## 1.1 The magnetic field of a plane wave propagating in free space is given by the following expression: H (r,t) = 0 .2 cos(6.28 × 109 [t – x/c] + π/4 ) az (amps/m).

## a. Write a similar expression for the electric field.

b. What are the frequency and the wavelength?

c. What is the direction of propagation and the direction of linear polarization?

## 1.2 Calculate the capacity (in bps) of communication channels with the following parameters:

## a. Center frequency, f0 = 85 kHz; Bandwidth, B = 0.01 f0; S/N = 10

b. Center frequency, f0 = 850 MHz; Bandwidth, B = 0.01 f0; S/N = 10

c. Center frequency, f0 = 850 MHz; Bandwidth, B = 0.01 f0; S/N = 2

## 1.3 A base station antenna with a gain of 16 dBi is supplied with 5 Watts. Calculate the EIRP.

## 1.4 Effective noise input power into a mobile receiver is –100 dBm and a signal-to-noise ratio of at least 5 dB is required for acceptable quality of reception. Calculate the maximum acceptable propagation loss, given that the transmitter power is 10 Watts, the transmitter feeder loss is 6 dB, the base station antenna gain is 12 dBi, the mobile antenna gain is 1 dBi, and the mobile feeder loss is 1.5 dB

## 1.5 RF power of 100 Watts is radiated isotropically in free space. Calculate the power density 3 km from the source. Making a local plane wave approximation, calculate the values of the electric field and magnetic field that corresponds to.

## 1.6 What are the power density and field strengths that might be realized in Problem 1.5 if a transmitting antenna with a gain of 15 dBi was used?

## 1.7 How many cells are required in a cell phone system cluster if the minimum acceptable ratio of in-cell power to interfering power is 20 dB?

## 1.8 A cell has 2000 users who generate an average busy-hour traffic of 2.5 mE each. How many channels are needed to serve these users with a blocking probability no greater than 4%?

## 1.9 With the same number of channels per cell as calculated in Problem 1.8, if some emergency were to cause the average traffic to rise to 30 mE per subscriber, what would be the new value of the probability of a blocked call? (Comment on the expected performance of a cell phone system during an emergency when an unusually large number of subscribers are trying to call home.)

## 1.10 With the same number of channels per cell as calculated in Problem 1.8 and with the same blocking probability of 4%, how many subscribers can be accommodated if the cell is divided into three sectors?

## 1.11 Perform a first-order layout design of a cell phone system to cover a metropolitan service area with 1.5 million subscribers and a total area of 64 sq km (i.e., calculate the number of cells in a cluster, the number of clusters needed to cover the service area and the radius of each cell). Choose the following service quality parameters:

Minimum signal-to-interference power ratio = 25 dB

Maximum blocking probability = 0.3%

Number of “busy hour” erlangs per subscriber = 0.006