Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
The equation above contains really only three variables in it: ID, VD, and T. All the other terms are constants. Since in most cases we assume temperature is fairly constant as well, we are really only dealing with two variables: diode current and diode voltage. a) Linearize the following equation

The equation above contains really only three variables in it: ID, VD, and T. All the other terms are constants. Since in most cases we assume temperature is fairly constant as well, we are really only dealing with two variables: diode current and diode voltage. a) Linearize the following equation

icon
Related questions
Question

The equation above contains really only three variables in it: ID, VD, and T. All the other terms are
constants. Since in most cases we assume temperature is fairly constant as well, we are really only
dealing with two variables: diode current and diode voltage.

a) Linearize the following equation

The relationship between voltage and current for a PN junction is described by the "diode equation", or "Shockley's diode equation": ID = Is (er - 1) where, ID = Current through the PN junction, in amps Is = PN junction saturation current, in amps (typically 1 picoamp) e = Euler's number = 2.718281828 q = Electron unit charge, 1.6 x10-19 coulombs VD = Voltage across the PN junction, in volts N = Nonideality coefficient, or emission coefficient (typically between 1 and 2) k = Boltzmann's constant, 1.38 x10-23 T = Junction temperature in Kelvin
Transcribed Image Text:The relationship between voltage and current for a PN junction is described by the "diode equation", or "Shockley's diode equation": ID = Is (er - 1) where, ID = Current through the PN junction, in amps Is = PN junction saturation current, in amps (typically 1 picoamp) e = Euler's number = 2.718281828 q = Electron unit charge, 1.6 x10-19 coulombs VD = Voltage across the PN junction, in volts N = Nonideality coefficient, or emission coefficient (typically between 1 and 2) k = Boltzmann's constant, 1.38 x10-23 T = Junction temperature in Kelvin
Expert Solution
Step 1

Shockley's diode equation describing the relationship between voltage and current is given as,

ID=ISeqVDNkT-1...........(1)

Here, only diode current ID and diode voltage VD are variables. All other parameters are constant.

q = Electron's charge = 1.6*10-19 coulomb

N = Emission coefficient (1 or 2)

k = Boltzmann constant

T = Temperature = 300 K (Room temperature)

IS = PN junction saturation current = 1 Pico-ampere = 10-12 amperes

Now, putting the above values in equation (1), we get,

ID=10-12×e1.6×10-19×VD1×300×1.38×10-23-1

Or,

ID=10-12×e3.8647×10-3×10-19×VD10-23-1

Or,

ID=10-12×e38.647VD-1.........(2)

Now, from the equation (2), if we put VD = 1 volt, we can observe that the exponential term is very large compared to 1.

i.e.

e38.647>>1

Thus, we can neglect "1"and rewrite the equation (2) as,

ID=10-12×e38.647VD...........(3)

 

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer