Ultra Wide Band Antenna with Defected Ground Plane and Microstrip Line Fed for Wi-Fi/Wi-Max/DCS/5G/Satellite Communications

*Ashish Singh, Krishnananda Shet and Durga Prasad*

## **Abstract**

In this chapter, ultra wide band angular ring antenna has been proposed for wireless applications. It has been observed that antenna resonate from 2.9 to 13.1 GHz which has 10.2 GHz bandwidth. Further, it is observed that antenna has nearly omni-directional radiation pattern for E and H-plane at 3.5, 5.8, and 8.5 GHz. The theoretical analysis of the proposed has been done using circuit theory analysis. It was also found using simulation that antenna has good input and output response of 0.2 ns. Proposed antenna measured, simulated, and theoretical results matches for antenna characteristics, i.e., reflection coefficient and radiation pattern. Bandwidth of antenna lies between 2.9 and 13.1 GHz, so this antenna is suitable for Wi-Fi, Wi-Max, digital communication system (DCS), satellite communication, and 5G applications.

**Keywords:** ultra wide band (UWB), angular ring, finite ground plane, microstrip line fed, circuit theory

## **1. Introduction**

Wireless communication systems are highly desired in various fields of security systems, Wi-Fi, Wi-Max, and mobile communication. These applications have special common devices, i.e., an antenna for efficient transmission and reception information. Presently, antennas are equipped in all communication devices and these devices are size and volume constrains. This leads to reduction of size for antenna in existing communication device. All communication devices have patch antennas for transmission and reception of signals. Scientists and researchers are investigating on these antennas since 1972 for reduction in size and increase in bandwidth. To achieve this, numbers of patch antenna designs and techniques were proposed. It was found by researchers that angular ring patch antenna is an efficient antenna which gives both size reduction and increased bandwidth.

Angular ring patch antenna was first reported in year 1985, by IJ Bahal for biomedical application. Thereafter, only few research have been reported on these antennas such as, theory and experiment on the annular-ring microstrip antenna,

shared aperture microstrip patch antenna array for L and S-Bands, analysis of a gap-coupled stacked annular-ring microstrip antenna, compact stacked circularly polarized annular-ring microstrip antenna for GPS applications, annular-ring microstrip patch antenna with finite ground plane for ultra-wideband applications, compact concentric annular-ring patch antenna for triple-frequency operation, comparison of several novel annular-ring microstrip patch antennas for circular polarization, analysis of two-concentric annular-ring microstrip antenna, and broadband circularly polarized annular-ring microstrip antenna [1–10]. All above reported papers has some limitations such as complicated geometry, lacks theoretical analysis for defected ground with microstrip line feed, circuit diagram at Radio frequency were not proposed for designed antenna and theoretical, simulated and experimental results were not compared.

In this chapter, ultra-wideband microstrip patch antenna is proposed for Wi-Fi, Wi-Max, DCS, and 5G applications. Partial ground plane with microstrip line fed techniques is used to achieve UWB band for various wireless applications. Detail descriptions of proposed antenna design are discussed in next section.

## **2. Geometrical consideration**

The microstrip line fed angular ring patch antenna with rectangular ground is shown in **Figure 1** and the antenna is fabricated on FR4 substrate and its top and bottom view is shown in **Figure 2**. The proposed antenna has been designed on FR4 substrate of height "h" and overall dimension of designed geometry is ð Þ <sup>12</sup> � <sup>14</sup> � <sup>1</sup>*:*<sup>57</sup> mm3. The proposed strip line fed angular ring antenna comprises of ground plane of dimension ð Þ *WG* � *LG* , and strip line of dimension ð Þ *WL* � *LL :* Further, antenna is excited via SMA connector fed via strip line. The design specification of complete antenna design is given in **Table 1**. Fabricated antenna picture

> is shown in **Figure 2(b)**. It can be observed from figure that antenna is very compact in size and can be utilized for compact communication devices.

FR-4 lossy, ε<sup>r</sup> 4.4 Radius of angular ring inner, *p* 3.5 mm Radius of angular ring outer, *q* 8.5 mm Circular path, *x* 5.0 mm Strip line length, *LL* 5.0 mm Strip line width, *WL* 3.5 mm Ground plane width, *WG* 2.5 mm Ground plane length, *LG* 12 mm Height of the substrate, *h* 1.57 mm

> *<sup>f</sup>* <sup>¼</sup> *<sup>χ</sup>nm* 2*πp* ffiffiffiffi *ϵr*

where c is the velocity of light in free space, *χnm* ¼ *knmp, knm* is for the resonant

The inner and outer radii of angular ring are given as *pe* ¼ *p* � ð Þ *xe* � *x =*2 and *qe* ¼ *q* � ð Þ *xe* � *x =*2, respectively. The pe, qe, and xe are the effective increase in

The angular ring patch antenna can be represented in circuit diagram as combi-

*<sup>n</sup> k*1*pe*

� � � *Gn*ð Þ *<sup>k</sup>*1*<sup>e</sup> <sup>J</sup>*

0 *<sup>n</sup> k*1*pe*

� � � � , (2)

nation of inductance, capacitance and conductance, as shown in **Figure 3**. The values of inductance *L*, capacitance *C*, and conductance *G* are calculated as.

*Jn*ð Þ *k*1*e G*<sup>0</sup>

p , (1)

The resonating frequency of angular ring [11] is given as

length of inner, outer, and path width, respectively.

*<sup>L</sup>* <sup>¼</sup> *<sup>μ</sup><sup>h</sup> πk*<sup>2</sup> ½ � *n*, *m*

**3. Theoretical investigations**

*Design specification of angular ring antenna.*

*Designed antenna (a) top view (b) fabricated antenna on FR4.*

*DOI: http://dx.doi.org/10.5772/intechopen.91428*

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip…*

TMnm modes.

**121**

**Figure 2.**

**Table 1.**

**Figure 1.** *Radiating structure for proposed antenna.*

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip… DOI: http://dx.doi.org/10.5772/intechopen.91428*

**Figure 2.** *Designed antenna (a) top view (b) fabricated antenna on FR4.*


#### **Table 1.**

shared aperture microstrip patch antenna array for L and S-Bands, analysis of a gap-coupled stacked annular-ring microstrip antenna, compact stacked circularly polarized annular-ring microstrip antenna for GPS applications, annular-ring microstrip patch antenna with finite ground plane for ultra-wideband applications, compact concentric annular-ring patch antenna for triple-frequency operation, comparison of several novel annular-ring microstrip patch antennas for circular polarization, analysis of two-concentric annular-ring microstrip antenna, and broadband circularly polarized annular-ring microstrip antenna [1–10]. All above reported papers has some limitations such as complicated geometry, lacks theoretical analysis for defected ground with microstrip line feed, circuit diagram at Radio frequency were not proposed for designed antenna and theoretical, simulated and

In this chapter, ultra-wideband microstrip patch antenna is proposed for Wi-Fi, Wi-Max, DCS, and 5G applications. Partial ground plane with microstrip line fed techniques is used to achieve UWB band for various wireless applications. Detail

The microstrip line fed angular ring patch antenna with rectangular ground is shown in **Figure 1** and the antenna is fabricated on FR4 substrate and its top and bottom view is shown in **Figure 2**. The proposed antenna has been designed on FR4 substrate of height "h" and overall dimension of designed geometry is

ð Þ <sup>12</sup> � <sup>14</sup> � <sup>1</sup>*:*<sup>57</sup> mm3. The proposed strip line fed angular ring antenna comprises of ground plane of dimension ð Þ *WG* � *LG* , and strip line of dimension ð Þ *WL* � *LL :* Further, antenna is excited via SMA connector fed via strip line. The design specification of complete antenna design is given in **Table 1**. Fabricated antenna picture

descriptions of proposed antenna design are discussed in next section.

experimental results were not compared.

*Modern Printed-Circuit Antennas*

**2. Geometrical consideration**

**Figure 1.**

**120**

*Radiating structure for proposed antenna.*

*Design specification of angular ring antenna.*

is shown in **Figure 2(b)**. It can be observed from figure that antenna is very compact in size and can be utilized for compact communication devices.

## **3. Theoretical investigations**

The resonating frequency of angular ring [11] is given as

$$f = \frac{\chi\_{nm}}{2\pi p\sqrt{c\_r}},\tag{1}$$

where c is the velocity of light in free space, *χnm* ¼ *knmp, knm* is for the resonant TMnm modes.

The inner and outer radii of angular ring are given as *pe* ¼ *p* � ð Þ *xe* � *x =*2 and *qe* ¼ *q* � ð Þ *xe* � *x =*2, respectively. The pe, qe, and xe are the effective increase in length of inner, outer, and path width, respectively.

The angular ring patch antenna can be represented in circuit diagram as combination of inductance, capacitance and conductance, as shown in **Figure 3**. The values of inductance *L*, capacitance *C*, and conductance *G* are calculated as.

$$L = \frac{\mu h}{\pi k^2 [n, m]} \left[ J\_n(k\_1 e) G\_n' \left( k\_1 p\_\epsilon \right) - G\_n(k\_1 e) J\_n' \left( k\_1 p\_\epsilon \right) \right],\tag{2}$$

**Figure 3.** *RF circuit representation of angular ring.*

$$C = \frac{\mu \varepsilon\_0 \varepsilon\_r}{Lk\_1^2},\tag{3}$$

The resonating frequency of the strip line is given as

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip…*

**Figure 5.**

**Figure 6.**

**123**

*RF circuit representation for ground plane.*

*DOI: http://dx.doi.org/10.5772/intechopen.91428*

ε<sup>e</sup> is the effective permittivity of the medium.

*f* ¼ *c=*2*Lse*

RG, inductance LGG, and capacitance CG. The RF circuit representation of the ground plane is shown in **Figure 5**, RG, CG, LGG can be calculated as [12, 13].

> *RG* <sup>¼</sup> *<sup>Q</sup> ω*2 *rCG*

*LGG* <sup>¼</sup> <sup>1</sup>

Quality factor, *<sup>Q</sup>* <sup>¼</sup> *<sup>c</sup>* ffiffiffiffi

Further, there will be strong electromagnetic field between top patch (i.e., angular ring and strip line) and ground plane (rectangular patch). Due to which inductance and capacitance are developed between them and its RF circuit representation is shown in **Figure 6**. Thereafter, on excitation of antenna the impedance is also developed between top and bottom patch [12–14] and represented as,

*jωLee*

*Zee* <sup>¼</sup> <sup>1</sup>*<sup>=</sup>* <sup>1</sup>

*RF circuit diagram of electromagnetically coupled between ground plane and radiating patch.*

*Lee* <sup>¼</sup> *Lg* � *Lan Lg* þ *Lan*

*CGω*<sup>2</sup> *r*

*CG* <sup>¼</sup> *LGWGε*0*ε<sup>e</sup>* 2*LG*

The ground plane patch is represented as RF circuit combination of Resistance

ffiffiffiffiffi

cos <sup>2</sup> *<sup>π</sup> LG*

> *εe* p

*<sup>ε</sup>re* <sup>p</sup> , (8)

� �, (9)

, (10)

, (11)

<sup>4</sup>*fh :* (12)

<sup>þ</sup> *<sup>j</sup>ωCee* � � (13)

þ *Lgan*, (14)

$$G = \frac{\mathbf{1}}{R} = \text{Re}\left[\frac{\pi}{h}\left\{ \left(\frac{E\_p}{E\_x}\right)^2 g(p, p) + \left(\frac{E\_q}{E\_c}\right)^2 g(q, q) - \frac{2E\_p E\_q}{E\_x} \eta(p, q) \right\} \right],\tag{4}$$

$$\text{where } [n, m] = \frac{1}{2k\_1^2} \left[ (k\_1^2 q\_\epsilon - 1) \left\{ I\_n (k\_1 q\_\epsilon) Y\_n' (k\_1 p\_\epsilon) - Y\_n (k\_1 q\_\epsilon) f\_n' (k\_1 p\_\epsilon) \right\} - \epsilon \right]$$

4 *π*2*k*<sup>2</sup> 1*pe k*2 1*q*2 *e* � -1)], *y*(*p,q*) is mutual admittance for angular ring between inner and outer radii, *g*(*p,p*) is conductance across inner periphery of angular ring, *g*(*q,q*) is conductance across outer periphery of angular ring, *Ep* is the radiation field around inner periphery of angular ring, *Eq* is the radiation field at outer periphery of angular ring, *Ez* is the radiation field considered due to ground plane.

