Communication Engineering

Resources

• Ma’am’s slide.

• Bangla :
  https://www.youtube.com/watch?v=AJ-QfSSgXTg&list=PLMjaJoGgWV1nNjZXvcps2TrjdloXQxwbn&index=1&ab_channel=RojibEEEAcademy (Recommended if you are following ma’am slide.)

• Superheterodyne Receive: [90,93]

  https://www.youtube.com/watch?v=gwW0MnNVevY&list=PLc3zKsWdO93e2I625YDlXi0LlbBth1QpB&index=92&ab_channel=RKClasses

• English :
  https://www.youtube.com/watch?v=kAs8OerKRmc&list=PLgwJf8NK-2e7uyUYrpgUUQowmRuKxRdwp&index=1&ab_channel=EngineeringFunda

• https://www.youtube.com/watch?v=tn5NgjzNq_w&ab_channel=TechnicalGuftgu

• https://www.youtube.com/playlist?list=PLgluYk4ut4L1P_fGHgGDsyfzK28nscPcX

Communication System

Classification of Electric Communication System

1. Unidirectional system or simplex system

2. Bidirectional system or duplex system
   • Half duplex system
   • Full duplex system

Time Domain Signal

---

• It is a plot of amplitude wrt time

---

• multiple signals make complex

---

Frequency Domain Signal

---

• wrt frequency

---

• complexity is very less

---

Advantages

• Filtering

• Less complexity

• Stability

• Convolution of two signal = multiplication in frequency domain

Modulation

It is a process of modification of carrier signal wrt modulating (message) signal.

Carrier signal can be defined as a high frequency signal that is modulated by the modulating or the information signal. 

Need of Modulation

1. Height of antenna : reduction of size in antenna

   $f_m , \lambda = \frac{c}{f}$,

   Length of antenna,

   dipole, $L = \frac{\lambda}{2}$

   monopole, $L = \frac{\lambda}{4}$

   small antenna, $L = \frac{\lambda}{50} or \frac{\lambda}{10}$

   We can increase $f$ to decrease the $L$.

2. Radiated power by antenna: $P_r \propto \frac{1}{\lambda^2}$, power increases when $f$ increases

3. Multiplexing: FDM, TDM, CDMA

4. High Bandwidth

5. Narrow Banding signal

Classification of Modulation

Amplitude Modulation

It is the process in Amplitude of carrier signal changes wrt message/ modulating/ information signal.

$s(t) = A_c(1+k_a m(t))\cos \omega_c t$

For single tone,

$s(t) = A_c\cos\omega_ct + \mu\frac{A_c}{2} [\cos(\omega_c+\omega _m)t + \cos(\omega_c-\omega _m)t]$

where, modulation index $\mu = k_a A_m = \frac{A_m}{A_c }$

Modulating Index

AM Signal Transmitted power

Total Transmitted Power, $P_t = P_c + P_{USB} + P_{LSB} = P_c + P_s$

Powe of carrier, $P_c = \frac{A_c^2}{2}$, It is redundancy → it doesn’t have information

$P_s$ has information, it is called power of sideband.

Power of Upper Sideband, $P_{USB} = \frac{1}{2} (\frac{A_c\mu}{2})^2 = \frac{1}{8} A_c^2 \mu^2$

Power of Lower Sideband, $P_{LSB} = \frac{1}{8} A_c^2 \mu^2$

Power of sideband, $P_s = P_{USB} + P_{LSB} = \frac{1}{4} A_c^2 \mu^2 = \frac{1}{2} P_c\mu^2$

Total Power, $P_t = \frac{A_c^2}{2} (1+ \frac{\mu^2}{2})$

Efficiency of AM Signal

It is based on $P_s$. Because, it has information.

$\eta = \frac{P_s}{P_t} = \frac{\mu^2}{2+\mu^2}$

Redundancy

$D = 1-\mu = \frac{2}{2+\mu^2}$

DSB-SC : Double Side Band Suppressed Carrier

Transmission in which frequencies produced by amplitude modulation are symmetrically spaced above and below the carrier frequency and the carrier level is reduced to the lowest practical level, ideally completely suppressed.

