4.9 A rectangular waveguide has wide dimension a of 2.3 cm. A wave travelling down this guide makes an angle of reflection of 60° at each wall. Calculate (a) the phase velocity, (b) the group velocity, (c) the frequency of opera- tion, (d) the guide wavelength, and (e) the cut-off wavelength.

4.9 A rectangular waveguide has wide dimension a of 2.3 cm. A wave travelling down this guide makes an angle of reflection of 60° at each wall. Calculate (a) the phase velocity, (b) the group velocity, (c) the frequency of opera- tion, (d) the guide wavelength, and (e) the cut-off wavelength.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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3) Solve the cutoff frequency for the first mode and second mode of WR975 Wave guide TABLE 7.1 Some Standard Rectangular Waveguides Waveguide de signation a (in) b (in) t (in) fe, (GHz) Frequency range (GHz) WR975 9.750 4.875 0.125 0.605 0.75-1.12 WR650 6.500 3.250 0.080 0.908 1.12–1.70 WR430 4.300 2.150 0.080 1.375 1.70-2.60 WR284 2.840 1.340 0.080 2.08 2.60-3.95 WR187 1.872 0.872 0.064 3.16 3.95-5.85 WR137 1.372 0.622 0.064 4.29 5.85-8.20 WR90 0.900 0.450 0.050 6.56 8.2–12.4 WR62 0.622 0.311 0.040 9.49 12.4–18
Solve the cutoff frequency for the first mode and third mode of WR430 waveguide.
What are em and he modes? How do they differ from te and tem modes? What is a single mode waveguide and why is it 0th order mode?
Imagine a two-dimensional system in which a sinusoidal waveform is excited at the exact center of a circular plate. The standing wave pattern is established when the excited wave two-dimensionalwaveforms for a stable equilibrium pattern of constructive and destructive interference with the reflected waves from the edge of the circular plate. Draw what you expect the standing wave patterns to look like in this two-dimensional system for increasing resonant harmonics, n. Explain what characteristics of the oscillating plate affect the value of those resonancefrequencies, and what geometric properties of the plate affect the patterns.
4. Again, from the zigzag-path waveguiding model, explain why the group velocity is always slower than the phase velocity in a waveguide with a cutoff frequency.
S=2.2
Phase shift due to finite length of circuit conductors. On a particular type of circuit board, assume a signal travels at 2/3 of the speed of light. Suppose a high-speed system using this type of board can tolerate a phase shift in a sine-wave signal due to propagation delay of only 15° before failing to work. Calculate the maximum length /MAX (in m, or a suitable subdivision such as cm or mm) that a circuit-board trace carrying this signal can have at each of the following frequencies without encountering excessive phase shift due to the propagation delay along the trace: (a) f=10MHz, (b) f=30MHz, (c) f=500 MHz, and (d) f=2.5 GHz.
3. Coaxial cable is used in applications requiring the propagation of high-frequency signal. Such cable consists of a solid conducting cylinder as the inner conductor and a solid conducting cylindrical shell as the outer conductor. A dielectric fills the region between these conductors. Consider the RG-59/U coaxial cable that is commonly used to connect a television/internet equipment. It has an inner conductor with a diameter of 0.584 mm, dielectric filler with a dielectric constant of K = 1.20, and an outer conductor with an inner diameter of 3.7084 mm. Assuming that these conductors are very long, calculate the capacitance per metre of the RG-59/U coaxial cable. Include a derivation of an equation for the capacitance per unit length of the coaxial cable and then use this equation to calculate your answer. (As discussed in class, assign a charge +Q and voltage V to the inner conductor and a charge -Q and 0 V to the outer conductor, solve for the voltage V, and then compute the…
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(V.3) A common commercial size of rectangular hollow-conductor waveguide has (inner) dimensions a = 2.286 cm by b = 1.016 cm. (a) What is the single-mode bandwidth of this size waveguide frequency range (in gigahertz) within which the TE10 mode propagates but the next higher mode does not? [Most practical waveguide systems are operated under this single-mode condition.] that is, what is the (b) The maximum field strength that air can support without breakdown is about 50,000 V/cm (at standard atmospheric pressure). What is the maximum power that can be trans- mitted by this size waveguide at frequencies within the single-mode band?
A wave signal travelling along an electrical transmission line (usually called incident wave) will be reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impe- dance. This can happen in real life if we join dissimilar transmission lines together. Signals travelling alone the line will be partially reflected at the junction (see illustration below; note that up to this point we have not asked you any question yet). Impedance Discontinuity Forward Current Propagating Voltage Wave Z01 Zo2 Return Current Z01 Zo2 Incident Wave Transmitted Wave Reflected Wave Transmission Line Reflection Suppose a transmission line with characteristic impedance Zo is terminated at one end with an impedance of ZL (recall that impedance is a complex number Z = X +iY where X is the resistance and Y is the reactance), then the reflection coefficient I' is given by the voltage reflection equation ZL – Zo ZL + Zo where I, ZL = XL + iYL, and Zo Xo +…
(B) A commercial 50 92 Radio Shake coaxial cable is used to carry RF signal power from a transmitter to an antenna of 300 2 as a load through flat antenna transmission line with 300 2 characterstic impedance as shown in Figure 3. The above situation would happen if we connect the coaxial cable to the antenna without a matching techinque. Determine: 1- The reflection coefficient at junction B. 2- The input impedance at point A. 3- The reflection coefficient at junction A. 4- The fraction of the reflected power. 5- The fraction of the transmitted power to the antenna. 1²=0 5052 30052 (B) Z₁ = 30052 Figure 3