# Why are G and H used for feedback block diagrams?

The symbols $G$ and $H$ are typically used for the forward gain and feedback fraction in negative feedback block diagrams like this:

The choice of $G$ is, I suppose, an obvious one, meant to be mnemonic for gain.

But $H$ I don't get. Is it just because it's the next letter in the alphabet and maybe $F$ was already taken? Or is there perhaps a historical reason that might lead one to see it as a less arbitrary choice?

Note: I understand these symbols are not universally used in these roles. I kind of grew up on $A_o$ and $\beta$ myself, but as I understand it, $G$ and $H$ are more common in the control systems world and do have some advantages over other choices. Certainly conforming to a convention has its own benefits, whatever that convention is.

• Hysteresis? Heuristic? – Ignacio Vazquez-Abrams Aug 17 '16 at 5:18
• Hmm. I'll guess that Harold Black popularized it and managed to sneak his first initial in there, besides. ;) Of course, I've no clue at all. – jonk Aug 17 '16 at 5:22
• $H(\cdot)$ is commonly used to refer to the transfer function of e.g. n LTI system: en.wikipedia.org/wiki/Transfer_function – Math1000 Aug 17 '16 at 6:06
• @Math1000: Hmm, that's right, I hadn't made that connection. I wonder if that has to do with it, like the transfer function of the feedback network or something. Although in a block diagram of any complexity there are a lot of transfer functions around :). And then of course, it raises the question of how $H$ was chosen for that role :) – scanny Aug 17 '16 at 6:18
• Do you have an example because I see something different i.e. H is used as in H(s) for the overall transfer function. – Andy aka Aug 17 '16 at 7:42

"H" isn't Abbreviation something special . this just a symbol for feedback . like "beta". but i think this method of Nomination should be something like declare a variable like u declare "X" and other variable is "y" and this is "G" for gain and next alphabet of that is "H".

• At first I thought this unlikely, but based on some videos I've been watching on control systems, I'm starting to think assigning symbols in these block diagrams is actually fairly arbitrary and generally in sequence. It makes more sense when you have a block diagram with a dozen blocks in it and need more symbols (or have to resort to subscripts). So you might have G, H, K, M, N, P, Q, R etc. I'm thinking I, J, L, O and a few others are avoided to avoid confusion with current, inductance, and zero :). Anyway, not definitive, but starting to make more sense than it did to me originally :) – scanny Aug 18 '16 at 19:00