Found 1006 Articles for Electronics & Electrical

Thermal Power PlantA generating station which converts the heat energy of combustion of coal into electrical energy is called a thermal power plant or steam power station.Schematic Arrangement of Thermal Power PlantThe thermal power plant has many arrangements for proper and efficient working. The schematic of a modern thermal power plant is shown in the figure. This whole schematic arrangement can be divided into the following segments −Coal and Ash Handling PlantThe coal is transported to the site of power plant from the coal mines by rail or road and it is stored in the coal storage plant. From the ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain. Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z\left [ x\left ( n \right ) \right ]\mathrm{\, =\, }X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )z^{-n}}}$$Solving Difference Equations by Z-TransformIn order to solve the difference equation, first it is converted into the algebraic equation by taking its Z-transform. Then, the solution of the equation is calculated in z-domain and ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain. Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z\left [ x\left ( n \right ) \right ]\mathrm{\, =\, }X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )z^{-n}}}$$Inverse Z-Transform using Residue MethodThe residue method is also known as complex inversion integral method. As the Z-transform of a discrete-time signal $\mathrm{\mathit{x\left ( n \right )}}$ is defined as$$\mathrm{\mathit{Z\left [ x\left ( n ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain. Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z\left [ x\left ( n \right ) \right ]\mathrm{\, =\, }X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )z^{-n}}}$$Time Expansion Property of Z-TransformStatement – The time expansion property of Z-transform states that if$$\mathrm{\mathit{x\left ( n \right )\overset{ZT}{\leftrightarrow}X\left ( z \right );\; \; \; \mathrm{ROC}\to \mathit{R}}} $$Then$$\mathrm{\mathit{x_{m}\left ( n \right )\overset{ZT}{\leftrightarrow}X\left ( z^{m} ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain. Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z\left [ x\left ( n \right ) \right ]\mathrm{\, =\, }X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )z^{-n}}}$$Multiplication Property of Z-TransformStatement – The multiplication property of Z-transform states that the multiplication of two signals in time domain corresponds to the complex convolution in z-domain. For this reason, the multiplication property is ... Read More

Frequency Response of Discrete-Time SystemsA spectrum of input sinusoids is applied to a linear time invariant discrete-time system to obtain the frequency response of the system. The frequency response of the discrete-time system gives the magnitude and phase response of the system to the input sinusoids at all frequencies.Now, let the impulse response of an LTI discrete-time system is $\mathit{h}\mathrm{\left(\mathit{n}\right)}$ and the input to the system is a complex exponential function, i.e., $\mathit{x}\mathrm{\left(\mathit{n}\right)}\:\mathrm{=}\:\mathit{e^{\mathit{j\omega n}}}$. Then, the output $\mathit{y}\mathrm{\left(\mathit{n}\right)}$ of the system is obtained by using the convolution theorem, i.e., $$\mathrm{\mathit{y}\mathrm{\left(\mathit{n}\right)}\:\mathrm{=}\:\mathit{h}\mathrm{\left(\mathit{n}\right)}*\mathit{x}\mathrm{\left(\mathit{n}\right)}\:\mathrm{=}\:\sum_{\mathit{k=-\infty} }^{\infty}\mathit{h}\mathrm{\left(\mathit{k}\right)}\mathit{x}\mathrm{\left(\mathit{n-k}\right)}}$$As the input to the system is $\mathit{x}\mathrm{\left(\mathit{n}\right)}\:\mathrm{=}\:\mathit{e^{\mathit{j\omega n}}}$ ,then, ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain. Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z\left [ x\left ( n \right ) \right ]\mathrm{\, =\, }X\left ( z \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )z^{-n}}}$$Time Reversal Property of Z-TransformStatement – The time reversal property of Z-transform states that the reversal or reflection of the sequence in time domain corresponds to the inversion in z-domain. Therefore, if$$\mathrm{\mathit{x\left ( n ... Read More

Z-TransformThe Z-transform is a mathematical tool which is used to convert the difference equations in discrete time domain into the algebraic equations in z-domain. Mathematically, if $\mathrm{\mathit{x\left ( n \right )}}$ is a discrete time function, then its Z-transform is defined as, $$\mathrm{\mathit{Z\left [ x\left ( n \right ) \right ]=X\left ( z \right )=\sum_{n=-\infty }^{\infty }x\left ( n \right )z^{-n}}}$$Time Shifting Property of Z-TransformStatement – The time shifting property of Z-transform states that if the sequence $\mathrm{\mathit{x\left ( n \right )}}$ is shifted by n0 in time domain, then it results in the multiplication by $\mathrm{\mathit{z^{-n_{\mathrm{0}}}}}$ in the z-domain. ... Read More

Discrete-Time Fourier TransformThe Fourier transform of a discrete-time sequence is known as the discrete-time Fourier transform (DTFT). Mathematically, the discrete-time Fourier transform of a discrete-time sequence $\mathrm{\mathit{x\left ( n \right )}}$ is defined as −$$\mathrm{\mathit{F\left [ x\left ( n \right ) \right ]=X\left ( \omega \right )=\sum_{n=-\infty }^{\infty }x\left ( n \right )e^{-j\, \omega n}}}$$Time Convolution Property of DTFTStatement – The time convolution property of DTFT states that the discretetime Fourier transform of convolution of two sequences in time domain is equivalent to multiplication of their discrete-time Fourier transforms. Therefore, if$$\mathrm{\mathit{x_{\mathrm{1}}\left ( n \right )\overset{FT}{\leftrightarrow}X_{\mathrm{1}}\left ( \omega \right )\: \: ... Read More

Discrete-Time Fourier TransformThe Fourier transform of a discrete-time sequence is known as the discrete-time Fourier transform (DTFT). Mathematically, the discrete-time Fourier transform of a discrete-time sequence $\mathrm{\mathit{x\left ( n \right )}}$ is defined as −$$\mathrm{\mathit{F\left [ x\left ( n \right ) \right ]\mathrm{\, =\, }X\left ( \omega \right )\mathrm{\, =\, }\sum_{n\mathrm{\, =\, }-\infty }^{\infty }x\left ( n \right )e^{-j\, \omega n}}}$$Linearity Property of Discrete-Time Fourier TransformStatement – The linearity property of discrete-time Fourier transform states that, the DTFT of a weighted sum of two discrete-time sequences is equal to the weighted sum of individual discrete-time Fourier transforms. Therefore, if$$\mathrm{\mathit{F\left [ ... Read More