Microelectronics

1. What regions are heavily doped n+ to form ohmic contacts?

2. On the plot to the right. label the horzontal and vertical axis. Indicate the triode and square law regions. The square law region of second curve up from the bottom is a drain current of 2 mA, at (V_gs - V_tn) = 1 volt. What is (V_gs - V_tn) for the top curve? Fill in approximate values for (V_gs - V_tn) for the other two curves. The maximum Vds is 10 volts.

Draw a load line on the above curve representing the resistor in the circuit below. Assume that Vtn = 1.2 volts. Using the load line, estimate the value of Vgs needed for Vds in the circuit to equal 4 volts.

Show your work.

3. how does construction set FET device parameters, how FETs are built, and reasoning behind the constant push for smaller and smaller gates.

4. Examine the curves in the problem below and describe what changes if we alter mobility, oxide parameters, width and length. Redraw the set of curves and indicate the effect of each of the above changes.

a) A MOSFET has V_tn = 1.2 volts and K_n = 1/1kohm. Plot curves in the Triode region and Pinch-off region on the same plot, for currents from 0 to 10 mA and volts from 0 to 12. Find at least 4 Vgs values that result in maximum current of 8 mA and reasonably spaced curves. Connect the two regions by sketching curved lines.

Now plot a load line representing a 9 volt power supply and 1k load resistor. Find the values of Vgs that will result in a quiescent current of 2mA, 4A, and 6mA.

b) how does a CMOS inverter work. How to adjust the threshold voltage so the NMOS device turns on as the PMOS device turns off.

c) In a NMOS small signal amplifier with gate bias circuit, load resistor, and dc blocking capacitors on the input and output. Use gmRL to estimate gain. Describe how it works.

d) NMOS transistor

5. Explain the following bullet points (mark in textbook if necessary)

- bipolar transistor, simplified circuit models, and biasing techniques. DC feedback and the 4-resistor bias circuit is introduced and applied to both bipolar and FET circuits.
- Bipolar Transistors
- Common Emitter, Common Collector, and Common Base circuits.
- Separating the AC and DC circuits using capacitors. (Discuss separating the ac signal and dc circuits using dc blocking capacitors. Then describe how each of the dc blocking capacitors sets frequency response.)
- Frequency Response.
- A simple model for the bipolar transistor using a 0.6-volt ideal diode, controlled current source, and re.
- gm and 1/gm, and their importance in bipolar transistor circuits
- The four-resistor bias circuit
- Gain calculation using the four-resistor circuit.
- Gain when re is the only emitter resistor.
- Gain when the total emitter resistor is re + Re
- Separating ac and dc emitter resistors.

6. Design a Common emitter amplifier with a gain of 20 and a load resistor of 5.6k that draws 2 mA from the power supply. choose any supply voltage that works--note that the voltage drop across the load resistor is a significant constraint. Use the four-resistor bias circuit, and design the amplifier for signals at 100 Hz and above. Use standard components. Design on LTSpice as well.

Electromagnetics

1. Write a MATLAB program to plot the scalar electric potential V and the vector electric field E in the region of several user-specified point charges. The user enters the number of charges, their charge values and their locations in the x-y plane. The program should output contour, mesh and/or surface plots of V and a quiver plot of E.

Try different plotting options to get the best-looking plots possible. One warning: if R = 0, V and E will be undefined.

Use comments to explain the steps, and paste an example of the output plots it produces.

2. Airplanes are frequently struck by lightning, about once per 100 hours of flying. Why aren't the passengers electrocuted?

Which reason is correct?

The electric field is due to the gradient of the electric potential. Since lightning strikes the plane at a single point, there is no potential gradient.

According to Gauss'law, the electric field is due to the charge enclosed. There is no charge and thus no field inside the plane.

Actually many passengers pet electrocuted every year, but the government conspires with the airlines to cover it up.

According to coulomb's Law, the electric field is due to point charges. There are no point charges in lightning.

3. Problems 4 - 6 refer to an infinitely long coaxial cable oriented along the z-axis. The inner conductor has radius a and a uniform surface charge distribution ρ_sa The outer conductor has radius b, and a charge equal and opposite to the inner conductor, so that from out the cable the total charge is zero. The intent of this problem is that you use Gauss Law, to find D.

What is D for r

4. Problems 4 - 6 refer to an infinitely long coaxial cable oriented along the z-axis. The inner conductor has radius a and a uniform surface charge distribution ρ_sa. The outer conductor has radius b, and a charge equal and opposite to the inner conductor, so that from outside the cable the total charge is zero. The intent of this problem is that you use Gauss's Law to find D.

What is D for a < r < b?

5. problems 4 - 6 refer to an infinitely long coaxial cable oriented along the z-axis. The inner conductor has radius a and a uniform surface charge distribution ρ_sb The outer conductor has radius b, and a charge equal and opposite to the inner conductor, so that from ouTaicle the cable the total charge is zero. The intent of this problem is that you use Gauss's Law to find D.

What is the surface charge distribution ρ_sb on the outer conductor?

6. An infinite line of charge with uniform charge distribution ρ_i is oriented along the z-axis in free space. From Example 4-6, the electric field is E = r^ρ_i/2Πε₀r (you don't need to derive this again!) Find V_BA, where point A is at (r, Φ, z) = (1, 0, 0) and point B is at (2, 0, 0). ρ_i is 20 nC/m.

7. Problems 8 - 10 refer to a copper wire which is 10 m long and has a radius of 2 cm- Find the resistance of the wire in each case. Use σ_cu = 5.8x10⁷ S/m and σ_steel = 8.5 x10⁶ Sim.

Find the resistance if the wire is solid copper.

Find the resistance if the wire consists of a copper sheath with a hollow core, with the radius of the core 1 cm.

rind the resistance if the wire consists of a copper sheath with a steel core, with the radius of the core 1 cm.

8. The interface between two dielectrics is the z - 0 plane. For z > 0, ε_r1 = 4 and for z < 0, ε_r2 = 3. For z > 0, E₁ = 5x^ - 2
Y^{^} + 3Z^{^}V/m. Assume no surface charge at the interface. What is E₂?

9. A parallel-plate capacitor has area A, separation d, free space between the plates and a fixed voltage V. A dielectric with ε_r = 2 is inserted between the plates, while the voltage is kept fixed, Consider the quantities E, D, ρ_s, Q, C and W_e. How will these quantities be affected when the dielectric is inserted?