Input impedance for the angular ring is given as,

$$Z\_{an} = \frac{1}{G + jo\mathcal{C} + 1/joL},\tag{5}$$

Angular ring is connected to strip line; the strip line can be represented into RF circuit as combination of *Ls*, *Cs*, and *Z0*. The RF circuit of the strip line angular patch antenna is shown in **Figure 4**, where Ls and Cs are inductance and capacitance of strip [12, 13].

$$L\_s = 100h\left(4\sqrt{W\_S/h} - 4.21\right), \text{nH} \tag{6}$$

$$C\_s = W\_s \{ (9.5\varepsilon\_r + 1.25)W\_s/h + 5.2\varepsilon\_r + 7.0 \}, \text{pF} \tag{7}$$

**Figure 4.** *RF circuit diagram for strip line.*

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip… DOI: http://dx.doi.org/10.5772/intechopen.91428*

**Figure 5.** *RF circuit representation for ground plane.*

*<sup>C</sup>* <sup>¼</sup> *μϵ*0*ϵ<sup>r</sup> Lk*<sup>2</sup> 1

> *Eq Ec* � �<sup>2</sup>

� �*Y*<sup>0</sup>

� -1)], *y*(*p,q*) is mutual admittance for angular ring between inner and outer radii, *g*(*p,p*) is conductance across inner periphery of angular ring, *g*(*q,q*) is conductance across outer periphery of angular ring, *Ep* is the radiation field around inner periphery of angular ring, *Eq* is the radiation field at outer periphery of

Angular ring is connected to strip line; the strip line can be represented into RF circuit as combination of *Ls*, *Cs*, and *Z0*. The RF circuit of the strip line angular patch antenna is shown in **Figure 4**, where Ls and Cs are inductance and capacitance of

> *WS=<sup>h</sup>* <sup>p</sup> � <sup>4</sup>*:*<sup>21</sup> � �

*Cs* ¼ *Ws*f g ð Þ 9*:*5*ε<sup>r</sup>* þ 1*:*25 *Ws=h* þ 5*:*2*ε<sup>r</sup>* þ 7*:*0 , pF (7)

" # ( )

*<sup>n</sup> k*1*pe*

*g q*ð Þ� , *q*

� � � *Yn <sup>k</sup>*1*qe*

� � � � �

*g p*ð Þþ , *p*

angular ring, *Ez* is the radiation field considered due to ground plane.

*Zan* <sup>¼</sup> <sup>1</sup>

*Ls* <sup>¼</sup> <sup>100</sup>*<sup>h</sup>* <sup>4</sup> ffiffiffiffiffiffiffiffiffiffiffiffi

<sup>1</sup>*qe* � <sup>1</sup> �� � *Jn <sup>k</sup>*1*qe*

Input impedance for the angular ring is given as,

*<sup>G</sup>* <sup>¼</sup> <sup>1</sup>

4 *π*2*k*<sup>2</sup> 1*pe k*2 1*q*2 *e*

**Figure 3.**

strip [12, 13].

**Figure 4.**

**122**

*RF circuit diagram for strip line.*

where ½ �¼ *<sup>n</sup>*, *<sup>m</sup>* <sup>1</sup>

*<sup>R</sup>* <sup>¼</sup> *Re <sup>π</sup>*

*RF circuit representation of angular ring.*

*Modern Printed-Circuit Antennas*

*h*

2*k*<sup>2</sup> 1 *k*2

*Ep Ez* � �<sup>2</sup> , (3)

*y p*ð Þ , *q*

, (4)

2*EpEq Ez*

> � �*J* 0 *<sup>n</sup> k*1*pe*

*<sup>G</sup>* <sup>þ</sup> *<sup>j</sup>ω<sup>C</sup>* <sup>þ</sup> <sup>1</sup>*=jω<sup>L</sup>* , (5)

, nH (6)

The resonating frequency of the strip line is given as

$$f = \mathfrak{c} / 2L\_{\mathfrak{e}} \sqrt{\mathfrak{e}\_{\mathfrak{re}}},\tag{8}$$

The ground plane patch is represented as RF circuit combination of Resistance RG, inductance LGG, and capacitance CG. The RF circuit representation of the ground plane is shown in **Figure 5**, RG, CG, LGG can be calculated as [12, 13].

$$\mathcal{L}\_G = \frac{L\_G W\_{G} \varepsilon\_0 \varepsilon\_\varepsilon}{2L\_G} \cos^2 \left(\frac{\pi}{L\_G}\right),\tag{9}$$

$$R\_G = \frac{Q}{a\rho\_r^2 C\_G},\tag{10}$$

$$L\_{GG} = \frac{1}{C\_{G}a\_{r}^{2}},\tag{11}$$

$$\text{Quality factor, } Q = \frac{c\sqrt{\varepsilon\_{\varepsilon}}}{4\hbar h}. \tag{12}$$

ε<sup>e</sup> is the effective permittivity of the medium.

Further, there will be strong electromagnetic field between top patch (i.e., angular ring and strip line) and ground plane (rectangular patch). Due to which inductance and capacitance are developed between them and its RF circuit representation is shown in **Figure 6**. Thereafter, on excitation of antenna the impedance is also developed between top and bottom patch [12–14] and represented as,

$$Z\_{\rm ee} = \mathbf{1} / \left[ \frac{\mathbf{1}}{j\alpha L\_{\rm ce}} + j\alpha \mathbf{C}\_{\rm ce} \right] \tag{13}$$

$$L\_{ee} = \frac{L\_{\rm g} \times L\_{am}}{L\_{\rm g} + L\_{am}} + L\_{gm},\tag{14}$$

**Figure 6.**

*RF circuit diagram of electromagnetically coupled between ground plane and radiating patch.*

*Modern Printed-Circuit Antennas*

$$\mathbf{C}\_{\text{ee}} = \frac{\left(\mathbf{C}\_{\text{g}} + \mathbf{C}\_{am}\right) \times \mathbf{C}\_{\text{g}am}}{\mathbf{C}\_{\text{g}} + \mathbf{C}\_{am} + \mathbf{C}\_{\text{g}am}} \tag{15}$$

where Z is the input impedance of the microstrip fed (*50 Ω*).

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip…*

*(a) Comparative results of proposed antenna; (b) measured result on VNA.*

*Input and output response for the excited proposed antenna.*

to frequency (GHz) is plotted.

*DOI: http://dx.doi.org/10.5772/intechopen.91428*

**4. Result and discussion**

**Figure 8.**

**Figure 9.**

**125**

*VSWR* <sup>¼</sup> <sup>1</sup> <sup>þ</sup> j j <sup>Γ</sup>

Using Eqs. (21)–(23) the theoretical plots for RL, VSWR, and RC with respect to frequency (GHz) can be plotted. In this chapter, theoretical plot for RC with respect

The comparison between simulated [14], measured, and theoretical results is shown in **Figure 8(a)**. It is observed from the figure that these three results are in approximately close with each other. Further, the bandwidth of theoretical, measured and simulated results is 10.63, 10.6, and 10.2 GHz, respectively. Bandwidth of antenna lies between 2.9 and 13.1 GHz, these bands are suitable for Wi-Max, Wi-Fi,

<sup>1</sup> � j j <sup>Γ</sup> , (22)

Return loss ðRLÞ ¼ 20 log j j Γ (23)

*Lee* and *Cee* are the equivalent inductance and capacitance developed because of electromagnetic coupling.

*Lan* and *Can* are electromagnetically developed mutual inductance and capacitance for angular ring.

$$\mathcal{L}\_{\text{gan}} = \frac{\mathbf{k}\_{\text{gc}}^2 \left(\mathbf{L}\_{\text{g}} + \mathbf{L}\_{\text{am}}\right) + \left[\mathbf{k}\_{\text{gc}}^4 \left(\mathbf{L}\_{\text{g}} + \mathbf{L}\_{\text{am}}\right)^2 + 4\mathbf{k}\_{\text{g}^c}^4 \left(\mathbf{1} - \mathbf{k}\_{\text{g}^c}^2\right) \mathbf{L}\_{\text{g}} \mathbf{L}\_{\text{am}}\right]^{1/2}}{2\left(\mathbf{1} - \mathbf{k}\_{\text{g}^c}^2\right)},\tag{16}$$

$$\mathbf{C}\_{\text{gen}} = \frac{-\left(\mathbf{C}\_{\text{g}} + \mathbf{C}\_{\text{an}}\right) + \left[\left(\mathbf{C}\_{\text{an}} + \mathbf{C}\_{\text{g}}\right)^{2} + \left(\mathbf{1} - \mathbf{1}/k\_{\text{g}c}^{2}\right)\mathbf{C}\_{\text{an}}\mathbf{C}\_{\text{g}}\right]^{1/2}}{2},\tag{17}$$

$$k\_{\rm gc} = \frac{1}{\sqrt{Q\_{\rm g} Q\_{\rm gg}}},\tag{18}$$

$$Q\_{\rm g} = R\_G \sqrt{\frac{C\_G}{L\_{GG}}},\tag{19}$$

*Qgg* ¼ *Ran* ffiffiffiffiffi *Can Lan* <sup>q</sup> , *Q <sup>g</sup>* and *Q gg* are quality factor for both the resonators, Ran impedance of microstrip.

The input impedance of strip line feed angular ring with defected ground plane and its RF circuit representation is shown in **Figure 7** and is calculated using Eqs. (2)–(19)

$$Z\_{in} = \frac{1}{\frac{1}{Z\_G} + \frac{1}{Z\_l} + \frac{1}{Z\_{au}} + \frac{1}{Z\_w}}\tag{20}$$

Using Eq. (20) the input impedance of proposed has been used to calculate reflection coefficient (RC), return loss (RL) and voltage standing wave ratio (VSWR) can be calculated as,

$$\text{Reflection Coefficient} \,\Gamma = \frac{Z - Z\_{in}}{Z + Z\_{in}},\tag{21}$$

**Figure 7.** *The equivalent RF circuit diagram of microstrip angular patch antenna.*

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip… DOI: http://dx.doi.org/10.5772/intechopen.91428*

where Z is the input impedance of the microstrip fed (*50 Ω*).

$$\text{VSWR} = \frac{\mathbf{1} + |\Gamma|}{\mathbf{1} - |\Gamma|},\tag{22}$$

$$\text{Return loss (RL)} = \text{20} \log |\Gamma| \tag{23}$$

Using Eqs. (21)–(23) the theoretical plots for RL, VSWR, and RC with respect to frequency (GHz) can be plotted. In this chapter, theoretical plot for RC with respect to frequency (GHz) is plotted.

