“Angle modulation is a non-linear process and transmission bandwidth is usually much greater than twice the message bandwidth. Because of larger bandwidth, this modulation provides increased signal to noise ratio without increased transmitted power.”
Basically, angle modulation is divided into two categories namely Frequency Modulation & Phase Modulation.
One significant characteristic of this type is that it can better classify in contrast to noise and interference signal than amplitude modulation. This adjustment in execution is accomplished in the expense of expanded transmission bandwidth; that is, this modulation gives us a method for improved signal to noise ratio.
Besides, this improvement in execution in angle modulation is achieved in the expense of complex circuitry in both the transmitter and receiver section and not possible in Amplitude one.
Mathematical Expression of Angle Modulation:
Let θi(t) signify the angle of a modulated sinusoidal carrier at time t; it is assumed to be a function of the information-bearing signal or message signal. The resultant angle-modulated signal is,
s(t) = Ac cos [θi(t)]
Where Ac is the carrier amplitude, a complete oscillation happens each and every time the angle θi (t) will changed by the value of 2π radians if θi (t) increases with time, then the average freq in hertz, over a trivial intervals of t to t+∆t.
The angle-modulated signal s(t) as a rotating phasor of length Ac and angle θi (t) respectively. Such a phasor’s angular velocity is dθi (t)/dt, measured in radians/sec. The angle θi (t) is represented for an unmodulated carrier signal,
θi (t) = 2πfct + kp m(t)
and the corresponding phasor rotating with a constant angular velocity measured in radians/sec. This constant specify the angle of the unmodulated carrier during that period.
There are various methods in which the angle θi (t) could be changed in a manner w.r.t to the message signal.
Diagram of different waveforms of angle modulation:
Diagram of AM, PM and FM waveform made by a single tone: a) the carrier wave b) the amplitude modulated c) the frequency modulated signal , Image Credit: Berserkerus, Amfm3-en-de, CC BY-SA 2.5
Frequency Modulation:
“Frequency Modulation is one form of angle modulation in that instantaneous freq of the carrier is changed proportionally with the instantaneous amplitude variation of the modulating signal”.
FM is one sort of angle modulation in with fi (t) is linearly proportional with the message signal m(t) as expressed below,
fi (t) = fc + kf m(t)
The steady value of fc presented to the frequency of the unmodulated carriers signal; the fixed kf termed as modulator’s ‘frequency-sensitivity factor’, measured in hertz per volt on the other hand m(t) is a voltage signal waveform. Integrating w.r.t time and multiply the result by a factor 2π, we can write
where the 2nd term for the increase or decrease in the instant phase θi(t) due to the message m(t) one. The frequency-modulated signal is consequently,
Phase Modulation:
Phase Modulation is such type of angle modulation in which the instantaneous angle θi(t) is linearly proportional with the message ‘ m(t)’ signal as presented by means of,
θi(t) = 2πfct + kp m(t)
The term 2πfct expresses to the un-modulated carrier angle Øc set to ‘0’ in the phase modulation. The fixed kp value phase sensitivity factor of the modulator, communicated in radians/volt and m(t) is the voltage signal. In the phase modulation, modulated signal s(t) is correspondingly depicted in the time-space by,
s(t) = Ac cos [2πfct + kp m(t)]
Show that FM and PM are basically same:
Let the carrier signal is = Ac cos (2πfct)
Let the message signal is = m(t)
So, the expression of F.M. signal is =
Now if the modulation method is Phase Modulation. then the expression of Phase Modulation signal is
= Acos [2πfct + mp . m(t)]
Where, mp is a constant for the Phase Modulation
Also the Phase Modulation signal can be treated as a Frequency Modulation signal where message signal is dm(t)/dt.
So, basically Frequency Modulation and Phase Modulation are basically same.
Pre-Emphasis and De-Emphasis in FM:
A random undesired signal or noise constantly comes with a triangular spectral distribution in a Frequency Modulation technique, together with the impact that noise happens at the maximum frequency of baseband.
This may be offset, to some restricted selection, by raising the frequencies prior to transmitting and decreasing them with a corresponding receiver number. If we decrease the high frequencies from the receiver, then, in addition, it reduces the high-frequency noise.
These practice of increasing and decreasing of these frequencies are called pre-emphasis and de-emphasis, respectively. Most frequently 50 µs time constant is employed.
The total quantity of pre-emphasis which may be implemented is restricted by the simple fact that lots of kinds of modern sound signal comprise higher frequency energy compared to the musical styles that have predominated at the beginning of FM broadcasting.
They cannot be pre-emphasized since it might cause excess deviation. (systems more contemporary compared to FM broadcasting often utilize either programmed-dependent variable pre-emphasis.)
What is Narrow Band FM (NBFM) and Wide Band FM (WBFM ?
The expression for the FM signals is given by
and hence the instantaneous frequency ωi is given by,
where, kf = constant of proportionality and kr . em (t) represents the deviation of carrier frequency from the quiescent value ωc. Constant Kf hence controls the frequency deviation. If the Kf is small the frequency deviation is also small and the spectrum of the FM signal is having a narrow band. On the other hand, for higher value of kf, we get wide frequency spectrum corresponding to wideband FM case.
NARROW BAND FM:
The modulation index for narrow band FM is generally near unity and hence for this case, the maximum deviation δ<<fmand the bandwidth is
B = 2fm.
This bandwidth is same as that occupied by AM signal. The narrowband FM is used wherein intelligible signals for communications are to be transmitted such as in mobile communication used by police, ambulance etc.
WIDE BAND FM:
The modulation index for wideband FM is greater than unity. The bandwidth of a wideband FM system is given by,
B = 2(δ+fm)
For wideband FM δ<<fmand hence B = 2δ
Thus, the bandwidth of wideband FM is twice the maximum frequency deviation. The wideband FM is used where the purpose is to transmit high fidelity signals such as in FM broadcasting and TV sound.
For more Modulation And Demodulation related article click here
“Modulation is the process of requiring information contained a lower frequency electronic signal onto a higher frequency signal.”
The higher freq signal is named carrier signal and the lower freq signal is termed as the modulating signal.
The upside of sending the higher freq signal is multiple: Firstly if all radio broadcasts broadcast at sound frequencies, they couldn’t be recognized from each other, and just a mix or jumbled signal will be there. Second, it is discovered that specific antenna with a range of 5 miles to 5000 miles is essential for the audio transmissions.
The expression of the modulated carrier wave is,
A sin 2πfct
If, for straightforwardness a particular audio signal is taken as the modulating signal, it can be characterized as,
B sin 2πfat
The modulated signal may be represented by,
(A + Bsin2πfat)(sin 2πfct)
V = Vc (1 + B/A sin2πfat) (sin2πfct)
Modulation Factor:
m = The ratio of “peak value of the modulating signal” with ‘the peak value of the un-modulated signal”
Percent Modulation:
M = B/A x 100
The modulation percentage may differ somewhere in the range of zero to 100 without distortion. When the per cent modulation is crossing 100 per cent, noisy frequencies are mixed, and hence distortion is the result.
Types of Modulation:
There are mainly 2 modulation types,
Analog modulation – It’s a technique of transferring analog baseband signal like audio or TV signal over a higher frequency signal.
Digital modulation – this is a digital technique of encoding digital info.
Again, Analog Modulation has different types; such as
Amplitude Modulation:
“A modulation process in that amplitude of carrier is differed in agreement by means of the instantaneous value of modulating signal is termed as Amplitude Modulation”.
Regarding correspondences, an essential thing for modulation is to encourage the transmission of the data-bearing sign over a radio channel with a recommended passband. In continuous-wave modulation, this is made operational by amplitude or changing the angle of the sinusoidal carrier.
Definitions related to Modulation and Demodulation
Modulation Index of Amplitude Modulation:
Modulation index demonstrates what amount modulated variable of the carrier signal converted around its unmodulated level. In AM , this amount otherwise called modulation depth indicate how much the modulated parameter variable differs around its unique level.Mathematically modulation index is, ma, well-defined by,
where, K = proportionality constant;
Vm = amplitude of modulating signal;
Vc = amplitude of carrier signal;
Angle Modulation
“Angle modulation is a non-linear process and transmission bandwidth is typically much more than the message band width.
Angle modulation is of two types. They are – Frequency Modulation and Phase Modulation.
A valuable component of angle modulation is that it can give better output in noisy and interference presence than AM technique. This improvement in execution is accomplished to the detriment of expanded transmission data transfer bandwidth; that is good methods for channel bandwidth with improved noise performance.
Also, in angle modulation, the improvement in execution is possible at the expense of system circuit complexity in both the transmitter and collector. This is not possible in case of amplitude modulation technique.
Angle Modulation can further be divided into:
Frequency Modulation:
Phase Modulation:
Frequency Modulation
“Frequency modulation is the form of angle modulation in which instantaneous frequency of the carrier is varied linearly with the instantaneous amplitude change of the modulating signal”.(link wiki)
Narrow band Frequency modulation has modulation-index around one. The greatest deviation is δ<<fm. The equation of bandwidth is given by the following equation. a
B = 2fm.
WIDE BAND FM:
Typically the Wider Band Frequency modulation has modulation index greater than the one. The equation of bandwidth is represented in the following equation.
B = 2(δ+fm)
For wideband FM δ<<fmand hence B = 2δ
Phase Modulation:
“Phase Modulation technique is an example for conditioning or tuning the correspondence communication signal for transmission.”
The period of a carrier signal is modulate to follow the changing sign degree of the message signal.
PM is the part of angle modulation where the θi (t) directly proportional to message signal m(t) as appeared by,
θi(t) = 2πfct + kp m(t)
Digital Modulation can further be divided into:
ASK (Amplitude Shift keying)
FSK (Frequency Shift Keying)
PSK (Phase Shift Keying)
What is Demodulation?
Definition of Demodulation:
“Demodulation is basically extracting the original information carrying signal from a carrier wave.”
Where as a demodulator is an circuitry that is utilized to recover original information or data from the modulated signal.