AM signal,

$s(t) = A_c[1+k_a m(t)] cos\omega_ct = A_c m(t) cos\omega_ct$ [$k_a =1$, $A_ccos\omega_c=0$]

$= A_c A_m cos \omega_m t cos\omega_ct = \frac{A_m A_c}{2} cos(\omega_c+\omega_m)t cos(\omega_c-\omega_m)t$

$P_{avg} = (\frac{\frac{A_m A_c}{2}}{\sqrt2})^2 + (\frac{\frac{A_m A_c}{2}}{\sqrt2})^2 = {\frac{A_m^2 A_c^2}{4}}$

Balance Modulator DSB-SC

• Consists of two identical AM modulation
  • one input m(t)
  • another input -m(t)

• The summer block is used to sum those

$s_1(t) = A_c[1+ k_a m(t)] cos \omega_ct$

$s_2(t) = A_c[1-k_a m(t)] cos \omega_ct$

$s(t) = s_1(t) - s_2(t) \\= 2k_a m (t) cos\omega_ct$

By comparing with the standard form of DSB-SC, we will get the scaling factor as $2k_a$

Ring Modulator DSB SCs

For Positive half cycle

• D1, D3 = on, D2, D4 = off

• message signal multiplied by +1

• $D_1, D_2, D_3, D_4$ are connected in ring structure

• Two center tapped transformers are used

• Carrier signal is applied between two transformer

• Carrier signal controls the diode

For Negative half cycle

• D2, D4 = on, D1, D3=off

• message signal multiplied by -1

We will get DSB SC wave s(t), which is just the product of the carrier signal c(t) and the message signal m(t), which represents DSB-SC wave and is obtained at the output transformer of the ring modulator.

SSB-SC : Single Sideband Suppressed Carrier

• Removes any of sideband along with carrier

• Bandwidth = $\omega_m = f_m$

$s(t) = \frac{A_mA_c}{2} cos(\omega_c + \omega_m) t$

or, $s(t) = \frac{A_mA_c}{2} cos(\omega_c - \omega_m) t$

We can use SSB-SC for Audio, Video signal but voice signal. Because of gap.

VSB : Vestigial Sideband Generator

Demodulation of AM

Envelope Detector

• It is a simple and highly effective system. This method is used in most of the commercial AM radio receivers

Positive Half Cycle

• Diode forward biased

• Capacitor charges rapidly

• Charge time constant (rf+Rs)C must be shorter than the carrier period

Negative/ Input signal falls

• Reverse

• Discharges through load resistor

• it continues until the positive next positive half cycle

• Discharging time constant $R_LC$ must be long enough to ensure that the capacitor discharges slowly through $R_l$ between the positive peak of the carrier wave.

[W’ is bandwidth of the message signal]

Synchronous Detection

if $\mu > 1$, we should use this.

Angle Modulation

Angle modulation is a modulation process in which the angle of the carrier wave or signal is changed with respect to the message signal or baseband signal.

Carrier Signal for Angle modulation,

$\omega_{ins} = \text{instantaneous angular frequency}$

$f_{ins} = \text{instantaneous frequency}$

$\Delta f = \text{Frequency derivation}$

Frequency Modulation

Frequency Modulation (FM) is that form of angle modulation in which the instantaneous frequency $f_{ins}$ is varied linearly with the baseband signal $m(t)$.

$\Delta f \propto m(t)$ ⇒ $\Delta f = k_{f} m(t)$, Unit of $k_f = \frac{Hz}{Volt}$

where $k_f = \text{frequency sensitivity of modulation}$

Expression

$s(t) = A_c cos(\omega_ct + \phi)$, we have to convert $\phi$ to frequency.