## **4. Result and discussion**

*Cee* <sup>¼</sup> *Cg* <sup>þ</sup> *Can*

*gc Lg* þ *Lan*

electromagnetic coupling.

*Modern Printed-Circuit Antennas*

k2

gc *Lg* þ *Lan* � � <sup>þ</sup> *<sup>k</sup>*<sup>4</sup>

� *Cg* þ *Can*

� � <sup>þ</sup> *Can* <sup>þ</sup> *Cg*

tance for angular ring.

Lgan ¼

*Cgan* ¼

*Qgg* ¼ *Ran*

Eqs. (2)–(19)

**Figure 7.**

**124**

ffiffiffiffiffi *Can Lan* q

impedance of microstrip.

(VSWR) can be calculated as,

� � � *Cgan Cg* þ *Can* þ *Cgan*

*Lee* and *Cee* are the equivalent inductance and capacitance developed because of

*Lan* and *Can* are electromagnetically developed mutual inductance and capaci-

� �<sup>2</sup> <sup>þ</sup> <sup>4</sup>*k*<sup>4</sup>

� �<sup>2</sup> <sup>þ</sup> <sup>1</sup> � <sup>1</sup>*=k*<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffi *QgQgg*

s

ffiffiffiffiffiffiffiffi *CG LGG*

, *Q <sup>g</sup>* and *Q gg* are quality factor for both the resonators, Ran

2 1 � *<sup>k</sup>*<sup>2</sup> *gc*

*kgc* <sup>¼</sup> <sup>1</sup>

*Qg* ¼ *RG*

The input impedance of strip line feed angular ring with defected ground plane and its RF circuit representation is shown in **Figure 7** and is calculated using

> *Zin* <sup>¼</sup> <sup>1</sup> 1 *ZG* <sup>þ</sup> <sup>1</sup> *Zs* <sup>þ</sup> <sup>1</sup> *Zan* <sup>þ</sup> <sup>1</sup> *Zee*

Using Eq. (20) the input impedance of proposed has been used to calculate reflection coefficient (RC), return loss (RL) and voltage standing wave ratio

Reflection Coefficient <sup>Γ</sup> <sup>¼</sup> *<sup>Z</sup>* � *Zin*

*The equivalent RF circuit diagram of microstrip angular patch antenna.*

*Z* þ *Zin*

*gc* <sup>1</sup> � *<sup>k</sup>*<sup>2</sup> *gc* � �

*gc* � �

h i1*=*<sup>2</sup>

h i1*=*<sup>2</sup>

*LgLan*

� � , (16)

*CanCg*

<sup>2</sup> , (17)

<sup>q</sup> , (18)

, (19)

(15)

(20)

, (21)

The comparison between simulated [14], measured, and theoretical results is shown in **Figure 8(a)**. It is observed from the figure that these three results are in approximately close with each other. Further, the bandwidth of theoretical, measured and simulated results is 10.63, 10.6, and 10.2 GHz, respectively. Bandwidth of antenna lies between 2.9 and 13.1 GHz, these bands are suitable for Wi-Max, Wi-Fi,

**Figure 8.** *(a) Comparative results of proposed antenna; (b) measured result on VNA.*

**Figure 9.** *Input and output response for the excited proposed antenna.*

Radiation pattern of the proposed antenna are shown in **Figures 10** and **11** for E and H-plane, respectively. **Figure 10(a)** shows the radiation pattern measurement setup, proposed antenna under test is kept 200 cm apart from the horn antenna. **Figure 10(b)** and **(c)** are measured and simulated radiation pattern at 3.5 and 5.8 GHz, respectively. Measured and simulated radiation pattern are in close agreement in both cases and omni-directional patterns are observed. **Figure 10(d)** shows radiation pattern at center frequency. Major and minor lobes have been observed of same beam width for measured, theoretical, and simulated antenna at center frequency 8.5 GHz for H-plane. **Figure 11(a)–(c)** shows the radiation pattern for Eplane at 3.5, 5.8, and 8.5 GHz, respectively. Antenna shows nearly omni-directional radiation pattern at 3.5 and 5.8 GHz; whereas at 8.5 GHz, it is partially eight shaped. Electric field intensity is more toward 180° for E-plane and antenna 3 dB beam width is 87.4°. Slightly mismatch is observed in radiation pattern results because of partially open anechoic chambers and fabrication defects. It has omni-directional

pattern so this antenna can be utilized for mobile communication.

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip…*

*DOI: http://dx.doi.org/10.5772/intechopen.91428*

**Figure 12.**

**Figure 13.**

**127**

*Current distributions at center frequency at 0° phase.*

*Current distribution at 90° phase.*

**Figures 12**–**14** show the surface current distribution of proposed antenna at center frequency for 90 and 0° phase, respectively. Further, from **Figure 12**, the

#### **Figure 10.**

*Radiation pattern for H-plane (a) anechoic chambers with antennas; (b) 3.5 GHz, (c) 5.8 GHz, and (d) 8.5 GHz.*

**Figure 11.** *Radiation pattern for E-plane (a) 3.5 GHz, (b) 5.8 GHz, and (c) 8.5 GHz.*

digital communication system, satellite communication, and 5G applications. Measured result picture on Vector Network Analyzer (VNA) of proposed antenna is shown in **Figure 8(b)**.

From **Figure 9**, it is observed that maximum input amplitude of the antenna is 1 sqrt W at 0.1 ns time interval, whereas maximum output amplitude is 0.34 sqrt W at a response time of 0.38 ns with phase reversal. The output response is not smooth because angular ring structure with rectangular ground plane.

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip… DOI: http://dx.doi.org/10.5772/intechopen.91428*

Radiation pattern of the proposed antenna are shown in **Figures 10** and **11** for E and H-plane, respectively. **Figure 10(a)** shows the radiation pattern measurement setup, proposed antenna under test is kept 200 cm apart from the horn antenna. **Figure 10(b)** and **(c)** are measured and simulated radiation pattern at 3.5 and 5.8 GHz, respectively. Measured and simulated radiation pattern are in close agreement in both cases and omni-directional patterns are observed. **Figure 10(d)** shows radiation pattern at center frequency. Major and minor lobes have been observed of same beam width for measured, theoretical, and simulated antenna at center frequency 8.5 GHz for H-plane. **Figure 11(a)–(c)** shows the radiation pattern for Eplane at 3.5, 5.8, and 8.5 GHz, respectively. Antenna shows nearly omni-directional radiation pattern at 3.5 and 5.8 GHz; whereas at 8.5 GHz, it is partially eight shaped. Electric field intensity is more toward 180° for E-plane and antenna 3 dB beam width is 87.4°. Slightly mismatch is observed in radiation pattern results because of partially open anechoic chambers and fabrication defects. It has omni-directional pattern so this antenna can be utilized for mobile communication.

**Figures 12**–**14** show the surface current distribution of proposed antenna at center frequency for 90 and 0° phase, respectively. Further, from **Figure 12**, the

**Figure 12.** *Current distribution at 90° phase.*

**Figure 13.** *Current distributions at center frequency at 0° phase.*

digital communication system, satellite communication, and 5G applications. Measured result picture on Vector Network Analyzer (VNA) of proposed antenna is

*Radiation pattern for H-plane (a) anechoic chambers with antennas; (b) 3.5 GHz, (c) 5.8 GHz, and*

From **Figure 9**, it is observed that maximum input amplitude of the antenna is 1 sqrt W at 0.1 ns time interval, whereas maximum output amplitude is 0.34 sqrt W at a response time of 0.38 ns with phase reversal. The output response is not smooth

because angular ring structure with rectangular ground plane.

*Radiation pattern for E-plane (a) 3.5 GHz, (b) 5.8 GHz, and (c) 8.5 GHz.*

shown in **Figure 8(b)**.

**Figure 10.**

*Modern Printed-Circuit Antennas*

*(d) 8.5 GHz.*

**Figure 11.**

**126**

**5. Conclusion**

**Acknowledgements**

antenna in their research lab.

**Author details**

**129**

Udupi, Karnataka, India

Ashish Singh\*, Krishnananda Shet and Durga Prasad

\*Address all correspondence to: ashsin09@rediffmail.com

provided the original work is properly cited.

From the above theoretical analysis, it is found that angular ring patch antenna can be utilized for UWB antenna. Further was observed that antenna cover frequency band between 2.9 and 13.1 GHz which has 125% bandwidth. From the results, it was also observed that antenna has good radiation characteristics and input and output response. Antenna has the gain and efficiency of 2.2 dBi and 70.79%. Simulated, measured, and theoretical results are matching for radiation pattern and reflection coefficient. Further, this antenna is suitable for digital communication system, satellite communication, and 5G applications.

The authors would like to thanks Nitte Education Trust for providing

Dr. K. Krishnamoorthy, Department of Electronics and Communications, National Institute of Technology, Surathkala, for providing measurement faculties of

Department of Electronics and Communication Engineering, N.M.A.M. Institute of Technology (Affiliated to Visvesvaraya Technological University, Belagavi) Nitte,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

the research Grant No. Res/NMAMIT/03. We would like to thank

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip…*

*DOI: http://dx.doi.org/10.5772/intechopen.91428*

**Figure 14.** *Gain and directivity of proposed antenna.*

**Figure 15.** *Radiation efficiency of proposed antenna.*

maximum surface current of 86.4766 A/m is observed at the outer perimeter of angular ring near the edges of strip line and surface current is evenly distributed along length of antenna at 90° phase. Whereas, the surface current at 0° phase is not evenly distributed along the length of antenna and more surface current observed near feed as shown in **Figure 13**.

**Figure 14** shows the gain and directivity of the antenna in dBi. It is observed that maximum gain of 2.75 dBi is achieved at 10.2 GHz; whereas, average gain of antenna is 2.1 dBi. Further, the directivity of the antenna at 10.2 GHz is maximum, i.e., 4.1 dBi and average directivity is 2.98 dBi.

The maximum radiation efficiency is achieved 1.5 dB (70.79%) at 10.2 GHz frequency as observed in **Figure 15** and total radiation efficiency of proposed antenna at 10.2 GHz is found to be (2.2 dB) 60.25%. This is because the loss occurs due to skin effect and conduction loss in antenna device.

*Ultra Wide Band Antenna with Defected Ground Plane and Microstrip… DOI: http://dx.doi.org/10.5772/intechopen.91428*

## **5. Conclusion**

From the above theoretical analysis, it is found that angular ring patch antenna can be utilized for UWB antenna. Further was observed that antenna cover frequency band between 2.9 and 13.1 GHz which has 125% bandwidth. From the results, it was also observed that antenna has good radiation characteristics and input and output response. Antenna has the gain and efficiency of 2.2 dBi and 70.79%. Simulated, measured, and theoretical results are matching for radiation pattern and reflection coefficient. Further, this antenna is suitable for digital communication system, satellite communication, and 5G applications.

## **Acknowledgements**

The authors would like to thanks Nitte Education Trust for providing the research Grant No. Res/NMAMIT/03. We would like to thank Dr. K. Krishnamoorthy, Department of Electronics and Communications, National Institute of Technology, Surathkala, for providing measurement faculties of antenna in their research lab.