Some important demodulators (detectors) used for demodulating are:
Square law demodulator
Envelope detector
There are different demodulation techniques available dependent on the base-band signal parameters, for example, amplitude, freq or phase angle are transmitted in the carrier signal. A synchronous detector could be utilized when a signal is modulated with a linear modulation technique. In contrast, a Frequency modulation demodulator or a Phase modulation demodulator can be utilized for a signal attuned with a unintended one.
Comparison between Modulation and Demodulation:
MODULATION
DEMODULATION
This is the process of influencing data information on the carrier.
This is the restoration of original information as collected from the carrier.
In modulation, unique message signal is at all times mixed with carrier signal whose parameters are required modifications
In the demodulation technique, the mixture of carrier and message signal is detached from each other, to produce actual signal.
Modulation prerequisites a modulator for the mixing of the two signals.
Demodulation prerequisites demodulator to recuperate the original signal.
Modulation is for transmit data to extensive distance.
Demodulation is utilized to regain the original message signal.
Modulation is comparatively simple in between Modulation and Demodulation technique..
Demodulation is comparatively complex in between Modulation and Demodulation technique.
Microscopes are essential tools in the fields of science, medicine, and research, allowing us to explore the microscopic world in unprecedented detail. From the basic brightfield microscope to the advanced super-resolution microscope, each type of microscope has its own unique technical specifications, capabilities, and applications. In this comprehensive guide, we will delve into the intricacies of the most common types of microscopes, providing you with a detailed understanding of their features and specifications.
Brightfield Microscope
The brightfield microscope is the most widely used and fundamental type of microscope. It utilizes a light source positioned below the specimen to illuminate it, producing a direct image. The technical specifications of a brightfield microscope include:
Magnification Range:
– 40x to 1000x
Resolution:
– 200 nanometers (nm) to 2 micrometers (μm)
Field of View:
– 0.6 millimeters (mm) to 1.2 mm
Light Source:
– Halogen or Light-Emitting Diode (LED)
The brightfield microscope is commonly used for a variety of applications, such as observing stained biological samples, examining thin sections of tissues, and analyzing the morphology of cells and microorganisms.
Fluorescence Microscope
Fluorescence microscopes utilize fluorescent dyes or proteins to label specific structures or molecules within a specimen. These microscopes excite the fluorophores with a specific wavelength of light and detect the emitted light at a longer wavelength, allowing for the visualization of targeted components. The technical specifications of a fluorescence microscope include:
Magnification Range:
– 10x to 100x
Resolution:
– 200 nm to 500 nm
Field of View:
– 0.2 mm to 2 mm
Light Source:
– Mercury or Xenon lamp, Light-Emitting Diode (LED), or laser
Excitation and Emission Filters:
– Filters that select the appropriate wavelengths for excitation and emission
Fluorescence microscopy is widely used in cell biology, molecular biology, and neuroscience research, enabling the visualization of specific proteins, organelles, or signaling pathways within living cells.
Phase Contrast Microscope
Phase contrast microscopes employ a specialized optical system to convert phase differences in the light passing through the specimen into amplitude differences, resulting in a high-contrast image. This technique is particularly useful for observing living cells and transparent specimens. The technical specifications of a phase contrast microscope include:
Magnification Range:
– 40x to 1000x
Resolution:
– 200 nm to 2 μm
Field of View:
– 0.6 mm to 1.2 mm
Light Source:
– Halogen or Light-Emitting Diode (LED)
Phase contrast microscopy is commonly used in cell biology, microbiology, and developmental biology to study the internal structures and dynamics of living cells without the need for staining or labeling.
Confocal Microscope
Confocal microscopes use a pinhole to eliminate out-of-focus light, producing high-resolution, three-dimensional images of thick specimens. They can also perform optical sectioning and generate Z-stack images. The technical specifications of a confocal microscope include:
Magnification Range:
– 10x to 100x
Resolution:
– 100 nm to 300 nm
Field of View:
– 0.1 mm to 1 mm
Light Source:
– Argon ion laser, Helium-Neon (HeNe) laser, diode laser, or Light-Emitting Diode (LED)
Pinhole Size and Position:
– The size and position of the pinhole are critical for achieving optimal resolution and contrast.
Confocal microscopy is widely used in cell biology, neuroscience, and developmental biology to study the three-dimensional structure and dynamics of cells and tissues, as well as to perform high-resolution imaging of fluorescently labeled samples.
Super-Resolution Microscope
Super-resolution microscopes employ advanced techniques, such as Stimulated Emission Depletion (STED), Photoactivated Localization Microscopy (PALM), and Stochastic Optical Reconstruction Microscopy (STORM), to overcome the diffraction limit of light and achieve resolutions below 100 nanometers. These microscopes are particularly useful for observing molecular structures and interactions in living cells. The technical specifications of a super-resolution microscope include:
Magnification Range:
– 60x to 100x
Resolution:
– 20 nm to 100 nm
Field of View:
– 0.05 mm to 0.2 mm
Light Source:
– Laser or Light-Emitting Diode (LED)
Excitation and Emission Filters:
– Filters that select the appropriate wavelengths for excitation and emission
Super-resolution microscopy has revolutionized the field of cell biology, allowing researchers to visualize and study the intricate details of cellular structures and processes at the nanoscale level.
DIY Microscope Kits
For those interested in exploring the world of microscopy on a budget, DIY microscope kits offer an affordable and accessible option. These kits typically include a lens, a light source, a stage, and a camera or smartphone adapter. The technical specifications of DIY microscope kits vary depending on the kit, but they generally have lower magnification and resolution compared to professional-grade microscopes. Typical specifications include:
Magnification Range:
– 10x to 40x
Resolution:
– 1 μm to 2 μm
DIY microscope kits provide an excellent opportunity for students, hobbyists, and amateur scientists to build their own microscopes and explore the microscopic world on a budget. While they may not match the performance of high-end professional microscopes, these kits can still be valuable tools for learning and experimentation.
Conclusion
In this comprehensive guide, we have explored the technical specifications and key features of the most common types of microscopes, from the basic brightfield microscope to the advanced super-resolution microscope. Each type of microscope has its own unique capabilities and applications, catering to the diverse needs of the scientific community. Whether you are a student, a researcher, or an enthusiast, understanding the intricacies of these microscopes will empower you to make informed decisions and unlock the secrets of the microscopic world.
Optical microscopes are versatile and powerful tools that have revolutionized scientific research and analysis across various disciplines, from biology and materials science to nanotechnology. These instruments allow researchers to observe and study the intricate details of microscopic structures, enabling them to gain valuable insights and make groundbreaking discoveries. In this comprehensive guide, we will delve into the key specifications and characteristics of optical microscopes, providing you with a deep understanding of their capabilities and how to optimize their performance for your research needs.
Magnification: Unlocking the Invisible World
The magnification of an optical microscope is a crucial parameter that determines how much larger the image appears compared to the actual object. This is typically expressed as a ratio, such as 10x, 40x, or 100x. The maximum practical magnification of an optical microscope is around 1500x, beyond which the image quality may start to deteriorate due to various optical aberrations and limitations.
The magnification of an optical microscope is determined by the combination of the objective lens and the eyepiece or camera. The objective lens is responsible for the primary magnification, while the eyepiece or camera further magnifies the image. To achieve higher magnifications, researchers can use objective lenses with higher numerical apertures (NA) and shorter focal lengths, as well as eyepieces or cameras with higher magnification factors.
Numerical Aperture (NA): The Key to Resolution
The numerical aperture (NA) of an objective lens is a measure of its ability to collect light and resolve fine details. It is defined as the sine of the half-angle of the cone of light that enters the objective lens, multiplied by the refractive index of the medium between the lens and the specimen. The higher the NA, the better the resolution and the smaller the depth of field.
The relationship between the NA and the resolution of an optical microscope is governed by the Rayleigh criterion, which states that the minimum distance between two resolvable points (d) is given by the equation:
d = 0.61 λ / NA
where λ is the wavelength of the illuminating light. This equation demonstrates that by increasing the NA of the objective lens, you can achieve a higher resolution and observe smaller details in your specimen.
Depth of Field: Balancing Focus and Clarity
The depth of field of an optical microscope is a measure of the distance over which the image remains in focus. It is inversely proportional to the square of the NA and is also affected by the magnification. A high NA and a low magnification result in a shallow depth of field, while a low NA and a high magnification result in a deep depth of field.
The depth of field (DOF) can be calculated using the following equation:
DOF = n λ / (NA)^2
where n is the refractive index of the medium between the objective lens and the specimen, and λ is the wavelength of the illuminating light.
By understanding the relationship between NA, magnification, and depth of field, researchers can optimize their microscope settings to achieve the desired balance between resolution, clarity, and the ability to observe the entire depth of the specimen.
Field of View: Capturing the Big Picture
The field of view (FOV) of an optical microscope is the area of the specimen that is visible through the eyepiece or camera. It is usually expressed in terms of the diameter of the circular field of view, and is inversely proportional to the magnification. A high magnification results in a small field of view, while a low magnification results in a large field of view.
The field of view can be calculated using the following equation:
FOV = (Eyepiece field number) / (Objective magnification)
where the eyepiece field number is a characteristic of the eyepiece and is typically provided by the manufacturer.
By adjusting the magnification and selecting the appropriate objective lens, researchers can balance the need for high-resolution imaging with the requirement to observe a larger area of the specimen.
Contrast: Enhancing Visibility
The contrast of an optical microscope is a measure of the difference in brightness between the object and its background. It is affected by the lighting, the objective lens, and the specimen itself. A high contrast results in a clear and distinct image, while a low contrast results in a faint and blurry image.
There are several techniques that can be used to enhance the contrast of an optical microscope, such as:
Bright-field illumination: This is the most common form of illumination, where the specimen is illuminated from below, and the contrast is created by the absorption or scattering of light by the specimen.
Dark-field illumination: In this technique, the specimen is illuminated at an angle, and the contrast is created by the scattering of light by the specimen.
Phase contrast: This method uses the phase shift of the light passing through the specimen to create contrast, making it particularly useful for observing transparent specimens.
