Fundamentals of Communication Systems
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. Noise Figure (NF): In communications, the Noise
Figure of a system or component, such as an amplifier or receiver, is crucial as it quantifies how much noise is added to the signal as it passes through. A lower noise figure indicates a better performance because it means less noise is introduced, thereby preserving the quality of the received signal. It is important in the design and analysis of communication systems to ensure high signal integrity. 2.
Noise Temperature:
Noise Temperature is used to characterize the noise performance of communication receivers and systems. It provides a way to express the noise power in terms of temperature, which can be particularly useful when comparing different systems or components. It helps engineers understand and minimize the noise contribution from various sources in the system.
3. Noise Bandwidth:
Noise Bandwidth in communication systems refers to the effective bandwidth within which noise power is measured and is relevant because it determines the total noise power that affects the signal. For instance, when designing filters, engineers must consider the noise bandwidth to ensure that only the desired signal frequencies are passed while minimizing the noise.
4. Noise Voltage: Noise Voltage is significant in the design and analysis of communication circuits, such as amplifiers and mixers. It affects the overall noise performance and sensitivity of the communication system. Engineers strive to minimize noise voltage to enhance the clarity and quality of the transmitted and received signals.
5. Modulation: Modulation is a fundamental principle in communications where the properties of a carrier signal (such as amplitude, frequency, or phase) are varied in accordance with the information signal. Modulation allows the transmission of data over various types of media (e.G., radio waves, optical fibers) and is essential for efficiently utilizing the bandwidth and reducing interference.
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Quantization Process
The Quantization Process is a critical aspect of digital communications, involving the conversion of analog signals to digital form. During this process, continuous amplitude values are mapped to discrete levels, introducing quantization noise. This process is essential in digital communication systems, such as analog-to-digital converters (ADCs) used in digital radios and telecommunications.
7. Signal-to-Noise Ratio (SNR): Signal-to-Noise Ratio is a key parameter in communications that measures the quality of the received signal relative to the background noise. A high SNR indicates a strong, clear signal with minimal noise interference, which is crucial for reliable data transmission. SNR impacts the error rate, data rate, and overall performance of communication systems, and engineers aim to maximize SNR to enhance system performance.
Feature : Signal Representation | Bandwidth Efficiency | Noise Sensitivity | Power Efficiency | Typical Use Cases
Pulse Amplitude Modulation : Amplitude of pulses varies in proportion to the modulating signal | Moderate bandwidth requirement | High (amplitude variations can introduce noise) | Less power efficient |Digital communication systems, Ethernet
Pulse Width Modulation : Pulse width varies while amplitude remains constant | Low bandwidth requirement | Low (less affected by amplitude noise) | More power efficient | Motor control, LED dimming, power electronics
Pulse Position Modulation : Pulse position varies while amplitude and width remain constant | High bandwidth requirement | Moderate (timing jitter can introduce noise) | Moderate power efficiency | Optical communication, radio navigation systems
Amplitude Shift Keying : Varies the amplitude of the carrier signal | Moderate bandwidth requirement | High (susceptible to amplitude noise) | Low (simpler to implement) | Optical communications, RFID
Phase Shift Keying :Varies the phase of the carrier signal |High bandwidth efficiency | Low (more robust against noise) | Moderate (requires more complex demodulation) | Wi-Fi, Bluetooth, satellite communications
Frequency Shift Keying :Varies the frequency of the carrier signal | Moderate bandwidth requirement | Moderate (susceptible to frequency noise) | Low to moderate (depends on the number of frequencies) | Radio communications, modem data transmission
Feature: Signal Representation | Bandwidth Efficiency | Noise Sensitivity | Complexity | Typical Use Cases
Feature: Frequency Range | Distance Coverage | Propagation
Mechanism | Signal Quality | Typical Applications
Ground Wave Propagation: Low frequency (LF) to Medium frequency (MF) | Short to medium range (up to a few hundred kilometers) | Follows the curvature of the Earth | Less affected by atmospheric conditions, stable | AM radio broadcasting, navigation systems
