# Difference between dynamic resistance of diode and resistance of PWL model of diode

What is the difference between dynamic resistance $r_{d}$ of a diode and resistance $R_{D}$ of piecewise linear model of a diode? The book "Microelectronic Circuits - Analysis and Design - Muhammad H. Rashid (2nd Edition)" says that $R_{D}=r_{d}$, but it seems so strange. In fact, to get $R_{D}$ it is necessary to drawn a straight line that passes always through the operating point Q and the point $\left(V_{threshold},0\right)$. Whereas to get $r_{d}$ it is necessary to drawn a straight line that passes through the Q-point and that is tangent to the diode characteristic. These two lines are not the same.

• Ask yourself this: What would $r_{d}$ be for the real (green) curve ? Would it be a constant value or would it vary over $V_{d}$ ? Now the PWL model. Note how I emphasized model, it's a simplification ! Now what will $r_{d}$ be in for the PWL model ? Distinguish between the flat part between $V_{d}=0$ and $V_{d}=V$ and the part where $V_{d}>V$ Commented Jun 12, 2016 at 15:23
• The same thing is on the book "Fundamentals of Electrical Engineering - Giorgio Rizzoni (McGraw Hill Higher Education)". Commented Jun 12, 2016 at 18:17

Neither for the "piecewise" (simplified) model nor for the real diode the static resistance RD is equal to the dynamic (differential) resistance rd. Rd is always the inverse slope of the connection line between the operating point and the origin. And the value of RD is always smaller than the differential resistance rd which is the inverse slope of the tangent drawn at the Q point.

## Those two resistances are not the same.

For starters, they are used in two different kind of analysis: the dynamic resistance is used in small signal analysis, the other one (the static series resistance) is used in large signal analysis (provided you decided to use the piecewise linear model for the diode).

The dynamic resistance accounts for the fact that a real diode is not an ideal diode, i.e. the voltage between its terminals changes if the current through it changes (instead of being the same for every current passing through, as happens in the ideal diode).

The static series resistance is simply part of the large signal model you chose, and accounts for the fact that, according to the piecewise linear model, then the voltage is greater than the threshold, the current increases linearly with the voltage applied.

• (1) The static resistance can be (and is in fact) used not only for the piecewise model but, of course, for the exponential response also. (2) The term "static resistance" does NOT mean that the current "increases linearly with the voltage". This would be the case for a constant RD only. However, because the linear part of the curve does not cross the origin, the slope of the connection line to the Q-point is not constant.
– LvW
Commented Jun 12, 2016 at 18:26