Differential interference contrast (DIC): This technique uses the interference of two polarized light beams to create contrast, highlighting the edges and surface topography of the specimen.
By selecting the appropriate illumination and contrast techniques, researchers can optimize the visibility of their specimens and extract valuable information from their observations.
Illumination: Controlling the Light
The illumination of an optical microscope is a measure of the amount and quality of light that is used to illuminate the specimen. It can be transmitted (bright field), reflected (dark field), or polarized (polarization microscopy). The type and quality of illumination can affect the contrast, resolution, and depth of field of the microscope.
One of the key techniques for optimizing the illumination of an optical microscope is Köhler illumination. This method involves the use of a condenser lens and a field diaphragm to create a uniform and well-defined illumination of the specimen, minimizing the effects of uneven illumination and improving the overall image quality.
In addition to Köhler illumination, researchers can also use specialized illumination techniques, such as fluorescence microscopy, to study specific features or components of their specimens. Fluorescence microscopy relies on the use of fluorescent dyes or proteins to label specific targets within the specimen, allowing for the visualization of these structures with high contrast and sensitivity.
Image Quality: Maximizing Performance
The image quality of an optical microscope is a measure of the overall performance of the microscope in terms of resolution, contrast, depth of field, and other factors. It can be affected by many factors, including the objective lens, the illumination, the specimen, and the camera or eyepiece.
To ensure the highest possible image quality, researchers can employ various techniques and strategies, such as:
Proper alignment and calibration: Ensuring that the optical components of the microscope are properly aligned and calibrated can significantly improve the image quality and reduce the effects of aberrations and distortions.
Careful specimen preparation: Proper sample preparation, such as fixation, staining, and mounting, can enhance the contrast and visibility of the specimen, leading to better image quality.
Optimization of imaging parameters: Adjusting parameters like exposure time, gain, and bit depth can help to maximize the dynamic range and signal-to-noise ratio of the acquired images.
Image processing and analysis: Utilizing advanced image processing techniques, such as deconvolution, can further improve the resolution and clarity of the images, enabling more accurate quantitative analysis.
By understanding and applying these principles, researchers can unlock the full potential of their optical microscopes, obtaining high-quality images that provide valuable insights into the microscopic world.
Conclusion
In this comprehensive guide, we have explored the key specifications and characteristics of optical microscopes, equipping you with the knowledge to master the art of quantitative microscopy. From understanding the fundamentals of magnification and numerical aperture to optimizing illumination and image quality, this guide has provided you with a deep dive into the technical aspects of these powerful instruments.
By applying the principles and techniques outlined in this guide, you can unlock the full potential of your optical microscope, enabling you to conduct cutting-edge research, make groundbreaking discoveries, and push the boundaries of scientific exploration. Remember, the journey of mastering optical microscopy is an ongoing one, and by continuously learning and adapting, you can become a true expert in this field.
VLSI is one of the most trending technologies in this digital era. Some of the frequently asked and important VLSI interview questions are given below for preparations. Study them for good result. To build up a solid concept on VLSI and VHDL, go through our detailed guideline -listed below. VLSI Interview Questions. Best of luck for your interview!
1. What is the range of integration can be designed using VLSI technology?
Ans:VLSI technology can incorporate ICs in a range of 2000 to 20,000.
2. What is Moore’s law?
Ans:Moor’s law is one of the most significant statements that describes large-scale integration technology growth. Gordon Moor, the co-founder of Intel, predicted that the number of transistors inside an integrated cheap would be doubled every 1.5 years.
3. What is BiCMOS?
Ans:BiCMOS is one of the kinds of integrated circuits that use Bipolar Junction Transistors and CMOS to design models.
4. What is Y- Chart?
Ans: Y chart is an illustration for the representation of IC design domains. Gajski-Kuhn introduced it.
5. Name the components of FPGA architectures.
Ans: FPGA or Field programmable gate array is a specially designed integrated circuit. The interconnections are programmable to design different logics. FPGA architecture consists of –
Logic block array (CLBs)
Input-Output Buffers
Programmable Interconnections
6. What is PLA and PAL? Write some differences between PAL and PLA.
Ans:PLA is acronym of Programmable Logic Array, and PAL is acronym of Programmable Array Logic. They are kinds of programmable logic devices.
PAL vs PLA, VLSI Interview Questions
7. What is the condition for a CMOS inverter to be a symmetric CMOS inverter?
Ans: The logic voltage for a symmetric CMOS inverter will be equal to half of the supplied voltage (VDD).
VINV = VDD / 2
8. Name and explain the design rules of VLSI technology.
Ans: There are two types of design rules – Micron rules and Lambda rules.
Micron Rules:This rule deals with some of the important parameters like – min. sizes of features, permissible feature separations, etc.
Lambda Rules:The Lambda is the primary length unit.
9. What is Antenna Effect regarding VLSI technology?
Ans: While the fabrication of interconnection is under process, some of the metal lines may be partially processed. Those metal lines further gather static charges inside the clot surroundings. Later, if those lines get interconnected with transistors, the previously stored charges may start discharging during operation in progress. That discharging may affect the gate oxide. This effect is known as Antenna Effect.
10. What is PLL?
Ans: PLL is Phase Locked Loop, which can track the frequency- coming inside. PLL can also work as a clock generator.
11. What is PDN and PUN?
Ans: PDN is Pull Down Network, and PUN is Pull Up Network. They are used to design desired CMOS logic.
12. Which type of transistors are used in Pass Transistor Logic?
Ans: Pass transistor logic uses NMOS transistors to design models.
13. What is Domino CMOS logic?
Ans: Domino CMOS logic is implemented by connecting a static CMOS inverter at each dynamic CMOS logic’s output.
14. What is the full form of VHDL?
Ans: VHDL stands for – Very High Speed Integrated Circuit Hardware Description Language or VHSICHDL.
15. How many MOSFETs and BJTs are required to design a BiCMOS two-input NAND gate? Draw the circuit diagram of a two-input BiCMOS NAND gate.
16. How many MOSFETs and BJTs are required to design a BiCMOS two-input NOR gate? Draw the circuit diagram of a BiCMOS NOR gate.
Ans: To build a BiCMOS two-input NOR gate, we need 7 MOSFETs and 2 BJTs.
BiCMOS NOR Gate, VLSI Interview Questions
17. What is ROBDD and OBDD?
Ans: OBDD is an Ordered Binary Decision Diagram, and ROBDD is Reduced Ordered Decision Diagram. These are Boolean space methodology for handling a large number of input signals.
18. Give some examples of Logic Synthesis Techniques of VLSI design.
Ans: Some of the logic synthesis techniques are – Instantiation, Macro expansion/ substitution, Inference, logic optimization, and structural reorganization.
19. What do you mean by Local-skew, Global Skew?
Ans:
Local Skew:Local skew is the change of clock to reach the launching flip-flop to reach the destination flip-flop.
Global Skew: Global skew is the alteration of first reaching flip-flop to the last reaching flip-flop.
20. What is FSM or Finite State Machines? Discuss the types of FSM.
Ans: FSM or Finite State Machines are devices consists of both combinational and sequential logic circuits. Input signals and current states help the machine to change its state.
The two kinds of Machines are –
Moore Machine:The FSM whose outcome is contingent upon the present state of the machine.
Mealy Machine:The FSM whose outcome is contingent upon the present state of the machine as well as upon the input signals.
21. What is HBM or Human body model regards to VLSI?
Ans: HBM or Human Body Module is a corresponding course to describe the electrostatic discharge models when the IC is in direct contact with the human figure.
22. What is Soft Error? What is SER?
Ans: Soft error occurs due to the striking of charged particles against the semiconductor devices. It can be described as a type of noise r glitch.
SER or Soft Error Rate is the prediction rate of a device to face a soft error.
23. Compare between FPGA and ASIC.
Ans: The comparative study between FPGA and ASIC is given in the below table.
Subject of Comparison
FPGA
ASIC
NAME
Field Programmable Gate Array
Application Specific Integrated Circuit
Application
The user designs the program on his own
The user gives the description of the need; the vendor provides the required model.
Production Set-up Costs
Minimal production set up cost.
Relatively costlier
Turnaround Time
Faster Turnaround Time
Slower turnaround time
Capability
Lower Capability
Higher capability and efficiency for a higher volume of production.
VLSI Interview Questions
24. What are the modes of SFF or Scan Flip Flop?
Ans: SFF or scan flip-flop has two types of operation modes. In the general model, the flip-flop function as conventional flip-flops. In the next mode or the scan mode, the flip-flops are connected so that they will work as a series of registers.
24. What is AD HOC testing?
Ans: AD HOC testing is a strategy or process to condense the number of trials from a huge set of test outlines. It is most useful for small models where ATPG, BIST are not available.
25. What is BIST?
Ans: BIST is a Built-in self-test. It is a testing logic circuit that is placed inside a chip. BIST consists of – PRSG or pseudo-random sequence generator and signature analyser.
26. Describe Slew Balancing.
Ans: Slew is a basic term related to the rise and fallen time of the input and output waveforms. Rise time is known as rising slew, whereas fall time is known as fall slew. Slew balancing is the process of making the rise slew and fall slew equal. To do so, the corresponding resistances of the transistors are kept equal.
27. Why CMOS is preferred over BJT in VLSI designs?
Ans: CMOS technology is preferred over BJTs for VLSI designs. Some of the reasons are –
CMOS has lower power indulgence.
CMOS uses lower area
Scaling of CMOS is easier than that of BJTs.
CMOS has a lower fabrication cost.
28. State some of the DSM issues.
Ans: Some of the DSM or deep sub-micron issues are – interconnect RC delays, IR drop, induction effects, antenna effects, capacitive and inductive coupling, etc.
29. What is the package of VLSI design?
Ans: Package: It is basically the storage of various datas. VHDL packages typically made up of Declaration and Body of the packages.
30. What are the future technologies of VLSI?
Ans: Future technologies of VLSI are – ULSI (Ultra Large Scale Integration) and GSI (Giga- Scale Integration). ULSI has a range of – 100,000 gates to 1,000,000 gates per IC, and GSI has a range greater than 1,000,000 gates per IC.
