# Isn't the GNT/GFT the same as Bode's theory, Rosenstark's AGM, Blackman's formula,...

Isn't the GNT/GFT the same as

• Bode's feedback theory
• Rosenstark's Asymptotic Gain Model
• Blackman's formula
• Kron's theorem
• ....

?

The GNT and its theorems have a long history. As with all scientific theories, it is based on previous knowledge which it seeks to expand. As Middlebrook mentions in his EET paper and in his video series, the EET is a rewrite of Bode's formule (p.11) in a much more maneable form. Bode was a mathematician and his book is not for the faint of heart.

Furthermore, the 2GFT is actually an expansion of Bode's feedback theory in two ways:

1. It allows for non-ideal injection points
2. It invokes the null-double injection technique to calculate the various components

Furthermore, the NEET and nested 2GFT expansions add extra levels of hierarchy in the decomposition, enabling e.g. numerical analysis of multiple-loop feedback circuits in terms of Mason's loop gain and allow application of the Nyquist theorem for the multiple-loop feedback case.

The asymptotic gain model (AGM), attributed to Rosenstark, is actually equal to the 1GFT and is therefore equal to Bode's theory. The rewrite of the formula in term of Ginf, T, H0 and Tn had been proposed already in 1967 by Middlebrook. GFT starts from the desired $$\Hinf$$ and calculates the loop gain  $$T$$ with respect to the injection point. Although $$T$$ is a generalized return ratio in Bode's sense, it is, in general, not equal to the return ratio of a single dependent source, as is the case for the AGM. Indeed, the starting point of AGM is a single dependent generator and requires an ideal injection point. The resulting $$\Hinf$$ just follows and could or could not be equal to the desired $$\Hinf$$. Furthermore, the AGM is difficult to simulate without direct access to the dependent generators or without manually crafting a small-signal equivalent schematic. The 2GFT can be simulated elegantly on any practical circuit.

Blackman's formula is equivalent to the EET.

In all, Middlebrook's approach and formalism is circuit- and design-oriented, while Bode's approach is mathematical and hard to use in practice (and hard to simulate without access to internals of the devices). It would be very hard to teach students the Bode approach to feedback circuits in his brute force mathematical way: setting up matrices, calculating determinants, etc,... Middlebrook's value lies in his design-oriented approach and rewrite/expansion of the theory in a unified, understandable, practically useful manner.