**4. Multiple band-notched characteristics using meander lines (MLs)**

#### **4.1. Design multiple band-notched antennas using MLs**

Meander line (ML), also known as serpentine line, consisting of a number of transmission lines closely packed and jointed to each others, as shown in Figure 24, is an effective way for size reduction of a transmission line [29-36]. The idea behind meandering is to increase the electrical length per unit area of circuit board space when the signal is propagating along the ML.

252 Ultra Wideband – Current Status and Future Trends

These results indicate that the

*3.6.2. Time-domain performance*

received pulses for both antennas.

achieve the fidelity of more than 94%.

characteristic for the antenna.

about 2.5 dBi to -5.4 dBi and the radiation efficiency is reduced from about 80% to 15%.

**Figure 22.** Simulated and measured (a) peak gains and (b) efficiencies of proposed antenna

**Figure 23.** Measured pulse responses for (a) reference and (b) single-band notched antennas

The fidelities *F* of the time responses using (1) are computed and shown in Table 4. In both the face-to-face and side-by-side arrangements, the fidelities are about the same. As expected, the reference UWB antenna has the fidelity of more than 97%, very close to the source signal. The results in Table 4 show that the antenna with a single-band notch can

The measurement procedure for the time-domain performance is described in the previous section. For comparison, the pulse responses of the reference UWB antenna (without having the notched characteristic) are also measured and shown in Figure 23. It can be seen that, the pulse responses in the face-to-face arrangements have larger amplitudes than those in the side-by-side arrangements. This agrees with the radiation patterns shown in Figure 21 where radiations in the x-direction are slightly larger than those in the y-direction in most of the frequencies tested. The pulse responses for the reference antenna are only slightly larger than those for the notched antenna in the same arrangements. Late time ringing (or distortion) and lower power are observed in the

/4-resonators effectively generate a single band-notched

λ

To design multiple band-notched characteristics for compact UWB antennas, the λ/4 resonator used in section 3 is too large to be used. By folding the λ/4-resonator into a ML, we can obtain a compact structure. Due to the mutual coupling between the adjacent segments of the ML, the total physical resonator length is no longer λ/4 long. Studies have shown that we can make the electrical length of the MLs to be λ/4 with a smaller size. With the compact structures of MLs, we can easily place several pairs of MLs in different positions of the antenna to obtain a multiple band-notched characteristic. In our proposed design, two different types of feeding techniques, known here as parallel-coupled feeding (PCF) and direct-connected feeding (DCF), as shown in Figures 25(a) and 25(b), respectively, are employed. In the PCF ML, the signal is coupled from the transmission line to the ML, while in the DCF ML, the signal is fed directly to the ML. Details of the different band-notched designs for a compact UWB antenna using MLs are described in the following sections.

**Figure 25.** MLs with (a) parallel-coupled fed and (b) direct-connected fed

**Figure 24.** Typical ML with 8 segments

The design procedure for our band-notched antennas is as follows. An UWB antenna without any ML is designed and used as a reference antenna for comparison. Several pairs of MLs are then added to the reference antenna to make it a multiple band-notched antenna. (A single notched-band antenna requires only one pair of MLs.) The dimensions of the individual MLs are adjusted to achieve the desirable center frequencies and bandwidths for the notches. For convenience, we use the same antenna in section 2 as the reference antenna for our band-notched antennas design here.

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 255

In the single and dual band-notched designs shown in Figures 26(a) and 26(b), respectively [10, 11, 37], the notches are designed at the frequencies of existing communication systems such as the WiMax system, upper and lower bands of the WLAN systems. In the triple band-notched design of Figure 26(c), the notches are designed at 3.5, 5.25 and 5.775 GHz. In the quadruple band-notched antenna design of Figure 26(d), we select four notch frequencies with around 1 GHz separation to show the flexibility in designing the notch frequencies. To avoid duplicated description, the quadruple band-notched antenna is used here to explain creating notches using MLs. In Figure 26(d), the four pairs of MLs, labeled as MLs #1, #2, #3 and #4, are designed to create the notches at 3.14, 4.34, 5.4 and 6.4 GHz, respectively. Detailed dimensions of the MLs for single, dual, triple and quadruple band-

*ML d1 d2 d3 d4 #1 0.3 0.3 0.4 1.9*

*ML d5 d6 d7 d8 w3 #1 0.25 0.25 0.25 2.9 5 #2 0.25 0.25 0.25 2.6 8.5*

*ML d1 d2 d3 d4 ML d5 d6 d7 d8 w3 #1 0.3 0.3 0.25 2.2 #3 0.3 0.3 0.3 2.7 5.2*

*ML d1 d2 d3 d4 ML d5 d6 d7 d8 w3 #1 0.3 0.3 0.25 3 #3 0.2 0.2 0.2 2.5 5.2 #2 0.3 0.3 0.25 2.1 #4 0.2 0.2 0.2 2.1 8.5*

The PCF MLs, i.e., MLs #1 and #2 in Figure 26(d), on both sides of the feed line have open circuit at one end and short circuit to the ground through a via at the other end. With an

feed line is coupled to the MLs and then flowing through the vias to the ground plane. This creates high impedance for the signal and prevents the signal from flowing into the radiator.

