Question

The continuous time system structure which uses minimum number of integrators is

• A. Direct form-I
• B. Direct form-II
• C. Cascade form
• D. Parallel form

Hint:

Canonical realization structures use the minimum number of memory elements (integrators for continuous-time, delay elements for discrete-time).
Direct Form-II is a canonical structure that requires N integrators for an Nth-order system.

Answer 1

The Correct Option is B

For a continuous-time LTI system of order N (highest power of \(s\) in the denominator of its transfer function), the minimum number of integrators required for its realization is N. This is achieved by canonical forms.
Direct Form-I generally uses M+N integrators (M zeros, N poles). Not minimal if M>0.
Direct Form-II is a canonical form that uses N integrators. It is derived from Direct Form-I by reordering operations.
Cascade Form realizes the system as a cascade of first and second-order sections. Each section is often realized canonically. The total number of integrators is N.
Parallel Form realizes the system as a sum of terms from partial fraction expansion. Each term is realized canonically. The total number of integrators is N.

While Cascade and Parallel forms also use N integrators overall, Direct Form-II is specifically known as a structure that directly achieves this minimum for the overall system representation in a single block diagram. It's often called the "canonical direct form." \[ \boxed{\text{Direct form-II}} \]