# Transformation: Differential Equation ↔ Signal Flow Graph

Given a system differential equation it is possible to derive a signal flow graph directly, but it is more convenient to go first derive the transfer function, and then go from the transfer function to the state space model, and then from the state space model to the signal flow graph.

##### Example: Diff Eq → Signal Flow Graph

Find a signal flow graph for the system described by the differential equation:

Step 1: Find the transfer function using the methods described here (1DE ↔ TF)

Step 2: Find a state space representation using the methods described here (TF ↔ SS).  In this case we are using a CCF form).

Step 3: Find a signal flow graph using the methods described here (TF ↔ SFG).

This example is not yet finished

##### Example: Signal Flow Graph→ Diff Eq

Repeat the previous example, but reverse the order (i.e., do step 3 (SFG → SS) then step 2 (SS → TF)then step 1 (TF → DE)).

Another option is to go directly from the Signal Flow Graph to the Transfer Function directly (using Mason's gain formula) and then go from the transfer function to the differential equation.

References