In the previous article, we have got an overview of VLSI design flow. In this article, we will learn about how different logic circuits can be implemented using VLSI design. VLSI is one of the key technologies in this era of digitalization. Transistors are used to implement logic circuits in VLSI design.
Digital logics are three types – the Inverter of the NOT gate, the AND gate, and the OR gate. More complex gates like -NAND, NOR, XNOR, and XOR can also be made using the basic gates. Let us discuss some of the methods of implementation of logic circuits.
CMOS Logic Design
Digital is everything about ZERO and ONE or HIGH or LOW. The input for a digital logic circuit will be either 0 or 1, so as the output value. Now, if a circuit takes input as 0 and 1, then the logic can be understood by the switch function as given-below.
Switching Operation for VLSI Design Flow
We can see in the image that when the s1 switch is opened and the s2 switch is closed, then the output will be 0; for vice versa, the output will be 1.
A digital inverter is a NOT gate that gives the inverted output for an input. For high input or input is digital ONE, then the output is low or digital ZERO. For low input or input is digital ZERO, then the output is high or digital ONE.
INPUT
OUTPUT
HIGH
LOW
LOW
HIGH
NOT gate truth table / Inverter truth table, VLSI Design Flow
A CMOS inverter is made of two enhancement-mode transistors – one is NMOS, and the other is PMOS. The NMOS works as a pull-down network, and the PMOS works as a pull up network. The input voltage controls both the transistors.
When the PMOS transistor is in the ON state, the NMOS transistor goes into the OFF state. Also, when the NMOS transistor stays OFF, the PMOS will be in an ON state. That is how both the transistors work in complementary mode.
The transistor, which remains in OFF state, provides a high impedance value, and the output value changes. Under the same rail, a CMOS logic-circuit has less noise than an NMOS logic-circuit.
The graph of the voltage transfer characteristics of a symmetrical CMOS is given below.
Voltage transfer characteristics of a symmetrical CMOS, VLSI Design Flow
Operation
The transistors are made in such a way that their threshold voltages should be of equal magnitude and opposite polarity. That is, the threshold voltage of NMOS will be equal to the magnitude of the threshold voltage of PMOS, given by the below expression.
VTN = – VTP
When the input voltage (Vin) is smaller than the threshold voltage of the NMOS transistor, then the NMOS transistor is in an OFF state. Then, the PMOS circuit will control the output voltage (Vout) with the supplied voltage (VDD). The AB region of the graph represents this operation.
Now, when the input voltage is greater than the difference of VDD and threshold voltage, then the PMOS logic circuit enters into an OFF state, and the NMOS gets activated. Then, NMOS controls the output voltage (Vout) with the ground voltage that is 0 V.
The graph’s BC region represents the saturated NMOS, and the CD part represents both the transistors are in saturated mode. VINV is the input voltage value for which the input voltage equals the output voltage.
From careful observation, we can say that the change is very high-pitched for the voltage swipe from 0 to VDD. That is why the CMOS inverter is a perfect inverter for logic design.
Now, when the input voltage is equal to the VINV, both the transistors are in saturation. The pull up network (PUN) will have VGS value =
VGS = Vin – VDD
Or, VGS = VINV – VDD
Current equation for saturation region is given as –
ID = μεW * (VGS – VTH )2 / 2 LD
This equation can be rewritten for pull up network–
IDpu = μpεWpu * (VINV – VDD – VTHP)2 / 2 D Lpu
The equation for pull down network will be –
IDpd = μnεWpd * (VINV – VTHN )2 / 2 D Lpd
Equating the drain current as per the characteristics –
CMOS logic-circuits dissipate less power than that of an NMOS logic-circuit for low frequency. The CMOS power degeneracy swings as per the switching frequency of the circuit.
Noise margins
Noise margin is the maximum allowable deviation that can be occurred without changing the main feature under noisy conditions. NML is given as the difference between the logical threshold voltage and the logic ZERO equivalent voltage for a CMOS inverter of low level. The noise margin is described as the difference between the logic high or ONE equivalent voltage and the logical threshold voltage for the high level.
CMOS two input NAND and NOR gates
NOR and NAND gates are known as universal logic gates, which can be used to implement any logic equation or any kind of other logic gates. These are the two most manufactured gates using the CMOS logic for VLSI technology. Let us discuss the implementation and design of both the gates using CMOS logic.
CMOS NOR gate
A NOR gate can be described as an inverted OR gate. The truth table of the NOR gate is given below, where A and B are the inputs.
NOR Gate Truth Table, VLSI Design Flow
A NOR gate can also be implemented using CMOS technology. The CMOS inverter circuit comes into work in this design. A pull-down network (transistor) is added with the basic CMOS NOT gate in a parallel connection to implement the NOR operation. For two input NOR gates, only one pull-down network is added. To incorporate more numbers of inputs, more transistors are added.
Operation
The logic implementation using CMOS is shown in the below image. When any of the inputs is logic high or logic ONE, then the pull-down way to the ground is locked. The output will be logic ZERO.
When both the inputs get HIGH voltage or logic – ONE value, then the output value will be logic high or ONE. The logical threshold voltage will be equal to the threshold voltage of an inverter. That is how NOR logic can be achieved using CMOS.
A NAND gate can be described as an inverted AND gate. The truth table of the NAND gate is given below, where A and B are the inputs.
NAND gate truth table, VLSI Design Flow
A NAND gate can also be implemented using CMOS technology. The CMOS inverter circuit also comes into work in this design. A pull-down network (transistor) in series and a depletion mode transistor are added with the basic CMOS NOT gate to implement the NAND operation. For two input NAND gates, only one transistor is added. To incorporate more numbers of inputs, more transistors are added to the series connection.
The logic implementation using CMOS is shown in the above image. When both the inputs are logic ZERO, both the NMOS transistors are in OFF state, while both the PMOS transistors are in ON state. The output gets connected to VDD, and that is how the output provides logic ONE or high value.
When input A gets a high value as input, and the input B gets a low value, the upside NMOS goes into ON state, and lower NMOS goes into OFF state. The ground connection cannot be established with the output value. In this condition, the left PMOS gets ON, whereas the right PMOS stays in the OFF state. The VDD finds a path through output and provides a high output value or logic 1.
When input B gets a high value as input, and input A gets a low value, the upside NMOS goes into OFF state, and lower NMOS goes into ON state. The ground connection cannot be established with the output value. Also, in this condition, the left PMOS gets OFF, whereas the right PMOS goes into the ON state. The VDD finds a path through output and provides a high output value or logic 1.
For the final logic, when both the input gets high input voltage or logic ONE value, both the NMOS transistors are in ON state. Both the PMOS transistors are in OFF state, providing a path for the ground voltage to connect with the output. The output thus provides logic ZERO or low value as output.
For more Electronics related article and VLSI design flow click here
To know about VLSI, we have to know about IC or integrated circuit. An IC is a chip or a processes package which contains transistors or digital circuits in lakhs of number.
VLSI or very large scale integration refers to the process to incorporate transistors (especially MOS transistors) to formulate IC.
VLSI devices consist of thousands of logic gates. They help to create big memory arrays .The arrays are used in microcontroller and microprocessors. It is possible to incorporate 104 to 109 components in a single chip in standard VLSI designing technique.
B. History and background of VLSI
The very first transistor was invented in the year 1947 by J. Barden, W. Shockley, W. Brattain in the Bell Laboratories. All three scientists got noble for the invention in the year 1956. The transistor size got reduced with progress in time and technology.
Jack Kilby and Robert Noyce came up with the idea of IC where components are connected within a single chip. This helped engineers to increase the speed of the operation of various circuits.
Moor’s Law: In the year 1998, Intel Corporation’s co-founder Gordon Moor predicted a trend on the number of components in an integrated circuit.
He predicted that –
“The transistor number inside a microchip gets doubled in every two years”.
The progress of integrated circuits leads to the discovery of very large scale integration or VLSI technology. Before the VLSI get invented, there were other technologies as steps. They are discussed below.
SSI or Small Scale Integration: These type of integrated circuits contains less than ten logic gates. These IC gates have several gates or flip-flops associated with one package.
MSI or Medium Scale Integration: These packages contain ten to thousand logic gates. MSI ICs can generate basic logic gates. The logic gates can be further used for making sequential and combinational circuits like – mux-demux, encoders-decoders, latch, flip flop, registers, etc.
LSI or Large Scale Integration: LSI units contain more than one hundred gates. LSI ICs creates more complex circuit structures like – calculators, mini-computers, etc.
VLSI or Very Large Scale Integration: Contains thousands of logic gates.
ULSI or Ultra Large Scale Integration: A single chip contains more than 10^9 components.
An overview of transformation is given below.
Different range for scale-integration design (in standard VLSI design > 10000 gates per IC are used )
A VLSI design has several parts. It needs right and perfect physical, structural, and behavioural representation of the circuit. Redundant and repetitive information is omitted to make a good artwork system. It is achieved by using graphical design description and symbolic representation of components and interconnections.
VLSI architectures use n-channel MOS field-effect transistors and complementary MOS. Complementary MOS or CMOS need both the n-channel and p-channel MOS FETs to be fabricated in the same substrate.
In the 1980s, the demand for increasing package density grew up, and it affected the power consumption of NMOS ICs. The power consumption became so high that the dissipation of the power posed a serious problem. To resolve the issue, the CMOS technology emerged as a solution.
CMOS provides high input impedance, high noise margin, and bidirectional operation. That is why it works smoothly as a switch.
The Metal Oxide Semiconductor Field Effect Transistor or MOSFET is the key component in high-density VLSI chips.
Why is FET used in VLSI?
FET or Field Effect Transistors are probably the simplest forms of the transistor. FETs are used widely in both analogue and digital applications. They are separated by a large value of input resistance and smaller area and size, and they can be used to form circuits with low power consumption. That is why they are widely used in very large scale integration.
CMOS and n-channel MOS are used for their power efficiency.
An NMOS field effect transistor is shown in the above image with the drain current and terminal voltage representations. For an NMOS FET, the source and drain terminals are symmetrical (bidirectional).