Sky Wave Propagation : High frequency (HF) | Long range (up to several thousand kilometers) | Reflects off the ionosphere back to Earth | Can be affected by ionospheric conditions, variable | International broadcasting, amateur radio, military
Tropospheric Scatter Propagation: Very high frequency (VHF) to Ultra high frequency (UHF) | Medium to long range (up to 1,000 km) | Scatters off irregularities in the troposphere
| Subject to fading and requires higher power | Long-distance communication for remote areas, military
Space Wave Propagation: VHF to Super high frequency (SHF) | Line-of-sight, up to a few hundred kilometers, satellite for global coverage | Travels in a straight line, can pass through the atmosphere to and from satellites | Generally clear, can be affected by obstacles and atmospheric conditions | TV broadcasting, FM radio, mobile communications, satellite communication
Ground Wave Propagation: Frequency Range:** Low Frequency (LF) to Medium Frequency (MF). | Distance Coverage:** Short to medium range, typically up to a few hundred kilometers. | Propagation Mechanism:** Follows the curvature of the Earth by diffracting around obstacles and over the surface. | Signal Quality:** Less affected by atmospheric conditions; generally stable and reliable. | Typical Applications:** AM radio broadcasting, navigation systems, and maritime communications
Sky Wave Propagation: Frequency Range:** High Frequency (HF). | Distance Coverage:** Long range, up to several thousand kilometers. | Propagation Mechanism:** Reflects off the ionosphere back to Earth, allowing signals to travel beyond the horizon. | Signal Quality:** Can be affected by ionospheric conditions, such as solar activity; variable signal quality. | Typical Applications:** International broadcasting, amateur radio, long-distance military communications.
Space Wave Propagation: Frequency Range:** Very High Frequency (VHF) to Super High Frequency (SHF). | Distance Coverage:** Line-of-sight communication, typically up to a few hundred kilometers; can extend to global coverage using satellites | Propagation Mechanism:** Travels in a straight line; can pass through the atmosphere to and from satellites. | Signal Quality:** Generally clear, but can be affected by physical obstructions and atmospheric conditions. | Typical Applications:** TV broadcasting, FM radio, mobile communications, satellite communication, and radar systems.
Modulation, the process of varying a carrier signal in accordance with an information signal, serves several crucial purposes in communication systems:
Bandwidth Efficiency: Modulation allows for the transmission of information over a limited frequency range. By varying the carrier signal’s characteristics (such as amplitude, frequency, or phase), multiple signals can be transmitted simultaneously without interfering with each other.
Noise Immunity: Modulation techniques can enhance the signal-to-noise ratio (SNR) of the transmitted signal. By modulating the carrier signal, the information is encoded in a way that makes it more resilient to noise and interference during transmission and reception.
Long-Distance Communication: Modulation enables the transmission of signals over long distances by overcoming attenuation and dispersion effects. By modulating the carrier signal, the transmitted signal can be efficiently propagated through various mediums such as air, water, or space.
Compatibility: Different communication systems and devices operate at various frequencies and standards. Modulation allows for the compatibility between these systems by enabling the transmission of signals at different frequencies and formats while ensuring interoperability.
Security: In certain applications, modulation techniques can enhance the security of transmitted information. Techniques such as spread spectrum modulation and encryption can make it difficult for unauthorized users to intercept or decipher the transmitted data.
PSK stands for Phase Shift Keying, which is a digital modulation technique used in telecommunications to encode digital data within the phase of a carrier wave. In PSK modulation, the phase of the carrier signal is varied to represent different symbols or bits of digital data. In PSK modulation, the carrier signal typically has two or more discrete phase states, each representing a different symbol or bit. The most common forms of PSK are Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), and Differential Phase Shift Keying (DPSK). In BPSK, for example, the carrier signal shifts between two phase states, typically 0 and 180 degrees, to represent binary data (0s and 1s). PSK modulation offers several advantages, including efficient use of bandwidth, robustness against noise and interference, and compatibility with existing modulation and demodulation techniques. It is widely used in various communication systems, including digital communication standards such as Wi-Fi, Bluetooth, GSM, and satellite communication.
