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ICE-079 Microwave Engineering (초고주파공학)

Homework Solutions

Week-14: Ch08 Wireless Communication Systems

Homework problems:

14.1 An antenna is at 100m height from the earth surface. Find the LOS distance (the radio horizon).

(Answer)

(km) 4 (m) 4 100 40 kmd h= = =

A radio communication system is specified by the following parameters.

Pt = 1W, R =100m, Gt = 0dB, Gr = 10dB, B = 100kHz, T = 290K, F = 10dB, Lsys = 10dB, f = 1GHz

14.2 Find the EIRP of the transmitter.

(Answer) 0 /10EIRP = 1 1 W10 t tP G = × =

14.3 Find the power density at the receiver.

(Answer)

2 2

4

22 EIR 10 W/P 1 =

4 4 4 1 0m

40t t

DP GS

R Rπ π π π

−= = =

×

14.4 Find the power received by the receivig antenna.

(Answer) 2 4 10 /10 20

2 2 10 /10

6

2 1 EIRP 10 10 0.3 =

4 449 1

4 4 100 W

16t t r

r ersys sys

P G GP AL LR R

λπ ππ π π π

− −×= =

×=

×

14.5 Find the signal-to-noise ratio at the output of the receiver.

(Answer)

02

0

174 /10 20.4

20.4 3 15.4

10 /10

60

2 2 15.40

1 14

174 dBm 10 mW =10 W for 1 Hz

10 100 10 10 W for 100 kHz

10 dB 10 10

1 1 9 10 14 16 10

t ter

sys

t ter

sys

S P G AN L kTBFR

kTB B

kTB B

F

S P G AN L kTBFR

π

π π

− −

− −

−

−

=

= − = =

= × × = =

= = =

×= =

8.4

2

70 010 0

0 0

7

1

9 1010 16

(dB) = 10log 10log (1.

1.4

43 10 )

3 10

71.6 dBS SN N

π×

= =×

= × =

×

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Week-13: Ch07 Radars (2)

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Homework problems:

13.1 A pulse radar with pulse with 10 μs, PRF 1 kHz. Find the range resoltion ΔR, the maximum range Rmax,

and the bandwidth B of the matched filter.

(Anwer)

8 61 1 3 10 10 110 m2

500 2

R cτ −∆ = = × × × × =

8 5max 3

1 1 13 10 1.5 10 m2 2 10

150 kmR cT= = × × × = × =

61 1

10 100.1 MHzB

τ −= = =×

13.2 A target is approaching a radar with 10 GHz RF signtal at a 45 degree angle form radar antenna beam

direction with a speed of 200 m/s. Find the Doppler frequency.

(Answer)

90 8

2 2 200cos 10 cos 453 10

4000 Hz3 2

rd

vf fc

θ ×= = × × ° =

×

13.3 A FMCW radar with modulation frequency fm of 5 kHz, frequency deviation Δf of 300 MHz, and the

bit frequency fR of 5 MHz. Find the range.

(Answer) 8 6 14

3 6 111 1 3 10 5 10 104 4 5 10 300 1

2500 4 10

mR

m

c fRf f

× × ×= = = =

∆ × × × ×

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Week-12: Ch07 Radars (1) Homework problems: If not given, assume K = 290 K (thermal noise power -174 dBm/Hz), Lsys = 1 (0 dB). Problem 12.1 An antenna with the maximum gain of 30dB transmits power of 1W. Find the power density at

a target 100m away from the antenna in the direction of the maximum gain. (Answer) S = [Pt /(4πR2)]G = [1/(4π×1002)]×1030/10 = 1/(40π) W/m2

Problem 12.2 In Problem 12.1, the frequency is 1GHz and the target's radar cross section is 1m2. Find the received power.

(Answer) Pr = PtG2σλ0

2/[(4π)3R4] = 1×(1030/10)2×1×(3×108/109)2/[(4π)3×1004] = 9×104/[(4π)3×1004] = 9×10–4/(64π3) W

Problem 12.3 In Problem 12.1, the antenna has beamwidth of 3 degrees, scan rate of 30°/s. The PRF is 1kHz. Find the number of pulses received from a target.

(Answer)

3

n = (θB / θS) × PRF = (3/30)1000 = 100

Problem 12.4 In Problems 12.1 to 12.3, we used a receiver with 10MHz bandwidth, 5 dB noise figure. The minium output SNR is 10dB. Find the maximum target detection range.