When there is no charge on the gate terminal, the drain to source path acts as an open switch. As a thin oxide layer separates the gate from the substrate, it gives a capacitance value. When the gate terminal accumulated enough positive charges, the voltage VGS exceeds a threshold voltage VTH. Thus, electrons are attracted in the region under the gate to give a conducting path between the drain and the source.
The gate voltage enhances the channel conductivity by entering into the enhancement mode operation. VTH ~= 0.2 VDD gives the VTH.
The majority carrier for this type of FET is holes. When the positive gate to source voltage or VGS is smaller than VTH, the majority carrier or holes are repelled into the substrate. Now, on the surface of the p-type there is no carrier. There is no current because of the depletion region.
Now, when the gate to source voltage get higher than the threshold voltage, a healthy amount of minority carriers gets attracted to the surface (Which in our case is the electron). Thus, a channel is formed of inversion layer between the source and drain terminal.
The below expression gives the drain current ID.
ID = Charge induced in the channel (Q) / transit time (τ)
The charge transit time τ is the time taken by a charge carrier to cross the channel from the source terminal to drain terminal. For small value of VDS,
τ = Drain to source distance (L) / Electron drift velocity (vd) = L / μ E = L2 / VDS μ
E is the electric field and given as, E = VDs / L.
μ is the electron mobility. We have said earlier that there is a capacitance value that generates. The capacitance is given as C = εA / D = εWL / D
W is the width, while D is the thickness of the di-oxide layer. ε represents the permittivity of the oxide layer. For silicone di-oxide, the ratio of ε / ε0 comes as 4. The charge in transit is –
The drain current is given as – ID = Q / τ = (μεW / LD) * (VGS – VTH – VDS/2)VDS
The resistance will be R = VDS / ID = LD / [ μεW * (VGS – VTH – VDS/2)]
The output characteristics of an NMOS transistor is shown in the below graph.
Output characteristics of an NMOS transistor
In the saturation region, the drain current is obtained as –
ID = (μεW / 2LD) (VGS – VTH)2
NMOS transistors can also be fabricated with the values of the threshold voltage VTH < = 0. The transistors are referred to as depletion-mode devices.
E. VLSI design rules
VLSI designing has some basic rules. The rules are specifically some geometric specifications simplifying the design of the layout mask. The rules provide details for the minimum dimensions, line layouts and other geometric measures which are obtained from the limits of certain dispensation expertise.
These rules help the designer to design a circuit in the smallest possible area that too without compromising with the performance and reliability.
There are two sets of design rules.
Rule of Micron – The rule evolves around implementation constrains such as – minimum feature size, smallest allowable feature separations. They are quoted with respect to micro-meter ranges.
Design rules based on Lambda: the constraints on the distance in the layout are expressed in terms of primary length unit lambda. The rules were developed to simplify the industry-standard micron rules. This allows scaling the capability for different processes. The length unit lambda is the distance by which the geometrical feature of a layer may overlap with that of another layer, and is determined by the limitations of the process technology.
If the length unit is lambda, then all widths, spacings and distances are expressed as m*lambda. M is the scaling factor. The diffused region has a scaling factor of a minimum of 2 lambdas. As per safe thumb rule, diffused regions, which are unconnected, have a separation of 3 lambdas. Metal lines have a minimum width and separation of 3 lambdas in standard VLSI Design.
F. Scaling in VLSI Design
The progress in technology allows us to reduce the size of the devices. This process of size reduction is known as scaling. The main advantages of scaling VLSI Design are that, when the dimensions of an integrated system are scaled to decreased size, the overall performance of the circuit gets improved. Other objectives of scaling are – larger package density, greater execution speed, reduced device cost.
Some of the most used scaling models are –
Constant Electric Field Scaling
Constant Voltage Scaling.
For the constant electric field, the nonlinear effects are eliminated as the electric field of the circuit remains the same. To understand the scaling in the VLSI Design, we take two parameters as α and β. For constant electric field, β = α and for voltage scaling, β = 1.
In this VBScript Tutorial, we are going to learn about different kinds of VBScript Conditional Statements (vbscript if else statement & vbscript select case statement) and VBScript Loop Statements (for loop, do while loop & while loop).
VBScript Tutorial #1:VBScript Conditional Statements and VBScript Loop
VBScript Conditional Statements:
Conditions are nothing but some criteria or comparison, based on which we can perform a certain task. VBScript conditional statements are the most important features in VBScript as a programming language. VBScript conditional statements perform different computations or actions based on certain ones or comparisons or conditions. Through the VBScript conditional statements, we can develop functional logic.
In this section, we are going to learn about different VBScript conditional statements, which are frequently used during programming. The frequently used conditional statements are –
· VBScript If Statement
· VBScript Case Statement
VBScript If Statement:
The VBScript If the statement is used to validate one or more conditions through the program. Multiple conditions can be added using logical boolean operators such as AND, OR, NOT, etc. Here, the conditions are the expressions that compare one value or variable with another with the help of comparison operators like equal(=), not equal(!=), Not (!), etc. Based on the verification result, we can perform a specific task.
The conditions should be kept between “If” and “Then” keywords. If there is any task need to be performed based on the false condition, the task has to be performed after the “Else” statement. At the end of the if statement block, we need to close the VBScript if statement by using the keyword “End If.” Structure of VBScript If Statement –
If <Condition1> AND <Condition2> AND .. <Condition3> Then
actions for success case
Else
actions for failure case
End If
VBScript ElseIf Statement:
Through the VBScript ElseIf Statement, we can add multiple VBScript If statements based on the result of the previous conditional result. Nested VBScript ElseIf statements are used while different actions or tasks need to be performed based on each of the conditions. Structure of VBScript If Statement –
If <Condition1> Then
actions for condition 1
ElseIF<Condition2> Then
actions for condition 2
ElseIF<Condition3> Then
actions for condition 3
Else
actions for else condition
End If
Example: Identify Saturday, Sunday, and Business Working Days using VBScript IF statement and VBScript ElseIf statement. Here, we will use more than one ElseIf statements to fulfill our requirements. Also, we can put multiple conditions along with the If statement with the help of ‘AND’ or ‘OR’ operators.
VBScript If Statement
VBScript Select Case Statement:
A VBScript Select Case Statement is an alternative approach to using multiple VBScript IfElse statements. VBScript Select Case statements are used while we have different logics/statements based on the different values against any variable. It’s also known as a switch-case statement. It helps us to write code more efficiently and readable.
A VBScript Select Case statement works with a single test expression that is executed once, at the beginning. The result of the expression will be compared in each case statement. For the match, the block of statements associated with that case will be executed. VBScript Select Case block always should end with the keyword “End Select.” Structure of VBScript Select Case Statement –
Select <Expression> // This Expression can have any value between 1-3
Case1
actions for expression value 1
Case 2
actions for expression value 2
Case 3
actions for expression value 3
Case Else
actions else condition
End Select
For example: Identify Saturday, Sunday, and Business Working Days using if conditions.
VB Scripting in UFT – Select – Case Conditional Statements in UFT
VBScript Loop:
When similar kinds of statements need to be executed repeatedly, it’s advisable to write looping statements to make the code more readable and efficient. The VBScript loop works repeatedly based on conditions or the iteration counter. Every VBScript loop has three parts –
· Loop Iterations – It’s basically the loop counter based on these statements that are getting executed.
· Loop Condition – Based on this loop will be executed, and once the condition meets, loop iteration will be completed.
· Loop Statements – it’s basically the repeated activities that are executed based on the condition.
Below VBScript Looping statements are frequently used during the coding –
VBScript For Loop
VBScript While Loop
VBScript Do While Loop
VBScript For Loop:
VBScript For Loop statements is used to execute repeated statements based on the predefined iteration counter. In this structure, the loop will continue until the iteration is reached to the predefined counter value as a condition. The VBScript For Loop should always start with the “For” keyword and end with the keyword “Next.”
While defining the counter in the after “For” keyword, we can specify the increment or decrement of the counter using the keyword “Step.” By default, if we do not use this keyword, VBScript For loop defined the increment by 1. Also, we can use the VBScript Exit For the statement to exit from the loop, which can be placed within any VBScript conditional statements within this looping structure. Structure for “VBScript For Loop” –
For nIteration = <start> to <end> Step <incremet/decrement by>
— Repeatative Statement 1
— Repeatative Statement 2
If <Condition> Then
Exit For
End If
Next
Example – here loop will be executed until the counter value has been reached to 10,
For nIteration = 1 to 10 Step 1
Msgbox “Current Iteration – “ & nIteration
Next
VBScript While Loop:
VBScript While Loop statements are used to execute repeated statements based on one or more conditions. In this structure, conditions are checked at the beginning of the loop. So, if the conditions are not met, the loop will not be executed. The keyword “While” is used to check the condition. We can use the “Exit While” statement to exit from VBScript while loop, which can be used in an IF statement within this looping structure. Structure for “VBScript While Loop” –
While <Loop Condition>
— Repeatative Statement 1
— Repeatative Statement 2
If <Exit Condition> Then
Exit While
End If
Wend
Example – here loop will be executed until the counter value has been reached to 10,
VBScript Loop – VBScript While Loop Statement
VBScript Do While Loop:
VBScript Do While Loop statements are used to execute repeated statements based on one or more conditions. This loop will be ontinued untill the loop conditions return False. VBScript Do While Loop structure, conditions are checked at the end of the loop. So, irrespective of the conditions are meet or not; the loop statements are always executed for the first iteration. We can use the “Exit Do” statement to exit from this loop, which can be placed in any conditional statement within this looping structure.
The keyword “While” is used to check the condition. The main difference between VBScript Do While Loop and VBScript While Loop statement is the position of the conditional statement. Structure for VBScript “Do While Loop” –
Do
— Repeatative Statement 1
— Repeatative Statement 2
If <Exit Condition> Then
Exit Do
End If
Loop While <Loop Condition>
Example – here loop will be executed until the counter value has been reached to 10,
VBScript Loop – VBScript Do While Loop
Conclusion:
In this VBScript article, we have learned about the VBScript Conditional Statements (vbscript if else statement & vbscript select case statement) and VBScript Loop Statements (for loop, do while loop & while loop).. We hope this tutorial has helped a lot to brush up on your basics of VB Scripting. If you want to learn more about VBScript, please click here.
