Static And Dynamic Resistance of a Diode

STATIC AND DYNAMIC RESISTANCE OF A DIODE

An ideal diode should offer zero resistance in forward bias and infinite resistance in the reverse bias Diode behaves as a perfect conductor in forward biased condition and act as insulator in reverse biased condition. In practical situations diode will not behave as ideal diode and thus offers minimum amount of resistance in forward bias.

Forward Resistance

The resistance offered by the p-n junction diode in forward biased condition is called forward resistance. There are two types of forward resistance.

i. Static resistance or dc resistance (R_F)

ii. Dynamic resistance or ac resistance (r_F)

Static Forward Resistance R_F

It is defined as the ratio of the voltage to the current when p - n junction is used in de circuit and forward de voltage is applied.

In the Fig.1.16 shown, at point X, the static forward resistance R_F is defined as the ratio of de voltage applied across the p - n junction to the dc current flowing through the p - n junction.

R_F = forward dc voltage / forward dc current = OA / OB

The dc resistance will be low when the diode current is high.

Dynamic Forward Resistance (r_F)

The resistance offered by the p - n junction under ac conditions is called dynamic resistance. It is defined as the reciprocal of the slope of the volt-ampere characteristics.

The change in applied voltage from point A to C in Fig. 1.16 is denoted as ∆ V. The change is forward current from point B to D is represented as ∆ I.

The dynamic resistance varies inversely with current. At room temperature ac resistance of a diode is the sum of ohmic resistance and junction resistance.

Reverse Resistance

It is the resistance offered by the PN junction diode under reverse bias condition.. It is very large compared to the forward resistance, in the order of MΩ.

Static Reverse Resistance (R_f)

It is the reverse resistance under dc applied voltage. It is defined as the ratio of applied reverse voltage to the reverse saturation current I_o.

Dynamic Reverse Resistance (r_r)

It is defined as the ratio of incremental change in the reverse voltage applied to the corresponding change in the reverse current. It is found under ac conditions.

V-I EQUATION OF A DIODE

The mathematical representation of V-I characteristics of diode is called V-I characteristic equation or diode current equation.

The diode current is represented as

Where

I = diode current, Amperes

I_o = reverse saturation current, Amperes

V = Applied voltage, Volts

V_T = voltage equivalent of temperature, Volts

η = emission co-efficient, η = 1 for Germanium and η = 2 for Silicon diode

The emission coefficient or ideality factor n represents the recombination occurring in the depletion region.

The voltage equivalent of temperature indicates the dependence of diode current on temperature.

V_T = KT Volts

K - Boltzmann's constant = 8.62 x 10^-5 e V/K

T - Temperature, K

At room temperature 27°C, T = 273 + 27 = 300 K

V_T = KT

= 8.62 x 10^-5 x 300

= 26 mV T

When voltage applied is zero ie., V = 0

ie., no current flows through the diode.

When forward bias is applied, current increases exponentially and 

During reverse bias, voltage applied is negative and  thus neglecting exponential term

The negative sign indicates the current flows in opposite direction to that of forward current.

SOLVED PROBLEMS

Problem 1.1

The reverse saturation current of a silicon PN junction diode is 10 μA. Calculate the diode current for the forward-bias voltage of 0.6 V at 25 °C. (AU/ECE – MAY 2007)

Solution:

Given:

 

Problem 1.2

The diode current is 0.6 mA when the applied voltage is 400 mV and 20 mA.

When the applied voltage is 500 mV. Determine η. Assume (AU/ECE - May 2008)

Solution:

Given:

Diode current I = 0.6 mA

Voltage V = 400 mV

Given:

I = 20 mA when V = 500 mV

Substitute in (1)

Dividing (3) by (2)

Taking l n on both sides

 

Problem 1.3

The voltage across a silicon diode at room temperature of 300 °K is 0.71 V when 2.5 mA current flows through it. If the voltage increases to 0.88 V, What is the value of diode current?

Solution:

Given:

V = 0.71 V

T = 300 K

I = 2.5 mA

When V = 0.8 V,

Problem 1.4

A Germanium diode has a saturation current of 10 μA at 300° K. Find the saturation current at 400°K. (AU/EEE - May 2008)

Given:

T₁ = 300° K = 27° C

T₂ = 400° K = 127° C

I_ol = 10 ΜΑ

Solution: