Question

Current Through a Diode. The current flowing through the semiconductor diode shown in Figure \(4.4\) is given by the equation $$ i_{\theta}=l_{e}\left(e^{\frac{w_{3}}{1 T}}-1\right) $$ where $$ \begin{aligned} &i_{D}=\text { the voltage across the diode, in volts } \\ &v_{n}=\text { the current flow through the diode, in amps } \\ &I_{e}=\text { the leakage current of the diode, in amps } \\ &q=\text { the charge on an electron, } 1.602 \times 10^{-19} \text { coulombs } \\ &k=\text { Boltzmann's constant, } 1.38 \times 10^{-23} \text { joule/K } \\ &T=\text { temperature, in kelvins }(\mathrm{K}) \end{aligned} $$ The leakage current \(I_{o}\) of the diode is \(2.0 \mu \mathrm{A}\). Write a program to calculate the current flowing through this diode for all voltages from \(-1.0 \mathrm{~V}\) to \(+0.6 \mathrm{~V}\), in \(0.1 \mathrm{~V}\) steps. Repeat this process for the following temperatures: \(75^{\circ} \mathrm{F}, 100^{\circ} \mathrm{F}\), and \(125^{\circ} \mathrm{F}\), Create a plot of the current as a function of applied voltage, with the curves for the three different temperatures appearing as different colors.

Short answer

In this problem, we are asked to calculate the current flowing through a diode using the given equation for different voltage values (-1.0 V to +0.6 V, in 0.1 V steps) and three temperatures (75°F, 100°F, and 125°F). After converting the temperatures to Kelvin (\(T_1 \approx 297.04 K\), \(T_2 \approx 310.93 K\), and \(T_3 \approx 324.82 K\)), we use the equation \(i_{D}=I_{e}\left(e^{\frac{qv_{D}}{kT}}-1\right)\) to calculate the current through the diode for each voltage step and temperature. Finally, we plot the currents as a function of applied voltage with different colors representing the different temperatures.

Step-by-step solution

Define constants

First, the constants given in the problem must be defined: - \(I_e = 2.0 \times 10^{-6} A\) (Leakage current) - \(q = 1.602 \times 10^{-19} C\) (Charge on an electron) - \(k = 1.38 \times 10^{-23} J/K\) (Boltzmann's constant)

Convert temperature to Kelvin

Next, the temperatures given in Fahrenheit should be converted to Kelvin: - \(T_1 = (75°F - 32) \times \frac{5}{9} + 273.15 K \approx 297.04 K\) - \(T_2 = (100°F - 32) \times \frac{5}{9} + 273.15 K \approx 310.93 K\) - \(T_3 = (125°F - 32) \times \frac{5}{9} + 273.15 K \approx 324.82 K\)

Calculate current through the diode

For each temperature, we will calculate the current through the diode for voltage values from -1.0 V to 0.6 V, in 0.1 V steps. To do this, we need to use the given equation: $$i_{D}=I_{e}\left(e^{\frac{qv_{D}}{kT}}-1\right)$$ For example, let's calculate the current for temperature \(T_1\) and voltage \(v_D = -1.0 V\): $$i_{D} = 2.0 \times 10^{-6}(e^{\frac{1.602 \times 10^{-19} \times -1.0}{1.38 \times 10^{-23} \times 297.04}} - 1) \approx -1.999 \times 10^{-6} A$$

Repeat for different temperatures and plot the results

Continue calculating the currents for each voltage step and temperature values, and plot these currents versus voltage. Use different colors to represent different temperatures on the graph.

Key concepts

Semiconductor Diode

A semiconductor diode is a fundamental electronic component with a simple yet crucial function. It allows current to flow in one direction while blocking it in the opposite direction. This uni-directional behavior makes it an essential part of electronic circuits. Semiconductor diodes are made from materials such as silicon or germanium. These materials have unique properties that change when impurities are added, becoming conductive only under certain conditions.

• When forward-biased, a diode allows electric current to pass, while reverse bias prevents it.
• The exponential relationship between the voltage and the current in a diode is described by the Shockley diode equation.
• Understanding these characteristics is vital for designing circuits that control where and how current flows.

Exploring how a diode reacts to changes in temperature and voltage is crucial in many applications, from power supplies to communication systems.

Temperature Conversion

Temperature conversion is an essential step when working with electronic components because their performance can vary with temperature changes. In electronics, temperatures are often given in Fahrenheit or Celsius, but scientific calculations require these temperatures to be in Kelvin. Kelvin is the scientific standard unit for temperature because it starts at absolute zero, the coldest possible temperature.

• The formula to convert Fahrenheit to Kelvin is: \[T(K) = (T(°F) - 32) \times \frac{5}{9} + 273.15\]
• For example, converting 75°F to Kelvin involves subtracting 32, multiplying by 5/9, and adding 273.15 to get approximately 297.04 K.
• Accurate temperature conversion is critical because many electronic properties rely on temperature calculations, particularly in semiconductor physics.

Make sure to convert all temperatures to Kelvin before performing any electronic simulations or calculations. This ensures consistency and accuracy in your results.

Current Calculation

Calculating the current through a semiconductor diode involves using the Shockley diode equation. This equation provides the relationship between the diode current, voltage, temperature, and material properties.

• The formula for current calculation is: \[i_{D}=I_{e}\left(e^{\frac{qv_{D}}{kT}}-1\right)\]
• Here, \(I_e\) is the leakage current, \(q\) is the electron charge, \(v_D\) is the voltage across the diode, \(k\) is Boltzmann's constant, and \(T\) is the temperature in Kelvin.
• For example, at 297.04 K and -1 V, inserting these values into the equation allows the calculation of the current passing through the diode.

Understanding the calculation of current flowing through a diode is crucial for predicting how a diode will behave under different conditions. This informs decisions in circuit design and component selection.

Plotting in MATLAB

MATLAB is a powerful tool used to simulate and visualize various electronic behaviors, including the current flow through diodes at different conditions. It excels in creating plots that can illustrate how different factors affect electronic components.

• Start by defining all necessary constants and variables such as voltage ranges and temperatures in your MATLAB script.
• Use loops or vector operations to calculate currents for each voltage and temperature combination, according to the diode equation.
• Finally, employ MATLAB plotting functions like `plot` to create a graph showing the relationship between voltage and current for each temperature.

This graphical representation is essential for easy comparison and analysis of the diode's behaviors across different temperatures. MATLAB's extensive functions make it an ideal choice for such simulations and allow for the presentation of complex data in an understandable manner.