Limitations of TRF receiver:
1] TRF receiver suffers from variations in BW over the tuning range ( s 40 – 1650 KHz) | 2] The gain of TRF RXr is not uniform over the tuning range. | 3] The TRF is unstable at high frequency. | 4] Gang tuning of more number of capacitors simultaneously is difficult.
Super hetrodyne Receiver :The features of hetrodyne RXr is that all incoming radio frequency s/gs are converted into intermediate frequency, If of 455KHz usually. The received s/g frequency fs, is mixed with local oscillator frequency, fo, to extract only the difference.
If = fo – fs = 455 KHz.
SHR can overcome limitations of TRF due to the following reasons: Since majority of amplification is done by IF amplifiers which are tuned by IF amplifiers which are tuned to IF, BW remains constant & therefore better selectivity can be obtained. | If amplifiers that provide max. Gain, are tuned to IF have fixed BW ∴ Gain provided is also constant over the AM tuning range. | The neutralization capacitor can be easily tuned to IF that is fixed ∴ unwanted feedback can be eliminated and hence removes the possibility of instability at high frequency. | Number of capacitors which are to be tuned simultaneously are less.
FRIss (to noise factor in cascade. )
Let the power gains of two amplifier be G1 and G2 respectively and le their noise factors be f1
and f2 respectively.
The total noise power at the i/p of the first amplifier is given as,
Pni (total)f1 K To B – – – – (1)
The total noise power at the o/p of amplifier 1 will be addition of two terms.
∴Noise e/p to amp2 = G1f1 K To B + (f2−1) K To B – – – -(2)
The first term represents the amplified noise power (by G1) and second terms represents the noise contributed by 2nd amp.
The noise power at the o/p of 2nd amp is G2 times the i/p noise power to amp 2.
∴ Pno=G2× (Noise i/p to amp 2)
∴Pno=G1G2F1 K To B + G2(f2−1) K To B
The overall gain of the cascade connection is given by,
G=G1G2
The overall noise factor F is defined as follows:
F=Pno/G1G2Pni
Here, Pni=K To B
Substituting the values of Pno and Pni we get,
F=G1G2F1K To B+G2(F2−1)K To B/G1G2K To B =F1+ (f2−1)/G1
The same logic can be extended for more number of amplifiers connected in cascade, then the overall noise factor F would be,
F=F1+(f1−1)/G1+(f3−1)/G1G2+(f4−1)/G1G2G3+−−− This is Knows as Friss Formula.
Reflection: Reflection occurs when a wave encounters a boundary between two different mediums and bounces back into the original medium. The angle of incidence (the angle between the incident wave and the normal to the surface) is equal to the angle of reflection. Significance: 1.Radio Wave Propagation: Urban Environments: Buildings and other structures reflect radio waves, enabling signal propagation in areas not in the direct line of sight of the transmitter. | Indoor Communication:** Walls and surfaces inside buildings reflect signals, allowing coverage throughout the structure.
Statement: A continuous time signal can be represented in its samples and can be recovered back when sampling frequency fs is greater than or equal to the twice the highest frequency component of message signal. I. E. | fs≥2fm.
Proof: Consider a continuous time signal x(t). The spectrum of x(t) is a band limited to fm Hz i.E. The spectrum of x(t) is zero for |ω|>ωm.
Sampling of input signal x(t) can be obtained by multiplying x(t) with an impulse train δ(t) of period Ts. The output of multiplier is a discrete signal called sampled signal which is represented with y(t) in the following diagrams:
Signal Sampling
Here, you can observe that the sampled signal takes the period of impulse. The process of sampling can be explained by the following mathematical expression:
Sampled signal y(t)=x(t).δ(t)……(1)
The trigonometric Fourier series representation of δ(t) is given by
δ(t)=a0+Σ∞n=1(ancosnωst+bnsinnωst)……(2)
Where a0=(1/Ts)∫T/2−T/2δ(t)dt=(1/Ts)δ(0)=1/Ts
an=(2/Ts)∫T/2−T/2δ(t)cosnωsdt=(2/T2)δ(0)cosnωs0=2/T
bn=(2/Ts)∫T/2−T/2δ(t)sinnωstdt=(2/Ts)δ(0)sinnωs0=0
Substitute above values in equation 2.
