# Pulse Down a line with Series terminations between transmission lines

I am interested in a relative edge case in transmission line of a simulation.

If send a pulse down the setup below, now obviously my rudimentary steady state electronics knows this is a basic voltage divider which will split the voltage of 3.3V between all resistors.

The setup goes from 0 to 10V from a source with a 50ohm source impedance, down a transmission line characteristic impedance of 50 ohm, series resistor of 50ohm, TL of 50ohm then a final resistor of 50ohms.

Now when the pulse goes down the line

1. It sees a transmission of 50 ohm and a source impedance of 50 ohms and the 10V voltage halves, so far so good.
2. This 5V goes down the transmission line and hits the 50ohm resistor and hits point b.
3. As soon as this hits point b, point b goes to 6.667V, as would be the case in steady state analysis.
4. the reflection of this then goes from b to a and a goes form 5V to 6.667V.

My questions

• Are why does the voltage at b from a +5V pulse to 6.667V.
• What is this reflection that causes point a to go from +5V to 6.667V as well.

As all connections are completely matched and there should be no reflection?

UPDATE

What I was specifically looking for was some kind of textbook or equation to explain this phenomena.

The terminology used to describe this in literature is 'discontinuity in the transmission line'

An overview of the equations governing this is shown below. This equation for the resistor specifically explains the resistor/voltages seen in my simulations.

Useful references include:

2. https://ece.illinois.edu/webooks/nnrao2004/06%20Rao%20Elements%202004%20ch6.pdf (from the textbook called Elements of Engineering Electromagnetics by Nannapaneni Narayana Rao)
• What are the differential and single ended characteristics of the transmission line? What is the electrical length of your transmission line? – EasyOhm Oct 18 '19 at 7:54
• I'm purely interested in the simulation which is taken from www.falstad.com Lets say the length is above the 1/10 rule of thumb. – Hart22 Oct 18 '19 at 8:06
• When the first edge from the wave is arriving at point 'b', it does not see a 50 Ohms load, because you have no direct GND path. (In difference to point d, where the impedance matching is OK). So mismatch at point 'b' can lead to increased voltage. – Stefan Wyss Oct 18 '19 at 8:46
• Okay, so what load value does it see? What is the equation in question? – Hart22 Oct 18 '19 at 8:47
• It ‚sees‘ 100 Ohms at ‚b’. The reflection factor will be 1/3. – Stefan Wyss Oct 18 '19 at 10:05

As all connections are completely matched and there should be no reflection?

No they are not. Point b looking from left to right should terminate in 50 ohms but you have 50 ohms in series with the 50 ohms of the t-line between c and d. This means you are terminating b in 100 ohms. So no, the termination at point b does not match the left hand t-line.

And clearly this is the case if you think about it - if b and c were shorted then you would have one continuous t-line between a and d and then it would be a perfectly matched line.

• I thought the transmission line theory was supposed to clear up the underlying theory of why voltage splits between loads in steady state. If the +5V way arrives at b, then gets to C, sure it can see the 50ohm characteristic impedance line but it can't see point d yet, i.e. the 50ohm load yet? so how does point d effect point b if it hasn't reached point d? It's a wave, it doesn't know what's down the line. – Hart22 Oct 18 '19 at 10:53
• An infinitely long 50 ohm transmission line looks like 50 ohms for all time and all input signals. Bringing it back to reality, if you apply 1 volt to a 50 ohm line then instantly 20 mA flows and, 20 mA will continue to flow when the wave hits the end of the line providing the line is terminated in 50 ohms. – Andy aka Oct 18 '19 at 11:39