Attend Lab 2: Time-Domain Reflectometry

In this lab, we will use calculated and measured reflection coefficients (S11), such as those you saw in Lab 1. We will calculate these the same way you did in Lab 1, and measure them the same way too. The only difference is you will only need S11 (so can do a single port calibration on the VNA, which is faster), and we will do that over the full frequency band of the VNA (300kHz to 6.5 GHz). That will give us as much bandwidth as possible. We will then use this data to convert to the time domain, to see our data in time domain reflectometry format.

• Review calibration of the VNA from Lab 0 if needed.
• Review calculation and measurement of reflection coefficient/S11 from Lab 1 if needed.
• Matlab code to calculate input impedance, reflection coefficient (Gamma), and convert it to TDR is given in the supporting documents.
• Matlab code to read the measured VNA data and convert it to TDR is also given.

You have learned about Transients on Transmission Lines (bounce diagrams) in class. Review this material if needed.

In this lab, we will look at both the impulse response and the step function response:

• The impulse response is what you get if the generator produces an infinitessimally short voltage pulse ( a spike), and it reverberates on the line. Producing such a short pulse is actually impossible (it would require an infinite bandwidth, and our VNA is limited to 6.5 GHz). You’ve seen this before, as the pulse response you’ve calculated in bounce diagrams. Just consider the case where the pulse gets very narrow in time. You also have seen/ will see the impulse response in ECE3500. The impulse response is a very handy calculation, because it lets us estimate what the response will be to any other shape of generator signal. This is done with a convolution. And that is how we will calculate the step function response…
• The step function response is what you get if the generator creates a voltage step function, which reverberates through the system. Voltage steps are produced when a switch is switched ‘on’, allowing voltage to enter the system. You’ve seen this before, in ECE 1240, where you calculated the switch response of a capacitive or inductive circuit.

Review: Textbook section 2-12 Transients on Transmission Lines

Supporting Materials:

• Dr. Furse's ECE3300 lectures on bounce diagrams https://utah.instructure.com/courses/578994/assignments/6490626
• Keysight application note on TDR: TDR_Keysight_Appnote_5966-4855E.pdf Download TDR_Keysight_Appnote_5966-4855E.pdf
• For more details on the ProcessTDR function, which converts from freq to time domain: ECE3305---2020Lab 2.pdf Download ECE3305---2020Lab 2.pdf
• BounceDiagramCalcs.m Download BounceDiagramCalcs.m 

In this lab, you will measure the step function response of capacitors and inductors. This is the response you see when you run a square wave generator (that's a step function, it just turns on and off repeatedly) through a capacitor or inductor.

• Step function response of capacitors and inductors:
  • Keysight application note on TDR: TDR_Keysight_Appnote_5966-4855E.pdf Download TDR_Keysight_Appnote_5966-4855E.pdf
• Review if needed:
  
  • ECE1240 lectures on capacitor step function response
  • ECE1240 lectures oninductor step function response
  • ECE1240 textbook sections 5.4 and 5.5 (Free download) Links to an external site.

Everything in this table is completely optional. For full understanding, you'll need a good understanding of both transient electromagnetics (ECE3300) and Fourier transforms (ECE3500).

• VNA-to-TDR Keysight Appnote 5989-5723.pdf Download VNA-to-TDR Keysight Appnote 5989-5723.pdf
• VNA-to-TDR Rhode Appnote 1ez44_0e.pdf Download VNA-to-TDR Rhode Appnote 1ez44_0e.pdf
• Matlab application note https://www.mathworks.com/help/rf/ug/modeling-a-high-speed-backplane-part-3-4-port-s-parameters-to-differential-tdr-and-tdt.html Links to an external site.