We’ll now move on to the DC analysis of diode circuits.
Let’s consider this very simple diode circuit:

We will assume that the diode is forward biased. Using KVL V_{DD}=IR+V_{D}
From the characteristic equation for the diode

Assuming n, I_{S}, and V_{T} are known, we have two equations for the two unknown quantities V_{D} and I. Substituting (2) into (1):

which is a transcendental equation for VD. There is no simple analytical solution to this equation.
So how do we solve such a circuit problem? Over the next
couple of pages we’ll mention five methods.
1. Graphical Analysis. Begin with the diode i-v characteristic curve:

2.
From (1), we can rearrange the equation in terms of I to also plot above. That is, from (1)

which is an equation for a straight line ( y b mx = + ):

We call this straight line the load line.
Now, plot both of these curves on the same graph:

The point where these two curves intersect is the simultaneous solution to the two equations (1) and (2).
This graphical method is an impractical solution method for
all but the simplest circuits. However, it is useful for a
qualitative understanding of these circuits. For example, what happens when:
(a) V_{DD} increases?

(b) R increases?
(c)
3. Simulation packages. SPICE, Agilent’s Advanced Design System (ADS), etc. Here is a simple example using ADS:
4.
3. Numerical methods. Use Mathematica, Matlab, Mathcad, etc.
Here is a simple example from Mathcad:

4. Iterative analysis. See example 3.4 in the text.
5. Approximate analysis. This is by far the most widely used approach for hand calculations. Approximate Diode Circuit Solutions There is often a need for us to perform design with pencil and paper. Remember: simulation packages don’t design for you, they only analyze circuits. There’s a big difference between design and analysis!
There are two very important approximate diode models that allow easier paper designs:
1. Constant-Voltage-Drop (CVD) Model.
2. Piecewise Linear (PWL) Model.

Constant-Voltage-Drop (CVD) Model
In this model, the characteristic curve is approximated as:

In words, this model says that if the diode is forward biased, then the voltage drop across the diode is VD. If not forward biased, the diode is then reversed biased and the current is zero and V_{D} can be any value < V_{D}.
VD is often set to 0.7 V for silicon diodes, as shown above, while set to 0.2 V for Schottky diodes, for example.
The CVD circuit model for diodes is

This is probably the most commonly used diode model for hand calculations.
Example N3.1. Determine the current I in the circuit below
using the CVD model and assuming a silicon diode.

Using the CVD model, the equivalent approximate circuit is:

Assuming the diode is forward conducting (i.e., “on”) with V_{D} = 0.7 V and using KVL in this circuit:

The positive value of this current indicates our original
assumption that the diode is “on” is correct.

Since I is negative, then D must be reversed biased. This means our initial forward conducting assumption was incorrect. Rather, in this situation I = 0 and V_{D} = 0.5 V.

Piecewise Linear (PWL) Diode Model

This is a “battery plus internal diode resistance model.” It is one step better than the CVD model by incorporating a slope to the interpolative line:

The finite slope to this curve means that the diode has a nonzero internal resistance, which we will label as rD. The
equivalent circuit for the PWL diode model is then

Example N3.2. Determine the current I in the circuit below using the PWL diode model shown in text Figure.
From Fig., we can determine VD0 and rD for the particular
diode whose characteristic equation is shown:

The equivalent circuit using the PWL model of the diode is then

Assuming the diode is “on,”, then by KVL:
This is close to the 1.3 mA we computed in the last example using the cruder CVD model. Again, the positive value of this current indicates that we made the correct choice that the diode is “on.”
What’s the forward voltage drop across the diode?

Is this enough to turn the diode on? Yes, referring to the
equivalent circuit above