1. Network Analysis and Synthesis
Chapter 1
Introduction

2. 1.1 Signal analysis
For electric networks, excitation and response are given in terms of voltages and currents.
These signals are a function of time and frequency.
We use transforms (Fourier and Laplace) to transform from time domain to frequency domain and vice versa.

3. Example:

4. 1.2 Network Analysis
Characterization of the excitation and response is only half of the problem.
The other half is describing the network.

5. Basic definations Linear system A network is linear if and only if
i.e. if it satisfies the principle of super postion and proportionality

6. Passive Reciprocal A linear network is passive if
The energy delivered is non negative for any excitation.
No voltages or currents appear between any two terminals before excitation is applied.
Reciprocal
A network is said to be reciprocal if when the point of excitation and response are interchanged, the relation between excitation and response remains the same.

7. Causal
A network is causal if the response is zero before any excitation.
Time invariant
A network is time invariant if
i.e. a network that doesn’t contain time variant components.

8. Ideal models
The following ideal models are useful in signal processing
Amplifier
Differentiator
Integrator
Time Delay

9. Ideal elements
The elements encountered most are resistor, capacitor and inductor.
When the currents and voltages are given as a function of time

10. In frequency domain, using Laplace transform

11. The end points of elements are called terminals.
A port is defined as any pair of two terminals into which energy is supplied, drawn or variables measrued.

12. 1.3 Network Synthesis
In network synthesis, we are given the excitation and response and we are required to synthesize the network from the system function.

13. Driving point synthesis
Deriving point immittance: the excitation and response are taken from the same port.
A driving point impedance is thus given as

14. Two Port Network
Transfer function: excitation and response are taken from different ports.
The transfer function can take different forms.

15. Filter Design
One of the most important aspect of transfer function synthesis.
A filter is defined as a network that passes a certain portion of a frequency and blocks the remainder of the spectrum.
Ideal Low pass filter

16. Two aspects of filter design
Obtaining a suitable and realizable transmittance H(s) given the specification.
Realizing the transmittance H(S).

17. The first step is an approximation step.
Because there are no ideal filters.

18. End!