Low pass filter A Low Pass Filter is a circuit that can be designed to modify, reshape or reject all unwanted high frequencies of an electrical signal and accept or pass only those signals wanted by the circuits designer Working: As the frequency is increased, the reactance of L increases so that a larger amount of the voltage appears across L.Also as the frequency increases, the reactance of C decreases. The capacitor thus provides a bypass for the higher frequency currents around the load resistance R. Because of the increased reactance of the inductor and decreased reactance of the capacitor at high frequencies, the higher frequencies appear only in small amounts across the load. Low frequencies develop higher voltages across the load. Low frequencies are passed, high frequencies are rejected. Circuit diagram: Derivation- we use the following equation to calculate the output voltage for two single resistors connected in series: Vout = Vin x R2 . R1+R2 Where R1+R2=RT, the total resistance of the circuit We know that the capacitive reactance of a capacitor in an AC circuit is given as: XC= 1 . ohms 2πfC the circuit impedance is calculated as: Then by substituting our equation for impedance above into the resistive potential divider equation gives us: High pass filter A High Pass Filter is the exact opposite to the low pass filter circuit as the two components have been inter interchanged changed with the filters output signal now being taken from across the resistor. High-pass pass filters pass chosen high-frequency frequency current and reject low-frequency currents. Working: As the frequency increases, XL increases and a higher voltage is developed across L and R in parallel. As frequency increases, XC decreases, providing a low- reactance path for high-frequency high frequency signals. Low frequencies are shunted or bypassed around the load R by the low reactance of L at low frequencies. Circuit diagram: Derivation: Band pass filter A band pass filter is an electronic device or circuit that allows signals between two specific frequencies to pass, but that discriminates against signals at other frequencies. Working: In a receiver, a band pass filter allows signals within a selected range of frequencies to be heard or decoded, while preventing signals at unwanted frequencies from getting through. A band pass filter also optimizes the signal-to-noise ratio (sensitivity) of a receiver. Circuit diagram: Derivations: 1) Calculation of the center frequency- 2) Calculation of the cut off frequencies- which then gives: The solution of this yields four values for the cutoff frequencies. Only two are positive and have physical significance. They are- 3) Calculation of the bandwidth- 4) Calculation of the quality factor- Band reject filter. A band stop filter is a device that enables the passage of various frequencies but rejects particular ones. By combining a basic RC lowpass filter with a RC high-pass filter we can form a simple band-pass filter that will pass a range or band of frequencies either side of two cutoff frequency points. Circuit diagram: The frequency response of band stop filter is shown below Working: In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels.[1] It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stop band. Network graph:: When all the elements in a network are replaced by lines with circles or dots at both ends, the configuration is then called the graph of network. The graph of network is drawn by keeping all the points of intersection of two more branches and representing the network elements of lines, voltages and current source by their internal impedance. Tree and co-tree: A tree is a connected sub graph of a network which consists of all the nodes of the original graph but no closed path. The number of nodes in a graph is equal to the number of node in the tree co-tree is a sub graph, which is formed with the branches that are removed while forming a tree. Hence it is called a complement of a tree. For every tree, there will be a corresponding co-tree and it's branches are called as links or chords. Duality of Network:: two electrical network ate said to be dual network,if the mesh equations of one network are equal to the node equation of others. Identical behaviour patterns in two crkts illustrate the principle of duality.the two dual network are based on kcl and kvl. Tie-set:: it is a unique set with respect to a given tree of a connected graph containing one chords and all of the free branches contained in the free formed between two vertices of the chord. Cut-set:: it is that set of elements or branches of a graph that separates two main ports of a network.if any branch of the cut set is not removed, the network remains connected. The term cut set is derived from the properly designated by the way which the network can be devided into two parts. A cut-set is shown on a dashed line, where the dashed line passes through the branches defining the cutset. Incidence Matrix:: Any oriented graph can be described completely in a compect Matrix from and the orientation of each branch in the graph and the nodes at which this branch is incident is incidence Matrix, the remaining Matrix is then termed as reduce incident.
