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Transfer Function Block Diagrams - Noise and Disturbances

Every system will be subjected to both noise and disturbances from a range of sources. These can be emitted externally from the environment or from internal circuit components.


Noise is present within internal circuits of the system itself and is also emitted by external sources such as equipment installed on the same power line (which conduct noise into the control system via the power input line) or from other devices physically located nearby.

Internal noise sources include:

  • Resistor shot noise
  • PWM switching frequency radiated noise
  • High current signal path conducted and emitted noise
  • Clock signal noise
  • Internal ADC noise

External noise sources include:

  • Conducted noise through power inlet from locally grid connected electronic equipment
  • Environmental radiated noise from other equipment, such as clock signals etc
  • Heavy local switching machinery, such as motors and welding machines

A system should be designed so that any noise, from internal and external sources, is adequately attenuated so that it does not interfere with the operation of the system. Noise can cause many issues including communication issues between subsystems on a digital level, as well as analogue noise which can affect sensor performance and control/plant behaviour.


Any control system that is eventually put into operation “in the field” should be able to maintain its desired output regardless of any disturbances placed upon the system.

Disturbances can be in the form of a varying terrain for an automotive cruise control system or a change of wind direction for an aircraft autopilot system.

D(s) represents the disturbance input to the system.

Systems should be designed to minimise the effects of any noise or disturbances, block diagram representation of a system allows the designer to model the effects of noise and disturbances upon the output (or upon intermediate stages) of the system.

Systems will have many inputs, these include the “intended” input signal as well as noise inputs, disturbances, temperature drifts and many more. When modelling the effect of these disturbances, each input is modelled individually by setting all other inputs to zero. As systems are modelled as linear time invariant (LTI) systems, the sum effect of all of the disturbances together is a simple addition of the individual effects. This serves as another reason to linearise systems before performing any in depth modelling.

Deriving the transfer function for a disturbance input:

Determine D(S)/Y(S)

Set all other inputs zero – R(s) = 0

D(S)/Y(S) = G2(s) / [1 + G1(s)G2(s)H(s)]