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Network analysis and synthesis

Introduction to Network analysis and synthesis.

An electric network is any possible interconnection of electric circuit elements, while an electric circuit is a closed energised network. An electric circuit is characterised by currents (I) in the elements and voltage (V) across them. A network is not necessarily and circuit.

Circuit's elements may be as follows

- Active or passive
- Unilateral or bilateral
- Linear or non linear
- Lumped or distributed.

Network analysis includes study of the network condition and its changes due to change by applied source or change in circuit elements. During this process branch currents and element voltage changes from earlier form to new one. This is called "transient" after this it attains study state.

V (voltage) I (current) relation is linear first order differential equation. R (resistance), L (inductance), C (capacitance) is parallel and series combinations or second order equations and can be solved and analysed.

Network analysis includes number of input and output terminals with components like resistance inductance and capacitance etc...It also includes driving signals like voltage source and current source. Signals may be time variant or time invariant. Analysis always includes response of input signal with components inters of solutions such analysis demands various methods like mathematical equations (first order and second order differential equations, Laplace transformations and Z transformations).

Different standard input signals are used like continuous AC sinusoidal signal, Step signal, Ramp signal, impulse signal, exponential signal and rectangular gate signal.

Circuits to be analysed are usually combination of series, parallel or combination of both. Tools used for analysis are Kirchhoff voltage law, Kirchhoff current law mesh and node analysis using various network theorems.

Network to be analysed may be fed with AC signal or DC signal and tools are available for both. Since all electrical electronics and instrumentation networks are combination of static or dynamic components with different signals and hence network analysis finds its importance in every field. Analysis provides information about the stability of the system.

In synthesis preliminary problem is to determine the response given the excitation in the network.

Synthesis procedure is to determine whether T(s) can be realised as physical passive network. Important considerations are causality and stability.

**Fundamentals of network analysis synthesis.**

Network analysis includes analysis of active and passive elements like RLC with various combinations like series parallel and input source. It includes basic fundamental system properties as follows,

- Continuous time and discreet time system: Continuous time system results in continuous time output signal. Discreet time input signal transfers into discreet time output. Continuous time signals can be solved using differential equations and Laplace transformations. Discreet time systems are described by difference equations and can be solved by Z transformations.
- Time variant and time invariant system: Time invariant system are fixed and its input output relation does not change with the time. Time varying system varies with the time.
- Linear and nonlinear system: A linear system holds the principle of superposition and homogeneity. It has the property of additively and scaling failing which it is said to be non linear.
- Instantaneous and dynamic system: In a system output is a function of input is said to be instantaneous at present time. In a dynamic system output depends on past or future values of the input.

The fundamentals also include casual and non casual systems invariability and inverse system.

It also includes Ideal voltage source and current source.

The fundamentals of synthesis include the realisation using reliability theory. Different task to synthesize a network are causality and stability. Test whether the network function can be realised as physical passive network. It considers causality and stability by causality mean voltage cannot appear between any pair of terminals in a network before current is impressed. For stability no poles on RHS of S-plane, cannot have multiple poles etc...

Another element of reliability is Hurwitz polynomial.

**What is the difference between analysis and synthesis:**

Difference between analysis and synthesis are as follows

- Analysis is the process of reducing bigger one into small. It breaks down complex into smaller concepts for better understanding.
- Synthesis resolves conflicts set between anti synthesis and thesis by setting a common truth between them and finally provides new proposition. Analysis is dependent on logic and mathematics.
- Synthesis is a higher process that creates something new it will be done at the end of study .Analysis starts from the beginning breaks into different simple ideas to gain a better understanding of entire network.
- In simple words network analysis is considered with determining the response, given the excitation and the network.
- On the other hand network synthesis, the problem is to design the network given the excitation and the desired response.

Note:

(Excitation and response are given in terms of voltage and current.

Signal can be described well in terms of spectral or frequency information.

Time and frequency translation can be done by Fourier series, Fourier integral and the Laplace transform. )

- In network analysis in the time domain voltage-current relationship are given in terms of differential equations.
- While in synthesis the complex frequency domain are in algebraic equations.
- The algebraic equation is the more easily solved than differential equation.
- In network analysis characteristic signals may be time variant or time invariant.
- In synthesis it may be periodic or periodic or it may be even or odd.

(Periodic signal repeats itself with the minimum fundamental period whereas periodic pulse pattern do not repeat).

**Six things every student should know to solve problems in network analysis and synthesis.**

- Usually electrical networks are complex in nature analysis requires techniques important techniques are remembering all theorems they are superposition theorem, the venin, Norton, maximum power transfer theorem ,reciprocity theorem and millmans theorem. Basic electrical parameters can be solved in simple way. To use theorems circuit must be linear in basic theorem like superposition theorem replace voltages and current sources except one of them .Kirchhoffs law or ohms law will be used to calculate voltage drop and current in the branch. Procedure must be repeated for every source and finally add all the voltage results due all sources and also current of each source.
- Basic concepts like components node, branch, mesh, port, circuit, transfer functions; component transfer function etc must be understood.
- Drawing equivalent circuits by reducing number of components can be done by replacing actual components with other components. Any two terminal networks can be reduced to single impedance by successive applications of impedance in series or parallel .Star and delta transformations must be remembered .Star to delta and series resistor transformation can be treated as special case of general resistor network node elimination algorithm.
- Nodal analysis requires labelling of nodes defining voltage variable for remaining nodes to the reference using KCL solving and obtaining the result.
- Mesh analysis leads to defining a mesh, assigning mesh current to the each window using KVL and solving the equations.
- Proper understanding of circuit and its source applying proper law and obtaining the solution using appropriate techniques is most important rule to be remembered while solving any network problem. For every network problem there will be alternative technique which can be used to cross check the result. For example simultaneous equation and matrix method.

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