First_Order_Systems

632 632 afterthreetimeconstantsie state 1 0950

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: input at ∞ . • The time constant, , is the time required for the output to reach 63.2% of the steady‐state value: 1 0.632 63.2% • After three time constants (i.e.; state: 1 0.950 • After four time constants (i.e.; state: 1 0.981 3 ), the output is within 5% of steady‐ 95% 4 ), the output is within 2% of steady‐ 98% • After 4.6 time constants (i.e.; state: 4.6 ), the output is within 1% of steady‐ 1 0.990 99% • Although a first‐order system theoretically never reaches steady‐state, the rule of thumb is that steady‐state conditions have been achieved after five time constants have elapsed. . EXAMPLES: • At ∞, the output, , therefore the steady‐state gain, 1. This can also be determined by replacing the capacitor with an open circuit at ∞ . • The time constant, . • For a step‐input, the current flowing around the loop is the i...
View Full Document

Ask a homework question - tutors are online