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# hwprob10 - Roblin EE 710 — Homework #1 Problem 1:...

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Unformatted text preview: Roblin EE 710 — Homework #1 Problem 1: Quarter-wave Transformer for Complex Load 1. A 50 Ω transmission line is to be terminated in a load of 50+j50 Ω at 3 GHz. We are going to match this load with a quarter wave transformer. Find the distance ‘ from the load to the transformer and the characteristic impedance Z of the quarter-wave transformer. Use the Smith Chart. Hint: The load impedance seen by the transformer must be pure real. λ/4 Γ 50 Ω l=? Z = ? o 50 Ω 50 Ω 50+j Figure 1: 2. Implement the circuit in ADS using ideal transmission lines. Plot the amplitude of the reflection coefficient ( mag ( S 11 )) from 1 GHz to 5 GHz. Using the optimizer calculates the exact length ‘ and impedance Z required so that the reflection coefficient Γ be zero ( mag ( S 11 ) = 0 ). 3. This transformer is going to be implemented with microstrips and will operate at 3 GHz. Using Linecalc (see Appendix 5.3 of the EE 710 Lab manual) calculate the physical length and width of the required microstrips at 3 GHz. Assume a Duroid substrate with a relative dielectric constant Er =1.98, substrate thickness H =60 mils and dielectric loss tangent T anD =0.0009. Assume that the microstrip lines are realized using a copper layer of thickness of T =1.2 mils and conductivity 4 . 878 × 10 7 Ω- 1 m- 1 . Assume that the metalic top cover is Hu = 3 inches from the microstrip line. Assume that the side walls are infinitely far from the microstrip lines. This is achieved by setting W all 1 = W all 2 = 0 Appendix 5.3 of the EE 710 Microwave Lab manual gives a short tutorial on Linecalc and ADS. A more extensive tutorial is also available on-line at: http://eewww.eng.ohio-state.edu/ads 4. Implement the circuit in ADS using microstrips and optimize the circuit. Plot the amplitude of the reflection coefficient (Γ = mag ( S 11 )) from 0.001 GHz to 6 GHz. Com- pare the performance the microstrip and ideal transmission line circuit performance by plotting | Γ | on a SAME graph . To do so either create a multiport device or simply plot the data of different simulations in a same graph in the display window, by specifying the dataset simulation name in the Plot & Traces Attributes window of your graph. 1 Problem 2:LC transformer and Transmission Line Implementation Given R L = 15Ω and Z = 75Ω, design the transmission-line equivalent of an LC transformer at 4.0 GHz (see Fig. 4.16 of the HW1 Appendix available in the EE710 class webpage and p. 252 in Pozar). Assume Z 01 = 0 . 1 Z 02 , Z 02 = 6 R L , and λ = 0 . 8 λ . Use the approximate design procedure to determine ‘ 1 and ‘ 2 . Compare these values with those obtained from Eqs. 4-14 and 4-15 of the HW1 Appendix. Problem 3: Impact of the Stub Impedance We wish to design a transformer at 4.0 GHz to match a 15 Ω resistor to a 75 Ω transmission line. The transformer used is a single shunt stub tuner. Using the Smith Chart design the transformer with: a) (Design 1) an open shunt stub of impedance 75 Ω....
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## This note was uploaded on 04/30/2011 for the course ECE 710 taught by Professor Roblin during the Spring '11 term at Ohio State.

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hwprob10 - Roblin EE 710 — Homework #1 Problem 1:...

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