Analysis Conc

Analysis:

In this experiment which is about mesh analysis we are required to investigate the effects of mesh analysis on the multiple active linear source in a network. We are also required to verify the linear response at any point in a mesh circuit is similar to Kirchhoff’s voltage law, to investigate the effects of nodal analysis on multiple active linear source in a network and lastly, we have to verify the linear response at any point in a nodal circuit is similar to Kirchhoff’s current law. What first is a mesh analysis? Mesh analysis is a technique applicable only to those networks which are planar. A planar circuit is a circuit where no branch passes over or under any other branch. A mesh is a property of a planar circuit and is not defined for non-planar circuit. In the experiment what we did first was draw and simulates the first mesh circuit diagram in the Tina pro worksheet. Then we obtain the mesh currents I1, I2 , and I3 and the voltages across the resistors V1, V2 , V3 , V4 and V5 and record the simulated reading on the table. We noted the polarities of each. After that we calculate the mesh currents and the voltages across the resistors using mesh analysis technique and record the calculated values on table 4.1. Then we draw and simulate the second nodal circuit diagram in Tina pro worksheet. Then we now obtain the node voltages V1, V2 , and V3 and the currents I1, I2 , and I3 from the figure 4.2 and record the measured readings on the table. We noted the polarities of the responses. Then after that we calculated the node voltages and the mesh currents nodal analysis technique and record the calculated values on the table.

Conclusion:

Mesh analysis (sometimes referred to as loop analysis or mesh current method) is a method that is used to solve planar circuits for the voltage and currents at any place in the circuit. Planar circuits are circuits that can be drawn on a plane with no wires overlapping each other. Mesh analysis uses Kirchhoff’s voltage law to solve these planar circuits. The advantage of using mesh analysis is that it creates a systematic approach to solving planar circuits and reduces the number of equations needed to solve the circuit for all of the voltages and currents Mesh analysis works by arbitrarily assigning mesh currents in the essential meshes. An essential mesh is a loop in the circuit that does not contain any other loop. When looking at a circuit schematic, the essential meshes look like a “window pane”. Figure 1 labels the essential meshes with one, two, and three. Once the essential meshes are found, the mesh currents need to be labelled. A mesh current is a current that loops around the essential mesh. The mesh current might not have a physical meaning but it is used to set up the mesh analysis equations. When assigning the mesh currents it is important to have all the mesh currents loop in the same direction. This will help prevent errors when writing out the equations. The convention is to have all the mesh currents looping in a clockwise direction. Figure 2 shows the same circuit shown before but with the mesh currents labelled. The reason to use mesh currents instead of just using KCL and KVL to solve a problem is that the mesh currents can account for any unnecessary currents that may be drawn in when using KCL and KVL. Mesh analysis ensures that the least possible number of equations regarding currents is used, greatly simplifying the problem.

A supermesh occurs when a current source is contained between two essential meshes. To handle the supermesh, first treat the circuit as if the current source is not there. This leads to one equation that incorporates two mesh currents. Once this equation is formed, an equation is needed that relates the two mesh currents with the current source. This will be an equation where the current source is equal to one of the mesh currents minus the other. The following is a simple example of dealing with a supermesh.

Circuit with dependent source. Ix is the current that the dependent voltage source depends on. A dependent source is a current source or voltage source that depends on the voltage or current on another element in the circuit. When a dependent source is contained within an essential mesh, the dependent source should be treated like a normal source. After the mesh equation is formed, a dependent source equation is needed. This equation is generally called a constraint equation. This is an equation that relates the dependent source’s variable to the voltage or current that the source depends on in the circuit. The following is a simple example of a dependent source

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

In analyzing a circuit using Kirchhoff's circuit laws, one can either do nodal analysis using Kirchhoff's current law (KCL) or mesh analysis using Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node, requiring that the branch currents incident at a node must sum to zero. The branch currents are written in terms of the circuit node voltages. As a consequence, each branch constitutive relation must give current as a function of voltage; an admittance representation. For instance, for a resistor, Ibranch = Vbranch * G, where G (=1/R) is the admittance of the resistor.

Nodal analysis is possible when all the circuit elements' branch constitutive relations have an admittance representation. Nodal analysis produces a compact set of equations for the network, which can be solved by hand if small, or can be quickly solved using linear algebra by computer. Because of the compact system of equations, many circuit simulation programs (e.g. SPICE) use nodal analysis as a basis. When elements do not have admittance representations, a more general extension of nodal analysis, modified nodal analysis, can be used. While simple examples of nodal analysis focus on linear elements, more complex nonlinear networks can also be solved with nodal analysis by using Newton's method to turn the nonlinear problem into a sequence of linear problems.

