Diode Resistances:
It is defined as the resistance offered by a diode. There are two types of diode resistances:
(1) Forward Resistance (2) reverse Resistance
Forward Resistance: It is defined as the resistance offered by the diode when connected in forward condition. It is represented by rf or Rf . Forward resistance of ideal diode is 0 𝛀 and that of practical diode is few 𝛀.
There are two types of forward resistances:
(a) Static or DC Resistance (Rs or Rdc): It is a type of resistance which is defined as the ratio of voltage across diode to the corresponding current in the diode at any fixed voltage applied.
Rs = V/I (at a constant voltage)
and I can be calculated by diode current equation
(b) Dynamic or AC Resistance (RD or Rac ): It is a type of resistance which is defined as the ratio of change in the voltage across diode to the corresponding change in the diode at any fixed voltage applied.
Mathematically RD = dVD / dI (at a constant voltage)
We can understand it by watching the figure.
Derivation:
(2) Reverse resistance: The resistance offered by the diode when connected in reverse bias condition, is called reverse resistance of diode. It is denoted by rr or Rr. It can be calculated as similar as the calculation of static resistance. It can also be expressed as static resistance of diode in reverse bias condition.
In reverse bias condition reverse current is fixed and it does not need to be calculated.
So,
reverse resistance = Rr = VD / I0 (At a constant Voltage)
Reverse resistance of ideal diode is ∾ 𝛀 and that of practical diode is few M𝛀 and onwards..
Example: A germanium diode is used in a rectifier circuit and is operating at a temperature of 25℃ with a reverse saturation current of 1000 𝜇A. calculate the value of forward resistance at a forward voltage 0.2 Volts.
Solution:
Given: VD = 0.2 V, I0 = 1000µA = 1000 x 10-6 A, η=1 (Ge diode)
T = 250 C = 273 + 25 K = 298 K
VT = 298 / 11600 = 0.026 volt
It is required to calculate forward resistance but static or dynamic, it is not clear, so we should calculate both the resistances.
Calculation of Static Resistance
putting all values in diode current equation
I = 1000 x 10-6 x (e(0.2/0.026) -1)
I = 2.19 A
Rs = VD / I = 0.2 Volt / 2.19 A = 0.0913 𝛀 (Answer: Rs = 0.0913 𝛀)
Calculation of Dynamic Resistance
We know that dynamic resistance Rd = 𝜼VT /
I (Using
third formula)
Rd = 1 × 0.026 / 2.19 = 0.012 𝛀 (Answer: Rd = 0.012 𝛀)
Diode Capacitance:
The capacitance offered by diode is known as diode capacitance. There are two types of diode capacitance. (1) Diffusion capacitance (2) Transition Capacitance
Transition Capacitance: This capacitance is found when diode is reverse biased. The space charge region behaves as a dielectric material with ε dielectric constant. P side with positive charges and N side with negative charges behave like positive plate and negative plate respectively. This capacitance uses property of variation in depletion width (d) with applied reverse voltage.
Transition capacitance can be calculated as CT
= εA /
d
This is the general formula of capacitance of a material and we have studied it from high school even and in all onward classes so it is very easy to remember.
Sometimes depletion width is denoted by W. Then CT = εA / W
In reverse bias condition, diode capacitance (Cj) can be calculated using the following formula: CT = εA / d where d is the depletion width.
ε depends upon the doping level, material and space charge and charge carriers passing through the junction. These parameters cannot be changed once diode is designed. So ε cannot be varied. This is an independent parameter. A is the cross sectional area which also be not changed once diode is fabricated. ‘d’ is the only parameter which depends on external factor i.e. battery potential.
So we can say that CT α 1/d
We know that d increase on increasing reverse voltage,
Therefore CT decreases on increasing reverse voltage.
VC curve or Voltage-Capacitance curve is shown in figure. CT decreases on increasing reverse voltage. C0 is the voltage when diode is unbiased i.e. battery is not connected or battery voltage is zero.
Diffusion capacitance:
This capacitance is found when diode is forward bias. Since depletion width does not vary much more so capacitance due to depletion width is constant in this case.
As the forward voltage increases, majority charge carrier also increases passing through the junction which results in incrementing the value of dielectric constant which directly depends upon the number of charge carriers passing through the junction.
With this theory we can conclude that the diffusion capacitance directly depends on the existence of free charge carriers. So it depends on two factors
1. Forward current (I) and
2. Carrier life time (ꞇ): It is defined as the average time duration for which charge carries exists i.e. time between generation and recombination.
Derivation of Diffusion Capacitance:
We know that the forward current exponentially increases with increasing voltage
Means I α exp (VD)
But CD α I
So, CD α exp (VD)
VC curve or Voltage-Capacitance curve is shown in figure. CD increases on increasing forward voltage. C0 is the voltage when diode is unbiased i.e. battery is not connected or battery voltage is zero.
Complete VC Curve:
The capacitance offered by diode is known as diode capacitance. There are two types of diode capacitance.
(1) Transition Capacitance (2) Diffusion capacitance
CT = εA / d CD = ꞇI / ηVT
This is the complete voltage capacitance VC curve of a PN junction diode.
CT reciprocal decreases on increasing reverse voltage.
CD exponentially increases on increasing forward voltage.
C0
is the voltage when diode is unbiased i.e. battery is not connected or battery
voltage is zero.
Example: Example: A germanium diode is used in a rectifier circuit and is operating at a temperature of 25℃ with a reverse saturation current of 1000 𝜇A. Calculate the value of Diffusion Capacitance at a forward voltage 0.2 Volts. Mean carrier life time is given as 50ns.
Solution:
Given: VD = 0.2 V, I0 = 1000µA = 1000 x 10-6 A, η=1 (Ge diode) and ꞇ=50 x 10-9 seconds
T = 250 C = 273 + 25 K = 298 K
VT = 298 / 11600 = 0.026 volt
Putting all values in diode current equation
I = 1000 x 10-6 x (e(0.2/0.026) -1)
I = 2.19 A
Now
CD = ꞇI / ηVT
CD = 50 x 10-9 x 2.19 / (1 x 0.026)
CD = 4211.53 x 10-9 F = 4.212 x 10-6 F = 4.212 µF (Answer: CD = 4.212 µF)
Questions
for Exercise
1. Forward resistance of a diode is
(a) few 𝛀 (b) few k𝛀 (c) few M𝛀 (d) few T𝛀
2. A reverse biased diode has a resistance of
(a) 10 𝛀 to 10 𝛀 (b) 1 k𝛀 (c) 0 𝛀 (d) few hundreds k𝛀
3. Transition capacitance CT ....................... with decrease in reverse voltage.
(a) decreases (b) increases (c) remains unchanged (d) data not complete
4. At which of the following values CD is maximum?
(a) VD = -4 volt (b) VD = 0 volt (c) VD = 0.2 volt (d) VD = 0.31 volt
5. The dynamic resistance is measured in
(a) Transient condition, (b) DC condition, (c) AC Condition (d) can not say
Answer: 1 - a 2 - d 3 - b 4 - d 5 - c
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