FYI: I am just getting into electromagnetics, so please keep explanations close to the basics and fundamentals, if possible. Thanks.

I have run across the claim, in numerous texts and online resources, that the real part of the normalized impedance (the ratio of load impedance to the characteristic impedance of the driving transmission line) can never be negative, except in the case of some active devices. The justification I have seen for this in several places is that, for passive circuits, negative resistance has no physical meaning.

Leaving all of that aside, my confusion stems from the fact that normalized impedance is not an impedance at all, it is the ratio of two impedances. Thus the real part of the ratio is not a "resistance" and the imaginary part is not a "reactance"; they are both dimensionless quantities.

More to the point, consider the following example:

Load: ZL = 50+j1000 ohms

Transmission line: Z0 = 50-j3 ohms

It would seem to me that the normalized impedance in this case would be:

Normalized impedance: Zn = ZL/Z0 = -0.2+j20

In fact, it would seem that as long as the transmission line has any reactive component at all, that a passive load could easily be constructed that would result in the real part of the normalized impedance being negative.

So what am I missing?

What would happen if I proceeded to build such a circuit? Is there something that makes such a circuit unrealizable?

I have run across the claim, in numerous texts and online resources, that the real part of the normalized impedance (the ratio of load impedance to the characteristic impedance of the driving transmission line) can never be negative, except in the case of some active devices. The justification I have seen for this in several places is that, for passive circuits, negative resistance has no physical meaning.

Leaving all of that aside, my confusion stems from the fact that normalized impedance is not an impedance at all, it is the ratio of two impedances. Thus the real part of the ratio is not a "resistance" and the imaginary part is not a "reactance"; they are both dimensionless quantities.

More to the point, consider the following example:

Load: ZL = 50+j1000 ohms

Transmission line: Z0 = 50-j3 ohms

It would seem to me that the normalized impedance in this case would be:

Normalized impedance: Zn = ZL/Z0 = -0.2+j20

In fact, it would seem that as long as the transmission line has any reactive component at all, that a passive load could easily be constructed that would result in the real part of the normalized impedance being negative.

So what am I missing?

What would happen if I proceeded to build such a circuit? Is there something that makes such a circuit unrealizable?

Last edited: