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A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, [1] but often called a Mason graph after Samuel Jefferson Mason who coined the term, [2] is a specialized flow graph, a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections between pairs of nodes.
Mason's Rule is also particularly useful for deriving the z-domain transfer function of discrete networks that have inner feedback loops embedded within outer feedback loops (nested loops). If the discrete network can be drawn as a signal flow graph, then the application of Mason's Rule will give that network's z-domain H(z) transfer function.
Figure 1 shows a block diagram that leads to the asymptotic gain expression. The asymptotic gain relation also can be expressed as a signal flow graph. See Figure 2. The asymptotic gain model is a special case of the extra element theorem. Figure 2: Possible equivalent signal-flow graph for the asymptotic gain model
An example of a signal-flow graph Flow graph for three simultaneous equations. The edges incident on each node are colored differently just for emphasis. An example of a flow graph connected to some starting equations is presented. The set of equations should be consistent and linearly independent. An example of such a set is: [2]
Paul Voigt patented a negative feedback amplifier in January 1924, though his theory lacked detail. [4] Harold Stephen Black independently invented the negative-feedback amplifier while he was a passenger on the Lackawanna Ferry (from Hoboken Terminal to Manhattan) on his way to work at Bell Laboratories (located in Manhattan instead of New Jersey in 1927) on August 2, 1927 [5] (US Patent ...
Example of a single industrial control loop; showing continuously modulated control of process flow. A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical ...
Angular position servo and signal flow graph. θ C = desired angle command, θ L = actual load angle, K P = position loop gain, V ωC = velocity command, V ωM = motor velocity sense voltage, K V = velocity loop gain, V IC = current command, V IM = current sense voltage, K C = current loop gain, V A = power amplifier output voltage, L M = motor inductance, I M = motor current, R M = motor ...
Blackman's theorem is a general procedure for calculating the change in an impedance due to feedback in a circuit. It was published by Ralph Beebe Blackman in 1943, [1] was connected to signal-flow analysis by John Choma, and was made popular in the extra element theorem by R. D. Middlebrook and the asymptotic gain model of Solomon Rosenstark.