Transfer Functions

What are Transfer Functions?

Transfer functions are the Laplace domain representation of signal modification in a system where the input = u(t) or U(s), output = y(t) or Y(s), and the transfer function = h(t) or H(s) where "s" indicates a function in the Laplace domain. The transfer function H(s) is defined as the ratio between the output and the input:

$$ H(s) = \frac{Y(s)}{U(s)} $$

Essentially this means that the output is equal to the input multiplied by the transfer function:

$$ Y(s) = H(s)*U(s) $$

For example, if you have a simple block diagram like this:

Pretty easy since it's just a multiplication of two fractions.

Another consideration of transfer functions is that they can be combined and simplified, like the components of an electrical circuit. Transfer functions in series are multipled together while those that are in "parallel" are added or subtracted.

This is a test: Reformat of copied example block

Example Problem: Consider the chemical reaction for photosynthesis. #undefined

Given the chemical formula for photosynthesis, balance the moles of glucose and oxygen. Does this system follow the rules of conservation?

$$ 6 CO_2 + 6 H_2O + light \rightarrow C_6H_{12}O_6 + 6O_2 $$

The product chemical species—1 mole of glucose and 6 moles of oxygen—are counted as generated. The total amount of glucose and oxygen gas has increased in the system and the universe. On the other hand, the reactant chemical species—6 moles of carbon dioxide and 6 moles of water—have been consumed simultaneously, because the total amount of carbon dioxide and water has decreased in the system and in the universe.

Now try an example problem that combines these aspects and use the table of common Laplace transforms (here) to convert your answer to the time domain.