Arrays are an essential data structure in programming that allow us to store and organize multiple values under a single variable name. They are a fundamental concept in many programming languages, including Python, Java, and C++. In this section, we will explore what arrays are, how they are used, their properties, advantages, indexing types, array types, and the time complexity associated with arrays.
What are Arrays?
An array is a collection of elements of the same type, grouped together under a single variable name. Each element in an array is assigned a unique index, starting from 0 for the first element. This index allows us to access and manipulate individual elements within the array. Arrays provide a convenient way to store and retrieve multiple values efficiently.
Example of Array
To better understand arrays, let’s consider an example. Suppose we want to store the temperatures of a week. We can create an array called “temperatures” and assign each day‘s temperature to a specific index. For instance, temperatures[0] can represent Monday’s temperature, temperatures[1] can represent Tuesday’s temperature, and so on. By using arrays, we can easily access and modify the temperatures for each day of the week.
Usages of Array
Arrays have various applications in programming. They are commonly used for tasks such as:
Storing and manipulating collections of data
Implementing data structures like stacks, queues, and matrices
Sorting and searching algorithms
Representing images, sound, and other multimedia data
Arrays provide a flexible and efficient way to handle large amounts of data, making them an indispensable tool for programmers.
Array Properties
Arrays have several important properties that make them useful in programming:
Fixed Size: Arrays have a fixed size, meaning the number of elements they can hold is predetermined at the time of creation. Once an array is created, its size cannot be changed.
Homogeneous Elements: Arrays can only store elements of the same type. For example, an array of integers can only hold integer values, and an array of strings can only hold string values.
Random Access: Elements in an array can be accessed directly using their index. This allows for efficient retrieval and modification of specific elements.
Array Advantages
Arrays offer several advantages that make them a popular choice for storing and manipulating data:
Efficient Access: Since elements in an array are stored in contiguous memory locations, accessing elements by their index is fast and efficient.
Easy Manipulation: Arrays provide simple and intuitive ways to add, remove, and modify elements. This makes it easy to perform operations on the entire collection of data.
Memory Efficiency: Arrays use a fixed amount of memory, which is determined by the size and type of elements they store. This makes them memory-efficient compared to other data structures.
Types of Indexing Available in Array
Arrays support two types of indexing:
Zero-based Indexing: In zero-based indexing, the first element of an array is assigned an index of 0. Subsequent elements are assigned sequential indices. For example, in an array with five elements, the indices would be 0, 1, 2, 3, and 4.
One-based Indexing: In one-based indexing, the first element of an array is assigned an index of 1. Subsequent elements are assigned sequential indices. One-based indexing is less common than zero-based indexing but is used in some programming languages.
Types of Arrays
There are several types of arrays, each with its own characteristics and use cases. Some common types of arrays include:
One-dimensional Array: A one-dimensional array is the simplest form of an array. It consists of a single row of elements and is often used to represent lists or sequences of data.
Two-dimensional Array: A two-dimensional array is an array of arrays. It is used to represent tables or matrices, where elements are organized in rows and columns.
Multi-dimensional Array: A multi-dimensional array is an array with more than two dimensions. It can be used to represent complex data structures, such as three-dimensional graphics or multi-dimensional datasets.
Time Complexity of Array
The time complexity of array operations is an important consideration when working with arrays. The time complexity refers to the amount of time it takes to perform an operation on an array, and it is typically expressed in terms of the number of elements in the array.
Accessing an element in an array using its index has a time complexity of O(1), which means it takes constant time regardless of the size of the array.
Inserting or deleting an element at the beginning or middle of an array has a time complexity of O(n), where n is the number of elements in the array. This is because shifting elements after the insertion or deletion point is required.
Inserting or deleting an element at the end of an array has a time complexity of O(1), as it does not require shifting elements.
Understanding the time complexity of array operations is crucial for writing efficient and optimized code.
In the next sections, we will dive deeper into each type of array and explore their syntax, manipulation techniques, and examples. Stay tuned to expand your knowledge of arrays!
How to Declare Arrays
Arrays are an essential data structure in programming that allow you to store multiple values of the same type in a single variable. They provide a convenient way to organize and manipulate data. In this section, we will explore how to declare arrays in different programming languages.
How to Declare Arrays in Java
In Java, declaring an array involves specifying the type of the elements it will hold, followed by the name of the array variable and square brackets. Here’s the syntax:
java
dataType[] arrayName;
For example, to declare an array of integers called numbers, you would write:
java
int[] numbers;
You can also declare and initialize an array in one line by providing the values inside curly braces:
java
int[] numbers = {1, 2, 3, 4, 5};
It’s important to note that arrays in Java have a fixed size, meaning you need to specify the number of elements the array can hold when declaring it. Once the size is defined, it cannot be changed.
How to Declare Arrays in Python
Python provides a more flexible approach to declaring arrays, known as lists. Lists in Python can hold elements of different types and can grow or shrink dynamically. To declare a list, you simply assign values to a variable using square brackets:
python
listName = [value1, value2, value3]
For example, to declare a list of strings called fruits, you would write:
python
fruits = ["apple", "banana", "orange"]
Unlike Java, you don’t need to specify the type of elements in a Python list. Python automatically determines the type based on the values you assign.
How to Declare Arrays in C
In C, declaring an array is similar to Java, where you specify the type of elements followed by the name of the array variable and square brackets. Here’s the syntax:
c
dataType arrayName[size];
For example, to declare an array of integers called numbers with a size of 5, you would write:
c
int numbers[5];
You can also declare and initialize an array in one line by providing the values inside curly braces:
c
int numbers[] = {1, 2, 3, 4, 5};
Similar to Java, arrays in C have a fixed size that cannot be changed once declared.
Summary
In this section, we learned how to declare arrays in Java, Python, and C. Java requires you to specify the type of elements and the size of the array, while Python allows for dynamic resizing and doesn’t require type specification. C, like Java, requires you to specify the type and size of the array. Understanding how to declare arrays is fundamental to working with arrays and manipulating data efficiently in different programming languages.
How to Access Array Elements
How to Access Array Elements in Java
In Java, arrays are a fundamental data structure that allows you to store and manipulate multiple values of the same type. Accessing array elements in Java is straightforward and can be done using the index of the element within the array.
To access an array element in Java, you need to specify the index of the element you want to retrieve. The index starts from 0 for the first element and increments by 1 for each subsequent element. For example, if you have an array called numbers with 5 elements, you can access the third element using numbers[2].
Here’s an example that demonstrates how to access array elements in Java:
java
int[] numbers = {1, 2, 3, 4, 5};
int thirdElement = numbers[2]; // Accessing the third element
System.out.println(thirdElement); // Output: 3
In the example above, we have an array numbers with 5 elements. We access the third element by using the index 2 within square brackets. The value of the third element, which is 3, is then assigned to the variable thirdElement. Finally, we print the value of thirdElement, which outputs 3.
How to Access Array Elements in Python
Python also provides a simple and intuitive way to access array elements. In Python, arrays are called lists, and you can access list elements using the same indexing approach as in Java.
To access an element in a Python list, you need to specify the index of the element within square brackets. Similar to Java, the index starts from 0 for the first element. For example, if you have a list called fruits with 4 elements, you can access the second element using fruits[1].
Let’s take a look at an example of accessing array elements in Python:
python
fruits = ["apple", "banana", "orange", "grape"]
second_element = fruits[1] # Accessing the second element
print(second_element) # Output: banana
In the example above, we have a list fruits with 4 elements. We access the second element by using the index 1 within square brackets. The value of the second element, which is "banana", is then assigned to the variable second_element. Finally, we print the value of second_element, which outputs "banana".
How to Access Array Elements in C
In C, accessing array elements follows a similar indexing approach as in Java and Python. C arrays are zero-indexed, meaning the first element has an index of 0, the second element has an index of 1, and so on.
To access an element in a C array, you need to specify the index of the element within square brackets. For example, if you have an array called scores with 3 elements, you can access the third element using scores[2].
Here’s an example of accessing array elements in C:
c
int scores[] = {85, 90, 95};
int third_element = scores[2]; // Accessing the third element
printf("%d\n", third_element); // Output: 95
In the example above, we have an array scores with 3 elements. We access the third element by using the index 2 within square brackets. The value of the third element, which is 95, is then assigned to the variable third_element. Finally, we print the value of third_element, which outputs 95.
Accessing array elements is a fundamental operation when working with arrays in any programming language. By understanding how to access array elements, you can retrieve and manipulate specific values within an array to perform various tasks in your programs.
Using Array Length
Arrays are a fundamental data structure in programming that allow us to store multiple values of the same type in a single variable. One important aspect of working with arrays is determining their length, which refers to the number of elements they contain. In this section, we will explore how to use array length in different programming languages such as Java, Python, and C.
How to Use Array Length in Java
In Java, arrays are objects that have a built-in property called length which returns the number of elements in the array. To access the length of an array, you simply append .length to the array variable. Let’s take a look at an example:
java
int[] numbers = {1, 2, 3, 4, 5};
int length = numbers.length;
System.out.println("The length of the array is: " + length);
In this example, we have an array called numbers that contains five elements. By calling numbers.length, we retrieve the length of the array and store it in the variable length. Finally, we print out the length using System.out.println().
How to Use Array Length in Python
Python also provides a way to determine the length of an array. However, in Python, arrays are called lists. To get the length of a list, we can use the len() function. Here’s an example:
python
numbers = [1, 2, 3, 4, 5]
length = len(numbers)
print("The length of the list is:", length)
In this Python example, we have a list called numbers that contains the same elements as the Java array. By calling len(numbers), we obtain the length of the list and assign it to the variable length. Finally, we print out the length using the print() function.
