EE3300/EE5300 Electronics Applications
Week 5 Tutorial

Written by A/Prof Bronson Philippa

College of Science and Engineering, James Cook University

Last updated 7 April 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?

Tutorial questions

Figure 1:
**(a)** An infinitely long transmission line with characteristic impedance . **(b)** Adding a new infinitesimal length must maintain the same characteristic impedance.
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Figure 1 (a) shows an infinitely long transmission line. The AC phasor voltage and current at the start of the line are denoted and , respectively. Therefore, the characteristic impedance is
Suppose that a new differential segment is added to the front of the line, as shown in Figure 1 (b). As a result of this new segment, the voltage at the start of the line is now and the current at the start of the line is .
1. Use Ohm’s law to find an expression for in terms of the AC impedance of the newly added capacitor.
2. Use Ohm’s law to find an expression for in terms of the AC impedance of the newly added inductor.
3. Since the two expressions for must be equal (adding this new segment did not change the characteristic impedance of the line), we have
  Substitute your previous answers into this equation to prove that the characteristic impedance of the line is given by
  Hint: variables labelled with are infinitesimal quantities (very small), so you can neglect terms where two infinitesimal quantities are multiplied together. For example, is negligible and can be neglected in comparison to terms with only one infinitesimal quantity in them.
(Solution)

Consider the RLC tank circuit shown in Figure 2.

Figure 2:
A RLC tank circuit.
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1. The resistor generates thermal noise. Draw the circuit diagram where the noise is represented as a current source having power spectral density (PSD) of .
2. Find the transfer function where is the noise current.
3. Write down an expression for the power spectral density of by using the formula
  where is the transfer function from part (b).
4. Sketch the shape of based upon the behaviour of the parallel RLC tank and the fact that is white noise.
(Solution)

Figure 3:
The high frequency op-amp circuit reproduced from the notes.
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In the notes, we considered a strategy for split-power rail DC biasing as shown in Figure 3.
The component values are Suppose that all capacitors are large enough that their impedance at the signal frequencies can be neglected. The input signal is driven by a voltage source whose output impedance is 50 Ω.
1. Calculate the power supply isolation in dB, given by
  where is treated as a small signal AC voltage signal. For this analysis, turn off the input voltage (i.e. consider it only as a 50 Ω resistor).
2. Design question: The power supply isolation from part (a) is insufficient. How can this be improved?
  In electronics design, it is always a good idea to review the literature of manufacturers’ application notes. In this case, you might find it interesting to see a Renesas application note entitled How to Bias Op-Amps Correctly.
  You have decided to try the design shown in Figure 8 of that application note. The key insight is to use a bypass capacitor to place a pole at . Careful placement of this pole will strongly attenuate power supply ripple. The divide by 2 arises because . Notice that this calculation of the pole location implicitly assumes so that the loading due to can be neglected when analysing the pole. The application note isn’t very clear on this assumption (perhaps because they consider it obvious to the professional electronics designer).
  Choose component values for , and such that your circuit will provide least dB of power supply isolation at low frequencies and at least at 100 MHz.
  Hint: Assume that the signal path for power supply ripple can be separated into three stages that can be analysed independently. Under this assumption, the power supply isolation is given by:
  1. The attenuation due to and , multiplied by
  2. The attenuation due to the voltage divider formed by and the output impedance of , multiplied by
  3. The gain of the amplifier.
3. Build a simulation model to verify your design.
(Solution)
(Extension question for those interested in physics) Upon learning about thermal noise, your friend is excited to use it to generate electricity. Their thinking goes like this: if noise behaves like a voltage source, then it must be possible to use it to power some load. Can you use this method to generate free electricity?
1. As a first attempt, consider placing two resistors and in parallel. Let be large (so that it has a large ) and treat it as a “power source.” Let be small and treat it as a “load.”
  Prove that thermodynamics always wins by showing that there is no net flow of energy despite the different noise levels. In other words, show that the noise power delivered by into matches the noise power flowing the other way, from into .
2. Realising the mistake of the first attempt (thermodynamics requires that heat can only do work when there is a temperature difference), your friend now has the idea of placing the two resistors at different temperatures.
  Suppose that is at room temperature while is cooled to absolute zero ). Since the temperature of is zero, it has no thermal noise and so its noise PSD vanishes.
  Show that the maximum possible noise power (i.e. under conditions of maximum power transfer) is (in units of W per Hz of bandwidth).
3. Using the result from part (b), if the load can accept power from DC to 1 GHz, how much power in W can be extracted when ? Is this a useful energy source?
(Solution)