## **Author details**

Ashish Singh\*, Krishnananda Shet and Durga Prasad Department of Electronics and Communication Engineering, N.M.A.M. Institute of Technology (Affiliated to Visvesvaraya Technological University, Belagavi) Nitte, Udupi, Karnataka, India

\*Address all correspondence to: ashsin09@rediffmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

maximum surface current of 86.4766 A/m is observed at the outer perimeter of angular ring near the edges of strip line and surface current is evenly distributed along length of antenna at 90° phase. Whereas, the surface current at 0° phase is not evenly distributed along the length of antenna and more surface current observed

maximum gain of 2.75 dBi is achieved at 10.2 GHz; whereas, average gain of antenna is 2.1 dBi. Further, the directivity of the antenna at 10.2 GHz is maximum,

**Figure 14** shows the gain and directivity of the antenna in dBi. It is observed that

The maximum radiation efficiency is achieved 1.5 dB (70.79%) at 10.2 GHz frequency as observed in **Figure 15** and total radiation efficiency of proposed antenna at 10.2 GHz is found to be (2.2 dB) 60.25%. This is because the loss occurs

near feed as shown in **Figure 13**.

*Radiation efficiency of proposed antenna.*

**Figure 14.**

**Figure 15.**

**128**

*Gain and directivity of proposed antenna.*

*Modern Printed-Circuit Antennas*

i.e., 4.1 dBi and average directivity is 2.98 dBi.

due to skin effect and conduction loss in antenna device.

## **References**

[1] Lee KF, Dahele JS. Theory and experiment on the annular-ring microstrip antenna. Annales des Telecommunications. 1985;**40**:508-515

[2] Dhiman J, Sharma A, Khah SK. Shared aperture microstrip patch antenna array for L and S-bands. Progress in Electromagnetics Research Letters. 2019;**86**:91-95

[3] Ansari JA, Ram RB, Singh P. Analysis of a gap-coupled stacked annular ring microstrip antenna. Progress in Electromagnetics Research B. 2008;**4**: 147-158

[4] Ding K, Yu T-B, Zhang Q. A compact stacked circularly polarized annularring microstrip antenna for GPS applications. Progress in Electromagnetics Research Letters. 2013;**40**:171-179

[5] Rawat S, Sharma KK. Annular ring microstrip patch antenna with finite ground plane for ultra-wideband applications. International Journal of Microwave and Wireless Technologies. 2015;**7**(2):179-184

[6] Bao XL, Ammann MJ. Compact concentric annular-ring patch antenna for triple-frequency operation. Electronics Letters. 2006;**42**:1129-1130

[7] Bao XL, Ammann MJ. Comparison of several novel annular-ring microstrip patch antennas for circular polarization. Journal of Electromagnetic Waves and Applications. 2006;**20**:1427-1438

[8] Kanaujia BK, Vishvakarma BR. Analysis of two-concentric annular ring microstrip antenna. Microwave and Optical Technology Letters. 2003;**36**: 104-108

[9] Guo Y-X, Bian L, Shi XQ. Broadband circularly polarized annular-ring microstrip antenna. IEEE Transactions

on Antennas and Propagation. 2009;**57**: 2474-2477

**Chapter 8**

Array Radar

noise figure for active phased array radar.

active phased array radar will be described in detail.

temperature of the two-port linear network is [1].

**2. Noise power and noise figure of two-port network**

active phased array radar

**1. Introduction**

**131**

*Yu Hongbiao*

**Abstract**

Noise Characteristic Analysis of

Noise figure and noise power are detailedly analyzed and deduced in theory for multi-port network in active phased array radar. The mathematical expressions of output noise power and noise figure of network are given out under various conditions. Accordingly, this provides a basis of theories for multi-port network and radar receiver system design, the test method of array noise figure. Finally, two application examples are given to verify the accuracy of the formulae. Making use of these formulas, the designer can use to calculate the dynamic range of the radar receive system, and the designer can also constitute a measure scheme of the array

Multi-Port Network in Phased

**Keywords:** noise power, noise figure, active network, passive network,

In modern active phased array radar, the active antenna array is generally composed of dozens to tens of thousands of active transmit/receive (T/R) modules. However, the feeding of T/R modules (receiving echo signal and transmitting excitation power) is usually realized by a multi-port feeding network. The calculation of noise power and the measurement method of system noise figure of active antenna array including multi-port feed network are essential work for radar system designers and receiver designers. Understanding the analysis and calculation of noise power and noise figure of multi-port network is the basis for design specification such as system dynamic range, so how to correctly analyze and calculate noise power and noise figure of active antenna array is an important factor in radar system design. Next, the analysis and calculation of noise power for multi-port network and the calculation and measurement method of system noise figure in

For a two-port linear network as shown in **Figure 1**, suppose that *G*(*L*) in the figure is the gain (loss) of the two-port network and NF is the noise figure of the two-port linear network. BW is the signal bandwidth, then the equivalent noise

[10] Rasool N, Kama H, Basit MA, Abdullah M. A low profile high gain ultra lightweight circularly polarized annular ring slot antenna for airborne and airship applications. IEEE Access. 2019;**7**:155048-155056

[11] Kumar G, Ray KP. Broadband Microstrip Antenna. USA: Artech House; 2003

[12] Bahal IJ, Bartia P. Microstrip Patch Antenna. USA: Artech House; 1980

[13] Meada M. Analysis of gap in microstrip transmission line. IEEE Transactions on Antennas and Propagation. 1972;**32**:1375-1379

[14] Computer Simulation Technology (CST). Microwave Studio Suite Version. Germany: Dassault Systèmes and Darmstadt; 2018

## **Chapter 8**

**References**

[1] Lee KF, Dahele JS. Theory and experiment on the annular-ring microstrip antenna. Annales des Telecommunications. 1985;**40**:508-515

*Modern Printed-Circuit Antennas*

on Antennas and Propagation. 2009;**57**:

[10] Rasool N, Kama H, Basit MA, Abdullah M. A low profile high gain ultra lightweight circularly polarized annular ring slot antenna for airborne and airship applications. IEEE Access.

[11] Kumar G, Ray KP. Broadband Microstrip Antenna. USA: Artech

[13] Meada M. Analysis of gap in microstrip transmission line. IEEE Transactions on Antennas and Propagation. 1972;**32**:1375-1379

[12] Bahal IJ, Bartia P. Microstrip Patch Antenna. USA: Artech House; 1980

[14] Computer Simulation Technology (CST). Microwave Studio Suite Version. Germany: Dassault Systèmes and

2019;**7**:155048-155056

House; 2003

Darmstadt; 2018

2474-2477

[2] Dhiman J, Sharma A, Khah SK. Shared aperture microstrip patch antenna array for L and S-bands. Progress in Electromagnetics Research

[3] Ansari JA, Ram RB, Singh P. Analysis of a gap-coupled stacked annular ring microstrip antenna. Progress in Electromagnetics Research B. 2008;**4**:

[4] Ding K, Yu T-B, Zhang Q. A compact stacked circularly polarized annularring microstrip antenna for GPS

Electromagnetics Research Letters.

[5] Rawat S, Sharma KK. Annular ring microstrip patch antenna with finite ground plane for ultra-wideband applications. International Journal of Microwave and Wireless Technologies.

[6] Bao XL, Ammann MJ. Compact concentric annular-ring patch antenna

Electronics Letters. 2006;**42**:1129-1130

[7] Bao XL, Ammann MJ. Comparison of several novel annular-ring microstrip patch antennas for circular polarization. Journal of Electromagnetic Waves and Applications. 2006;**20**:1427-1438

[8] Kanaujia BK, Vishvakarma BR. Analysis of two-concentric annular ring microstrip antenna. Microwave and Optical Technology Letters. 2003;**36**:

[9] Guo Y-X, Bian L, Shi XQ. Broadband

circularly polarized annular-ring microstrip antenna. IEEE Transactions

for triple-frequency operation.

Letters. 2019;**86**:91-95

applications. Progress in

2013;**40**:171-179

2015;**7**(2):179-184

104-108

**130**

147-158

## Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar

*Yu Hongbiao*

## **Abstract**

Noise figure and noise power are detailedly analyzed and deduced in theory for multi-port network in active phased array radar. The mathematical expressions of output noise power and noise figure of network are given out under various conditions. Accordingly, this provides a basis of theories for multi-port network and radar receiver system design, the test method of array noise figure. Finally, two application examples are given to verify the accuracy of the formulae. Making use of these formulas, the designer can use to calculate the dynamic range of the radar receive system, and the designer can also constitute a measure scheme of the array noise figure for active phased array radar.

**Keywords:** noise power, noise figure, active network, passive network, active phased array radar

## **1. Introduction**

In modern active phased array radar, the active antenna array is generally composed of dozens to tens of thousands of active transmit/receive (T/R) modules. However, the feeding of T/R modules (receiving echo signal and transmitting excitation power) is usually realized by a multi-port feeding network. The calculation of noise power and the measurement method of system noise figure of active antenna array including multi-port feed network are essential work for radar system designers and receiver designers. Understanding the analysis and calculation of noise power and noise figure of multi-port network is the basis for design specification such as system dynamic range, so how to correctly analyze and calculate noise power and noise figure of active antenna array is an important factor in radar system design. Next, the analysis and calculation of noise power for multi-port network and the calculation and measurement method of system noise figure in active phased array radar will be described in detail.

## **2. Noise power and noise figure of two-port network**

For a two-port linear network as shown in **Figure 1**, suppose that *G*(*L*) in the figure is the gain (loss) of the two-port network and NF is the noise figure of the two-port linear network. BW is the signal bandwidth, then the equivalent noise temperature of the two-port linear network is [1].

**Figure 1.**

*Noise characteristics of a two-port network.*

$$T\_\mathbf{e} = (\mathbf{NF} - \mathbf{1})T\_\mathbf{0} \tag{1}$$

noise power at the input of the passive two-port network, and PNo is the noise

PNoi <sup>¼</sup> *kT*iBW

The equivalent noise temperature of the passive two-port lossy network

The noise power generated by the passive two-port lossy network at the

*L*

*L* þ

Therefore, the total noise power generated by the passive two-port lossy net-

PNoL <sup>¼</sup> <sup>1</sup> � <sup>1</sup>

*kT*0BW <sup>¼</sup> *kT*0BW

**4. Analysis of noise characteristics of multi-port linear passive**

Next, we will analyze the noise characteristics of the multi-port linear passive network as shown in **Figure 3**. It is assumed that the multi-port linear passive network has *n* input ports and one output port, the active power loss of the network

Let the noise temperature of the *j*th input port of the multi-port linear passive

Then the noise power generated by the *j*th input port at the output of the multi-

BW

PNo*<sup>j</sup>* <sup>¼</sup> *k T*<sup>0</sup> <sup>þ</sup> *<sup>T</sup>*ei*<sup>j</sup>*

*T*<sup>i</sup> ¼ *T*<sup>0</sup> þ *T*ei (7)

*T*eL ¼ ð Þ *L* � 1 *T*<sup>0</sup> (10)

*kT*0BW (11)

*<sup>L</sup>* <sup>þ</sup> <sup>1</sup> � <sup>1</sup>

*L kT*0BW

(12)

*kT*eiBW

*T*i*<sup>j</sup>* ¼ *T*<sup>0</sup> þ *T*ei*<sup>j</sup>* (13)

*nL* (14)

*<sup>L</sup>* (9)

PNi ¼ *kT*iBW ¼ *k T*ð Þ <sup>0</sup> þ *T*ei BW (8)

power at the output of the passive two-port network.