Analysis:

In this experiment which is about superposition theorem and linearity we are required to do three things. First we must investigate the effects of multiple active linear sources in a network, second we must verify that the linear response at any point in a linear circuit having several independent linear sources is equivalent to the algebraic sum of individual source acting alone and lastly, we must illustrate the principle of linearity. In this experiment what we first did was measure the resistances R1 R2 R3 R 4 R5 and connect the resistances in the circuit. Then we connected the power supply unit (psu) to the main power supply line. We did not turn on the power supply we first check the connection if it is correct to avoid accidents. We ensure that the output voltages of the supply is set and adjusted to 20V dc (VS1) and 15V (VS2) then we connected the supply to the circuit. The we measured the currents I1, I2 , and I3 and the voltages V1, V2 , V3 , V4 and V5 and record the measured readings in the table provided. We noted the polarities of the response. After that we removed the 15V dc source by “”shorting” the terminals in the circuit. We then checked the circuit connection before switching on the power supply. We ensured that output voltages of the power supply is set and adjusted to 20V dc (VS1) then connect the supply to the circuit. Then we measured the currents I1’, I2 ‘, and I3’ and the voltages V1’, V2’ , V3 ‘, V4’ and V5’ and record the measured

readings on the provided table. We again noted the polarities of responses. After that we removed the 20V dc source by “shorting” the terminals in the circuit. We now checked the circuit connection before switching on the power supply. We ensured that the output voltages of the power supply is set and adjusted to 15V dc (VS2) then we connected the supply t to the circuit. We now measured the currents I1’’, I2 ‘’, and I3’’ and the voltages V1’’, V2’’ , V3 ‘’, V4’’ and V5’’ and measured the readings on the table. Then we computed for the calculated values and recorded the calculated values.

Conclusion:

In an electric circuit, a linear element is an electrical element with a linear relationship between current and voltage. Resistors are the most common example of a linear element; other examples include capacitors, inductors, and transformers. Fundamentally nonlinear devices like transistors are often used to build approximately linear circuits. For example, an op-amp is designed to behave like a linear amplifier, as long as its input voltages remain within certain limits A linear circuit is an electronic circuit in which, for a sinusoidal input voltage of frequency f, any output of the circuit (the current through any component, or the voltage between any two points) is also sinusoidal with frequency f. Note that the output need not be in phase with the input. A linear element is a passive element that has a linear voltage-current relationship. By a “linear voltage-current relationship” it means that by multiplying a current through the element by a constant K results in multiplying the voltage across the element by the same constant K. One passive element that is defined to have linear voltage-current relationship is the resistor. A linear circuit is defined as a circuit composed entirely of independent sources and linear elements. From this definition it is then possible to show that response is proportional to the source.

The superposition theorem for electrical circuits states that the response (Voltage or Current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, while all other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by: 1.Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential. i.e. V=0, internal impedance of ideal voltage source is ZERO (short circuit)). 2.Replacing all other independent current sources with an open circuit (thereby eliminating current. i.e. I=0, internal impedance of ideal current source is infinite (open circuit). This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources. The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent. Applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements Resistors, Inductors, Capacitors and linear transformers. Because they obey the superposition principle, linear circuits can be analyzed with powerful mathematical frequency domain techniques, including Fourier analysis and the Laplace transform. These also give an

intuitive understanding of the qualitative behavior of the circuit, characterizing it using terms such as gain, phase shift, resonant frequency, bandwidth, Q-factor, poles, and zeros. The analysis of a linear circuit can often be done by hand using a scientific calculator.

In contrast, nonlinear circuits usually don't have exact solutions. They must be analyzed using approximate numerical methods by electronic circuit simulation computer programs such as Spice, if accurate results are desired. These can give solutions for any specific circuit, but not much insight into the operation of the circuit in general with different component values or inputs. The behavior of such linear circuit elements as resistors, capacitors, and inductors can be specified by a single number (resistance, capacitance, inductance, respectively). In contrast, a nonlinear element's behavior is specified by its detailed transfer function, which may be given as a graph. So specifying the characteristics of a nonlinear circuit requires more information than is needed for a linear circuit.

Linear circuits and systems form a separate category within electronic manufacturing. Manufacturers of transistors and integrated circuits divide their product lines into 'linear' and 'digital' lines, for example. In their linear components, manufacturers work to reduce nonlinear behavior to a minimum, to make the real component conform as closely as possible to the 'ideal' model used in circuit theory