$\Delta f = \frac{1}{2\pi} \frac{d\phi}{dt}$ ⇒ $\int k_f m(t) = \frac{1}{2\pi} \phi$

⇒ $\phi = 2\pi \int k_f m(t) dt$

$s(t) = A_c cos [\omega_ct + 2\pi k_f\int m(t)dt]$ [$k_f = Hz/Volt$]

$s(t) = A_c cos [\omega_ct + k_f\int m(t)dt]$ [$k_f = rad/Volt$]

For single tone

$m(t) = A_m cos(2\pi f_m t)$

$s(t) = A_c cos [\omega_ct + 2\pi k_f \int A_m cos 2\pi f_m t ]$

$=A_c cos[\omega_c t + \frac{k_f A_m}{f_m} sin (\omega_mt) ]$

$=A_c cos[\omega_c t + \beta sin (\omega_mt) ]$

Modulation index, $\beta = \frac{k_f A_m}{f_m} = \frac{(\Delta_f)_{max}}{f_m}$

Types of FM:

1. Narrowband FM $(\beta \le 1)$

   This frequency modulation has a small bandwidth when compared to wideband FM. The modulation index β is small, i.e., less than 1. Its spectrum consists of the carrier, the upper sideband and the lower sideband. This is used in mobile communications such as police wireless, ambulances, taxicabs, etc.

   $s(t)=A_c cos[\omega_c t + \beta sin (\omega_mt) ]$

   ⇒ $s(t) = A_c cos(\omega_ct) cos[\beta sin(\omega_m t)] - A_c sin(\omega_ct) sin[\beta sin(\omega_m t)]$

   where, $cos[\beta sin(\omega_m t)] \approx 1$

   $sin[\beta sin(\omega_m t)] \approx \beta sin(\omega_m t)$

   $\text{Hence, } s(t) = A_ccos(\omega_ct) - \beta A_c sin(\omega_ct) sin(\omega_m t)$

   

2. Wideband FM $(\beta \gt 1)$

Ideal Bandwidth = $\infin$

To get rid off this infinite bandwidth,

Carson’s Law :

• estimates the transmission bandwidth necessary for efficiently sending an FM signal without excessive bandwidth consumption

• Carson's rule states that the bandwidth required to transmit an angle modulated wave is twice the sum of the peak frequency deviation and highest modulating signal frequency.

$B = 2 (\Delta f_{max} + f_m) = 2f_m(\beta + 1)$

• 90% power transmit

Phase Modulation

Phase modulation (PM) is a type of angle modulation where the phase of the carrier signal is varied in proportion to the the modulating signa $m(t)$.

$\phi \propto m(t)$ ⇒ $\phi = k_p m(t)$

where, $k_p$ = phase sensitivity of modulation = $\frac{rad}{volt}$

Expression

$s(t) = A_c cos(\omega_ct + \phi) = A_c cos(\omega_ct + k_p m(t))$

For single tone,

$s(t) = A_c cos[\omega_ct + k_p A_m cos(\omega_mt)] = A_c cos[\omega_ct + \beta cos(\omega_mt)]$

Modulation index, $\beta = k_p A_m = \frac{\Delta f_{max}}{\delta f_min}$

$\Delta f = \frac{k_p}{2\pi} \frac{d}{dt} m(t)$

$\Delta f_{max} = \frac{k_p}{2\pi} [\frac{d}{dt} m(t) ] _{max} = \frac{k_p}{2\pi} A_m \omega_m [ (-sin\omega_mt)] _{max}$

$\Delta f_{max} = k_p A_m f_m$, $[ (-sin\omega_mt) _{max} = 1]$

$\Delta f_{min} = -k_p A_m f_m$ $[ (-sin\omega_mt) _{max} = -1]$

Phase derivation: Difference between phase of modulated carrier and phase of unmodulated carrier.

Unmodulated carrier = $A_c cos(\omega_ct + 0 \degree)$

Modulated carrier = $A_c cos(\omega_ct + k_p m(t))$

$\text{Phase derivation}, \Delta \phi = k_p m(t)$

$\Delta \phi_{max} = _{max}(k_p m(t))$

Single tone,

$\Delta \phi_{max} = k_p A_m$ [$cosw_mt = 1$]

$\Delta \phi_{min} = -k_p A_m$

Receivers

In radio communications, a radio receiver or receiver is an electronic device that receive radio waves and converts the information carried by them to a usable form.

