 Likewise the reflected voltage is given by

The total voltage on the line is given by

It is often convenient to express this in terms of hyperbolic functions

Similarly, the total current on the line is

The voltage nodes (current nodes are not at the same locations) and anti-nodes occur when

Because of the absolute value bars, the general case analytical solution is tiresomely complicated, but in the case of lossless lines (or lines that are short enough that the losses can be neglected) formula_76 can be replaced by formula_77 where formula_78 is the phase change constant.The voltage equation then reduces to trigonometric functions

and the partial differential of the magnitude of this yields the condition,

Expressing formula_78 in terms of wavelength, formula_82, allows formula_7 to be solved in terms of formula_82