*DOI: http://dx.doi.org/10.5772/intechopen.91198*

converted to the input of the two-port network is:

work at the output is PNo ¼ PNoi þ PNoL

*<sup>L</sup>* <sup>þ</sup> <sup>1</sup> � <sup>1</sup>

is *L*, and the signal bandwidth is BW.

port linear passive network is:

*L*

*kT*eiBW *L*

PNo <sup>¼</sup> *kT*iBW

**networks**

network be:

**133**

¼ *kT*0BW þ

The noise power generated by PNi at the network output is:

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar*

Let:

Then:

output is:

where *T*<sup>e</sup> is the equivalent noise temperature and *T*<sup>0</sup> is the room temperature, equal to 290 K.

The white noise power PN0 is [2]:

$$\text{PN}\_0 = kT\_0 \text{BW} \tag{2}$$

where *<sup>k</sup>* is the Boltzmann constant, equal to 1.381� <sup>10</sup>�<sup>23</sup> J/K.

Assuming that the noise temperature of the input port is *T*i, the input noise power PNi is:

$$\text{PN}\_{\text{i}} = kT\_{\text{i}} \text{BW} \tag{3}$$

The noise power PNa of a two-port linear network caused by equivalent noise temperature is:

$$\text{PN}\_{\text{a}} = kT\_{\text{e}} \text{BW} \tag{4}$$

The noise figure NF is expressed by noise power as:

$$\text{NF} = \mathbf{1} + \frac{\text{PN}\_{\mathbf{a}}}{\text{PN}\_{0}} \tag{5}$$

The output noise power PNo of the two-port linear network is:

$$\text{PN}\_{\bullet} = \text{GPN}\_{\text{i}} + \text{GPN}\_{\bullet} \tag{6}$$

Note that *T*<sup>i</sup> in the formula is not necessarily equal to *T*0.

## **3. Analysis of noise characteristics of passive two-port linear network**

We first analyze the noise characteristics of the passive two-port linear network as shown in **Figure 2**. In the figure, *L* is the insertion loss of the passive two-port network, BW is the operating bandwidth of the passive two-port linear network,*T*<sup>i</sup> is the noise temperature at the input of the passive two-port network, PNi is the

**Figure 2.** *Passive two-port linear network.*

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar DOI: http://dx.doi.org/10.5772/intechopen.91198*

noise power at the input of the passive two-port network, and PNo is the noise power at the output of the passive two-port network.

Let:

$$T\_{\text{i}} = T\_{\text{0}} + T\_{\text{ei}} \tag{7}$$

Then:

*T*<sup>e</sup> ¼ ð Þ NF � 1 *T*<sup>0</sup> (1)

PN0 ¼ *kT*0BW (2)

PNi ¼ *kT*iBW (3)

PNa ¼ *kT*eBW (4)

PNo ¼ *G*PNi þ *G*PNa (6)

(5)

where *T*<sup>e</sup> is the equivalent noise temperature and *T*<sup>0</sup> is the room temperature,

Assuming that the noise temperature of the input port is *T*i, the input noise

The noise power PNa of a two-port linear network caused by equivalent noise

NF ¼ 1 þ

**3. Analysis of noise characteristics of passive two-port linear network**

We first analyze the noise characteristics of the passive two-port linear network as shown in **Figure 2**. In the figure, *L* is the insertion loss of the passive two-port network, BW is the operating bandwidth of the passive two-port linear network,*T*<sup>i</sup> is the noise temperature at the input of the passive two-port network, PNi is the

The output noise power PNo of the two-port linear network is:

Note that *T*<sup>i</sup> in the formula is not necessarily equal to *T*0.

PNa PN0

where *<sup>k</sup>* is the Boltzmann constant, equal to 1.381� <sup>10</sup>�<sup>23</sup> J/K.

The noise figure NF is expressed by noise power as:

equal to 290 K.

**Figure 1.**

power PNi is:

temperature is:

**Figure 2.**

**132**

*Passive two-port linear network.*

The white noise power PN0 is [2]:

*Noise characteristics of a two-port network.*

*Modern Printed-Circuit Antennas*

$$\text{PN}\_{\text{i}} = k T\_{\text{i}} \text{BW} = k (T\_0 + T\_{\text{ei}}) \text{BW} \tag{8}$$

The noise power generated by PNi at the network output is:

$$\text{PN}\_{\text{oi}} = \frac{kT\_{\text{i}} \text{BW}}{L} \tag{9}$$

The equivalent noise temperature of the passive two-port lossy network converted to the input of the two-port network is:

$$T\_{\rm eL} = (L - \mathbf{1})T\_0 \tag{10}$$

The noise power generated by the passive two-port lossy network at the output is:

$$\text{PN}\_{\text{oL}} = \left(1 - \frac{1}{L}\right) k T\_0 \text{BW} \tag{11}$$

Therefore, the total noise power generated by the passive two-port lossy network at the output is PNo ¼ PNoi þ PNoL

$$\begin{split} \text{PN}\_{0} &= \frac{kT\_{\text{i}}\text{BW}}{L} + \left(1 - \frac{1}{L}\right) kT\_{0}\text{BW} = \frac{kT\_{0}\text{BW}}{L} + \frac{kT\_{\text{ei}}\text{BW}}{L} + \left(1 - \frac{1}{L}\right) kT\_{0}\text{BW} \\ &= kT\_{0}\text{BW} + \frac{kT\_{\text{ei}}\text{BW}}{L} \end{split} \tag{12}$$

## **4. Analysis of noise characteristics of multi-port linear passive networks**

Next, we will analyze the noise characteristics of the multi-port linear passive network as shown in **Figure 3**. It is assumed that the multi-port linear passive network has *n* input ports and one output port, the active power loss of the network is *L*, and the signal bandwidth is BW.

Let the noise temperature of the *j*th input port of the multi-port linear passive network be:

$$T\_{\circ} = T\_{\bullet} + T\_{\text{e}\circ} \tag{13}$$

Then the noise power generated by the *j*th input port at the output of the multiport linear passive network is:

$$\text{PN}\_{\text{oj}} = \frac{k \left(T\_0 + T\_{\text{e}\circ j}\right) \text{BW}}{nL} \tag{14}$$

**Figure 3.** *Multi-port linear passive network.*

Then the total noise power generated by the *n* input ports at the network output is:

$$\text{PN}\_{\text{on}} = \sum\_{j=1}^{n} \text{PN}\_{\text{oj}} = \frac{k \text{BW}}{nL} \sum\_{j=1}^{n} (T\_0 + T\_{\text{ej}}) = \frac{kT\_0 \text{BW}}{L} + \frac{k \text{BW}}{nL} \sum\_{j=1}^{n} T\_{\text{ej}} \tag{15}$$

The equivalent noise temperature of the multi-port lossy passive network converted to each input is of the same formula (10), and then the noise power generated by the lossy network at the output is:

$$\text{PN}\_{\text{oL}} = \frac{nkT\_{\text{eL}} \text{BW}}{nL} = \left(1 - \frac{1}{L}\right) kT\_0 \text{BW} \tag{16}$$

The equivalent noise temperature of the two-port active network converted to

The equivalent noise temperature of a two-port passive network converted to its input is of the same formula (10). The noise power at the output of the two-port

The noise power PNa at the output of the two-port active network produces the

*L* þ

The noise power generated by the two-port passive network itself at the output is shown in Eq. (11), so the total noise power at the output of the two-port synthetic

*kT*eaBW*G*

following noise power at the output of the passive network:

*Cascade of two-port active network and two-port passive network.*

*DOI: http://dx.doi.org/10.5772/intechopen.91198*

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar*

*G* � 1 *L* 

and the two-port passive network are cascaded is:

NF <sup>¼</sup> PNo

PNo <sup>¼</sup> PNoa <sup>þ</sup> PNoL <sup>¼</sup> *kT*0BW*<sup>G</sup>*

¼ *kT*0BW 1 þ

PNoa <sup>¼</sup> *kT*0BW*<sup>G</sup>*

*L* þ

*kT*eaBW*G*

**6. Analysis of network noise characteristics after cascaded two-port**

Cascade *n* two-port active linear networks and a passive linear network

characteristics of *n* two-port active networks and multi-port passive networks after

As before, we assume that the active power loss of the multi-port passive network is *L*, the noise figure of the *i*th two-port active network is NFi, and the gain is *G*i. To facilitate analysis, if the operating signal bandwidth of both networks is BW,

The total noise figure of the synthetic network after the two-port active network

*G* þ

þ

*kT*0BW*G=<sup>L</sup>* <sup>¼</sup> *<sup>L</sup>* <sup>þ</sup> *<sup>G</sup>* � <sup>1</sup>

with *n* input ports, as shown in **Figure 5**. Next, let's analyze the noise

the equivalent noise temperature of the *i*th two-port active network is:

**active network and multi-port passive network**

*T*ea ¼ ð Þ NF1 � 1 *T*<sup>0</sup> (19)

PNa ¼ *kT*0BW*G* þ *kT*eaBW*G* (20)

*kT*eaBW*G*

*<sup>L</sup>* <sup>þ</sup> <sup>1</sup> � <sup>1</sup>

*T*ea *T*<sup>0</sup>

*L kT*0BW

*<sup>L</sup>* (22)

*L* � 1

*<sup>G</sup>* (23)

¼ NF1 þ

*T*ea*<sup>i</sup>* ¼ ð Þ NF*<sup>i</sup>* � 1 *T*<sup>0</sup> (24)

*<sup>L</sup>* (21)

its input is [3]:

**Figure 4.**

network is:

cascading.

**135**

active network is thus:

The total noise power generated at the output of the multi-port linear passive network is:

$$\text{PN}\_{\text{o}} = \text{PN}\_{\text{o}\text{u}} + \text{PN}\_{\text{o}\text{L}} = kT\_0 \text{BW} + \frac{k \text{BW}}{\text{nL}} \sum\_{j=1}^{n} T\_{\text{e}\text{j}} \tag{17}$$

If *T*ei*<sup>j</sup>* of each input port of the multi-port linear passive network is the same as *T*ei, then:

$$\text{PN}\_{\text{o}} = kT\_0 \text{BW} + \frac{kT\_{\text{ei}} \text{BW}}{L} \tag{18}$$

By comparing Eq. (12) with Eq. (18), we can find that when *T*ei = 0, i.e., each input port of the passive lossy network is connected to a matching load with a noise temperature of *T*0, the noise power generated by the passive lossy network at the output port is equal, i.e., PNo = *kT*0BW.

## **5. Analysis of network noise characteristics after cascade of two-port active network and two-port passive network**

If the two-port active network and the two-port passive network are cascaded, as shown in **Figure 4**, what is the noise characteristic of the cascaded two-port network? For the convenience of analysis, we make the noise figure of the two-port active network to be NF1, the gain *G*, and the insertion loss *L*. For the convenience of analysis, it is assumed that the operating signal bandwidths of both are the same and both are BW.

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar DOI: http://dx.doi.org/10.5772/intechopen.91198*

**Figure 4.**

Then the total noise power generated by the *n* input ports at the network

*T*<sup>0</sup> þ *T*ei*<sup>j</sup>*

The equivalent noise temperature of the multi-port lossy passive network converted to each input is of the same formula (10), and then the noise power

*nL* <sup>¼</sup> <sup>1</sup> � <sup>1</sup>

The total noise power generated at the output of the multi-port linear passive

If *T*ei*<sup>j</sup>* of each input port of the multi-port linear passive network is the same as

By comparing Eq. (12) with Eq. (18), we can find that when *T*ei = 0, i.e., each input port of the passive lossy network is connected to a matching load with a noise temperature of *T*0, the noise power generated by the passive lossy network at the

**5. Analysis of network noise characteristics after cascade of two-port**

If the two-port active network and the two-port passive network are cascaded, as shown in **Figure 4**, what is the noise characteristic of the cascaded two-port network? For the convenience of analysis, we make the noise figure of the two-port active network to be NF1, the gain *G*, and the insertion loss *L*. For the convenience of analysis, it is assumed that the operating signal bandwidths of both are the same

� � <sup>¼</sup> *kT*0BW

*L* þ

*L* � �

*kT*eiBW

*k*BW n*L*

X*n j*¼1

*k*BW *nL*

X*n j*¼1

*kT*0BW (16)

*<sup>L</sup>* (18)

*T*ei*<sup>j</sup>* (17)

*T*ei*<sup>j</sup>* (15)

output is:

**Figure 3.**

network is:

*T*ei, then:

and both are BW.