*g*/4-resonators with parallel-coupled fed. At resonant frequencies, the signal on the

*g* is the guided wavelength approximately given by (2), the

λ

*g*/4-length standing wave

**Table 5.** Dimensions of PCF MLs and DCF MLs for Single Band-Notched Antenna

**Table 6.** Dimensions of PCF MLs and DCF MLs for Dual Band-Notched Antenna

**Table 7.** Dimensions of PCF MLs and DCF MLs for Triple Band-Notched Antenna

**Table 8.** Dimensions of PCF MLs and DCF MLs for Quadruple Band-Notched Antenna

**4.2. Parallel-coupled fed (PCF) and direct-connected fed (DCF) MLs**

notched antennas are listed in Tables 5 to 8, respectively.

*#2 0.3 0.3 0.3 2*

λ

*g*/4, where

λ

*g*/4-resonator operating in the fundamental mode will have a

electrical length of

λ

MLs are

A λ

As previously described and shown in Figure 14, the surface current concentrates most at the edges of the feed line, the ground plane and the radiator. So we can place the resonators implemented using MLs along these edges as shown in Figures 26(a), 26(b), 26(c) and 26(d) to create a single-, dual-, triple- and quadruple-band notches, respectively, for the antenna. Two different types of feeding techniques, i.e. PCF and DCF, are used. The MLs with PCF are etched on the same side as the radiator on the substrate and connected to ground through vias, while the MLs with DCF are etched on the ground plane on the other side of the substrate.

**Figure 26.** Top views and side views of (a) single, (b) dual, (c) triple, (d) quadruple band-notched antennas, (e) PCF and (f) DCF MLs

In the single and dual band-notched designs shown in Figures 26(a) and 26(b), respectively [10, 11, 37], the notches are designed at the frequencies of existing communication systems such as the WiMax system, upper and lower bands of the WLAN systems. In the triple band-notched design of Figure 26(c), the notches are designed at 3.5, 5.25 and 5.775 GHz. In the quadruple band-notched antenna design of Figure 26(d), we select four notch frequencies with around 1 GHz separation to show the flexibility in designing the notch frequencies. To avoid duplicated description, the quadruple band-notched antenna is used here to explain creating notches using MLs. In Figure 26(d), the four pairs of MLs, labeled as MLs #1, #2, #3 and #4, are designed to create the notches at 3.14, 4.34, 5.4 and 6.4 GHz, respectively. Detailed dimensions of the MLs for single, dual, triple and quadruple bandnotched antennas are listed in Tables 5 to 8, respectively.

254 Ultra Wideband – Current Status and Future Trends

for our band-notched antennas design here.

the substrate.

antennas, (e) PCF and (f) DCF MLs

The design procedure for our band-notched antennas is as follows. An UWB antenna without any ML is designed and used as a reference antenna for comparison. Several pairs of MLs are then added to the reference antenna to make it a multiple band-notched antenna. (A single notched-band antenna requires only one pair of MLs.) The dimensions of the individual MLs are adjusted to achieve the desirable center frequencies and bandwidths for the notches. For convenience, we use the same antenna in section 2 as the reference antenna

As previously described and shown in Figure 14, the surface current concentrates most at the edges of the feed line, the ground plane and the radiator. So we can place the resonators implemented using MLs along these edges as shown in Figures 26(a), 26(b), 26(c) and 26(d) to create a single-, dual-, triple- and quadruple-band notches, respectively, for the antenna. Two different types of feeding techniques, i.e. PCF and DCF, are used. The MLs with PCF are etched on the same side as the radiator on the substrate and connected to ground through vias, while the MLs with DCF are etched on the ground plane on the other side of

