Problems

Section 4.7 Problems

For each of the following circuit inputs, graph by hand 1) the input waveform and 2) the output waveform after passing through the circuit in Figure 4.7.1. These waveforms should appear on the same axes and should be as accurate and numerical as reasonably possible. Please use different colors (or solid vs dashed lines) for your two waveforms.
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You should use the diode behavior shown in Figure 4.2.2 with $V_F=0.6$V to analyze this circuit analytically.
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Figure 4.7.1.
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1. Input waveform: two cycles of a triangle wave alternating between $\pm 1.0$V.
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2. Input waveform: two cycles of a triangle wave alternating between 0.0V and +2.0V.
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Assume an input waveform that is two cycles of a triangle wave alternating between $\pm 2.0$V in Figure 4.7.2. Then, graph by hand 1) the input waveform and 2) the output waveform. These waveforms should appear on the same axes and should be as accurate and numerical as reasonably possible. Please use different colors (or solid vs dashed lines) for your two waveforms.
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You should use the diode behavior shown in Figure 4.2.2 with $V_F=0.6$V to analyze this circuit analytically.
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Figure 4.7.2.
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Assume an input waveform that is two cycles of a triangle wave alternating between $\pm 4.0$V in Figure 4.7.3. Then, graph by hand 1) the input waveform and 2) the output waveform. These waveforms should appear on the same axes and should be as accurate and numerical as reasonably possible. Please use different colors (or solid vs dashed lines) for your two waveforms.
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You should use the diode behavior shown in Figure 4.2.2 with $V_F=0.6$V to analyze this circuit analytically.
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Figure 4.7.3.
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A red light-emitting diode (LED) has a forward voltage drop of 1.8V and has to be operated with a 10.0mA diode current. One possible circuit that can achieve these requirements is shown in Figure 4.7.4.

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Figure 4.7.4.
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Figure 4.7.5.
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1. Find the Thévenin equivalent circuit parameters when leaving the diode out of the circuit in Figure 4.7.4.
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2. Using the Thévenin equivalent circuit in Figure 4.7.5, calculate the resistance $R$ that will ensure the desired diode operating conditions.
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Analyze the circuit in Figure 4.7.6 using the analytical circuit treatment from Subsection 4.4.1 with $V_F=0.6$V.
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Figure 4.7.6.
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1. At what minimum $V_b$ does the diode just barely begin to conduct current?
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2. Calculate all of the labeled currents for $V_b=2.8$V.
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3. Calculate all of the labeled currents for $V_b=10.5$V.
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4. Calculate all of the labeled currents for $V_b=14.0$V.
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Hint: Consider the voltage drop across the $700\Omega$ resistor if the diode were missing, and then determine the effect of the diode when it is present.

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Calculate the three unknown currents in Figure 4.7.7 using the analytical circuit treatment from Subsection 4.4.1 with $V_F=0.6$V.
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Figure 4.7.7.
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Analyze the circuit in Figure 4.7.8 using two different methods. Assume a sinusoidal $V_\text{in}$ that has a 10V peak-to-peak amplitude and $f=1$kHz.
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Figure 4.7.8.
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1. Numerical methods: Use Newton’s method in Python to analyze the circuit assuming the exponential description of diode behavior. Then, generate the following two figures using Python. The first figure should show $V_\text{in},\ V_\text{out},\text{ and } V_D$ vs time on the same axes (with labels). The second figure should show $I_1,\ I_2,$ and $I_D$ vs time on the same axes. Figure 2 should appear below Figure 1 and the time axes of the two figures should align with each other. Submit your code along with your figures and any analytic work that you needed to perform before writing the Python code.
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2. Analytic methods: Use the analytical circuit treatment from Subsection 4.4.1 to explain how we could have achieved similar results to what you found above with the analytic diode analysis using the cartoon diode behavior (with $V_F=0.6$V). You do not need to reproduce the graphs from the previous part, but you must provide narrative and equations to explain how you come to essentially the same plots.
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For the circuit in Figure 4.7.9, use Python to plot $V_\text{in}$ and $V_\text{out}$ as a function of time and on the same axes. Assume a sinusoidal $V_\text{in}$ with a peak-to-peak voltage of 10V and $f=1$kHz.
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Figure 4.7.9.
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