝑡) is the original signal, then  x(at) is the time-scaled version. If a>1: signal compresses (plays faster). If 0<a<1: signal expands (plays slower) Frequency shifting is a transformation where the frequency content of a signal is shifted by multiplying the signal with a sinusoidal wave. This shifts the entire spectrum of the signal to a different frequency range. Example: Let x(t)=cos(2πft) | Multiply with carrier cos(2πfct): | x(t)⋅cos(2πfct)= 1/2 [cos2π(f+fc)t+cos2π(f−fc)t]. This creates new frequency components at f+fc and f−fc. ​Used in modulation and wireless comms. Time shifting means delaying or advancing a signal in time. X(t−t0): delay by t0 units x(t+t0): advance by t0 units Example: Let x(t)=t²    x(t−3)=(t−3) ²→ signal delayed by 3 units| x(t+2)=(t+2)²→ signal advanced by 2 units. Used in systems with time offsets, communication signals, radar, etc.

Convolution is a mathematical operation used to find the output of a Linear Time-Invariant (LTI) system when input and impulse response are known. Formula: y(t)=x(t)∗h(t)=_−∞ ∫ ^∞ x(τ)h(t−τ)dτ

Noise Figure is a measure of how much noise a device adds to the signal compared to an ideal noiseless device. Formula: Noise Figure (NF) = SNR at input/SNR at output. It is usually expressed in decibels (dB): NF_dB=10log₁₀( SNR_out/SNR _in)  ...Noise Temperature is the temperature at which a resistor would generate the same amount of thermal noise power as the actual noisy component. Formula: N=kTB, Where: N = noise power, k = Boltzmann's constant, T = noise temperature, B = bandwidth . Bandwidth is the range of frequencies over which a system or signal operates effectively. In terms of signalsBandwidth=f _high−f_low.  Noise Voltage is the random voltage generated by resistors, circuits, or components due to thermal agitation or other effects. Formula (for resistor): Vn= root(4kTRB). Where: k = Boltzmann constant, T = temperature (K), R = resistance, B = bandwidth

Friis formula gives the overall noise figure of a system made up of multiple connected amplifier stages (cascade connection). It shows how the first few stages dominate the total noise.Formula: If a system has multiple stages: 𝐹_total=F1+ (F2−1/G1)+ (F3−1/G1G2) +......  | Where: 𝐹1, 𝐹2, 𝐹3= Noise figures of stages (in linear, not dB) | 𝐺1, 𝐺2, 𝐺3= Gains of the stages (also in linear) | 𝐹total= Overall noise figure...... A cascade connection is when multiple amplifier stages are connected one after another to achieve higher gain or performance. Why it's used: To increase overall gain, To control noise and bandwidth, Used in radio receivers, communication systems, signal chains Total Gain in Cascade: If individual gains are: 𝐺total= 𝐺1×𝐺2×𝐺3  Or in dB: 𝐺total(dB)=G1(dB)+(dB)+G3(dB)

 ASK – Amplitude Shift Keying: ASK is a digital modulation technique in which the amplitude of a carrier wave is varied according to the digital data (0s and 1s). Working: For binary 1: transmit high amplitude signal. For binary 0: transmit low or zero amplitude signal. Frequency and phase remain constant. Use Case: Used in optical fiber communication (e.G., On-Off Keying). Simple but highly affected by noise

Thermal Noise (Johnson-Nyquist Noise): Cause: Due to random motion of electrons in a resistor or any conductor at temperature T. Noise Power: Pn=kTB Where: k = Boltzmann constant. T = temperature (Kelvin). B = bandwidth (Hz) | Key Points: White noise (uniform across frequency). Exists in all passive components. Cannot be eliminated, only minimized

Shot Noise : Cause: Due to random emission or flow of electrons across a potential barrier (e.G., in diodes, BJTs). Noise Current: I_n²=2qIB . Where: q = charge of electron. I = DC current. B = bandwidth| Key Points: Occurs in active devices. More significant at low currents .Also white noise

Flicker Noise: Cause: Due to imperfections in materials and recombination/trapping of carriers in semiconductors. Power Spectrum: S(f)∝ f1 | Key Points: Dominant at low frequencies (< few kHz). Common in MOSFETs, JFETs. Decreases with increase in frequency

Burst Noise: Cause: Due to sudden transitions in current/voltage levels in semiconductors caused by imperfections or traps. Key Points: Appears as random step-like transitions. Affects low-frequency precision analog circuits,. Often device-specific

Transit-Time Noise: Cause: Due to time delay in carrier transit across a junction or device at high frequencies. Key Points: Increases with frequency. Significant in microwave and high-speed devices. Signal-to-Noise Ratio (SNR) is the ratio of the power of a useful signal to the power of background noise present in the system. It shows how much clear signal is available compared to unwanted noise — higher the SNR, better the signal quality. Formula: SNR = 𝑃signal/𝑃noise. Expressed as a unitless ratio or in decibels (dB): SNR_𝑑𝐵 =10log₁₀( Pnoise / Psignal). Meaning: High SNR → signal is strong and clear. Low SNR → signal is buried in noise | Example: If signal power = 100 mW, noise power = 1 mW: SNR = 100/1= 100 ⇒ SNR_𝑑𝐵 =10log₁₀( 100)=20| Used In: Communication systems. Audio and video quality. Data transmission reliability. RF and wireless systems

PAM is a modulation technique in which the amplitude of regularly spaced pulses is varied according to the instantaneous value of the analog message signal.