1. TRF : Tuned Radio Frequency

2. SHR : Super Heterodyne Radio Receiver

Heterodyne Process

It is a process of mixing two signals having different frequencies in a non-linear manner to produce a signal with new frequency.

A special type of receiver that is used for this operation is caller Super heterodyne receiver (Superhet).

Superhet receiver sections

• RF Section

• Mixer Section/IF section

• Detector/Demodulator Section

Preselector

• used to select the desire carrier frequency of AM wave

• It rejects unwanted RF signal or image frequency

RF Amplifiers

• It amplifies the incoming signals in the required range of frequencies.

• One or more RF amplifiers can be cascaded to increase the gain.

• It determines the sensitivity of the receiver

• The output of the RF section is given to the mixer stage

Frequency used in Superhet receiver

1. Radio Frequency $(f_{RF} \text{ or } f_S)$: Centre frequency of the signal transmitted/received.

2. Intermediate Frequency $(f_{IF})$: Fixed frequency lower than $f_c$

3. Local Oscillator Frequency $(f_{LO} \text{ or } f_o)$

   $f_{LO} \ge f_c$

   $f_{LO} = f_{RF} + f_{IF} = f_{s} + f_{IF}$

Image Frequency $(f_{si})$:

Image signal is the unwanted signal present at $f_{si}$

$f_{si} = f_{LO} + f_{IF} = f_{RF} + 2 f_{IF}$

The image frequency must be rejected.

Image frequency rejection ration $(IFRR)$:

The value of IFRR should be high.

Applications

All radio and TV receivers operate on the principle of super heterodyne methos.

Sampling

• Sampling is the reduction of a continuous-time signal to a discrete time signal.

• Sampling is a process performed by a sampler

• Analog signal is samples every $T_s$ secs, called sampling interval.

• Sampling rate/ frequency = $f_s$

When the continuous signal $m(t)$ is sampled at regular intervals multiplied by a periodic pulse train $s(t)$/ impulse train $\delta(t)$ , the produced signal is the sampled signal.

Sampling Theorem: A continuous time signal can be represented in its samples and can be recovered back when sampling frequency $f_s$ is greater than or equal to the twice highest frequency component of message signal.

[$f_m \text{ is the maximum frequency of the input or message signal}$]

Condition: $f_s \ge 2f_m$

Sampling rate is defined as the number of samples taken per second from a continuous signal for a finite set of values. $f_s = \frac{1}{T_s}$

Nyquist rate: The theoretical minimum sampling rate /inline eq at which a signal can be sampled and still can be reconstruct samples without any distortion.

$f_s = 2f_m$

Nyquist Interval: Nyquist interval is the reciprocal of the Nyquist rate. $T_s = \frac{1}{2f_m}$

Methods of Sampling

1. Ideal Sampling

• Known as instantaneous sampling/impulse sampling

• multiplied by a impulse train signal

• Sampling rate in infinite

• Bandwidth is large

2. Natural Sampling

• considered as efficient multiplexing method in Pulse Amplitude Modulation

• multiplied by the uniformly spaced rectangular pulses

• pulses do not have flat tops, they are curved

• their tops follow the waveform of input or message signal

3. Flat-top Sampling

• easier than natural sampling

• amplitude of sampled pulses are constant

• pulses have flat top

• Aperture effect: The loss of high frequency content because of constant amplitude. Example:

Quantization

Quantization is the process in which continuous amplitude (analog) signals is converted into discrete amplitude (digital) signals.

Given a real number $x$m we denote the quantized value of $x$ as,

$\hat x = Q(x) = x + \epsilon$, where $\epsilon$ is the quantization error.