How to Use Array Length in C
In C, arrays do not have a built-in property or function to directly retrieve their length. However, we can calculate the length of an array by dividing the total size of the array by the size of each element. Let’s see an example:
“`c
include
int main() {
int numbers[] = {1, 2, 3, 4, 5};
int length = sizeof(numbers) / sizeof(numbers[0]); printf(“The length of the array is: %d\n”, length);
return 0;
}
“`
In this C example, we declare an array called numbers and initialize it with five elements. To calculate the length, we use the sizeof() operator to get the total size of the array and divide it by the size of each element (sizeof(numbers[0])). Finally, we print out the length using printf().
By understanding how to use array length in different programming languages, you can effectively manipulate arrays and perform various operations based on the number of elements they contain. Whether you’re working with Java, Python, or C, the ability to determine array length is a valuable skill that will enhance your programming capabilities.
Looping through Arrays
Arrays are a fundamental data structure used in programming to store multiple values of the same type. Once we have created an array and populated it with elements, we often need to perform operations on each element. This is where looping through arrays becomes essential. In this section, we will explore how to use loops to iterate through arrays in different programming languages.
How to Use a Loop in Array in Java
Java provides several ways to loop through an array. One common approach is to use a for loop. Here’s an example:
“`java
int[] numbers = {1, 2, 3, 4, 5};
for (int i = 0; i < numbers.length; i++) {
System.out.println(numbers[i]);
}
“`
In this code snippet, we declare an array called numbers and initialize it with some values. Then, we use a for loop to iterate through the array. The loop starts at index 0 and continues until it reaches the last index (numbers.length - 1). Inside the loop, we access each element of the array using the index i and perform the desired operation.
Another way to loop through an array in Java is by using a for-each loop. This type of loop simplifies the syntax and makes the code more readable. Here’s an example:
“`java
int[] numbers = {1, 2, 3, 4, 5};
for (int number : numbers) {
System.out.println(number);
}
“`
In this code snippet, we declare an array called numbers and initialize it with some values. Then, we use a for-each loop to iterate through the array. The loop automatically assigns each element of the array to the variable number, allowing us to directly access and manipulate the elements without worrying about indices.
How to Use a Loop in Array in Python
Python offers various ways to loop through an array. One common approach is to use a for loop. Here’s an example:
“`python
numbers = [1, 2, 3, 4, 5]
for number in numbers:
print(number)
“`
In this code snippet, we define a list called numbers and populate it with some values. Then, we use a for loop to iterate through the list. The loop assigns each element of the list to the variable number, allowing us to perform operations on each element.
Another way to loop through an array-like structure in Python is by using the range() function and a for loop. Here’s an example:
“`python
numbers = [1, 2, 3, 4, 5]
for i in range(len(numbers)):
print(numbers[i])
“`
In this code snippet, we use the range() function to generate a sequence of indices that correspond to the elements in the numbers list. We then use a for loop to iterate through these indices and access the elements of the list using the index i.
How to Use a Loop in Array in C
C provides different ways to loop through an array. One common approach is to use a for loop. Here’s an example:
“`c
include
int main() {
int numbers[] = {1, 2, 3, 4, 5};
int length = sizeof(numbers) / sizeof(numbers[0]);
for (int i = 0; i < length; i++) {
printf("%d\n", numbers[i]);
}
return 0;
}
“`
In this code snippet, we declare an array called numbers and initialize it with some values. We also calculate the length of the array using the formula sizeof(numbers) / sizeof(numbers[0]). Then, we use a for loop to iterate through the array. The loop starts at index 0 and continues until it reaches the last index (length - 1). Inside the loop, we access each element of the array using the index i and perform the desired operation.
Another way to loop through an array in C is by using a while loop. Here’s an example:
“`c
include
int main() {
int numbers[] = {1, 2, 3, 4, 5};
int length = sizeof(numbers) / sizeof(numbers[0]);
int i = 0;
while (i < length) {
printf("%d\n", numbers[i]);
i++;
}
return 0;
}
“`
In this code snippet, we declare an array called numbers and initialize it with some values. We also calculate the length of the array using the formula sizeof(numbers) / sizeof(numbers[0]). Then, we use a while loop to iterate through the array. The loop continues as long as the conditioni < length is true. Inside the loop, we access each element of the array using the index i and perform the desired operation.
By using loops, we can efficiently iterate through arrays and perform operations on each element. Whether you’re working with Java, Python, or C, understanding how to loop through arrays is a crucial skill in programming.
Important Questions on Arrays
Qn 1: Can we change the Array size in Java?
In Java, the size of an array is fixed once it is declared. This means that once you create an array with a specific size, you cannot change its size later on. The size of an array is determined at the time of its creation and cannot be modified dynamically. If you need to store more elements in an array than its initial size allows, you would need to create a new array with a larger size and copy the elements from the old array to the new one.
Qn 2: What is ArrayStoreException?
An ArrayStoreException is a type of exception that is thrown when you try to store an element of an incompatible type in an array. In Java, arrays are homogeneous, which means that they can only store elements of the same type. If you attempt to store an element of a different type in an array, the JVM will throw an ArrayStoreException. For example, if you have an array of integers and you try to store a string in it, an ArrayStoreException will be thrown.
Qn 3: What is ArrayIndexOutOfBoundsException?
An ArrayIndexOutOfBoundsException is a type of exception that is thrown when you try to access an array element using an invalid index. In Java, array indices start from 0 and go up to array.length - 1. If you try to access an element using an index that is outside this range, the JVM will throw an ArrayIndexOutOfBoundsException. For example, if you have an array of size 5 and you try to access the element at index 6, an ArrayIndexOutOfBoundsException will be thrown.
Qn 4: What is the difference between ArrayStoreException and ArrayIndexOutOfBoundsException?
The main difference between an ArrayStoreException and an ArrayIndexOutOfBoundsException is the cause of the exception.
ArrayStoreException is thrown when you try to store an element of an incompatible type in an array.
ArrayIndexOutOfBoundsException is thrown when you try to access an array element using an invalid index.
In other words, ArrayStoreException occurs during the assignment of values to an array, while ArrayIndexOutOfBoundsException occurs during the retrieval of values from an array. Both exceptions indicate that there is an issue with the array operation being performed.
Qn 5: How to initialize an array with array size in Java?
To initialize an array with a specific size in Java, you can use the array declaration syntax and specify the desired size within square brackets. Here’s an example:
java
int[] numbers = new int[5];
In this example, we declare an integer array named numbers with a size of 5. This means that the array can store 5 integer values. The elements of the array are automatically initialized to their default values (0 in the case of integers). You can then assign values to individual elements of the array using their indices.
Qn 6: How to initialize an array with predefined values?
To initialize an array with predefined values in Java, you can use the array initializer syntax. Here’s an example:
java
int[] numbers = {1, 2, 3, 4, 5};
In this example, we declare an integer array named numbers and initialize it with the values 1, 2, 3, 4, and 5. The size of the array is automatically determined based on the number of elements specified within the curly braces. You can access individual elements of the array using their indices, starting from 0.
Qn 7: How to sort an array in Java?
To sort an array in Java, you can use the Arrays.sort() method from the java.util package. Here’s an example:
In this example, we have an integer array named numbers with the values 5, 2, 8, 1, and 9. By calling Arrays.sort(numbers), the elements of the array will be rearranged in ascending order. After sorting, the numbers array will contain the values 1, 2, 5, 8, and 9.
Qn 8: How to convert an array to a String?
To convert an array to a string representation in Java, you can use the Arrays.toString() method from the java.util package. Here’s an example:
In this example, we have an integer array named numbers with the values 1, 2, 3, 4, and 5. By calling Arrays.toString(numbers), the array is converted to a string representation. The resulting string will be “[1, 2, 3, 4, 5]”. This can be useful when you need to display the contents of an array as a string or when you want to concatenate the array with other strings.
Qn 9: How to copy an array?
Copying an array is a common operation in programming, and it allows you to create a new array with the same elements as an existing array. This can be useful when you want to manipulate the elements of an array without modifying the original array. In this section, we will explore different methods to copy an array in various programming languages.
Method 1: Using a loop
One way to copy an array is by using a loop. This method is straightforward and can be implemented in most programming languages. Here’s an example in Python:
“`python
Original array
original_array = [1, 2, 3, 4, 5]
Create a new array
copied_array = []
Copy the elements using a loop
for element in original_array:
copied_array.append(element)
Print the copied array
print(copied_array)
“`
In the above example, we iterate over each element in the original array and append it to the new array. This creates a copy of the original array.
Method 2: Using the slice operator
Another method to copy an array is by using the slice operator. The slice operator allows you to extract a portion of an array, and by specifying the entire array, you can create a copy of it. Here’s an example in JavaScript:
// Copy the array using the slice operator
const copiedArray = originalArray.slice();
// Print the copied array
console.log(copiedArray);
“`
In the above example, we use the slice() method without specifying any arguments. This creates a copy of the original array.
Method 3: Using library functions
Many programming languages provide library functions or methods specifically designed for copying arrays. These functions can simplify the process and make the code more concise. Here’s an example in Java:
“`java
import java.util.Arrays;
public class Main {
public static void main(String[] args) {
// Original array
int[] originalArray = {1, 2, 3, 4, 5};
// Copy the array using the copyOf() method
int[] copiedArray = Arrays.copyOf(originalArray, originalArray.length);
// Print the copied array
System.out.println(Arrays.toString(copiedArray));
}
}
“`
In the above example, we use the copyOf() method from the Arrays class in Java to copy the array. This method takes the original array and the length of the array as arguments and returns a new array with the same elements.
Method 4: Using built-in functions
Some programming languages have built-in functions that allow you to copy arrays directly. These functions are often optimized for performance and can be more efficient than other methods. Here’s an example in C++:
“`cpp
include
include
int main() {
// Original array
std::vector originalArray = {1, 2, 3, 4, 5};
// Copy the array using the assignment operator
std::vector<int> copiedArray = originalArray;
// Print the copied array
for (int element : copiedArray) {
std::cout << element << " ";
}
return 0;
}
“`
In the above example, we use the assignment operator (=) to copy the array. This creates a new vector with the same elements as the original vector.
