課程名稱︰微波系統導論 課程性質︰選修(含複選必修) 課程教師︰吳宗霖 開課學院：電機資訊學院 開課系所︰電機工程學系 考試日期（年月日）︰104.4.21 考試時限（分鐘）：130分鐘 試題 : Microwave and RF Design of Wireless System - Midterm There are 6 problems, with 20 points for each, total 120 points. --------- Problem 1 --------- A lossless transmission line with characteristic impedance Z_0 and propagation delay T can be modeled as a lumped element circuit in term of π-model as shown in Fig.1. (1)Please derive the transmission (ABCD) matrix for the transmission line.[8%] (2)Please derive the transmission (ABCD) matrix for the equivalent circuit.[8%] (3)Please apply Taylor series and compare your answer for (1) and (2). Then express the equivalent L and C in terms of Z_0 and T.[4%] http://i.imgur.com/30aFX9f.jpg --------- Problem 2 --------- (1)For the two-element cascaded circuit shown in Fig.2, prove that the overall noise factor F = F_1 + (F_2－1)/G_1.[10%] http://i.imgur.com/1EnDqfv.jpg (2)Calculate the overall noise figure and gain in decibels for the system (at room temperature,290K) shown in Fig.3. The Boltzmann coefficient k = 1.38 x 10^-23.[10%] http://i.imgur.com/USSFAV1.jpg --------- Problem 3 --------- Fig.4 describes the relationship between input power and output power of signal with radius frequency ω_1 and 2ω_1－ω_2, respectively, for an amplifier. (1)Please write down the definition of "1dB compression point (P_1dB)" and mark it in Fig.4.[4%] (2)Please write down the definition of "third-order intercept point (P_3)" and mark it in Fig.4.[4%] (3)Please write down the definition of "linear dynamic range (DR_l)" and mark it in Fig.4.[4%] (4)Please write down the definition of "spurious-free dynamic range (DR_f)" and mark it in Fig.4.[4%] (5)Please derive the formula of DR_f in terms of P_3 and noise level N_0.[4%] http://i.imgur.com/LWnYIe4.jpg --------- Problem 4 --------- (1)Please derive the Friis equation that describe the relationship between transmitting power P_t and receiving power P_r for a wireless transmission system. Assume that the transmitting and receiving antenna are with gain of G_t, G_r, respectively, and are placed in a distance R. The wavelength of the transmitted signal is λ.[10%] (2)A satellite orbitting 50,000 km above the earth has an antenna with gain of 40 dB and left-hand circular polarization (LHCP). If the receiving station on earth has an antenna with radiation efficiency of 0.8, far-zone electic field pattern of F=(cosθ)^2, polarization factor of 0.8e_R + 0.6e_L, where e_R is the unit vector for right-hand circular polarization (RHCP), and e_L is the unit vector for LHCP. Find the minimum required transmitted power if the received power should be larger than -120dBm. Assume that the main beams of these two antennas are directed to one another, and that operating fre- quency is 20 GHz. Ignore the propagation loss effect.[10%] --------- Problem 5 --------- Consider the receiver system with an antenna shown in Fig.5. The radiated sig- nal from θ= 0 degree at frequency of 1000 MHz is at such a power level S_i= -150 dBm if received by an antenna on Earth whose gain is 0dB. Now the antenna of this system has a gain G_A and background temperature T_B as shown below. The amplifier has a gain G=10dB and noise figure F=3dB while the transmission line has a loss L=6dB. The bandwidth of signal B is 1 kHz. (1)Find the noise temperature T_A of the antenna.[10%] (2)Find the carrier-to-noise ratio (C/N).[10%] http://i.imgur.com/Q0o7j1X.jpg --------- Problem 6 --------- In a RF system, mixer (shown in Fig.6) is a non-linear component to convert the signal frequency. There are three ports in a mixer, IF, LO, and RF. The RF sig- nal is the multiplication of IF and LO signals. For example, a 6 GHz IF signal and a 32 GHz LO signal can lead to 26 GHz and 38 GHz RF signals. Conversion loss is the power transfer efficiency from IF to RF. For example, if 38 GHz is the desired signal, the conversion loss is the power ratio of 38 GHz RF signal and 6 GHz IF signal in dB. LO-RF isolation is the power leakage from LO to RF port measured in dB. http://i.imgur.com/jgjf8yi.jpg Fig.7 is a RF transmitting system. The IF signal is at 6 GHz and with a power of -10 dBm. The LO frequency is 32 GHz and the desired RF frequency is 38 GHz. The conversion loss of the mixer is 5 dB and LO-RF isolation is -20 dB. http://i.imgur.com/NNliecC.jpg We hope the output power is larger than +22 dBm and the undesired tones should be at least 20 dB lower than the main signal (please referred to Fig.8). The PA2 can offer 20 dB gain from 25 GHz to 40 GHz. http://i.imgur.com/AhHZrkA.jpg Please design a filter of this system by using Appendix and Fig.8. Assume the system reference impedance is 50Ω. (1)Specify which kind of filter should be used.(LPF,HPF,BPF,or BSF)[5%] (2)Specify the minimum order of the filter and explain the reason.[5%] (3)Draw the filter with all the parameters on it.[10%] http://i.imgur.com/oT4f9n5.jpg http://i.imgur.com/3qRjfpX.jpg --

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