**Figure 26.** Top views and side views of (a) single, (b) dual, (c) triple, (d) quadruple band-notched

**Table 6.** Dimensions of PCF MLs and DCF MLs for Dual Band-Notched Antenna

**Table 7.** Dimensions of PCF MLs and DCF MLs for Triple Band-Notched Antenna

**Table 8.** Dimensions of PCF MLs and DCF MLs for Quadruple Band-Notched Antenna

#### **4.2. Parallel-coupled fed (PCF) and direct-connected fed (DCF) MLs**

The PCF MLs, i.e., MLs #1 and #2 in Figure 26(d), on both sides of the feed line have open circuit at one end and short circuit to the ground through a via at the other end. With an electrical length of λ*g*/4, where λ*g* is the guided wavelength approximately given by (2), the MLs are λ*g*/4-resonators with parallel-coupled fed. At resonant frequencies, the signal on the feed line is coupled to the MLs and then flowing through the vias to the ground plane. This creates high impedance for the signal and prevents the signal from flowing into the radiator. A λ*g*/4-resonator operating in the fundamental mode will have a λ*g*/4-length standing wave

formed along it. Computer simulation has been carried out to study the surface current on ML #2 at the resonant frequency of 4.34 GHz and results show that, at any instance, the currents on the whole ML always have the same phase (in the same direction), i.e. a standing wave is formed on the ML which is expected for a λ*g*/4-resonator operating in the fundamental mode. This confirmed that MLs #1 & #2 are λ*g*/4-resonators. Figure 27(a) shows a snap-shot from the simulation result on the surface current of ML #2. It can be seen that, the current is quite small at the open end of the ML but substantially larger near the via, which is typical for a λ*g*/4-resonator.

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 257

*g*/4=9.27 and 7.825 mm when computed using (2).

*f L C* ∝ (3)

*f* proportional to

6.4 GHz computed using Table 8 are 16.2 and 15 mm, respectively, which again are very

These results show that (2) cannot be used in our MLs to determine the notch frequencies for

(2) is derived using the distributed-elements model and can be applied quite accurately to a straight microstrip line. For complicated structures which are many times, say 10, less than the free space wavelength, the lumped-elements model should be used [38]. In our design, the sizes of MLs #1, #2, #3 and #4 are 3×4.5 mm2, 2.1×4.5 mm2, 2.8×2.7 mm2, 2.8×2.3 mm2, respectively. The maximum lengths of these structures are less than 1/10th of the corresponding guided wavelengths of 51.18, 38.82, 29.76 and 25.11 mm at the resonant frequencies of 3.14, 4.34, 5.4 and 6.4 GHz, respectively, thus both the distributed-elements model and the lumped-elements model together should be used [38-40]. In the lumpedelement model, there will be capacitance formed by the shunt capacitance between the ML and the substrate, series capacitance formed between segments of the ML, inductance formed by the series inductance along the ML plus shunt inductance formed between the segments of the ML, and inductance formed by the via [41], so the models are extremely complicated [35, 42-44]. These models will have different resonant modes of operation. In the fundamental mode, only the largest capacitances and inductances are in effect and form

1

where *Leq* and *Ceq* are the equivalent inductance and capacitance, respectively, resulted from

For the PCF MLs, at resonance, the signals will be electrically coupled from the feed line to MLs #1 and #2 via a mutual coupling capacitor *Cm* between them [38]. This coupling will detune the resonant frequency as will be shown later. For the DCF MLs, the signals will be directly fed to MLs #3 and #4. Since it is not easy, if not impossible at all, to relate *Leq* and *Ceq*

Parametric study of the quadruple band-notched antenna is carried out using computer simulation to explore how the dimensions of the MLs affect the characteristics of the band

For the PCF resonators, ML #1 is used for studies. The smallest dimension we can make for our antenna using the prototype-machine in our laboratory is 0.1 mm. So for convenience in our design process, we fix the segment width *d1* and segment spacing *d2* of the ML to be the same value. Simulation results show that, with *d1* = *d2* < 0.2 mm, the notch bandwidth is too

*eq eq*

λ

an *LC* resonator which will have the fundamental resonant frequency *r*

*r*

to the dimensions of the MLs, full-wave simulation needs to be used for the design.

**4.4. Setting the notch center frequencies and bandwidths**

different from the corresponding lengths

1/ *eq eq L C* , i.e.,

notches.

the antennas. The reason can be explained as follows.

the self inductance and self capacitance of the ML.

The DCF MLs, i.e., MLs #3 and #4 in Figure 26(d), at the upper edges of the ground plane are stubs having open circuit at one end and directly connect to ground at the other end. With an electrical length of λ*g*/4, the MLs are λ*g*/4-resonators with direct-connected fed. At resonance, the MLs prevent the signal from passing through, creating high input impedance. This causes severely mismatching to the antenna and reduces the return loss. As mentioned before, a λ*g*/4-resonator operating in the fundamental mode has a λ*g*/4-length standing wave formed along it. Computer simulation has also been carried out on the surface current of ML #3 at the resonant frequency of 5.4 GHz. Results show that, at any instance, the currents along the ML all have the same phase (in the same direction), as expected for a λ*g*/4-resonator operating in the fundamental mode. This again confirms that MLs #3 & #4 are λ*g*/4-resonators. Figure 27(b) shows a snap shot from the simulation result on the surface current of ML #3. The current is substantially smaller at the open end of the ML than that at the connected end, which is expected for a λ*g*/4-resonator.

