# Is a transfer function of a LTI system the same and valid for all operating points of the system?

Let's say that we have a LTI system (speaking strictly theoretical at the moment) and it has a transfer function H(s). Is this transfer function the same over all the operating points that the system can be in ?

For example a purely theoretical circuit, composed with ideal passive elements, has one input, one output and couple of nodes where we can set DC voltages. Will the output of that circuit be predictable with it's transfer function acquired with a certain set of DC voltages at it's nodes, and will that function be valid if I change the DC voltages on the nodes (implying a different operating point)?

• An LTI system has a unique representation in terms of its transfer function. It is the same for all inputs. I am not sure what you mean by valid because validity is not a problem in theoretical setting. – Rodrigo Amarante Nov 21 '16 at 22:35
• What do you meaning by 'setting' voltages at the nodes? – Chu Nov 22 '16 at 0:24
• Yes, because it is linear. – mkeith Nov 22 '16 at 6:13

Yes. This is the whole point of LTI systems. They utilize superposition. Consider this: $$V_{\mathrm{in}} H = (V_{\mathrm{DC}} + V) H = V_{\mathrm{DC}} H + V H$$
On the other hand, if the system is not linear, you cannot use the superposition principle. It is due to the fact that you can express the response of a linear system as: $$H = \frac{V_{\mathrm{out}}}{V_{\mathrm{in}}}$$ For a non-linear system you cannot reduce it as a fraction of this type. You get he input in the numerator for example.