Solution: What is the length of an antenna one-half wavelength long

Problem Statement: Transmission and Antenna Systems

The audio power of the human voice is concentrated at about 300 Hz. Antennas of the appropriate size for this frequency are impracticably large, so that to send voice by radio the voice signal must be used to modulate a higher (carrier) frequency for which the natural antenna size is smaller.

a) What is the length of an antenna one-half wavelength long for sending radio at 300 Hz?

b) Suppose we would like a half-wave antenna to have a length of 2 m. What carrier frequency would we use?

c) Suppose a transmitter produces 100W of power. Express the transmit power in units of dBm and dBW.

d) If the transmitter’s power is applied to a unity gain antenna with a 900-MHz carrier frequency, what is the received power in dBm at a free space distance of 100 m?

Problem Answer:

a) The length of an antenna one-half wavelength long is equal to 500 km.

b) The carrier frequency is equal to 75 MHz.

c) The transmit power is equal to 50 dBm and also equal to 20 dBW.

d) The received power is equal to -21.52 dBm

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