Copying an array is a fundamental operation in programming, and understanding different methods to accomplish this task can be beneficial. Whether you choose to use a loop, the slice operator, library functions, or built-in functions, the goal remains the same – creating a new array with the same elements as the original array. Experiment with these methods in your preferred programming language to gain a better understanding of how arrays can be copied. Conclusion
In conclusion, arrays are a fundamental concept in programming that allow us to store and manipulate multiple values of the same data type. They provide a convenient way to organize and access data efficiently. In this tutorial, we have learned the basics of arrays, including how to declare and initialize them, how to access and modify elements, and how to perform common operations such as sorting and searching. We have also explored some advanced topics like multidimensional arrays and arrays of objects. By understanding arrays and practicing their usage, we can become more proficient in solving problems and writing efficient code. Arrays are an essential tool in any programmer’s toolkit, and mastering them will greatly enhance our ability to write robust and efficient programs.
Frequently Asked Questions
Q1: When should I use arrays?
A1: Arrays are useful when you need to store and access multiple values of the same type. They provide a convenient way to organize and manipulate data efficiently.
Q2: How can I learn arrays?
A2: To learn arrays, you can start by understanding the basics of array concepts and syntax. Then, you can explore array manipulation, operations, and indexing. There are various tutorials and resources available online to help you learn arrays in different programming languages like JavaScript and Java.
Q3: What are the basics of arrays?
A3: Array basics involve understanding the array data structure, its implementation, and the various functions and methods available for working with arrays. It is essential to grasp concepts like array elements, array indexing, and how to perform common operations on arrays.
Q4: Are there any array tutorials for beginners?
A4: Yes, there are many array tutorials available for beginners. These tutorials provide step-by-step guidance on understanding arrays, their syntax, and how to work with them effectively. They often include examples and exercises to reinforce your learning.
Q5: How can I learn arrays in JavaScript?
A5: To learn arrays in JavaScript, you can start with online resources that offer tutorials specifically focused on JavaScript arrays. These tutorials cover array basics, array methods, and provide examples to help you understand and practice working with arrays in JavaScript.
Q6: Can you provide some examples of array exercises?
A6: Sure! Here are a few examples of array exercises you can try:
– Write a program to find the sum of all elements in an array.
– Sort an array in ascending order.
– Remove duplicate elements from an array.
– Find the maximum and minimum values in an array.
– Reverse the order of elements in an array.
Q7: What is the difference between array fundamentals and array introduction?
A7: Array fundamentals refer to the core concepts and principles of arrays, such as their structure, indexing, and operations. Array introduction, on the other hand, provides a basic overview and introduction to arrays, including their purpose and usage.
Q8: Are there any specific array functions or methods?
A8: Yes, arrays come with built-in functions and methods that allow you to perform various operations on them. Some common array functions include length, push, pop, slice, and concat. These functions help you manipulate and work with arrays more efficiently.
Q9: How can I understand arrays better?
A9: To understand arrays better, it is recommended to practice working with them through examples and exercises. Additionally, studying array concepts, syntax, and exploring different array manipulation techniques will help you gain a deeper understanding of arrays.
Q10: Are arrays used in basic algebra?
A10: Arrays are not typically used in basic algebra. Basic algebra focuses on mathematical equations and formulas rather than data structures like arrays. However, arrays can be used in programming to solve algebraic problems or store algebraic expressions if needed.
Virtues, Limitations and Modifications of Amplitude Modulation
VSBSC Modulation
DSBSC Modulation
SSB Modulation
DSBSC vs SSBSC
Advantages & disadvantages
What is Amplitude Modulation?
Define Amplitude Modulation:
“A modulation procedure where amplitude of carrier is varied with respect to the instantaneous value of modulating signal is called Amplitude Modulation”.
From the context of communications, a main motivation for the modulation would be to ease transmission of this information-carrying signal over a communication channel or radio station via a prescribed pass-band. On this basis, we might classify continuous-wave modulation to two broad category: amplitude modulation and angle modulation. Both of these modulation differentiate themselves by providing absolutely distinctive spectral features and as a result distinct functional advantages. The classification is completed on the basis of if the amplitude of the sinusoidal carrier wave, or the frequency or phase the angle of the sinusoidal carrier wave, is varied in nature with the information signal.
Here, AC is the carrier signal amplitude and fc is the carrier signal freq. The information or message signal is indicated by term m(t); An amplitude-modulated (AM) wave may thus be described as a function of time as follows:
s(t) = Ac[1+Kam(t)]cos(2πfct)
Where Ka is a constant termed as the amplitude sensitivity. Characteristically, the carrier amplitude, message signal are stated in volts, and amplitude sensitivity is represented in volt-1
The amplitude of |Kam(t)| is generally less than unity;
|Kam(t)|<1, for all t
The carrier freq. ( fc ) is much higher than the maximum freq. element represented by W of the message signal m(t);
fc >>W
For +ve freq., the maximum freq. of the Amplitude modulation wave is equal to (fc + W), and the lowest freq. element is equal to (fc – W). The difference between these two freq. terms as the transmission bandwidth (BT) of the amplitude modulation wave, which is precisely double the message signal bandwidth (W). So
BT = 2W
Modulation Index of Amplitude Modulation:
Modulation index indicates how much modulated variable of the carrier signal fluctuates around its unmodulated level. In Amplitude modulation, this quantity also termed as modulation depth, specifies by exactly how much the modulated variable differs around its original level.
Mathematically modulation index is, ma, defined by,
where, K = proportionality constant;
Vm = amplitude of modulating signal;
Vc = amplitude of carrier signal;
We know that,
A = amplitude of modulated signal = Vc(1+masinωmt)
So, Amax = Vc(1+ma) and Amin = Vc(1-ma)
Finally, modulation index,
What is VSB-SC Modulation?
Define Vestigial Side Band System Modulation in Amplitude Modulation:
Single sideband modulation works reasonably for an info signal with an energy gap centred around ‘0’ frequency. If more information is to be broadcasted in a given time then corresponding larger B.W. is required, for example: television
SSB can play important role in reducing the bandwidth
We can analyse the case of video transmission for television system
Bandwidth occupied by T.V. video signal minimum 4MHz. So, a transmitted B.W. of 9 MHz at least would be required. So SSB is used for saving the B.W.
While using SSB, care must be taken to see at the receiver end. No problem of demodulation arises. So the carrier passed undiminished or as it is.
As the phase response of the filter at the edges of the flat pass band is loud to have bad effect on video signals received in a T.V. receiver a part of the unwanted i.e., lower sideband also transmitted. The effect of this is to produce a vestigial transmission system also known as AGC. A typical frequency spectrum of this type is shown :
1.25 MHz of the lower side band gets transmitted along with the USB so that the lowest frequencies of the required USB will not be distorted in their phase by the vestigial sideband filter as only 1.25 MHz of the LSB is transmitted; a saving of nearly 3 MHz of V.H.F spectrum is produced with every T.V channel. This makes it promising to allow multiple number of channel is in the same bandwidth.
In the above figure, it was observed that the receiver video amplifier frequency response the sound occupies a frequency band near the video amplifier frequency response. The sound occupies a frequency band near the video as it is required with the picture and in practice it is not possible to have separate receiver to receive the sound operating at distant frequency i.e., away from Video Frequency.
In television receiver attenuation is intentionally delivered for video frequency from 0 to 1.25MHz. the reason for this is the extra power is transmitted for this part of the information of the video signal as it is transmitted in both sideband this would have produced unnecessary emphasis in the video output of the receiver if the attenuation had been absent.
What is DSB-SC Modulation?
Define Double Side Band Modulation in Amplitude Modulation:
Fundamentally, the double side band suppressed carrier (DSB-SC) modulation comprises of the product of the message signal and the carrier wave as shown in the equation
s(t) = c(t)m(t)
= Ac cos (2πfc t) m(t)
Consequently, the device utilized to produce the DSB-SC modulated signal is the denoted to as ‘product modulator’. It is also identified fact that not like AM, DSB-SC modulation is reduced to ‘0’ at whatever time the message signal is not present.
Thus, the apparatus used to create the DSB-SC controlled wave is termed as product modulator. In addition, we understand that unlike any amplitude modulation, DSB-SC modulation is decreased to zero if the message code is switched off.
Mostly, the signal goes into a phase change if the message signal is not zero. The packet of a DSB-SC controlled signal is so dissimilar from the message one, meaning that simple demodulation with the packet detection isn’t a feasible choice for DSB-SC modulation.
DSB-SC features:
Only two side-band with suppressed carrier is transmitted
With carrier suppressed power saving for m=1 is 66%
It requires lesser bandwidth
It has balanced modulation
What is SSB-SC Modulation?
Define Single Side Band (SSB-SC) Modulation:
In suppressing the carrier, DSB-SC modulation have a significant limit of Amplitude modulation when it is to this wastage of transmitted electricity. To look after another significant restriction of Amplitude modulation when it comes to station bandwidth, we will have to suppress one of both sidebands from the DSB-SC modulated wave. This adjustment of DSB-SC modulation is exactly what implemented in SSB modulation. In significance, SSB modulation be subject to entirely on the lower-sideband and upper-sideband to transmit the message transfer through communication channels based on which side-band is in fact is communicated.
Single Side Band can be represented mathematically as;
Where, s(t) is the message, ŝ(t) is its Hilbert Transform, and f0 is the radio carrier frequency.
SSBSC Features:
A SSBSC has the following features:
Only one side band is transmitted
With one side boundary for m=1 it is 83.3%
Its bandwidth is least
This is a phase shift method modulator.
Comparison between DSB-SC and SSB-SC:
DSB-SC
SSB-SC
Only two side-band with suppressed carrier is transmitted.With carrier suppressed power saving for m=1 is 66%It requires lesser bandwidthIt has balanced modulation
Only one side band is transmittedWith one side boundary for m=1 it is 83.3%Its bandwidth is leastThis is a phase shift method modulator.
Advantages and disadvantages of Amplitude Modulation:
ADVANTAGES of AM
Small antenna size.
Long range communication.
Using repeater any distance communication is possible.
