abstract.
In this lab the diode, a simple nonlinear device in a circuit was explored by exploring the difficulties inherent in characterizing and working with it. Three models for the circuit element were explored: real, ideal, and model diode.
Diode Exploration
Calculating I_{s} and n
The common model used to characterize the diode is given by the Shockley diode equation shown below.
_{ }
The currentvoltage relationship is dictated by the following parameters:
q is the charge on an electron
v is the voltage across the diode
n is the emission coefficient, usually between 1 and 2
k is Boltzman's constant
T is the absolute temperature
I_{s} is the saturation current
I_{s} and n are values obtainable by experiment by measuring voltage and current. Two diodes—1N4001 and 1N914—were chosen diodes for the characterization experiment.
Figures 1 and 2 show the experimental voltagecurrent curves for the two diodes of interest. m1 is the fit value for I s and m2 is the fit value for n. As shown in the exponential fit, the values are well within reason considering the uncertainty in the manufacturer’s specified values. The value of n should be between 1 and 2, and is true for the 1N4001 diode but not for the 1N914. The value for the latter diode, however, has a significant error (.303) associated with it.
Figure 1. VoltageCurrent Curve for 1N914 Diode.
Figure 2. VoltageCurrent Curve for 1N4001 Diode.
Comparing our experimental I s values to the ones given by the manufacturer’s indicates that it is a difficult parameter to predict accurately. It is important to note that the data for the voltagecurrent plots from which the two diode parameters were obtained were recorded using an oscilloscope that is only accurate to a certain degree. However, I s and n values obtained were reasonable.
Task 2: Comparing the Real, Ideal and Shockley Model for Diodes
A simple circuit with the 1N914 diode in series with a 1kOhm resistor was built. Using an AC source of 2V at 2 kHz, we looked at how V_{out} changed relative to V_{in} by considering the three diode models. Figure 3 below shows the experimental output V_{in} and V_{out} after the diode.
Figure 3. Experimental Vout and Vin
The diode is clipping for the negative voltages of the sinusoid, and a voltage drop is existent. The three diode models were used to model the diode clipping and voltage drop shown in Figure 4.
Figure 4. Comparison of Diode Models
For the ideal diode model, there is no diode voltage drop for positive input voltages, so V_{out} is clipped at 0 for the negative part of the sinusoid. The Shockley Model for diodes assumes a .7V across the diode, so V_{out} is .7 volts below the input signal at all times.
We found the value for V_{diode }using a graphical method using the two equations shown below. By using the Shockley diode model and writing the Kirchoff loop expression for i in a circuit in which the diode was in series with a 1kOhm resistor, we can solve the two for V_{diode}.
and
Using the known values for k, T and q as well as calculated values for I_{s} and n for the 1N914 diode, we obtained graphs of both equations for i as a function of V_{diode}. The intersection point yielded the value for V_{diode} and the corresponding i value. Graph 3 shows an example of our graphical method.
Figure 5. Example of the graphical method used to find the right V_{diode} values.
In this case, V_{in} = 2V produced V_{diode} = 0.24 V and i = 1.78e3 A. Repeating for a range of voltage values between 2 V and +2 V, values for V_{diode }and i were obtained.
Circuit 2 Data 
V_{in} 
V_{diode} 
I_{diode}(mA) 
V_{out} (V) 
2.00 
0.24 
1.78 
1.76 
1.50 
0.22 
1.30 
1.28 
1.00 
0.20 
0.81 
0.80 
0.50 
0.16 
0.35 
0.34 
0.10 
0.06 
0.04 
0.04 
0.00 
0.00 
0.00 
0.00 
0.10 
0.09 
0.02 
0.02 
0.50 
0.48 
0.02 
0.02 
1.00 
0.98 
0.02 
0.02 
1.50 
1.48 
0.02 
0.02 
2.00 
1.98 
0.02 
0.02 
Table 1. V _{diode} and I _{diode} for various input voltages
Considering the three different models, the constant drop diode model (Figure 4) matches the experimental data best (Figure 3). It clips for negative voltages as the diode is reversedbiased and has approximately the same output amplitude.
conclusion.
Modeling and characterizing the diode is tricky due to its nonlinear relationship between current and voltage. Obtaining the correct I_{s} and n parameters for the real diode is important to accurately model its nonlinear behavior, and is a limitation to applying it in the circuit for Task 2. The constant drop diode model works best from what we have found.
