ECE3300 Lecture 6 4 Standing wave ratio

Summary

This video explains the key concepts behind standing waves, focusing on their voltage and current envelopes. It introduces the parameters V_max and V_min, which define the maximum and minimum amplitude values of the standing wave. The video also covers the Voltage Standing Wave Ratio (VSWR), explaining how it relates to the reflection coefficient and provides insights on how to calculate it. Additionally, it highlights the inverse relationship between the voltage and current envelopes in standing waves, where the voltage peak corresponds to the current minimum, and vice versa.

Takeaways

• 😀 Standing waves are described by the envelopes of the wave, which show the maximum and minimum amplitudes.
• 😀 V_max represents the maximum value of the envelope, while V_min represents the minimum value, which is not the time-domain minimum.
• 😀 The Voltage Standing Wave Ratio (VSWR), or Standing Wave Ratio (SWR), is calculated as the ratio of V_max to V_min.
• 😀 VSWR is also related to the reflection coefficient and can be used to calculate it.
• 😀 The equation for VSWR is 1 + the reflection coefficient divided by 1 - the reflection coefficient.
• 😀 A typical VSWR in the example is about 1.3, indicating a ratio of V_max to V_min.
• 😀 The reflection coefficient can be calculated by measuring the VSWR, which is often easier than measuring the reflection coefficient directly.
• 😀 Two plots of standing waves are shown: one for voltage and one for current.
• 😀 The voltage and current standing waves are inversely related: when voltage is at its maximum (V_max), the current is at its minimum (I_min), and vice versa.
• 😀 The relationship between voltage and current standing wave patterns is key for understanding how waves behave in different systems.
• 😀 The ability to calculate the reflection coefficient from VSWR is essential for analyzing signal integrity in systems like transmission lines.

Q & A

What are the two key values associated with the standing wave envelope discussed in the video?

The two key values are V_max (the maximum value of the standing wave envelope) and V_min (the minimum value of the standing wave envelope).

What is the significance of V_max and V_min in the context of standing waves?

V_max represents the largest amplitude reached by the time-domain waveform at any point along the line, while V_min represents the smallest amplitude reached by the time-domain waveform.

How is the Voltage Standing Wave Ratio (VSWR) calculated?

The Voltage Standing Wave Ratio (VSWR) is calculated by dividing V_max by V_min, which represents the ratio of the maximum to the minimum voltage in the standing wave.

What is the relationship between VSWR and the reflection coefficient?

VSWR is related to the reflection coefficient through the formula: VSWR = (1 + reflection coefficient) / (1 - reflection coefficient). By measuring the VSWR, we can calculate the reflection coefficient.

How does the video describe the voltage and current standing waves in terms of their relationship?

The video notes that the peak of the voltage standing wave corresponds to the minimum of the current standing wave, and the minimum of the voltage corresponds to the maximum of the current.

What does the term 'envelope' refer to in the context of standing waves?

The envelope refers to the smooth curve that outlines the maximum and minimum amplitudes of the standing wave, essentially representing the overall pattern of voltage or current variations.

What does the term SWR stand for, and what is its alternate name?

SWR stands for Standing Wave Ratio, and it is sometimes called the Voltage Standing Wave Ratio (VSWR).

Why is it important to measure the VSWR in most cases?

It is important to measure the VSWR because, while the reflection coefficient cannot usually be measured directly, VSWR can be measured and then used to calculate the reflection coefficient.

What value of VSWR is observed in the example shown in the video?

In the video, the VSWR value is approximately 1.3, which is calculated as V_max divided by V_min (about 1.3/0.7).

What is the practical significance of understanding the relationship between voltage and current in standing waves?

Understanding the relationship helps in visualizing how energy is distributed in the standing wave pattern. Knowing where voltage maxima and minima occur relative to current maxima and minima can be useful for designing systems like antennas, where impedance matching is crucial.