In the previous sections we studied the analysis of circuit having diodes: considering the diodes to be ideal: " Short Circuit " or " Open Circuit ".
Now we want to analyze circuit with real diode: having the exponential model
Consider the circuit shown:
Analyze the circuit to find I
D
=? and V
D
=?
1.
Applying ohm's law to R: ⇒ 𝐼
𝐷
=
𝑉
𝐷𝐷
𝑅
−𝑉
𝐷
2.
V
DD
> 0.5 V; Diode is forward: ⇒ 𝐼
𝐷
I
D
and V
D
are solution to equations (1) and (2)
= 𝐼
𝑆 exp(
𝑉
𝐷 𝑛𝑉
𝑇
)
(1)
(2)
Two alternative ways to solve these two equations:
1.
Graphical analysis
2.
Iterative analysis

Graphical analysis:
Plot the two relations given by equations (1) and (2) in the same I
D
V
D
plane:
 Blue line: Diode characteristics the exponential relation, Eq. (2)
 Red line: Load Line, represents Eq.(1)
 Eq. (1) ≡ Load line equation
The solution is the coordinate of the point of intersection of the two graphs. The Operating Point Q
For V
DD
= 6 V and R = 500 Ω
I
D
≈ 10.4 mA
V
D
≈ 0.80 V

Iterative analysis:
For V
DD
=5V and R = 1kΩ
Diode: has I
D1
= 1 mA at V
D1
= 0.7V,
Its voltage drop change by 0.1V/decade
( 2.3𝑛𝑉
𝑇
= 0.1 𝑉 )
⇒ 𝑉
𝐷
− 𝑉
𝐷1
= 2.3𝑛𝑉
𝑇 log
𝐼
𝐷
𝐼
𝐷1
⇒ 𝑉
𝐷
= 0.7 + 0.1 log
1.
𝐼
𝐷
=
𝑉
𝐷𝐷
𝑅
−𝑉
𝐷 (1)
2.
𝑉
𝐷
= 0.7 + 0.1 log
𝐼
𝐷
1
(2)
𝐼
𝐷
1
Iterative analysis solves these two equations (1) and (2) alternatively by trying different values of I
D reaching values that satisfy both equations:
and V
D
until
Start iteration by choosing a value for V
D
= 0.7V:
I
D

5  V
D
R
V
D
0.7 V
( 1 ) V
D
 0 .
7  0 .
1  log(
I
D
1
I
D
) ( 2 )
Eq. (1) 4.3 mA
0.763 V
Eq. (2)
Eq. (1)
Eq. (2)
4.237 mA
0.762 V


 Both Graphical and Iterative analysis gives accurate results but takes long time and become very hard for complex circuits with many diodes.
 Rapid circuit analysis is necessary for design of complex circuit in the first stage of design
 Speed up analysis we need give up the accuracy of the result and leave the precise analysis at the end of the process.
 Simpler models for the diode are necessary:

 Piecewise Linear Model:
Replace the exponential model (cause of the complexity) by linear relations that describe very closely the diode characteristics.
Two straight lines (red lines) are shown to approximate the exponential characteristics (blue line)
 Straight line A horizental zero slope
𝐼
𝐷
= 0, 𝑉
𝐷
≤ 𝑉
These lines are not unique: ( 𝑉
𝐷𝑂
 Straight line B with slope = 𝑟
1
𝐼
𝐷
=
(𝑉
𝐷
−𝑉 𝑟
𝐷
𝐷𝑂
)
, 𝑉
𝐷
𝐷𝑂
𝐷
≥ 𝑉
𝐷𝑂
= 0.68𝑉 , 𝑟
𝐷
= 12Ω
An ideal diode is included in the equivalent circuit to
) allow the current to flow in the forward direction only.

 Constant Voltage Drop Model:
A simpler model is obtained by using a vertical line at the place of line B
The model: a conducting Diode has a constant voltage drop V
D
across its terminal.
Usually V
D
= 0.7 V for Si diode
The constant voltage drop model is the most frequently used model for the diode
An ideal diode is included in the equivalent circuit to allow the current to flow in the forward direction only.
 Ideal Diode Model:
The ideal model as seen previously: is used when the voltage sources involved are much larger than the forward voltage drop across the diode (0.6 → 0.8 V).