(Answer) N = kTB = –174 dBm/Hz = 10–174/10 mW for B = 1Hz at 290 K. Rmax = PtG2σλ0

2n/[(4π)3kTBF (S0/N0)min]1/4= 1×(1030/10)2×1×(3×108/109)2×100/[(4π)3×(10–174/10×10–

3×107×105/10×1010/10]1/4 = [ 9×106/(64π3×10–11.9)]1/4 = 9×1017.9/(64π3)1/4 m = 7747 m

Problem 12.5 Convert 2m2 RCS into dBSm. (Answer) σ (dBsm) = 10log10σ = 10log102 = 3.0

Problem 12.6 Find the radar output SNR for detection probability of 0.99 and false alarm rate of 10–5. (Answer)

From the charg on p. 16 of the lecture slide, we find

SNR = 14 dB

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Week-11: Ch06 Transmitters (2)

Problem 11.1 After viewing the above videos, come up with an idea of your capstone design project

(졸업작품). Give a) the name or title of your project and b) the block diagram of your system.

(Answer)

a1) Project title: SmartHome with Amartphone and WiFi

a2) Project concept:

Use a smartphone's WiFi communication functionality, three Arduino modules with a WiFi communication

and an AC power swith relay to turn off and turn on a room lamp, an electric fan, and a room air conditioner.

b) Block diagram of the project

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Week-10: Ch06 Transmitters (1)

Problem 10.1 The RF output power of a resonator is 10 mW with 5 V/ 10 mA bias. Find the power

conversion efficiency.

(Answer)

e = PRF/PDC = 10 mW / (5×10 mW) = 10/50 = 0.2 = 20%

Problem 10.2 A resonator has a center frequency 30 GHz at 20 °C with stability of +1 ppm/°C. Find the

resonator's frequency at 30 °C.

(Answer)

f = f0 + sΔT = 30 + (30)(10-6)(30-20) = 30.0004 GHz

Problem 10.3 A resonator has output power of 10 mW with -100 dBc/Hz phase noiset at 100 kHz offset.

Find the phase noise power containted in 10-kHz bandwidth at 100 kHz offset.

(Answer)

Pn = Pc × Nd × Δf = 10(10-100/10)(10×103) = (10)(10-6) = 10-5 mW = -50 dBm

Problem 10.4 What is the primary type of an oscillator in the AM transmitter?

(Answer) A crystal oscillator

Problem 10.5 What is the typical efficiency of a class C power amplifier?

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(Answer) 90%

Problem 10.6 Draw the symbol of the oscillator used in the above video. What is the type of the ocillator?

(Answer)

Symbol:

Oscillator type: The crystal oscillator

Problem 10.7 What's the output power of the CC1120 chip used in the experiment?

(Answer) 27 dBm

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Week-09: Ch05 Receivers

Problem 9.1 Problem 9.1 At 290 K, calculate the thermal noise power for 1 MHz bandwidth.

(Answer)

N = kTB, N = -174 dBm for B = 1 Hz at T = 290 K

B = 1 Hz → 0 dB

B = 1 MHz → 10log10(106) = 60 dB

N = -174 + 60 = -114 dBm

Problem 9.2 Amplifier 1: Pin = -80dBm, Pout = -60dBm, Noise_in = -95dBm, Noise_out = -70dBm

1) Find the input signal to noise ratio.

2) Find the noise figure.

(Answer)

1) SNRin = -80 - (-95) = 15 dB

2) SNRout = -60 - (70) = 10 dB → NF = SNRin (dB) - SNRout (dB) = 5 dB

(Note) G1 of Amp 1 = -60 - (-80) = 20 dB

Problem 9.3 Amplifier 2: Pin = -80dBm, Noise_in = -95dBm, Gain = 30dB, Noise figure = 10dB. Amplifier

1 of Problem 9.2 and Amplifier of Problem 9.3 are connected in cascade as shown in the following

shematic.

(Input signal) → (Amplifier 1) → (Amplifier 2) → (Output signal)

1) Find the output power.

2) Find the noise power at the output.

3) Find the noise figure.

(Answer)

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1) Pout (of Amp 2) = Pin (dB)(of Amp 1) + G1 (dB) + G2 (dB) = -80 + 20 + 30 = -30 dBm

(Note) Use Pin of Amp 1, which is -80 dBm.

