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Chapter 10: Problem 7

A transmitter and receiver are connected using a cascaded pair of transmission lines. At the operating frequency, line 1 has a measured loss of \(0.1 \mathrm{~dB} / \mathrm{m}\), and line 2 is rated at \(0.2 \mathrm{~dB} / \mathrm{m}\). The link is composed of \(40 \mathrm{~m}\) of line 1 joined to \(25 \mathrm{~m}\) of line 2 . At the joint, a splice loss of \(2 \mathrm{~dB}\) is measured. If the transmitted power is \(100 \mathrm{~mW}\), what is the received power?

Short Answer

Expert verified
Question: Calculate the received power at the end of the transmission system when the transmitted power is 100mW, and the transmission system consists of two lines in cascade with given losses and lengths. The splice loss at the joint between the two lines is 2dB. Line 1 has a loss of 0.1 dB/m and a length of 40m. Line 2 has a loss of 0.2 dB/m and a length of 25m. Answer: The received power at the end of the transmission system is approximately 7.943 mW.

Step by step solution

01

Calculate the loss in each transmission line due to its length

We have the following losses and lengths for each transmission line: - Line 1: Loss of \(0.1 \textrm{dB/m}\) for a length of \(40 \textrm{m}\) - Line 2: Loss of \(0.2 \textrm{dB/m}\) for a length of \(25 \textrm{m}\) So the loss in each transmission line can be calculated by multiplying the given loss per meter by the respective lengths: Loss in Line 1: \(0.1\textrm{dB/m} \times 40\textrm{m} = 4\textrm{dB}\) Loss in Line 2: \(0.2\textrm{dB/m} \times 25\textrm{m} = 5\textrm{dB}\)
02

Sum up the total losses in the transmission system

To find the total loss in the transmission system, add the losses from Line 1, Line 2, and the splice at the joint: Total Loss = Loss in Line 1 + Splice Loss + Loss in Line 2 Total Loss = \(4\textrm{dB} + 2\textrm{dB} + 5\textrm{dB} = 11\textrm{dB}\)
03

Calculate the received power

To calculate the received power, we will use the formula for power loss in decibels: \(P_\textrm{received} = P_\textrm{transmitted} \times 10^{-\frac{L}{10}}\) Where \(P_\textrm{received}\) is the received power in milliwatts, \(P_\textrm{transmitted}\) is the transmitted power, and \(L\) is the total loss in decibels. Plug in the total loss and transmitted power into the formula: $P_\textrm{received} = 100\textrm{mW} \times 10^{-\frac{11}{10}} = 100\textrm{mW} \times 10^{-1.1} = 100\textrm{mW} \times 0.07943 = 7.943 \textrm{mW}$ So the received power is approximately \(7.943 \textrm{mW}\).

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Most popular questions from this chapter

The characteristic impedance of a certain lossless transmission line is \(72 \Omega\). If \(L=0.5 \mu \mathrm{H} / \mathrm{m}\), find \((a) C ;(b) v_{p} ;(c) \beta\) if \(f=80 \mathrm{MHz} .(d)\) The line is terminated with a load of \(60 \Omega\). Find \(\Gamma\) and \(s\).

A sinusoidal wave on a transmission line is specified by voltage and current in phasor form: $$V_{s}(z)=V_{0} e^{\alpha z} e^{j \beta z} \quad \text { and } \quad I_{s}(z)=I_{0} e^{\alpha z} e^{j \beta z} e^{j \phi}$$ where \(V_{0}\) and \(I_{0}\) are both real. (a) In which direction does this wave propagate and why? \((b)\) It is found that \(\alpha=0, Z_{0}=50 \Omega\), and the wave velocity is \(v_{p}=2.5 \times 10^{8} \mathrm{~m} / \mathrm{s}\), with \(\omega=10^{8} \mathrm{~s}^{-1}\). Evaluate \(R, G, L, C, \lambda\) and \(\phi\).

A sinusoidal voltage source drives the series combination of an impedance, \(Z_{g}=50-j 50 \Omega\), and a lossless transmission line of length \(L\), shorted at the load end. The line characteristic impedance is \(50 \Omega\), and wavelength \(\lambda\) is measured on the line. \((a)\) Determine, in terms of wavelength, the shortest line length that will result in the voltage source driving a total impedance of \(50 \Omega .(b)\) Will other line lengths meet the requirements of part \((a)\) ? If so, what are they?

A lossless transmission line having characteristic impedance \(Z_{0}=50 \Omega\) is driven by a source at the input end that consists of the series combination of a 10 -V sinusoidal generator and a \(50-\Omega\) resistor. The line is one- quarter wavelength long. At the other end of the line, a load impedance, \(Z_{L}=50-j 50 \Omega\) is attached. (a) Evaluate the input impedance to the line seen by the voltage source-resistor combination; \((b)\) evaluate the power that is dissipated by the load; \((c)\) evaluate the voltage amplitude that appears across the load.

A standing wave ratio of \(2.5\) exists on a lossless \(60 \Omega\) line. Probe measurements locate a voltage minimum on the line whose location is marked by a small scratch on the line. When the load is replaced by a short circuit, the minima are \(25 \mathrm{~cm}\) apart, and one minimum is located at a point \(7 \mathrm{~cm}\) toward the source from the scratch. Find \(Z_{L}\).
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