**4.1 Cylindrical surface with radius of curvature** *r* **= 8 cm**

The four-element microstrip patch antenna array on a cylindrical surface with radius *r* = 8 cm in **Figure 2** was simulated in CST simulator. The inter-element spacing was *L* = λ/2 at *f* = 2.45 GHz. The compensated phases for broadside pattern recovery were computed using Eq. (2) for projection method, and are tabulated in **Table 1**. For uncorrected pattern, the complex weights *wn* = 1∠0° were applied on all antenna elements in CST simulator. Next, the weights (phase correction only) for broadside pattern recovery were calculated using the optimization algorithm in Section 3 and are also tabulated in **Table 1**. The analytical and CST simulation results for *r* = 8 cm are shown in **Figure 4**. Next, the difference in gain (*Gref*) between flat array and compensated gain of conformal array were calculated and are also given in **Table 1**. It can be seen from **Figure 4** and **Table 1** that the broadside compensated gain *Gc* of conformal antenna array is greater than the uncorrected gain and is less than the gain of flat array using both projection and convex optimization (phase correction only) methods. This is the fundamental limitation of both the compensation methods for broadside pattern recovery of conformal antenna arrays and should be kept in mind while designing conformal antenna array. It should be noted that convex optimization has more degrees of freedom than projection method in the sense that convex optimization gives complex weights (amplitude tapering plus phase correction), while projection method gives only phase correction (one degree of freedom). However, for broadside pattern recovery, convex optimization gives uniform amplitudes (equal to 1) and compensated phases and thus its performance is equal to projection method for broadside pattern recovery.


**97**

**Figure 4.**

*Broadside Pattern Correction Techniques for Conformal Antenna Arrays*

**4.2 Cylindrical surface with radii of curvatures** *r* **= 10, 12, 15 cm**

When radii of curvatures of cylindrical surface array increase (less deformation), both the projection and convex optimization (phase correction only) methods recover the broadside radiation pattern with decreasing gap between corrected and uncorrected gains as shown in **Figures 5–7** and are also tabulated in **Table 1**. The gain *Gc* (between uncorrected and corrected) and *Gref* (between corrected and linear) decreases with increase in *r*. However, it is obvious that in all cases, the

*(a) Analytical results for phase compensation of a conformal cylindrical antenna array with r = 8 cm. (b) CST* 

*simulation results for phase compensation of a conformal cylindrical antenna array with r = 8 cm.*

*DOI: http://dx.doi.org/10.5772/intechopen.90957*

## **Table 1.**

*Computed parameters of conformal cylindrical array for various radii of curvatures.*

*Broadside Pattern Correction Techniques for Conformal Antenna Arrays DOI: http://dx.doi.org/10.5772/intechopen.90957*

*Advances in Array Optimization*

The compensated (corrected) weights were computed using projection method in Section 2 and convex optimization in Section 3. The analytical results using Eq. (5)

The four-element microstrip patch antenna array on a cylindrical surface with radius *r* = 8 cm in **Figure 2** was simulated in CST simulator. The inter-element spacing was *L* = λ/2 at *f* = 2.45 GHz. The compensated phases for broadside pattern recovery were computed using Eq. (2) for projection method, and are tabulated in

all antenna elements in CST simulator. Next, the weights (phase correction only) for broadside pattern recovery were calculated using the optimization algorithm in Section 3 and are also tabulated in **Table 1**. The analytical and CST simulation results for *r* = 8 cm are shown in **Figure 4**. Next, the difference in gain (*Gref*) between flat array and compensated gain of conformal array were calculated and are also given in **Table 1**. It can be seen from **Figure 4** and **Table 1** that the broadside compensated gain *Gc* of conformal antenna array is greater than the uncorrected gain and is less than the gain of flat array using both projection and convex optimization (phase correction only) methods. This is the fundamental limitation of both the compensation methods for broadside pattern recovery of conformal antenna arrays and should be kept in mind while designing conformal antenna array. It should be noted that convex optimization has more degrees of freedom than projection method in the sense that convex optimization gives complex weights (amplitude tapering plus phase correction), while projection method gives only phase correction (one degree of freedom). However, for broadside pattern recovery, convex optimization gives uniform amplitudes (equal to 1) and compensated phases and thus its performance is equal to projection method for broadside

*r* **(cm) Parameter Projection method Convex optimization**

*Gc* (dB) 4 *Gref* (dB) 0.53

*Gc* (dB) 2.74 *Gref* (dB) 0.4

*Gc* (dB) 1.765 *Gref* (dB) 0.24

*Gc* (dB) 0.5 *Gref* (dB) 0

*Computed parameters of conformal cylindrical array for various radii of curvatures.*

(deg) [121.67,0,0,121.67] [−89.49,146.95,146.95,-89.49]

(deg) [101.84,0,0,101.84] [−170.44,85.95,85.95,−170.44]

(deg) [86.95,0,0,86.95] [114.61,26.05,26.05,114.61]

(deg) [70.95,0,0,70.95] [9.66,−62.66,−62.66,9.66]

(deg) [36.42,0,0,36.42] [−102.2,−139.3,−139.3,−102.2]

*Gc* (dB) 6.17 6.17 *Gref* (dB) 0.8 0.8

were applied on

and CST simulation results using **Figure 2** are discussed next.

**Table 1**. For uncorrected pattern, the complex weights *wn* = 1∠0°

**4.1 Cylindrical surface with radius of curvature** *r* **= 8 cm**

**96**

**Table 1.**

pattern recovery.

8 δ*<sup>c</sup>*

10 δ*<sup>c</sup>*

12 δ*<sup>c</sup>*

15 δ*<sup>c</sup>*

30 δ*<sup>c</sup>*
