EE 461G Introduction to Electronics

 

Homework # 1 Due September 2, 1999

Chapters 1 and 2 in Sedra and Smith are a review of circuits 1 and 2. Review these chapters. Start reading chapter 3 with sections 3.1, 3.2, 3.4, and 3.5. Skim section 3.3. You are not responsible for all of section 3.3, just what is covered in class.

 

In Sedra and Smith do problem 2.45. What is the important result from this problem?

 

Problem 1

You are using a data acquisition system to monitor the voltage from a velocity sensor. The maximum voltage the sensor can put out is 50V while the maximum input voltage the data acquisition system can handle is 15V. You propose to use a resistor voltage divider to insure the voltage into the data acquisition system never exceeds its maximum value as shown below. The input impedance of the data acquisition system

is 10megW. Model the velocity sensor as an ideal voltage source. It is required that the input impedance of the combined resistor divider and data acquisition system be greater than or equal to 10megW.

 

  1. Draw the circuit model to be used for your calculations. Label the source voltage and the known quantities from the problem statement.
  2. What is R1 + R2//Rin? What are R1 and R2//Rin so that the input to the data acquisition system is 15V when the velocity sensor is putting out 50V?
  3. What is R1 and what is R2?
  4. Make a Spice model of your circuit and show that you meet the design requirements. Put a 50Vdc input voltage and plot the DC voltage into the data acquisition system by doing a transient analysis. Run your simulation for 1ms with a 20ms step size.
  5. Repeat part d) for a 1kHz 50V-peak sine wave. How long must you run your simulation and what is the maximum step size now?

 

Problem 2

R1 = 5kW, R2 = 20KW, C = 0.01mF, and Vc(0) = 1V.

 

  1. Find the Thevenin equivalent circuit for the circuit to the left of the capacitor. You will have to write the Thevenin voltage in terms of Vin.
  2. Using your Thevenin equivalent circuit, write down the differential equation that the capacitor voltage must satisfy.
  3. What are the homogenous solution, particular solution, and total solution for a stepped on DC input voltage Vin equal to 12V? How long will it take the circuit to reach steady state and what is the steady state capacitor voltage?
  4. What are the homogenous solution, particular solution, and total solution for a stepped 125V-peak sine wave input voltage Vin(t)? How long will it take the circuit to reach steady state and what is the steady state capacitor voltage in terms of the frequency and time?
  5. Plot Vin(t) and Vc(t) for a frequency of 1kHz. Label both the x and y axis.
  6. Make a Spice model of the above circuit. Do a transient analysis to find the circuits step response for Vin = 12V with a 1 V initial condition. What tstep and tend do you need to use? Plot the Spice solution and verify it is correct by comparing it to your analytical solution.
  7. Repeat part f) for a 125V-peak sine wave input voltage Vin(t). Choose the frequency so Xc is equal to Rth. Make sure you run to steady state.