1. Resistance & Nonlinearity of Diode
AC & DC Approach
Engr . Fazal Ur Rehman

2. Contents Linear & Nonlinear Devices
V-I Curves of Linear & Nonlinear Devices
AC & DC Resistances

3. Linear Elements
The elements which have a linear relation between the voltage applied across them and current through them, are known as linear devices
V = aI + b
I = cV + d
a, b, c and d are constants
For example; voltage and current for resistor are related to each other as:
V = IR a = R b = 0
or I = VG c = G d = 0
G = 1/R
Resistor, capacitor and inductor are linear devices and their equations are given as:
R  V = IR R is resistance
C  V = IXC XC is capacitive reactance
L  V = IXL XL is inductive reactance
Current through linear devices does not alter its linearity property.

4. Graphs of Linear ElementsV V2 ΔV
ΔV = V2 – V1 V1 ΔI I1 I2 I
ΔV / ΔI = R
ΔI = I2 – I1

5. Nonlinear Elements
The elements which have a nonlinear relation between the current through them and voltage applied across them are known as nonlinear elements. For example, the diode equation is given as:
This is a nonlinear equation and hence the element is nonlinear one

6. Graph of Diode Behavior
Forward Bias Region ID r2 ΔI ΔV r1 ΔI ΔV VD
r1 > r2
Reverse Bias Region

7. Nonlinear Elements
Unlike linear device, the resistance of a nonlinear device depends on the voltage across it (or current through it)
I-V characteristics becomes very nearly horizontal at low values of current and in the reverse-biased region. So, in these regions, large change in voltage create very small change in current so the value of “r” is very large.
The region on the I-V curve where the transition from high resistance to low resistance takes place is called the Knee of the curve.

8. AC & DC Resistance
ΔV/ΔI is called ac (dynamic) resistance of the diode because we consider small change in voltage
We would not want to calculate ac resistance between V=0.55V and V=0.65V
rd= ΔV/ΔI ohms
The dc resistance of a diode is found by dividing the dc voltage across it by dc current through it. DC resistance also called the static resistance.
Rd=V/I ohms
Diode is nonlinear in both the dc & the ac sense, that is, both its dc & c resistance change over a wide range.

9. AC & DC Resistance I (mA) rD = VT / I 40 30 DC Resistance
AC Resistance
RD = V / I 20
rD = ΔV / ΔI ΔI 10 ΔV
0.1
0.2
0.3
0.4
0.5
0.6
V (V)

10. AC & DC Resistance
The DC current in the diode has a value somewhere above the knee.
When the dc current in the diode has a value somewhere above the knee, the ac resistance is closely approximate by rd=Vt/I, so at room temp rd=0.026/I ohms

11. Bulk Resistance
Resistance between the contacts and semiconductor material is called “Bulk Resistance”. Its value is less than 1 Ω - + P N + -

12. Bulk Resistance Total AC resistance=AC resistance + Bulk resistance
At low current bulk resistance can be neglected.
At high currents Bulk resistance is typically on the order of 0.1 Ω
When diode is connected in a circuit in a way that results in the diode being forward biased, there should always be resistance in series with the diode to limit the current that flows through it.

13. An Example R VD
6312
0.55
4269
0.56
2877
0.57
599
0.61
405
0.62
274
0.63 85
0.66
57.5
0.67 39
0.68 5V R
Find the approximate ac resistance when the diode voltages are 0.56 V, 0.62 V, and 0.67 V. Assume bulk resistances of 0.8 Ω, 0.5 Ω and 0.1 Ω respectively.
Find the dc resistance of the diode when the voltage across it is 0.56, 0.62, and 0.67 V
Find the ac resistance presented by the diode to an ac signal generator that causes the voltage across the diode to vary between 0.55 V and 0.57 V, between 0.61 V and 0.63 V, and between 0.66 V and 0.68 V

14. Ideal Diode Model Equivalent Circuit + - ON Short Circuit - + OFF
Open Circuit

15. Practical Diode Model Equivalent Circuit + - ON 0.7 V - + OFF
Open Circuit

16. Actual Diode Model Equivalent Circuit + - ON rD 0.7 V - + OFF
Reverse Biased Resistance

17. Loop Equation
0.7 V E R
E = IR I

18. Home Work
Example: 3.1
End Problems: 3.1  3.13

19. Any Questions?