**134**

PNo*<sup>n</sup>* <sup>¼</sup> <sup>X</sup>*<sup>n</sup>*

*Multi-port linear passive network.*

*Modern Printed-Circuit Antennas*

*j*¼1

PNo*<sup>j</sup>* <sup>¼</sup> *<sup>k</sup>*BW *nL*

generated by the lossy network at the output is:

output port is equal, i.e., PNo = *kT*0BW.

**active network and two-port passive network**

X*n j*¼1

PNoL <sup>¼</sup> *nkT*eLBW

PNo ¼ PNo*<sup>n</sup>* þ PNoL ¼ *kT*0BW þ

PNo ¼ *kT*0BW þ

*Cascade of two-port active network and two-port passive network.*

The equivalent noise temperature of the two-port active network converted to its input is [3]:

$$T\_{\mathbf{ea}} = (\mathbf{NF\_1} - \mathbf{1})T\_0 \tag{19}$$

The equivalent noise temperature of a two-port passive network converted to its input is of the same formula (10). The noise power at the output of the two-port active network is thus:

$$\text{PN}\_{\text{a}} = kT\_0 \text{BWG} + kT\_{\text{ea}} \text{BWG} \tag{20}$$

The noise power PNa at the output of the two-port active network produces the following noise power at the output of the passive network:

$$\text{PN}\_{\text{oa}} = \frac{kT\_0 \text{BWG}}{L} + \frac{kT\_{\text{ea}} \text{BWG}}{L} \tag{21}$$

The noise power generated by the two-port passive network itself at the output is shown in Eq. (11), so the total noise power at the output of the two-port synthetic network is:

$$\begin{split} \text{PN}\_{\text{o}} &= \text{PN}\_{\text{oa}} + \text{PN}\_{\text{oL}} = \frac{kT\_0 \text{BWG}}{L} + \frac{kT\_{\text{ea}} \text{BWG}}{L} + \left(1 - \frac{1}{L}\right) kT\_0 \text{BW} \\ &= kT\_0 \text{BW} \left(1 + \frac{G-1}{L}\right) + \frac{kT\_{\text{ea}} \text{BWG}}{L} \end{split} \tag{22}$$

The total noise figure of the synthetic network after the two-port active network and the two-port passive network are cascaded is:

$$\text{NF} = \frac{\text{PN}\_o}{kT\_0 \text{BWG}/L} = \frac{L+G-1}{G} + \frac{T\_{\text{ea}}}{T\_0} = \text{NF}\_1 + \frac{L-1}{G} \tag{23}$$

## **6. Analysis of network noise characteristics after cascaded two-port active network and multi-port passive network**

Cascade *n* two-port active linear networks and a passive linear network with *n* input ports, as shown in **Figure 5**. Next, let's analyze the noise characteristics of *n* two-port active networks and multi-port passive networks after cascading.

As before, we assume that the active power loss of the multi-port passive network is *L*, the noise figure of the *i*th two-port active network is NFi, and the gain is *G*i. To facilitate analysis, if the operating signal bandwidth of both networks is BW, the equivalent noise temperature of the *i*th two-port active network is:

$$T\_{\text{eui}} = (\mathbf{NF}\_i - \mathbf{1})T\_0 \tag{24}$$

**Figure 5.** *Cascade of n two-port active networks and multi-port passive networks.*

The noise power of the *i*th two-port active network at its output is:

$$\text{PNN}\_{\text{ai}} = kT\_0 \text{BW} G\_{\text{i}} + kT\_{\text{ea}} \text{BW} G\_{\text{i}} \tag{25}$$

**6.1 Analysis of noise characteristics of active and passive synthetic networks with** *n* � **1 input ports connected to a matching load with a noise**

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar*

into a two-port network, but the total noise power at its output remains unchanged, the same as Eq. (27). At this time, the total noise figure NF of the

> . *kT*0BW*Gi nL* � �

> > *k*BW *nL*

1 þ *T*ea*<sup>i</sup> T*<sup>0</sup> � �*Gi* " #.

> *T*ea*<sup>i</sup> T*<sup>0</sup> þ *L* � 1 *G*

� �

**6.2 It is stated in Section 6.1 that if** *n* � **1 two-port active networks are not operating, the noise characteristics of the synthetic network are analyzed**

ports in the synthetic network are connected to a matching load with a noise temperature of *T*<sup>0</sup> and the *n* � 1 active networks do not operating, what will happen to the noise characteristics of the synthetic network at this time? In order to facilitate the analysis, it is assumed that the two-port active network matches the passive network in both operating and nonoperating states. At this time, the synthetic network degenerates into a two-port network with *nL* loss. As mentioned in Section 5, the noise power of the two-port active network at the output port of the synthetic

PNoa <sup>¼</sup> *kT*0BW*<sup>G</sup>*

*nL* <sup>þ</sup> ð Þ *<sup>n</sup>* � <sup>1</sup> *kT*0BW

Then the total noise power at that output port of the synthetic network is:

Following the previous analysis, when the *n* � 1 two-port active network input

*nL* þ

As mentioned in Section 4, the noise power of the passive network at the output

X*n i*¼1

( ) " # . *kT*0BW*Gi*

If the gain and noise figure of the two-port active network are the same (*Gi* = *G*,

ð Þ *T*<sup>0</sup> þ *T*ea*<sup>i</sup> Gi*

¼ *n* NF1 þ

*kT*eaBW*G*

*nL* <sup>¼</sup> *kT*0BW 1 � <sup>1</sup>

*nL* <sup>þ</sup> <sup>1</sup> � <sup>1</sup>

*nL* � �

*Gi* (30)

*L* � 1 *G*

� � (31)

*nL* (32)

*nL* � � *kT*0BW (34)

*nL* � � (33)

The previous analysis is to analyze the noise characteristics of *n* two-port active networks under normal operation. If the *n* � 1 input ports of the synthesis network are connected to a matching load with a noise temperature of *T*<sup>0</sup> and all two-port active networks operate normally, what will happen to the noise characteristics of the synthesis network? At this time, the multi-port synthesis network degenerates

**temperature of** *T***<sup>0</sup>**

*DOI: http://dx.doi.org/10.5772/intechopen.91198*

synthesis network is:

NF <sup>¼</sup> PNo

network is:

**137**

port of the synthetic network is:

PNoL <sup>¼</sup> *nk L*ð Þ � <sup>1</sup> *<sup>T</sup>*0BW

PNo <sup>¼</sup> PNoa <sup>þ</sup> PNoL <sup>¼</sup> *k T*ð Þ <sup>0</sup> <sup>þ</sup> *<sup>T</sup>*ea BW*<sup>G</sup>*

*kT*0BW*G*<sup>Σ</sup>

*L* � � *kT*0BW <sup>þ</sup>

<sup>¼</sup> *n L*ð Þ � <sup>1</sup> *<sup>=</sup>Gi* <sup>þ</sup> <sup>X</sup>*<sup>n</sup>*

NF*<sup>i</sup>* = NF1), the above equation becomes:

<sup>¼</sup> <sup>1</sup> � <sup>1</sup>

¼ PNo

*i*¼1

NF ¼ *n* 1 þ

The noise power generated by the *i*th two-port active network at the output of the passive network is:

$$\text{PN}\_{\text{out}} = \frac{kT\_0 \text{BW} G\_i + kT\_{\text{cal}} \text{BW} G\_i}{nL} \tag{26}$$

The total noise power at the output of the synthesis network is obtained from Eqs. (16) and (26):

$$\begin{split} \text{PN}\_{o} &= \text{PN}\_{o\text{L}} + \sum\_{i=1}^{n} \text{PN}\_{oai} = \left(1 - \frac{1}{L}\right) k T\_{0} \text{BW} + \sum\_{i=1}^{n} \frac{k T\_{0} \text{BWG}\_{i} + k T\_{\text{eui}} \text{BWG}\_{i}}{nL} \\ &= \left(1 - \frac{1}{L}\right) k T\_{0} \text{BW} + \left[\frac{k \text{BW}}{nL} \sum\_{i=1}^{n} (T\_{0} + T\_{\text{eui}}) \text{G}\_{i}\right] \end{split} \tag{27}$$

We can calculate the total noise figure NF of the synthetic network as follows:

$$\begin{split} \text{NF} &= \frac{\text{PN}\_{o}}{kT\_{0}\text{BWG}\_{\Sigma}} = \text{PN}\_{o} \Big/ \left( kT\_{0} \text{BW} \sum\_{i=1}^{n} \frac{G\_{i}}{nL} \right) \\ &= \left\{ \left( 1 - \frac{1}{L} \right) kT\_{0} \text{BW} + \left[ \frac{k \text{BW}}{nL} \sum\_{i=1}^{n} (T\_{0} + T\_{\text{eai}}) G\_{i} \right] \right\} \Big/ \left( kT\_{0} \text{BW} \sum\_{i=1}^{n} \frac{G\_{i}}{nL} \right) \\ &= n(L - 1) \Big/ \sum\_{i=1}^{n} G\_{i} + \left[ \sum\_{i=1}^{n} \left( 1 + \frac{T\_{\text{eai}}}{T\_{0}} \right) G\_{i} \right] \Big/ \sum\_{i=1}^{n} G\_{i} \end{split} \tag{28}$$

where *G*P is the gain of the synthetic network.

