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ECE410 Spring 2012

ECE410 Spring 2012. Lecture #31 Unbounded Response and Integrating Amplifier. Homework Due 3/16/2012. Chapter 7 – Problems 33, 35, 48, 50, 55, 70, 73, 74, 78, 89

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ECE410 Spring 2012

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  1. ECE410 Spring 2012 Lecture #31 Unbounded Response and Integrating Amplifier

  2. Homework Due 3/16/2012 • Chapter 7 – Problems 33, 35, 48, 50, 55, 70, 73, 74, 78, 89 • PSpice – Model the circuit from problem 89 from your homework assignment. This circuit is shown below as well as the input waveform:

  3. Homework (cont) • Plot voltage v0 vs. time. • Ignore the switch in the circuit and model the input waveform using VPWL, a piecewise linear voltage source. Using this source you can specify the voltage at multiple times (t1,t2,t3,…) and the corresponding voltages at those times (v1, v2, v3, …) and the points will be connected by straight lines. In order to model the vertical transitions use two times that are close together.. (let t1=0, v1=0; t2=1ns, v2=-200mV) to simulate the initial voltage change from 0V to -200mV at time zero. • My suggestion: • Run the simulation for 750ms • Use a LM741 or similar op-amp in your simulation

  4. Unbounded Response • When dependent sources are used in a circuit it is possible to have a negative Thevenin Resistance • When a negative resistance is used in an RC circuit, the time constant becomes negative • The results in a positive exponential… meaning the voltage across the capacitor blows up with time.

  5. Plot of Unbounded Response • Both responses start at an initial voltage (1V in our plot) • Unbounded response rises rapidly instead of decaying • Unbounded response has not set final voltage… it will increase forever, so we cannot use the general expression for step and natural responses from RC and RL circuits

  6. Example When the switch closes, the capacitor has 10V across it. We then can look use the test voltage method to look into the circuit from the capacitor’s point of view and find the Thevenin Resistance (Rth) since we have a dependent current source in the circuit.

  7. Unbounded Response Example Continued From node voltage: So:

  8. Unbounded Response Example Continued From Node Voltage:

  9. Unbounded Response Example Continued • Given How long would it take before the voltage across the capacitor reached 150V and the capacitor failed… shorting out?

  10. The Integrating Amplifier • We can use an op-amp circuit to integrate the input waveform. This is an inverting amplifier with the feedback resistor replaced by a capacitor

  11. Integrating Amp continued • Using our typical method for solving an ideal opamp circuit • First find Vp • Then find an expression for Vout in terms of Vn • Set Vn = Vp Vp=0 Vn=Vp=0

  12. Integrating Op-Amp If at time t0 there is no voltage on the resistor then v0(0) = 0 Output is the integrated input waveform multiplied by a negative constant

  13. Example Input and Output Waveforms Integral from 0 – t1 will be a ramp with slope Vm*t1 Integral from t1 – 2t1 will be a ramp with slope -Vm*t2 Actual Output is the integral of vs multiplied by

  14. Examples • Work Assessment 7.9 and 7.10

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