1

My professor had told us that Bilateral elements have V-I characteristics which are symmetric about the origin.

In an exam, we were asked to draw the V-I characteristics of a non linear, bilateral element.

The given answer was:

enter image description here

Shouldn't "symmetric about origin" imply something like this?

enter image description here

Have I misinterpreted the term "symmetric about the origin"? I am fairly sure that in the normal context, this corresponds to curves like my second image.

JRE
  • 67,678
  • 8
  • 104
  • 179
satan 29
  • 189
  • 5
  • 2
    Yes - I would agree to you. Second function is symm. to the origin. For example, the slope at the origin of both functions in the 1st figure is not identical. – LvW Feb 09 '21 at 17:01
  • What does searching on the internet tell you about this? I've never heard of the term but that shouldn't stop you searching for this. – Andy aka Feb 09 '21 at 17:02
  • 1
    There are different kind of symmetries, mainy odd symmetry (think x^3 or sinus) and even symmetry (think x^2 or cosinus). The second one is odd simmetry. The first one… well, I don't think is symmetric. The first one is neither bilateral nor symmetric, I'd classify it as unilateral non-linear. – Lorenzo Marcantonio Feb 09 '21 at 17:03
  • I’d invent a classification of the 1st as a bipolar exponential conjugate with a PN or NPN type positive voltage controlled current sink to a Pch negative voltage controlled conductance. The origin has 2 axes which makes the bilateral definition vague for symmetry – Tony Stewart EE75 Feb 09 '21 at 17:16

1 Answers1

1

I was unfamiliar with the term "bilateral", so I visited a few websites to learn about it, and they all agree with you.

Bilateral elements present the same resistance to current flow for some given current in either direction, which amounts to this algebraic relationship:

$$ V(I) = -V(-I)\\ \text{for } I < 0 $$

Bilateral behaviour is manifest in the characteristic curve as 180° rotational symmetry about the origin, like this:

enter image description here

Your first image shows mirror symmetry about the line \$V=-I\$ (in red), which is not at all the same thing. That symmetry is a result of this unilateral I-V relationship:

$$ V(I) = -V^{-1}(-I) \\ \text{for } I < 0 $$

enter image description here

Here are a couple of sites I used, which support this:

Classification of Element | Network Theory

Active,Passive,Linear,Non-Linear,Unilateral, Bilateral Elements

Simon Fitch
  • 27,759
  • 2
  • 16
  • 87