text: # Transmission Line attenuation
  
  Suppose I have an experimental lossy transmission line, being fed a sine voltage wave of known frequency and amplitude, with a known characteristic impedance that is terminated by a perfectly matched load impedance. With the aid of R', G', L', and C', how can I find the amplitude at the end of the transmission line? It is fair to assume that there are no reflections.
  
  I have already found the phase difference, but am struggling to get the correct answer for amplitude. I've found the propagation constant (K) and attempted to find V~(z) = V0+ * e^(-Kz), where z is the length of the transmission line, and then taking the modulus of V~(z), but am getting a much smaller value compared to an experimentally determined value. Thanks for any help.
  
  • What Andy said. Also note that transmission line formulae often use nepers for loss, rather than decibels, which changes the calculations. Commented Feb 24, 2023 at 22:09
  
  A propagation constant is composed with attenuation and phase constants.
  
  $$\gamma = \alpha + i\beta$$
  
  , where α is the attenuation constant and β is the phase constant.
  
  Your goal is to get the amplitude of the signal at the given position z, which can be calculated like this,
  
  $$A_z = A_0 \times e^{-\gamma z} = A_0 \times e^{- (\alpha + i\beta)z}$$ $$\left| \frac{A_0}{A_z} \right| = e^{\alpha z}$$
  
  In your question, there was not mentioning about the attenuation constant. Thus, I cannot assure if you calculated the amplitude correctly using the attenuation constant, which is the real term of the propagation constant.
  
  ### 2. Check your experiment setup
  
  Note that the above calculation is only valid for the infinite length transmission line with correct impedance matching between instruments and the transmission line. Did you check impedance of signal generator, spectrum analyzer (or oscilloscope), and the transmission line itself?
  
  For example, if the instrument's input impedance doesn't match to the transmission line, there will be reflections and will lead you to incorrect result.
explanation: The document describes a scenario involving a lossy transmission line and a sine voltage wave. The user is trying to determine the amplitude of the signal at the end of the transmission line, given the propagation constant and the length of the line. The user mentions that they have already found the phase difference but are struggling with the amplitude calculation. The document also includes a comment suggesting that transmission line formulae often use nepers for loss, which can affect the calculations. Additionally, the document provides a detailed explanation of the propagation constant and how to calculate the amplitude at a given position.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Transmission Line attenuation
  
  Suppose I have an experimental lossy transmission line, being fed a sine voltage wave of known frequency and amplitude, with a known characteristic impedance that is terminated by a perfectly matched load impedance. With the aid of R', G', L', and C', how can I find the amplitude at the end of the transmission line? It is fair to assume that there are no reflections.
  
  I have already found the phase difference, but am struggling to get the correct answer for amplitude. I've found the propagation constant (K) and attempted to find V~(z) = V0+ * e^(-Kz), where z is the length of the transmission line, and then taking the modulus of V~(z), but am getting a much smaller value compared to an experimentally determined value. Thanks for any help.
  
  • What Andy said. Also note that transmission line formulae often use nepers for loss, rather than decibels, which changes the calculations. Commented Feb 24, 2023 at 22:09
  
  A propagation constant is composed with attenuation and phase constants.
  
  $$\gamma = \alpha + i\beta$$
  
  , where α is the attenuation constant and β is the phase constant.
  
  Your goal is to get the amplitude of the signal at the given position z, which can be calculated like this,
  
  $$A_z = A_0 \times e^{-\gamma z} = A_0 \times e^{- (\alpha + i\beta)z}$$ $$\left| \frac{A_0}{A_z} \right| = e^{\alpha z}$$
  
  In your question, there was not mentioning about the attenuation constant. Thus, I cannot assure if you calculated the amplitude correctly using the attenuation constant, which is the real term of the propagation constant.
  
  ### 2. Check your experiment setup
  
  Note that the above calculation is only valid for the infinite length transmission line with correct impedance matching between instruments and the transmission line. Did you check impedance of signal generator, spectrum analyzer (or oscilloscope), and the transmission line itself?
  
  For example, if the instrument's input impedance doesn't match to the transmission line, there will be reflections and will lead you to incorrect result.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document describes a scenario involving a lossy transmission line and a sine voltage wave. The user is trying to determine the amplitude of the signal at the end of the transmission line, given the propagation constant and the length of the line. The user mentions that they have already found the phase difference but are struggling with the amplitude calculation. The document also includes a comment suggesting that transmission line formulae often use nepers for loss, which can affect the calculations. Additionally, the document provides a detailed explanation of the propagation constant and how to calculate the amplitude at a given position.
  
  Label: question-and-answer