Solutions to Practice Problems
Practice Problem 24.1
A radio station has an EIRP of 25 kW and a transmit power of 1.73 kW. What is the gain of the antenna?
EIRP = Pt Gt so Gt = EIRP / Pt = 25 kW / 1.73 kW = 14.45
Practice Problem 24.2
Consider the antenna with this radiation pattern:
1. What is the beamwidth of this directional antenna?
Beamwidth = 40° as shown
2. What is the sidelobe level?
SLLdB = Gmainlobe (dB) – Gsidelobe(dB)
= 0 dB – (−11 dB) = 11 dB
3. What is the front-to-back ratio?
FBRdB = Gmainlobe (dB) – Gbacklobe(dB)
= 0 dB – (−7 dB) = 7 dB
4. Will a station transmitting bearing 90° interfere with
me? Will I interfere with it?
No interference; no sidelobes in that direction.
5. Will a station bearing 240° be able to eavesdrop on my communications?
Yes, it is possible; our antenna does have a sidelobe in the 240° direction.
6. Suppose the receiver I am communicating with (at 0°) requires that the signal received be at least 1 pW. Will I have to
transmit more power or less power using this antenna than if I were using an isotropic antenna? Why?
Less power is needed, since this antenna can focus the transmitted power in a certain direction.
Practice Problem 24.3
A transmitter feeds a half-wave dipole antenna with 100 watts of power. Calculate the Effective Isotropic Radiated Power
(EIRP).
For a dipole antenna, Gt = 1.64. EIRP = Pt Gt = 164 W.
Practice Problem 24.4
How long would a dipole antenna be for AM 1100?
For AM 1100, the transmit frequency is 1100 kHz, so wavelength is
λ = c / f = 3x108 / 1100x103 = 272.7 m
For a dipole antenna, antenna length is λ/2 = 136.35 m
Practice Problem 24.5
The ballistic submarine, USS Alaska, has gone alert. They must stream a floating wire monopole antenna to get their alert
signal. If the alert signal is transmitted at 30 kHz, how far should they stream their antenna? (note: the antenna being
streamed is a straight wire)
For a 30 kHz signal the wavelength is λ = c / f = 3x10 8 / 30x103 = 10,000 m
For a monopole antenna, antenna length is λ/4 = 2500 m
Practice Problem 24.6
What is the length of the driven element in a Yagi at 290 MHz?
For a 290 MHz signal the wavelength is λ = c / f = 3x10 8 / 290x106 = 1.03 m
For a Yagi antenna, the driven element is a dipole antenna, so length is λ/2 = 0.517 m