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Q1 A linear circuit is shown below in Figure 1.
Figure 1
The elements elements in this circuit have have the following values: \(R_1 = 1000 1 000 \Omega\), \(R_2 = 400 \Omega\), \(R_3 = 600 \Omega\), \(V = 6 V\), and \(I = 0.002 A\). Determine the potentials drops \(v_A\) \(v_A\) and \(v_B\) \(v_B\) across resistors \(R_1\) and \(R_2\) \(R_2\) r espectively. espectively. What is the value of voltage \(v_A\) in Volts?
What is the value of voltage \(v_B\) in Volts?
Now let us determine if the answers you came up with satisfy the laws of physics. What is the power (in Watts) dissipated in resistor \(R_1\)?
What is the power (in Watts) dissipated in resistor \(R_2\)?
What is the power (in Watts) dissipated in resistor \(R_3\)?
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What is the power (in Watts) coming out of the voltage source \(V\)?
What is the power (in Watts) coming out of the current source \(I\)?
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Q2: PART 1 In this problem we will look at a bridge circuit, shown in Figure 2.
Figure 2
Write an expression for \(v_X\) in terms of \(V\), \(R_1\), \(R_2\), \(R_3\), and \(R_4\).
This circuit can be used to measure a resistor to determine its resistance. Imagine we have an unknown resistor \(R_?\), which we place in the \(R_4\) position from the circuit in Figure 2, and known resistors \(R_1=20\) and \(R_3=30\). We then change the resistance of resistor \(R_2\) until \(v_X=0\). We find that \(R_2=30\) results in \(v_X=0\). This setup is shown in Figure 3.
Figure 3
What is the resistance (in Ohms) of \(R_?\)?
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Q2: PART 2
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We can take a different approach with the bridge circuit and put a voltage source in the middle of the bridge as shown in Figure 4. Determine the thevenin equivalent for the circuit given below as viewed from the indicated terminals.
Figure 4
The values circuit parameters as follows: \( R_1 = 30 \Omega\), \( R_2 = 15 \Omega\), \( R_3 = 15 \Omega\), \( R_4 = 30 \Omega\),\( V = 15 V\) What is the thevenin equivalent voltage \(V_{TH}\) in Volts:
What is the thevenin equivalent resistance \(R_{TH}\) in Ohms:
The bridge circuit in Figure 4 is then modified by adding a dependent source as shown in Figure 5.
Figure 5
What is the thevenin equivalent voltage (in Volts) of the modified circuit in Figure 5
What is the thevenin equivalent resistance (in Ohms) of the modified circuit in Figure 5
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Q2: PART 3
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We can use this bridge topology, but instead of a resistive bridge, we can use diodes to build something called a voltage rectifier seen in Figure 6. In the middle of the bridge is a resistor \(R\) with current \(i_R\) through it. Assume that the diodes are ideal. The ideal diode model is given for convenience in Figure 7.
Figure 6
Figure 7
The voltage source, \(V\) is a ramp voltage with amplitude \(V_S=5 V\) seen in Figure 8. What is the maximum and minimum current \(i_R\) (in Amps) throught the resistor \(R=25 \Omega\)?
Figure 8
\(i_{R,max}\) in Amps:
\(i_{R,min}\) in Amps:
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Q3
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A junction field-effect transistor (JFET) with its gate and source connected together form a two terminal nonlinear device. The current in this device saturates to a current level \(I_{DSS}\) for \(v_D\) larger than \(V_P\) called the pinch-off voltage. The device and I-V characteristic are shown in Figure 9.
Figure 9
We can describe t his relationship with the equation:
This device is used in the circuit in Figure 10, which includes a resistor, \(R\), and voltage source, \(V_S\).
Figure 10
Assuming that \(I_{DSS}=0.003 A\), \(V_P=1.5 V\), \(R=750 \Omega \), and \(V_S=3 V\), find the operating point of the circuit by evaluating \(v_D\) and \(i_D\). \(v_D\) (in Volts):
\(i_D\) (in Amps):
At what value of \(V_S\) (in Volts) does the current through the JFET stabilize at \(I_{DSS}\)?
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Q4 The startup company WidgetCorp has invented a MOS-gated transistor called M-Plify, with the symbol and terminal i-v characteristics given in Figure 11.
Figure 11
WidgetCorp wants to determine the usefulness of their invention by examining the large-signal input-output characteristics of two amplifiers built using M-Plify. They hire you to figure this out. First the amplifier in Figure 12 is built.