2) Noise added by a device:

Na = kTBG(NF–1)

Ni = kTB = -95 dBm (at the input of Amp 1)

No1 (at the output of Amp 1) = Ni G1+Na1 = kTBG1NF1 = -95 + 20 + 5 = -70 dBm = Ni2 (at the input of

Amp 2)

No2 (at the output of Amp 2) = Ni2G2 + kTBG2(NF2–1) = 10-4.0 + 10-5.546 = 1.0284×10-4 mW = -39.88 dBm

(Note)

Ni2G2 = -70 + 30 = -40 dBm = 10-4.0 mW

kTBG2(NF2–1) = -95 + 30 + 10log10 (1010/10–1) = -95 + 30 + 9.54 = -55.46 dBm = 10-5.546 mW

3) Input SNR = -80 - (-95) = 15 dB

Output SNR = -30 - (-39.88) = 9.88 dB

Noise Figure = Input SNR (dB) – Output SNR = 15 - 9.88 = 5.12 dB

(Note) Using the noise figure formula of a cascaded system:

NF = F1 + (F2-1)/G1 = 105/10 + (1010/10-1)/102 = 3.162 + 0.09 = 3.252 = 5.12 dB

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Week-08: Mid-term exam, no homework.

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Week-07: Ch04 Components(2)

Problem 7.1 Draw symbols of a) a circulator and b) a mixer.

(Answer)

Circulator:

Mixer:

Problem 7.2 Directional coupler: Input power = 1W (1000mW=30dBm), Coupling = 20dB, Directivity =

50dB. Find a) the power at the coupled port and b) the power at the isolated port.

(Answer)

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a) (dB) /10 20 /101 1 110 3

3 3

1000 mW(dB) 10log 10 10 100 10 mW100 100

CP P PC PP P

= → = = = → = = =

b) (dB) /10 50 /10 5 43 3 310 4 5 5

4 4

10 mW(dB) 10log 10 10 10 10 mW = 100 nW10 10

DP P PD PP P

−= → = = = → = = =

Problem 7.3 Swith: ON-state attenuation = 1dB, OFF-state isolation = 40dB. Find the Pout when a) the

switch is ON and b) the switch is OFF.

(Answer)

a)

in 100.001 mW0.001 mW 10log 30 dBm

1 mWP = = = −

out in filter 1 ON 2 30 1 10 4 1 30 4 dBmcP P L G L L G= − + − − + = − − + − − + =

b)

out in filter 1 ON 2 30 1 10 4 40 30 35 dBmcP P L G L L G= − + − − + = − − + − − + = −

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Week-06: Ch04 Components(1)

Problem 6.1 How many ports are there in a directional coupler?

(Answer) 4

Problem 6.2 What is a dual directional coupler?

(Answer) A dual direction coupler is a type of direction coupler where one output port gives a sampling (or

coupling) of the forward-traveling wave and the other output port gives a sampling of the reverse-traveling

wave.

Problem 6.3 Name the components used in the 24GHz Doppler radar in Lecture 06-3.

(Answer) Oscillator, Coupled line, Power splitter, Rat race couper, Mixer, Antenna

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Week-05: Ch03 Antenna systems(2)

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Problem 5.1 What is the circular polarization?

(Answer) The electric wave vector is rotating in the right or left hand direction as the wave propagates. The

locus of the of the electric field vector is a circle.

Problem 5.2 What is the MIMO antenna technology?

(Answer) The MIMO antenna technology refers to a technique where a signal is transmitted using multiple

antennas (multipole input) and received using multiple antennas (multiple output). The MIMO antenna

technology increases the signal transmission rate and reduces the multi-path interference.

Problem 5.3 What is the phased array antenna?

(Answer) The phased array antenna is a type of an array antenna where the phase of each array element is

electronically adjusted to rapidly scan the antenna beam.

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Week-04: Ch03 Antenna systems(1)

Problem 4.1 Convert 17 dBm power into mW?

(Answer) 17 dBm = 1017/10 mW = 50.1 mW

Problem 4.2 With Gt = 20 dB (linear 100), Gr = 10 dB (linear), frequency = 1 GHz, distance r = PIN (m), Pt

= 10 dBm (10 mW), find the received power.

(Answer)

PIN = 3194 8

93 10 0.3 m

10cf

λ ×= = =

2 220 /10 10 /10 70.310 mW 10 10 5.59 10 mW 62.5 dBm

4 4 3194r t t rP P G Gr

λπ π

− = = × × × = × = − ×

Problem 4.3 With λ = PIN (m), design a six-turn helical antenna and find its Zin, G, and HPBW.

(Answer)

3194 1017 mC D Dπ λ= = = → =

1tan tan , 13 3194 tan13 737 mS S C SC

α α α−= → = = °→ = ° =

N = 6

PIN = 3194

in 140 140 140 CZ λλ λ

= = = Ω

2 2

3 36.2 6.2 3194 6 737 8.6 9.3 dB

3194C NSGλ

× × ×= = = =

9

65 65 3194HPBW 55.2/ 3194 6 737 / 3194C NS

λλ

×= = = °

×

Problem 4.4 With f0 = PIN (MHz), design a three-element Yagi antenna with a folded dipole driver.