If the gain and noise figure of the two-port active network are the same, i.e., *Gi* = *G* and NF*<sup>i</sup>* = NF1, then Eq. (28) is simplified as:

$$\text{NF} = \mathbf{1} + \frac{T\_{\text{eui}}}{T\_0} + \frac{L-\mathbf{1}}{G} = \text{NF}\_1 + \frac{L-\mathbf{1}}{G} \tag{29}$$

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar DOI: http://dx.doi.org/10.5772/intechopen.91198*

## **6.1 Analysis of noise characteristics of active and passive synthetic networks with** *n* � **1 input ports connected to a matching load with a noise temperature of** *T***<sup>0</sup>**

The previous analysis is to analyze the noise characteristics of *n* two-port active networks under normal operation. If the *n* � 1 input ports of the synthesis network are connected to a matching load with a noise temperature of *T*<sup>0</sup> and all two-port active networks operate normally, what will happen to the noise characteristics of the synthesis network? At this time, the multi-port synthesis network degenerates into a two-port network, but the total noise power at its output remains unchanged, the same as Eq. (27). At this time, the total noise figure NF of the synthesis network is:

$$\begin{split} \text{NF} &= \frac{\text{PN}\_{o}}{kT\_{0}\text{BWG}\_{\Sigma}} = \text{PN}\_{o} \Big/ \left(\frac{kT\_{0}\text{BWG}\_{i}}{nL}\right) \\ &= \left\{ \left(1 - \frac{1}{L}\right) kT\_{0}\text{BW} + \left[\frac{k\text{BW}}{nL}\sum\_{i=1}^{n} (T\_{0} + T\_{\text{eai}})G\_{i}\right] \right\} \Big/ \left(\frac{kT\_{0}\text{BWG}\_{i}}{nL}\right) \\ &= n(L-1)/G\_{i} + \left[\sum\_{i=1}^{n} \left(1 + \frac{T\_{\text{eai}}}{T\_{0}}\right) G\_{i}\right] \Big/ G\_{i} \end{split} \tag{30}$$

If the gain and noise figure of the two-port active network are the same (*Gi* = *G*, NF*<sup>i</sup>* = NF1), the above equation becomes:

$$\text{NF} = n\left(\mathbf{1} + \frac{T\_{\text{ea}}}{T\_0} + \frac{L-1}{G}\right) = n\left(\text{NF}\_1 + \frac{L-1}{G}\right) \tag{31}$$

## **6.2 It is stated in Section 6.1 that if** *n* � **1 two-port active networks are not operating, the noise characteristics of the synthetic network are analyzed**

Following the previous analysis, when the *n* � 1 two-port active network input ports in the synthetic network are connected to a matching load with a noise temperature of *T*<sup>0</sup> and the *n* � 1 active networks do not operating, what will happen to the noise characteristics of the synthetic network at this time? In order to facilitate the analysis, it is assumed that the two-port active network matches the passive network in both operating and nonoperating states. At this time, the synthetic network degenerates into a two-port network with *nL* loss. As mentioned in Section 5, the noise power of the two-port active network at the output port of the synthetic network is:

$$\text{PN}\_{\text{oa}} = \frac{kT\_0 \text{BWG}}{nL} + \frac{kT\_{\text{ea}} \text{BWG}}{nL} \tag{32}$$

As mentioned in Section 4, the noise power of the passive network at the output port of the synthetic network is:

$$\text{PN}\_{\text{oL}} = \frac{nk(L-1)T\_0 \text{BW}}{nL} + \frac{(n-1)kT\_0 \text{BW}}{nL} = kT\_0 \text{BW} \left(1 - \frac{1}{nL}\right) \tag{33}$$

Then the total noise power at that output port of the synthetic network is:

$$\text{PN}\_{\text{o}} = \text{PN}\_{\text{ca}} + \text{PN}\_{\text{oL}} = \frac{k(T\_0 + T\_{\text{ea}})\text{BWG}}{nL} + \left(1 - \frac{1}{nL}\right)kT\_0\text{BW} \tag{34}$$

The noise power of the *i*th two-port active network at its output is:

the passive network is:

*Modern Printed-Circuit Antennas*

**Figure 5.**

Eqs. (16) and (26):

PNo <sup>¼</sup> PNoL <sup>þ</sup>X*<sup>n</sup>*

<sup>¼</sup> <sup>1</sup> � <sup>1</sup> *L* � �

NF <sup>¼</sup> PNo

*kT*0BW*G*<sup>Σ</sup>

*L* � �

> .X*<sup>n</sup> i*¼1

<sup>¼</sup> <sup>1</sup> � <sup>1</sup>

¼ *n L*ð Þ � 1

**136**

*i*¼1

*kT*0BW þ

¼ PNo

*kT*0BW þ

where *G*P is the gain of the synthetic network.

*Gi* = *G* and NF*<sup>i</sup>* = NF1, then Eq. (28) is simplified as:

NF ¼ 1 þ

PNoa*<sup>i</sup>* <sup>¼</sup> <sup>1</sup> � <sup>1</sup>

*Cascade of n two-port active networks and multi-port passive networks.*

*L* � �

> X*n i*¼1

" #

*k*BW *nL*

.

*Gi* <sup>þ</sup> <sup>X</sup>*<sup>n</sup>*

*i*¼1

*T*ea*<sup>i</sup> T*<sup>0</sup> þ *L* � 1

The noise power generated by the *i*th two-port active network at the output of

PNoa*<sup>i</sup>* <sup>¼</sup> *kT*0BW*Gi* <sup>þ</sup> *kT*ea*<sup>i</sup>*BW*Gi*

The total noise power at the output of the synthesis network is obtained from

*kT*0BW <sup>þ</sup>X*<sup>n</sup>*

ð Þ *T*<sup>0</sup> þ *T*ea*<sup>i</sup> Gi*

We can calculate the total noise figure NF of the synthetic network as follows:

*i*¼1

*Gi nL*

ð Þ *T*<sup>0</sup> þ *T*ea*<sup>i</sup> Gi*

*i*¼1 *Gi*

*L* � 1

*Gi* " #,X*<sup>n</sup>*

*<sup>G</sup>* <sup>¼</sup> NF1 <sup>þ</sup>

*kT*0BWX*<sup>n</sup>*

X*n i*¼1

If the gain and noise figure of the two-port active network are the same, i.e.,

*k*BW *nL*

> 1 þ *T*ea*<sup>i</sup> T*<sup>0</sup> � �

( " #),

!

*i*¼1

PNa*<sup>i</sup>* ¼ *kT*0BW*Gi* þ *kT*ea*<sup>i</sup>*BW*Gi* (25)

*nL* (26)

*kT*0BW*Gi* þ *kT*ea*<sup>i</sup>*BW*Gi nL*

*kT*0BWX*<sup>n</sup>*

*<sup>G</sup>* (29)

!

*i*¼1

*Gi nL*

(28)

(27)

The noise figure NF of the synthetic network is:

$$\text{NF} = \frac{\text{PN}\_o}{kT\_0 \text{BWG}\_\Sigma} = \text{PN}\_o / \left(\frac{kT\_0 \text{BWG}}{nL}\right) = \left(1 + \frac{T\_{\text{eai}}}{T\_0} + \frac{nL - 1}{G}\right) = \text{NF}\_1 + \frac{nL - 1}{G} \tag{35}$$

Next, we will calculate the dynamic range of the output signal of the synthesis

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar*

We assume that the input signal power received by each T/R module of the array is �105 dBm and the phases of the input signals are the same, then the output signal

The input dynamic range of signal power relative noise power (regardless of

After the signal is synthesized by the network, the output dynamics of the signal

Note that when calculating the input and output noise power above, the band-

Through the calculation of the above practical examples, we can draw a conclusion that when calculating the dynamic range of the network output signals synthesized by the active network and the multi-port passive in-phase network, we must remember that the total noise power output by the network is not added, only the in-phase signals can be added, and the dynamic range of the signal to noise will

In the active phased array radar, we design a T/R module, which consists of four identical receiving channels. Finally, the four receiving channels are output through a 4:1 power synthesis network. How to measure the noise figure of the T/R module in practical engineering application? Our common noise figure instruments, such as HP8970B and Agilent N8975A, have only one noise source. At first, engineers measured the noise figure of each receiving channel to be about 8 dB under the condition of normal operation of the four channels. This measurement data is quite different from the actual design specification, and there are obvious problems. Later, when measuring the noise figure of one receiving channel, we turned off the other three receiving channels and measured the noise figure of each channel in turn. At this time, the noise figure of each channel was measured to be about 2 dB,

**7.2 Method for testing noise figure of synthesis network after cascading**

It is not difficult for us to understand the above phenomena by using the previous analysis and derivation results. Obviously, it can be seen from Eq. (29) that the noise figure of the synthetic network is basically close to that of a single active channel (when *G* is much larger than *nL*). Looking at Eq. (31), we find that when all four channels are operating, if we measure the noise figure of one channel, it will increase by *n* times than the theoretical value, where *n* is 4, i.e. 6 dB, so the noise figure we measure is about 8 dB. When one receiving channel is measured and the other three receiving channels are turned off, the noise figure measured at this time is the result given by Eq. (35), and the measurement result is close to the noise figure of a single active channel (when *G* is much larger than *nL*). Therefore, when

**two-port active network and multi-port passive network**

*S*<sup>o</sup> ¼ �105 þ 25–5 þ 18 ¼ �67 dBm (40)

DRi ¼ �105 � �ð Þ¼ 14 þ 6 3 dB (41)

DRo ¼ �67 � �ð Þ¼ 86 19 dB (42)

network.

power of the synthesis network is:

*DOI: http://dx.doi.org/10.5772/intechopen.91198*

noise introduced by antenna) is:

power relative noise power is as follows:

width of both must be the same; both are 4 MHz.

increase after passing through the synthesized network.

and the result basically met the design requirements.

**139**

when *n* = 1, the synthetic network degrades to section 5 state, that is, the cascade of two-port active network and two-port passive network.

## **7. Design, application, and verification**

### **7.1 Calculation of array receiving dynamics of phased array radar**

An active phased array radar is composed of 64 identical T/R modules and a 64:1 multi-port passive in-phase power synthesis network. Its structure is similar to that of **Figure 5**. In the engineering design, the design specification of the gain and noise figure of all T/R modules are the same, so we use the same noise figure NF1 and gain *G* in the analysis and calculation. The error caused by the inconsistent indexes of different T/R modules is always acceptable and reasonable in the engineering design and calculation. Then the total noise power of the synthetic output received by the radar array can be calculated from Eq. (27):

$$\text{PN}\_0 = kT\_0 \text{BW} \left( \frac{\text{NF}\_1 G}{L} + \mathbf{1} - \frac{\mathbf{1}}{L} \right) \tag{36}$$

Using Eq. (29), NF1 is expressed by the total noise figure NF of the synthesis network and substituted into the simplified equation above to obtain:

$$\text{PN}\_{\text{o}} = kT\_0 \text{BW} \frac{\text{NFG}}{L} \tag{37}$$

Assuming that the baseband signal bandwidth of the receiver is 4 MHz, the noise figure of the T/R module is 2 dB, the gain is 25 dB, and the active power loss of the 64:1 power synthesis network is 5 dB, the total output noise power of the synthesis network can be calculated by using Eq. (36) as follows:

$$\text{PN}\_{\bullet} = -\mathbf{1}\mathbf{1}\mathbf{4} + \mathbf{6} + \mathbf{2}\mathbf{2}.\mathbf{02} = -\mathbf{85}.\mathbf{98} \text{ dBm} \tag{38}$$

In order to facilitate calculation in engineering application, we use T/R module noise figure NF1 to replace the total noise figure NF of the synthesis network and use Eq. (37) to calculate the total output noise power of the synthesis network, then:

$$\text{PN}\_{\text{o}} = -\mathbf{1}\mathbf{1} \mathbf{4} + \mathbf{6} + \mathbf{2} + \mathbf{25} \mathbf{5} = -\mathbf{86} \text{ dBm} \tag{39}$$

We compare the calculation results of the above two different methods and find that the difference between them is only 0.02 dB. Therefore, as long as the gain of the active network is much larger than the active power loss of the passive network in engineering application, the error caused by using the noise figure of the active network instead of the noise figure of the synthesis network to calculate the total output noise power of the synthesis network can be ignored, which is enough to meet the requirements of engineering design.

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar DOI: http://dx.doi.org/10.5772/intechopen.91198*

Next, we will calculate the dynamic range of the output signal of the synthesis network.

We assume that the input signal power received by each T/R module of the array is �105 dBm and the phases of the input signals are the same, then the output signal power of the synthesis network is:

$$S\_o = -105 + 25 \text{--} 5 + 18 = -67 \text{ dBm} \tag{40}$$

The input dynamic range of signal power relative noise power (regardless of noise introduced by antenna) is:

$$\text{DR}\_{\text{i}} = -\mathbf{105} - (-\mathbf{14} + \mathbf{6}) = \mathbf{3} \,\text{dB} \tag{41}$$

After the signal is synthesized by the network, the output dynamics of the signal power relative noise power is as follows:

$$\text{DR}\_0 = -\mathsf{67} - (-\mathsf{86}) = \mathsf{19}\ \text{dB} \tag{42}$$

Note that when calculating the input and output noise power above, the bandwidth of both must be the same; both are 4 MHz.

