# Problems

# Sections 10.1 to 10.4: Satellite Communication Systems

1. *10.1 A remote sensing satellite is in circular orbit around Earth at an altitude of 1,100 km above Earth’s surface. What is its orbital period?

2. 10-2 A transponder with a bandwidth of 400 MHz uses polarization diversity. If the bandwidth allocated to transmit a single telephone channel is 4 kHz, how many telephone channels can be carried by the transponder?

3. *10.3 Repeat Problem 10.2 for TV channels with each requiring a bandwidth of 6 MHz.

4. 10.4 A geostationary satellite is at a distance of 40,000 km from a ground receiving station. The satellite transmitting antenna is a circular aperture with a 1 m diameter, and the ground station uses a parabolic dish antenna with an effective diameter of 20 cm. If the satellite transmits 1 kW of power at 12 GHz and the ground receiver is characterized by a system noise temperature of 1,000 K, what would be the signal-to-noise ratio of a received TV signal with a bandwidth of 6 MHz? The antennas and the atmosphere may be assumed lossless.

# Sections 10.5 to 10.8: Radar Sensors

1. *10.5 A collision avoidance automotive radar is designed to detect the presence of vehicles up to a range of 0.5 km. What is the maximum usable PRF?

2. 10.6 A 10 GHz weather radar uses a 15-cm diameter lossless antenna. At a distance of 1 km, what are the dimensions of the volume resolvable by the radar if the pulse length is 1 μ s?

3. *10.7 A radar system is characterized by the following parameters: P t=1 kW, τ=0.1 μ s, G=30 dB, λ=3 cm, and T sys=1,500 K. The radar cross section of a car is typically 5 m 2. How far away can the car be and remain detectable by the radar with a minimum signal-to-noise ratio of 13 dB?

4. 10.8 A 3-cm wavelength radar is located at the origin of an x–y coordinate system. A car located at x=100 m and y=200 m is heading east (x direction) at a speed of 120 km/hr. What is the Doppler frequency measured by the radar?

Test Your Understanding of Chapter 10:
http://em8e.eecs.umich.edu/all_qs/chapter10.phtml​