2.3.3.7 Voltage Source

The constitutive relation for an ideal voltage source is given as V = V₀(t). The voltage can be arbitrarily time-dependent and several common curve shapes have been implemented. However, no dependence on solution variables is allowed as this would result in a voltage or current controlled source (see Section 2.3.3.10 and Section 2.3.3.11). The stamp is given as

yx, y	$\varphi_{1}^{}$	$\varphi_{2}^{}$	I	f
n1			-1	I
n2			1	- I
I	1	-1		V0 - V

Again, the sign of the current is different as compared to the passive elements as it is defined to flow out of the source. Generalizing the branch relation to V = V₀(t) - I ^. R, that is to a voltage source with series resistance, gives the following stamp

yx, y	$\varphi_{1}^{}$	$\varphi_{2}^{}$	I	f
n1			-1	I
n2			1	- I
I	1	-1	R	V0 - V

Eliminating the current I results in the stamp for the current source with shunt resistance and corresponds to a Norton-Thevenin transformation of the source. For V₀ = 0 one gets the stamp of the linear resistor.