Through the calculation of the above practical examples, we can draw a conclusion that when calculating the dynamic range of the network output signals synthesized by the active network and the multi-port passive in-phase network, we must remember that the total noise power output by the network is not added, only the in-phase signals can be added, and the dynamic range of the signal to noise will increase after passing through the synthesized network.

## **7.2 Method for testing noise figure of synthesis network after cascading two-port active network and multi-port passive network**

In the active phased array radar, we design a T/R module, which consists of four identical receiving channels. Finally, the four receiving channels are output through a 4:1 power synthesis network. How to measure the noise figure of the T/R module in practical engineering application? Our common noise figure instruments, such as HP8970B and Agilent N8975A, have only one noise source. At first, engineers measured the noise figure of each receiving channel to be about 8 dB under the condition of normal operation of the four channels. This measurement data is quite different from the actual design specification, and there are obvious problems. Later, when measuring the noise figure of one receiving channel, we turned off the other three receiving channels and measured the noise figure of each channel in turn. At this time, the noise figure of each channel was measured to be about 2 dB, and the result basically met the design requirements.

It is not difficult for us to understand the above phenomena by using the previous analysis and derivation results. Obviously, it can be seen from Eq. (29) that the noise figure of the synthetic network is basically close to that of a single active channel (when *G* is much larger than *nL*). Looking at Eq. (31), we find that when all four channels are operating, if we measure the noise figure of one channel, it will increase by *n* times than the theoretical value, where *n* is 4, i.e. 6 dB, so the noise figure we measure is about 8 dB. When one receiving channel is measured and the other three receiving channels are turned off, the noise figure measured at this time is the result given by Eq. (35), and the measurement result is close to the noise figure of a single active channel (when *G* is much larger than *nL*). Therefore, when

The noise figure NF of the synthetic network is:

<sup>¼</sup> PNo*<sup>=</sup> kT*0BW*<sup>G</sup>*

of two-port active network and two-port passive network.

**7. Design, application, and verification**

radar array can be calculated from Eq. (27):

*nL* 

**7.1 Calculation of array receiving dynamics of phased array radar**

PNo <sup>¼</sup> *kT*0BW NF1*<sup>G</sup>*

network and substituted into the simplified equation above to obtain:

network can be calculated by using Eq. (36) as follows:

meet the requirements of engineering design.

**138**

Using Eq. (29), NF1 is expressed by the total noise figure NF of the synthesis

PNo <sup>¼</sup> *kT*0BWNF*<sup>G</sup>*

Assuming that the baseband signal bandwidth of the receiver is 4 MHz, the noise figure of the T/R module is 2 dB, the gain is 25 dB, and the active power loss of the 64:1 power synthesis network is 5 dB, the total output noise power of the synthesis

In order to facilitate calculation in engineering application, we use T/R module noise figure NF1 to replace the total noise figure NF of the synthesis network and use Eq. (37) to calculate the total output noise power of the synthesis network, then:

We compare the calculation results of the above two different methods and find that the difference between them is only 0.02 dB. Therefore, as long as the gain of the active network is much larger than the active power loss of the passive network in engineering application, the error caused by using the noise figure of the active network instead of the noise figure of the synthesis network to calculate the total output noise power of the synthesis network can be ignored, which is enough to

¼ 1 þ

when *n* = 1, the synthetic network degrades to section 5 state, that is, the cascade

An active phased array radar is composed of 64 identical T/R modules and a 64:1 multi-port passive in-phase power synthesis network. Its structure is similar to that of **Figure 5**. In the engineering design, the design specification of the gain and noise figure of all T/R modules are the same, so we use the same noise figure NF1 and gain *G* in the analysis and calculation. The error caused by the inconsistent indexes of different T/R modules is always acceptable and reasonable in the engineering design and calculation. Then the total noise power of the synthetic output received by the

*<sup>L</sup>* <sup>þ</sup> <sup>1</sup> � <sup>1</sup>

PNo ¼ �114 þ 6 þ 22*:*02 ¼ �85*:*98 dBm (38)

PNo ¼ �114 þ 6 þ 2 þ 25–5 ¼ �86 dBm (39)

*L*

*<sup>L</sup>* (37)

*T*ea*<sup>i</sup> T*<sup>0</sup> þ

*nL* � 1 *G*

¼ NF1 þ

*nL* � 1 *G* (35)

(36)

NF <sup>¼</sup> PNo

*kT*0BW*G*<sup>Σ</sup>

*Modern Printed-Circuit Antennas*


**References**

pp. 207-213

Press; 1982. p. 72

[1] Connor FR. Noise. Beijing: Science

*DOI: http://dx.doi.org/10.5772/intechopen.91198*

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar*

[2] Sklar B. In: PingPing X et al., editors. Digital Communications Fundamentals and Applications. 2nd ed. Beijing: Electronics Industry Press; 2002.

[3] Guangyi Z. Phased Array Radar System. Beijing: National Defense Industry Press; 2000. p. 218

measurement of active phased array receiver system. Modern Radar, China.

[5] Chuandong H. Measurement of equivalent noise temperature of phased array radar receiving system. In: National Conference on Microwave

[4] Lin GM, Yuan LS. Noise

2004;**26**(3):54-57

Measurement. 2000

**141**

**Table 1.**

*Noise figure of multi-port active synthesis network under different test conditions.*

*G* is much larger than *nL* (which can be realized in engineering), it can be considered that Eq. (35) is close to Eq. (29). See **Table 1** for noise figure of multi-port active synthesis network under different test conditions.

In engineering applications, we use the existing noise figure test instruments and adopt the above method to measure the noise figure of the multi-port active synthesis network. We must remember that there is a condition that the gain of a single active channel is much larger than the loss of the passive synthesis network (including the distribution loss at this time); otherwise the measurement result will be greatly different from the theoretical value. We can also average the measured values of each channel to characterize the noise figure of the whole synthetic network. For example, the active channel gain *G* is only 15 dB, while the passive network is 32:1. When the noise figure of the synthesis network is measured by the above test method, the result will cause a large error. The specific reason can be seen in the previous correlation analysis and calculation formula (35). Of course, we can also correct the measurement by setting the loss of the DUT in the noise figure testing instrument, so that we can also obtain the correct measurement value. For specific operation settings, please refer to the relevant operating instructions of the noise figure test instrument.

In this chapter, the mathematical expressions of the total output noise power and noise figure of the multi-port network in many common cases are given. Using these formulas, designers can calculate the dynamic range of the active phased array radar receiving system and can also use the calculation formula of noise figure to formulate the testing scheme of the active phased array radar noise figure [4, 5].

## **Author details**

Yu Hongbiao Nanjing Research Institute of Electronics Technology (NRIET), China

\*Address all correspondence to: sssyhb@126.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Noise Characteristic Analysis of Multi-Port Network in Phased Array Radar DOI: http://dx.doi.org/10.5772/intechopen.91198*

## **References**

*G* is much larger than *nL* (which can be realized in engineering), it can be considered that Eq. (35) is close to Eq. (29). See **Table 1** for noise figure of multi-port

Noise figure in single-channel operation/dB 2.28 2.20 2.26 2.24 Noise figure in four-channel operation/dB 8.20 8.12 8.16 8.15

active channel is much larger than the loss of the passive synthesis network

In engineering applications, we use the existing noise figure test instruments and adopt the above method to measure the noise figure of the multi-port active synthesis network. We must remember that there is a condition that the gain of a single

*f***<sup>1</sup>** *f***<sup>2</sup>** *f***<sup>3</sup>** *f***<sup>4</sup>**

(including the distribution loss at this time); otherwise the measurement result will be greatly different from the theoretical value. We can also average the measured values of each channel to characterize the noise figure of the whole synthetic network. For example, the active channel gain *G* is only 15 dB, while the passive network is 32:1. When the noise figure of the synthesis network is measured by the above test method, the result will cause a large error. The specific reason can be seen in the previous correlation analysis and calculation formula (35). Of course, we can also correct the measurement by setting the loss of the DUT in the noise figure testing instrument, so that we can also obtain the correct measurement value. For specific operation settings, please refer to the relevant operating instructions of the

In this chapter, the mathematical expressions of the total output noise power and noise figure of the multi-port network in many common cases are given. Using these formulas, designers can calculate the dynamic range of the active phased array radar receiving system and can also use the calculation formula of noise figure to formulate the testing scheme of the active phased array radar noise figure [4, 5].

Nanjing Research Institute of Electronics Technology (NRIET), China

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: sssyhb@126.com

provided the original work is properly cited.

active synthesis network under different test conditions.

*Noise figure of multi-port active synthesis network under different test conditions.*

noise figure test instrument.

**Table 1.**

*Modern Printed-Circuit Antennas*

**Author details**

Yu Hongbiao

**140**

[1] Connor FR. Noise. Beijing: Science Press; 1982. p. 72

[2] Sklar B. In: PingPing X et al., editors. Digital Communications Fundamentals and Applications. 2nd ed. Beijing: Electronics Industry Press; 2002. pp. 207-213

[3] Guangyi Z. Phased Array Radar System. Beijing: National Defense Industry Press; 2000. p. 218

[4] Lin GM, Yuan LS. Noise measurement of active phased array receiver system. Modern Radar, China. 2004;**26**(3):54-57

[5] Chuandong H. Measurement of equivalent noise temperature of phased array radar receiving system. In: National Conference on Microwave Measurement. 2000

**143**

antenna.

**Chapter 9**

**Abstract**

Wearable Textile Antennas with

This chapter provides a brief overview of the types of wearable antennas with high body-antenna isolation. The main parameters and characteristics of wearable antennas and their design requirements are discussed. Next, procedures (passive and active) to test the performance of wearable antennas are presented. The electromagnetic properties of the commercially available textiles used as antenna substrates are investigated and summarized here, followed by a more detailed examination of their effects on the performance of wearable antennas with high body-antenna isolation. A trade-off between substrate electromagnetic properties and resonant frequency, bandwidth, radiation efficiency, and maximum gain is presented. Finally, a case study is presented with detailed analyses and investigations of the low-profile all-textile wearable antennas with high body-antenna isolation and low SAR. Their interaction with a semisolid homogeneous human body phantom is discussed. The simulations and experimental results from different (in free-space and on-body)

**Keywords:** wearable antenna, flexible antenna, textile antenna, design requirements,

The wearables are identified as 1 of the 10 technologies which will change our lives [1]. They offer attractive solutions in diverse areas including healthcare, education, finance, sport, and entertainment. For example, in the area of the healthcare, wearable devices can collect data (on blood pressure, temperature, heart rate, steps, calories burned, and even glucose levels) in real-time and send this information to nearby node (on-body communication between two wearable devices) or remote station (off-body communication between a wearable device and mobile phone, tablet, or personal computer) using body area networks (BANs). In order to realize remote monitoring and real-time feedback to the user, the wearable device needs to be equipped with a sensor, processor, memory, power unit, transceiver, and an

SAR, antenna measurements, antenna performance, human body phantom

High Body-Antenna Isolation:

Design, Fabrication, and

Characterization Aspects

*Nikolay Atanasov, Gabriela Atanasova* 

*and Blagovest Atanasov*

scenarios are presented.

**1. Introduction**

## **Chapter 9**