Time Division Multiplexing is a technique where multiple signals are transmitted over the same communication channel by allocating different time slots to each signal. How it Works: Each user gets a fixed time slot in a repeating frame. The signals are sampled, and each sample is sent in its allocated time slot. At the receiver, a demultiplexer separates the time slots to reconstruct individual signals. Types of TDM: Synchronous TDM ->Fixed time slots, even if some users have no data. Simple but wastes bandwidth|| Asynchronous (Statistical) TDM->Slots assigned only when users have data. More efficient, but needs overhead info

Synchronization in TDM: Why It’s Needed: To make sure that the receiver knows which time slot belongs to which user. If synchronization fails → wrong data sent to wrong user = disaster |  How  Synchronization is Done: Frame Synchronization Bit (FSB): A unique sync pattern is added at the start of every frame Helps receiver detect the beginning of the frame Clock Synchronization: Both transmitter and receiver use same timing reference Ensures accurate sampling and slot timing

PWM is a technique where the width (duration) of each pulse is varied in proportion to the analog signal, while the amplitude and position remain constant.

PPM is a modulation method where the position (time delay) of each pulse is varied according to the analog signal, while amplitude and width remain constant.

FSK – Frequency Shift Keying: FSK is a modulation technique where the frequency of the carrier signal is varied depending on the digital data. Working:  For binary 1: transmit a carrier with higher frequency 𝑓1. For binary 0: transmit a carrier with lower frequency 𝑓0. Amplitude and phase are constant| Use Case: Used in modems, paging systems, walkie-talkies. Better noise immunity than ASK

PSK – Phase Shift Keying: PSK is a digital modulation method where the phase of the carrier wave is changed based on the binary data. Working: For binary 1: use carrier with 0° phase. For binary 0: use carrier with 180° phase (inverted signal). Frequency and amplitude are constant. More advanced versions like QPSK use 4 phases to send 2 bits per symbol!| Use Case: Used in Wi-Fi, satellite comms, Bluetooth, 4G/5G. Best noise immunity, but complex design

Fiber optic communication is a method of transmitting information as light pulses through a glass or plastic fiber.

Quantization is the process of mapping a continuous range of amplitude values into a finite set of levels during analog-to-digital conversion. In simple terms: Infinite amplitude values → Limited fixed values. When It Happens? Quantization happens after sampling in an ADC (Analog-to-Digital Converter). Sampling → Picks signal value at regular time intervals Quantization → Rounds off each sampled value to the nearest fixed level. Encoding → Converts each quantized value to binary. Why We Need Quantization: Digital systems (computers, microcontrollers) can’t handle infinite values. So we reduce the amplitude resolution to finite steps. Quantization Error: The difference between actual sample value and the quantized level. This introduces noise called quantization noise. Higher number of levels → lower error

Sampling theorem : A process of converting a continuous analog signal  into a discrete time signal. The sampled signal should be able to recover the original signal  back. The sampled signal should take as  many signals from modulating signal as possible

Modulation is the process of varying a carrier signal (usually a high-frequency sine wave) in accordance with the information signal (low-frequency baseband signal like voice, video, data, etc). Why is Modulation Needed? 1. To Transmit Signals Over Long Distances: Low-frequency signals (like human voice, 300 Hz – 3.4 kHz) cannot travel far without losing strength. High-frequency carrier waves (like 100 kHz or more) travel much farther, especially via antennas. Modulation helps attach the information to a powerful carrier, allowing long-range transmission. Example: You can’t hear someone whisper from 100 meters away. But if they use a loudspeaker (carrier wave), you can hear them — the whisper is modulated on the loudspeaker sound. 2. To Reduce Antenna Size: For efficient transmission, antenna height should be λ/4 (quarter wavelength). At 1 kHz (baseband signal), λ = 300 km → antenna = 75 km || At 100 MHz (carrier), λ = 3 m → antenna = 0.75 m || Example: Your FM radio (at 100 MHz) works with a small antenna, thanks to modulation. 3. To Avoid Mixing of Signals (Multiplexing). If all signals were sent at baseband frequencies, they would overlap and interfere. Modulation allows frequency division multiplexing (FDM) — each user gets a unique frequency band. Example: Different radio stations (98.3 MHz, 104.8 MHz, etc.) can broadcast at the same time without mixing.

Ground or surface waves progress along the surface of the earth. Must be vertically polarized to prevent short circuiting of the electric component with the earth. Wavefront tilts over because of diffraction, over some distance the wave “dies down”. Lower the frequency of EM wave, it will lose strength faster. In VLF, power may be increased to increase transmission range.

SKY WAVES Medium and high frequencies transmission. Reflection of EM waves from the ionized region in the upper part of the atmosphere (ionosphere) of the earth is used for transmission of waves to longer distances. Ionosphere is at about 70-400 km height from earth surface.  Ionosphere reflects back the EM waves if the frequency is between 2 to 30 MHz. This mode of propagation is also called as Short wave propagation. Applications : Point to point communication over long distances, MW and SW radio and amateur radio

PCM Advantages High noise immunity| Easy signal regeneration | Suitable for digital transmission

PCM DisadvantagesRequires more bandwidth | Quantization introduces distortion