Transfer function

In engineering, a transfer function (also known as system function^[1] or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input.^[2]^[3]^[4] It is widely used in electronic engineering tools like circuit simulators and control systems. In simple cases, this function can be represented as a two-dimensional graph of an independent scalar input versus the dependent scalar output (known as a transfer curve or characteristic curve). Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.

Dimensions and units of the transfer function model the output response of the device for a range of possible inputs. The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric current applied to the device; the transfer function of a photodetector might be the output voltage as a function of the luminous intensity of incident light of a given wavelength.

The term "transfer function" is also used in the frequency domain analysis of systems using transform methods, such as the Laplace transform; it is the amplitude of the output as a function of the frequency of the input signal. The transfer function of an electronic filter is the amplitude at the output as a function of the frequency of a constant amplitude sine wave applied to the input. For optical imaging devices, the optical transfer function is the Fourier transform of the point spread function (a function of spatial frequency).

^ Bernd Girod, Rudolf Rabenstein, Alexander Stenger, Signals and systems, 2nd ed., Wiley, 2001, ISBN 0-471-98800-6 p. 50
^ M. A. Laughton; D.F. Warne (27 September 2002). Electrical Engineer's Reference Book (16 ed.). Newnes. pp. 14/9–14/10. ISBN 978-0-08-052354-5.
^ E. A. Parr (1993). Logic Designer's Handbook: Circuits and Systems (2nd ed.). Newness. pp. 65–66. ISBN 978-1-4832-9280-9.
^ Ian Sinclair; John Dunton (2007). Electronic and Electrical Servicing: Consumer and Commercial Electronics. Routledge. p. 172. ISBN 978-0-7506-6988-7.

[1] Bernd Girod, Rudolf Rabenstein, Alexander Stenger, Signals and systems, 2nd ed., Wiley, 2001, ISBN 0-471-98800-6 p. 50

[LaughtonWarne2002-2] M. A. Laughton; D.F. Warne (27 September 2002). Electrical Engineer's Reference Book (16 ed.). Newnes. pp. 14/9–14/10. ISBN 978-0-08-052354-5.

[Parr1993-3] E. A. Parr (1993). Logic Designer's Handbook: Circuits and Systems (2nd ed.). Newness. pp. 65–66. ISBN 978-1-4832-9280-9.

[SinclairDunton2007-4] Ian Sinclair; John Dunton (2007). Electronic and Electrical Servicing: Consumer and Commercial Electronics. Routledge. p. 172. ISBN 978-0-7506-6988-7.

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