# Simulation and Modelling - Old Questions

1. Differentiate between analog and digital methods of simulation. Explain the analog method of simulation with the help of suitable example.

Analog simulation and Digital simulation differs in the following ways:

- The goal of digital simulation is much simpler to achieve than analog simulation because the circuit is discrete in nature and has no circuit constraints to meet, such as Kirchhoff's Current Law (KCL).
- Digital simulation runs orders of magnitude faster than analog simulation because digital simulation deals with high-level behavior only, while in analog simulation the same elements have analog implementations.
- Digital simulation abstracts away important electrical characteristics that might be revealed by the analog simulation.

__Analog Method of simulation__

Analog computers are those computers that are unified with devices like adder and integral so as to simulate the continuous mathematical model of the system, which generates continuous outputs.

Analog method of system simulation is for use of analog computer and other analog devices in the simulation of continuous system. The analog computation is sometimes called differential analyser. Electronics analog computers for simulation are based on the use of high gain dc amplifiers called operational amplifier (op amps). In such analog computer, voltages are equated to mathematical variables and the op amps can add and integrate the voltages. The proper configurations can handle addition of several input voltages each representing the input variables. The analog computer provides limited accuracy because op amps have many assumptions which can never be true in reality.

The general method to apply analog computers for the simulation of continuous system models involves following components:

*Example:* Automobile Suspension Problem

The general method by which analog computers are applied can be demonstrated using second order differential equation.

M x" + D x' + K x = K F(t)

Solving the equation for the highest order derivate gives,

M x" = K F(t) – D x' - K x

*Fig: Automobile suspension problem*

Suppose a variable representing the input F(t) is supplied, assume there exist variables representing -x and -x'. These three variables can be scaled and added to produce Mx". Integrating it with a scale factor 1/M produces X'. Changing sign produces -x', further integrating produces -x, a further sign inverter is included to produce +x as output.