Figure 12
What is the expression for \(v_{OUT}\) in terms of \(v_{IN}\), \(V_{S}\), \(R\), and \(m\) when \(v_{IN}\) is greater than \ (0V\)?
`{::}` The output voltage relationship to the input voltage is: \(v_{OUT}\) increases linearly with increasing \(v_{IN}\) \(v_{OUT}\) decreases linearly with increasing \(v_{IN}\) \(v_{OUT}\) increases quadratically with increasing \(v_{IN}\) \(v_{OUT}\) decreases quadratically with increasing \(v_{IN}\) The amplifier in Figure 12 is changed by adding more M-Plify transistors to build the circuit in Figure 13.
Figure 13
What is the expression for \(v_{OUT}\) in terms of \(v_{IN}\), \(V_S\), \(R\), and \(m\) for this amplifier when \(v_{IN}\) is greater than \(0V\)?
`{::}` The output voltage relationship to the input voltage is: \(v_{OUT}\) increases linearly with increasing \(v_{IN}\) \(v_{OUT}\) decreases linearly with increasing \(v_{IN}\) \(v_{OUT}\) increases quadratically with increasing \(v_{IN}\) \(v_{OUT}\) decreases quadratically with increasing \(v_{IN}\)
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Q5 The startup company WidgetCorp has invented a MOS-gated transistor called TurboK, with the symbol and terminal i-v characteristics given in Figure 14.
Figure 14
Engineers of WidgetCorp build an amplifier using TurboK shown in Figure 15.
Figure 15
Here, \(V_S = 5 V\), \(R = 7.5 k \Omega\), and the transistor parameter \(k = 3 \frac{mA}{\sqrt{V}}\). The amplifier is biased with \(V_{IN} = 2 V\). What is the dc operating point (bias) output voltage \(V_{OUT}\) (in Volts) of this amplifier?
What is the small signal gain \( ( \frac{v_{out}}{v_{in}} )\) of this amplifier when it is biased as above? (Hint: \( \frac{\delta y}{\delta x} \rvert _{x=x_0} = ( \frac{\delta x}{\delta y} \rvert _{y=y_0})^{-1} \) where \((x_0, y_0)\) is a coordinate pair on the x-y curve.)
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Q6: PART 1 Here we examine noise in a digital channel between an AND gate and an inverter shown in Figure 16. The channel has a length of \(D=28 m\) and noise is added in at the rate of \(0.5 \frac{V}{m}\).
Figure 16
To correct for that noise, we introduce non-inverting buffers into the channel. The purpose of a buffer is to take an input and replicate it at the buffer's output. This buffer is useful because it clean up a signal which no longer meets the ouptut specification of the static discipline due to noise, so that it once again meets the out put specifications of the static discipline. The buffered channel is show in Figure 17 below.
Figure 17
These buffers, as well as the gates shown, obey the following static discipline: \( V_{OL} = 0.5 V, V_{IL} = 2 V, V_{IH} = 3 V ,V_{OH} = 4.5 V \). What is the minimum number of buffers required to connect between the digital links in order to ensure correct operation?
Now let's consider the NOR gate in Figure 18 which has \(V_S = 5V\) and the following given static discipline: \( V_{OL} = 0.6 V, V_{IL} = 2 V, V_{IH} = 3 V, V_{OH} = 4.3 V \).
Figure 18
Assume that both MOSFETs have the same \(V_T\) and \(R_{ON} = 7 k\Omega\). What is the minimum value of \(V_T\) in Volts that allows the NOR gate to satisfy the given static discipline?
What is the maximum value of \(V_T\) in Volts that allows the NOR gate to satisfy the given static discipline?
What is the minimum value of \(R_L\) (in \(k \Omega\)) that allows the NOR gate to satisfy the given static discipline?
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Q6: PART 2 Consider the circuit in Figure 19 below.
Figure 19
Write a boolean expression for \(Z\) in terms of \(A, B, C, D,\) and \(E\). You need not simplify your expression. Use your expression to fill out the truth table below.
\(A\) \(B\) \(C\) \(D\) \(E\) \(Z\) ---
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1
1
0
0
1
\(z_0\)
1
1
1
0
1
\(z_1\)
0
0
1
1
1
\(z_2\)
0
1
1
0
1
\(z_3\)
Enter the unknown values for the ouputs as one stream of bits in the form \(z_0z_1z_2z_3\)
How many distinct boolean-valued functions are there of \(n\) boolean-valued signals? Write an expression in terms of \ (n\). =
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