There are two main types of quantization

1. Truncation

Just discard the least significant bits

2. Rounding

just choose the closet value

Peak to peak value = $2m_p$

• Dividing by decision boundaries (Here 5)

• Quantization level ($L$) : Decision Boundaries - 1

• Step size, $\Delta = \frac{V_H - V_L}{L} = \frac{2m_p}{L}$

• Number of bits to represent each sample (Level), $n= log_2^L$

Quantization Error: The difference between an input and output of a quantizer is known as a quantization error.

Quantization Error, $q = x(t) - y(t)$

Range of quantization error : $-\frac{\Delta}{2} \le q \le \frac{\Delta}{2}$

Signal-to-noise Ration

$P = \frac{V^2}{R} = \frac{A^2}{R}$

$SNR = \frac{\text{Wanted Component}}{\text{Unwanted Component}} = \frac{P_{signal}}{P_{noise}} = (\frac{A_{signal}}{A_{noise}})^2$,

Unit : Watt or $\text{dB}$, $1 \ dB = 10 log_{10}^P$

$SNR_{dB} = 10\log_{10}^{ SNR} = 10 \log_{10}( \frac{P_{signal}}{P_{noise}} )= 20 \log_{10} (\frac{V_{signal}}{v_{noise}})$

Signal Power, $P_{signal} = \frac{m_p^2}{2}$

Quantization noise power/ Average Quantization power / Mean square value of quantization error ,

$Nq = \frac{1}{\Delta} \int_{-\frac{\Delta}{2}}^{\frac{\Delta}{2}} q^2 dq = \frac{\Delta^2}{12}$

Noise power, $P_{noise} \text{ or } Nq = \frac{\Delta^2}{12} = \frac{4m_p^2}{12 L^2}$ [Derivation below]

$SNR = \frac{3}{2} L^2$

$SNR_{dB} = 10\log_{10} \frac{3}{2} L^2 = 1.76 + 10\log_{10}L^2 = 1.76 + 6n$

[$n = \text{Number of bits to represent each sample or level}$ ]

Bit Rate: The total bits transmitted in one unit time. It means the total bits that travel per second.

$R_b = \frac{bits}{samples} \times \frac{samples}{sec} = n \times f_s$, Unit : $bits/sec^{-1}$, bits per second

Shannon Capacity or Channel Capacity: Shannon’s Channel Capacity theorem states that the maximum rate at which information can be transmitted over a communication channel of a specified bandwidth in the presence of noise.

$C = B \log_2 (1+SNR)$

$C = \text{Channel Capacity, Unit : bits/sec}^{-1}$

$B= \text{Bandwidth}$

It tells us the theoretical highest limit in which any channel can transmit signals with the presence of noise. [Ref]

Baud Rate: The total number of signal units transmitted in one second.

$\text{Baud Rate } = \frac{R_b}{n}$

[Ref]

Pulse Code Modulation (PCM)

Information is transmitted in the form of “code words”. PCM output is in coded digital form.

Decoder

Pulse Amplitude Modulation

• amplitude of the pulse carrier signal is changed according to the amplitude of the message signal.

• Sampling Method: Flat Top PAM, Natural PAM

Applications: Ethernet, Photo biology, Driver for LED lighting, Micro controller

Demodulation

Reconstruction Filter:

• Cut off frequency $f_c > f_m$

Equalizer:

• Reduce aperture effect and attenuation

Pulse Width Modulation (PWM)

• Amplitude of $x(t) \uparrow$ → Width of PWM Signal $\uparrow$

• Amplitude of $x(t) \downarrow$ → Width of PWM Signal $\downarrow$

• Leading edges of PWM waveform coincide with the falling edges of ramp signal

Comparator

• Output High, $x(t) > c(t)$

• Output Low, $x(t) < c(t)$

Generation of PWM

• non-inverting $x(t)$

• inverting $c(t)$

Demodulation

Pulse Position Modulation (PPM)

Position of pulse varies according to modulating signal.

PPM can be derived from PWM.

Generation

Monostable:

• One stable state (Low)

• Give Trigger pulse → output = High (for some time)

• “Some time” depends on Register and Capacitor (RC) component

• Width and Amplitude Constant

• Position varies

Demodulation