This article explains the creation of a bounce diagram for a transmission line circuit (see [1] for transmission line reflections).
Consider the circuit shown in Figure 1.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig1.png)
When the switch closes the forward voltage wave travels toward the load and reaches it at t = T (T = one-way travel time). Since the line and the load are mismatched a reflection is created and travels back to the source, reaching it at t = 2T (assuming zero rise-time). Since the line and the source are mismatched, another reflection is created which travels forward to the load reaching it at t = 3T.
This process theoretically continues indefinitely; practically, it continues until the steady-state voltages are reached at the source and at the load. A bounce diagram is a plot of the voltage (or current) at the source or the load (or any other location) after each reflection.
The experimental setup for reflection measurements is shown in Figure 2.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig2.png)
The initial voltage at the location z = 0 is
This is shown in Figure 3.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig3.png)
The reflection coefficient at the load is
The initial voltage wave of 6V travels to the load and reaches it at t = T creating a reflection
V – = ΓLV + = (0.4845)(6) = 2.907 V
The total voltage at the load (at t = T) is
VL = V + + V – = 6 + 2.907 = 8.907 V
This is shown in Figure 4.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig4.png)
Voltage reflected at the load (V –= 2.907 V) travels back to the source. The reflection coefficient at the source is
The re-reflected voltage at the source is
V -+ = ΓSV – = (-0.2)(2.907) = -0.5814 V
The total voltage at the source at t = 2T is
VS = V + + V – + V -+ = 6 + 2.907 – 0.5814 = 8.3256 V
This is shown in Figure 5.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig5.png)
The voltage reflected at the source (V -+ = -0.5814 V) travels toward the load where it will create another reflection which will travel toward the source. This process will continue until the steady-state is reached.
The bounce diagram showing the voltages at the source and the load after each reflection is shown in Figure 6.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig6.png)
Figure 7 shows the voltages at the source (z = 0) while the Figure 8 shows the voltage at the load (z = L) during the period 0 ≤ t < 8T .
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig7.png)
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig8.png)
It is apparent the source and load voltages eventually reach the steady state. Recall that a transmission line can be modeled as a sequence of in-line inductors and shunt capacitors (assuming a lossless line) [2], as shown in Figure 9.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig9.png)
Under dc conditions (steady-state when driven by a dc source) inductors act as short circuits and capacitors act as open circuits.
Thus in steady state the circuit in Figure 1 is equivalent to the circuit in Figure 10 where the transmission line is modeled as an ideal conductor.
![](https://incompliancemag.com/wp-content/uploads/2023/12/1810_ECE_fig10.png)
The steady state value of the voltage at z = 0 is the same as the value at z = L and can be obtained from the voltage divider as
Note that both the source and the load voltages converge to this value as the reflection process approaches a steady state.
References
- Adamczyk, B., Transmission Line Reflections at a Resistive Load, In Compliance Magazine, January 2017.
- Adamczyk, B. Foundations of Electromagnetic Compatibility with Practical Applications, Wiley, 2017.