(Answer) 8

63 10 94 mm

3194 10λ ×= =

×

Reflector length = 492/f0(MHz) feet = 492/3194 feet = 47.0 mm

Reflector-director spacing = 0.04λ = 3.76 mm

Driver length = 479/f0(MHz) feet = 479/3194 feet = 45.7 mm

Driver-director spacing: no information in the lecture video

Director length = 461.5/f0(MHz) feet = 461.5/3194 feet = 44.0 mm

Problem 4.5 With f0 = PIN (MHz), design a full-wave loop antenn. What is its input impedance?

(Answer) 8

63 10 94 mm

3194 10λ ×= =

×

Square loop side length / 4 / 4 94 / 4 23.5 mmL C λ= = = =

Input impedance Zin = 100 Ω

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Week-03: Ch02 Transmission lines and impedance matching (2)

Problem 3.1 Define S11 and S21 of a two-port network.

(Answer)

Probem 3.2 Draw the r =1 circle on the Smith chart.

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Problem 3.3 What is the impedance matching?

(Answer) Transforming of the load impedance into the characteristic impedance of the transmission line

Problem 3.4 List three methods of the impedance matching.

(Answer)

1) Impedance matching with series and parallel lumped elements

2) Impedance matching with series or parallel stubs

3) Impedance matching with a quarter-wave transformer

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Week-02: Ch02 Transmission lines and impedance matching (1)

Problem 2.1 A transmission line (전 전 전 ) has a length L. On what condition can it be treated as a lumped-element

circuit (전 전 전 전 전 전 )?

(Answer) L is much smaller than the wavelength.

Problem 2.2 Draw an lumped-element equivalent circuit (전 전 전 전 ) of a short section of a transmission line.

(Answer)

Problem 2.3 Write down the formulas for the complex propagation contant γ (전 전 전 전 전 전 ) and the characteristic

impeance Z0 (전 전 전 전 전 전 ).

(Answer)

Complex propagation constant:

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Characteristic impedance Z0:

Problem 2.4 Write down the formulas for the reflection coefficient (반사계수) in terms of ZL (전 전 전 전 전 전 ) and Z0

(전 전 전 전 전 전 ).

(Answer)

Problem 2.5 Write down the reflection coefficient Гo of an open circuit, Гs of a short circuit, and Гm of a (matched) load.

(Answer)

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Week-01: Ch01 Introduction

Problem 1.1 Explain the operation of OOK modulation.

(Answer) AM modulation with RF signal on when the modulating digital signal is 1 (high) and RF signal off

when 0.

Problem 1.2 Explain the Fourier transformation of a signal?

(Answer) When a signal is Fourier-transformed, the amplitude and phase of the signal is obtained versus the

frequency.

Problem 1.3 What is the difference between a half-duplex system and a full-duplex system. Give an example

of a full-dulex system.

(Answer)

Half-duplex system: Transmission and reception not at the same time but at different times.

Full-duplex system: Transmission and reception at the same time.

Example of a full-duplex system: Telephone (mobile cellular phone or home wired phone)

Problem 1.4 What do the following acronyms stand for? (spell out each acronym)

a) LNA (low noise amplifier)

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b) PLL (phased locked loop)

c) PA (power amplifier)

d) PD (phase detector)

e) VCO (voltage controlled oscillator)

f) VGA (variable gain amplifier)

g) OSC (oscillator)

Problem 1.5 What is the channel spacing?

(Answer) Frequency separation between communication channels used to avoid interference between

adjacent channels.

Problem 1.6 What is the definition of ACPR?

(Answer) ACPR (adjacent channel power ratio): The ratio of the average power in the adjacent frequency

channel to the average power in the transmitted frequency channel)

Problem 1.7 What is the definition of SNR?

(Answer) SNR (signal to noise ratio): The radio of the signal power to the noise power

Problem 1.8 What is the definition of NF?

(Answer) NF (noise figure): The ratio of the signal-to-noise ratio (SNR) at the output to the SNR at the input

Problem 1.9 What is the difference between the bit rate and the symbol rate?

(Answer)

Bit rate: The number of digital signal bits transmitted per second

Symbol rate: The number of symbols (a symbol is a ground of bits) transmitted per second

Problem 1.10 What is the definition of BER?

(Answer) The ratio of bits in error to the total number of bits received

Problem 1.11 What is the defintion of P1dB?

(Answer) The output power level at which the gain decreases 1dB from its constant gain value