Design a Microstrip Antennas using CAD circuit model

Microstrip Antennas, CAD circuit model

Design a probe-fed rectangular patch antenna on a substrate having a relative permittivity of 2.33 and a thickness of 62 mils (0.1575 cm). (This is Rogers RT Duroid 5870.) Choose an aspect ratio of W / L = 1.5. The patch should resonate at the operating frequency of 1.575 GHz (the GPS L1 frequency). Ignore the probe inductance in your design, but account for fringing at the patch edges when you determine the dimensions. At the operating frequency the input impedance should be 50 Ω (ignoring the probe inductance). Assume an SMA connector is used to feed the patch along the centerline (at y = W / 2), and that the inner conductor of the SMA connector has a radius of 0.635 mm. The copper patch and ground plane have a conductivity of σ = 3.0 ×10^7 S/m and the dielectric substrate has a loss tangent of tanδ = 0.001.

1) Calculate the following: 

 The final patch dimensions L and W (in cm) 

 The feed location x0 (distance of the feed from the closest patch edge, in cm) 

 The bandwidth of the antenna (SWR < 2 definition, expressed in percent) 

 The radiation efficiency of the antenna (accounting for conductor, dielectric, and surface-wave loss, and expressed in percent) 

 The probe reactance Xp at the operating frequency (in Ω) 

 The expected complex input impedance (in Ω) at the operating frequency, accounting for the probe inductance 

 Directivity 

 Gain

2) Plot the input impedance vs. frequency.

MATLAB Code

15 EUR 

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Calculation of second moment of area

MODULAR PROGRAMME COURSEWORK ASSESSMENT SPECIFICATION

Problem: The concrete beam in question has been randomly reinforced with steel rebars as shown in Figure 7, and we need to calculate its second moment of area and neutral axis using code.

Figure 7: Reinforced concrete beam

Methodology: Under tension, ignore the contribution of concrete and calculate the equivalent area of steel rebars according to the Theory; Under compression, both the contribution of concrete and steel rebars would need to be considered which means the Theory needs to be slightly revised if the steel rebars are also under compression.

Inputs: The Young’s modulus of steel Es = 200GPa, and the Young’s modulus of concrete Ec = 25GPa. It is assumed that Es is the same for tension and compression, but Ec can be ignored under tension. The overall cross-sectional dimensions of the reinforced concrete beam are 600mm in width and 140mm in height. A total of 5 steel rebars with a diameter of 16mm are evenly spaced (150mm) horizontally but each of their vertical position through the depth is a random integer between 0 and 140. The direction of the moment My has been given.

Expected outputs:

1. Plot the distribution of 5 steel rebars.

2. Calculate the neutral axis by solving the equation according to the Theory. 

3. Calculate the second moment of area Iyy. 

4. Calculate the maximum tensile stress in the steel rebars and maximum compressive

stress in the concrete under a constant moment of My = 9 kNm

MATLAB Code

25 EUR 

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Structural analysis under variable loads (Structure 4)

MODULAR PROGRAMME COURSEWORK ASSESSMENT SPECIFICATION

When dealing with variable (live) loads the internal forces or reactions that a structure generates will vary according to a probability distribution. In order to determine the design value of a live load, we multiply the characteristic load by a partial safety factor, leading to a design live load value, which represents a worst case scenario associated with that load. However, when multiple loads interact together it might not be evident if applied partial safety factors should amplify or minimise each individual load. A probabilistic analysis has then to be performed, so as to determine how the internal forces or reactions will vary, and determine the output values of these distributions which have a small probability, on an absolute basis, of being exceeded. A workflow of this process is shown in Fig. 1. 

Figure 1: Diagram of probabilistic analysis for a supported beam subjected to two variable uniformly distributed loads (UDL). At the centre, three bending moment diagrams illustrate the variability which can be expected due to the UDL distributions. The histograms represent the distributions of the bending moments at one support and one mid-span of the beam, and the vertical dashed lines are the  corresponding threshold output values.

Structure 4: Reaction force at support 1 and bending moment at 4 towards 2

MATLAB Code

30 EUR 

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Structural analysis under variable loads (Structure 3)

MODULAR PROGRAMME COURSEWORK ASSESSMENT SPECIFICATION

When dealing with variable (live) loads the internal forces or reactions that a structure generates will vary according to a probability distribution. In order to determine the design value of a live load, we multiply the characteristic load by a partial safety factor, leading to a design live load value, which represents a worst case scenario associated with that load. However, when multiple loads interact together it might not be evident if applied partial safety factors should amplify or minimise each individual load. A probabilistic analysis has then to be performed, so as to determine how the internal forces or reactions will vary, and determine the output values of these distributions which have a small probability, on an absolute basis, of being exceeded. A workflow of this process is shown in Fig. 1.

Figure 1: Diagram of probabilistic analysis for a supported beam subjected to two variable uniformly distributed loads (UDL). At the centre, three bending moment diagrams illustrate the variability which can be expected due to the UDL distributions. The histograms represent the distributions of the bending moments at one support and one mid-span of the beam, and the vertical dashed lines are the  corresponding threshold output values.

Structure 3: Vertical reaction at 3 and bending moment at 6 towards 5

MATLAB Code

30 EUR 

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