EE3300/EE5300 Electronics Applications
Week 3 Tutorial

Written by A/Prof Bronson Philippa
College of Science and Engineering, James Cook University
Last updated 6 March 2025

Workshop warm-up

  • From this week’s notes, what material were you most comfortable with? What material were you the least comfortable with?
  • Is there anything that you’d like clarification on?

Workshop discussion question 1

Feedback circuit oscillation can be thought of as the situation where the feedback signal arrives in phase with the input signal, so that the two waves add together constructively and the overall amplitude is increased.

“Wait a moment!” you might say. Constructive interference occurs when the two waves are in-phase. Doesn’t that mean that we should worry about a 360° phase shift? Why have we been talking about 180° phase shift?

Workshop discussion question 2

In the lecture notes, we improved the phase margin of an op-amp circuit by adding a series resistor.

Does this make intuitive sense to you? How does placing a resistor in the circuit add a zero? Poles are associated with low-pass characteristics, and zeros are associated with high-pass characteristics. What is the high-pass character that was introduced by the resistor?

Hint: Draw the original circuit in the limit of high frequency when the capacitor is a short circuit. Then draw the modified circuit in the limit of high frequencies. Using these circuits, can you explain how the modified circuit has some high-pass character and therefore must include a zero?

Workshop discussion question 3

An improvement to the series resistor is the split feedback design (AoE Figure 4.78B, p. 264).

Without going into the detailed algebra, explain intuitively how this design works.

Hint: Draw the circuit as it appears to DC (i.e. with capacitors as open circuits). What is the output voltage? Now draw the circuit as it appears when the frequency is high enough that . Do you recognise this circuit?

Tutorial questions

  1. In the lecture notes, we considered the three-stage amplifier shown in Figure 1. As we determined in the lecture notes, for certain values of and , this circuit is unstable and therefore will oscillate. Use the Barkhausen criterion to find the frequency of oscillation. (Hint: find the frequency at which the loop gain equals -1.) (Solution)

Figure 1
Figure 1:

The three-stage amplifier that was considered in the lecture notes.

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  1. Now suppose that the circuit in Figure 1 is modified to include a voltage divider in the feedback path that attenuates the voltage by a factor of 10. In other words, the feedback factor is . What is the condition (in terms of and ) for the circuit to be stable? (Solution)

  2. Will the circuit in Figure 2 oscillate? Why/why not? (Solution)

Figure 2
Figure 2:

The common-source amplifier has negative gain, i.e. 180° phase shift. Could this be the simplest oscillator ever designed?

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  1. Suppose an amplifier with an open-loop transfer function

    is connected in a feedback network with . Assume that is large. Find the phase margin. (Solution)

Figure 3
Figure 3:

A phase shift oscillator.

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  1. Consider the oscillator shown in Figure 3. Assume that and are large enough that they can be considered as short-circuits at the oscillation frequency. Also assume that , and the input impedance of the transistor are large enough that they do not load the phase shift network.

    1. Given that the transfer function of the feedback network is

      prove that the frequency of oscillation is

      Hint: Use the Barkhausen criterion.

    2. Find the minimum transistor transconductance for this oscillator to start up.

    (Solution)

  2. (Extension question) Prove the value of that was given in the previous question. (Solution)