∴δ(t)=(1/Ts)+Σ∞n=1((2/Ts)cosnωst+0)
Substitute δ(t) in equation 1.
→y(t)=x(t).δ(t)
=x(t)[(1/Ts)+Σ∞n=1((2/Ts)cosnωst)]
=(1/Ts)[x(t)+2Σ∞n=1(cosnωst)x(t)]
y(t)=(1/Ts) [x(t)+2cosωst.X(t)+2cos2ωst.X(t)+2cos3ωst.X(t)……]
Take Fourier transform on both sides.
Y(ω)=(1/Ts) [X(ω)+X(ω−ωs)+X(ω+ωs)+X(ω−2ωs)+X(ω+2ωs)+…]
∴Y(ω)=(1/Ts) Σ∞n=−∞X(ω−nωs) where n=0,±1,±2,…
To reconstruct x(t), you must recover input signal spectrum X(ω) from sampled signal spectrum Y(ω), which is possible when there is no overlapping between the cycles of Y(ω).
Possibility of sampled frequency spectrum with different conditions is given by the following diagrams:
Aliasing Effect
The overlapped region in case of under sampling represents aliasing effect, which can be removed by
considering fs >2fm
By using anti aliasing filters.
A basic radio detector, also known as a demodulator, is used to extract the audio or information signal from a modulated carrier wave. Here, we will consider a simple diode-based AM (Amplitude Modulation) radio detector, which is commonly used in communication systems.
Antenna: Captures the modulated RF signal.
Tuning Circuit (L and C): Selects the desired frequency.
Diode: Rectifies the RF signal to a pulsating DC signal.
Capacitor (after diode): Filters out high-frequency components.
Resistor (R) and Capacitor (C): Further smooth the signal, recovering the audio signal.
Audio Output: Sends the audio signal to headphones, a speaker, or an amplifier.
Working Principle:
1. Reception: The antenna captures the modulated RF signal.
2. Tuning: The LC circuit selects the desired frequency from the wide range of frequencies received by the antenna
3. Demodulation: The diode rectifies the selected RF signal, converting it into a pulsating DC signal that contains the audio information.
4. Filtering: The capacitor and resistor filter out the high-frequency components, leaving the original audio signal.
5. Audio Output: The filtered audio signal is sent to the output device, making the transmitted information audible.
1. Time Scaling
If ( x(t) has a Fourier transform ( X(f), then the scaled signal x(at) has a Fourier transform (1/|a|)X(f/a)
x(at) ↔F (1/|a|)X(f/a)
Significance: Compression/Expansion: Scaling time compresses or expands the signal in time, affecting frequency content.
Resolution Analysis: Helps analyze signals at different resolutions (e.G., wavelet transforms).
2. Frequency Shifting
If x(t) has a Fourier transform X(f), then the modulated signal x(t)e j2Π f0t has a Fourier transform
X(f – f0)
x(t)e j2Π f0t ↔F X(f – f0)
Significance: Modulation: Enables shifting signals to different frequency bands, essential for communication systems.
Signal Processing
Used in mixing and heterodyning to shift signals to intermediate frequencies for processing.
3. Convolution in Time Domain
The convolution of two time-domain signals x(t) and h(t) corresponds to the multiplication of their Fourier transforms X(f) and H(f)
x(t)*h(t) ↔F X(f) H(f)
Significance: LTI Systems: Simplifies the analysis of system responses by converting convolution to multiplication. | Filtering: Easier filter design and application in the frequency domain through multiplication.
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REFLECTIN CONTINUED
Satellite Communication: Earth’s Surface:** Signals from satellites reflect off the Earth’s surface to reach receivers in shadowed areas.
3. Multipath Propagation: Signal Quality:** Reflected signals can cause multipath propagation, where multiple delayed signals reach the receiver, potentially leading to interference and signal fading. Techniques like diversity reception and equalization are used to mitigate these effects.