**Figure 27.** Current distribution on (a) ML #2 at 4.34 GHz and (b) ML #3 at 5.4 GHz

#### **4.3. Discussions on electrical lengths of PCF and DCF MLs**

For a λ*g*/4-resonator implemented using a straight microstrip line, if ε*r* in (2) is known, the physical length of the microstrip line, for the λ*g*/4-resonator to work at a particular frequency, can easily be calculated. Unfortunately, this does not work with the MLs in our design. For example, the total lengths measured along the internal perimeters of MLs #1 and #2 in Figure 26(d) for the resonant frequencies of 3.14 and 4.34 GHz are 26.1 and 17.7 mm, respectively, which are quite different from the computed λ*g*/4=15.95 and 11.54 mm using (2). Then for MLs #3 and #4, the internal perimeters for the resonant frequencies of 5.4 and 6.4 GHz computed using Table 8 are 16.2 and 15 mm, respectively, which again are very different from the corresponding lengths λ*g*/4=9.27 and 7.825 mm when computed using (2). These results show that (2) cannot be used in our MLs to determine the notch frequencies for the antennas. The reason can be explained as follows.

256 Ultra Wideband – Current Status and Future Trends

which is typical for a

mentioned before, a

expected for a

For a λ

MLs #3 & #4 are

With an electrical length of

λ

λ

standing wave is formed on the ML which is expected for a

fundamental mode. This confirmed that MLs #1 & #2 are

*g*/4-resonator.

λ

ML than that at the connected end, which is expected for a

**Figure 27.** Current distribution on (a) ML #2 at 4.34 GHz and (b) ML #3 at 5.4 GHz

*g*/4-resonator implemented using a straight microstrip line, if

**4.3. Discussions on electrical lengths of PCF and DCF MLs**

physical length of the microstrip line, for the

respectively, which are quite different from the computed

*g*/4, the MLs are

λ

λ

formed along it. Computer simulation has been carried out to study the surface current on ML #2 at the resonant frequency of 4.34 GHz and results show that, at any instance, the currents on the whole ML always have the same phase (in the same direction), i.e. a

a snap-shot from the simulation result on the surface current of ML #2. It can be seen that, the current is quite small at the open end of the ML but substantially larger near the via,

The DCF MLs, i.e., MLs #3 and #4 in Figure 26(d), at the upper edges of the ground plane are stubs having open circuit at one end and directly connect to ground at the other end.

resonance, the MLs prevent the signal from passing through, creating high input impedance. This causes severely mismatching to the antenna and reduces the return loss. As

standing wave formed along it. Computer simulation has also been carried out on the surface current of ML #3 at the resonant frequency of 5.4 GHz. Results show that, at any instance, the currents along the ML all have the same phase (in the same direction), as

on the surface current of ML #3. The current is substantially smaller at the open end of the

λ

*g*/4-resonator operating in the fundamental mode has a

*g*/4-resonator operating in the fundamental mode. This again confirms that

λ

λ

frequency, can easily be calculated. Unfortunately, this does not work with the MLs in our design. For example, the total lengths measured along the internal perimeters of MLs #1 and #2 in Figure 26(d) for the resonant frequencies of 3.14 and 4.34 GHz are 26.1 and 17.7 mm,

(2). Then for MLs #3 and #4, the internal perimeters for the resonant frequencies of 5.4 and

*g*/4-resonators. Figure 27(b) shows a snap shot from the simulation result

λ

*g*/4-resonator.

ε

*g*/4-resonator to work at a particular

*g*/4=15.95 and 11.54 mm using

*r* in (2) is known, the

λ

λ

*g*/4-resonator operating in the

λ

*g*/4-length

*g*/4-resonators. Figure 27(a) shows

*g*/4-resonators with direct-connected fed. At

(2) is derived using the distributed-elements model and can be applied quite accurately to a straight microstrip line. For complicated structures which are many times, say 10, less than the free space wavelength, the lumped-elements model should be used [38]. In our design, the sizes of MLs #1, #2, #3 and #4 are 3×4.5 mm2, 2.1×4.5 mm2, 2.8×2.7 mm2, 2.8×2.3 mm2, respectively. The maximum lengths of these structures are less than 1/10th of the corresponding guided wavelengths of 51.18, 38.82, 29.76 and 25.11 mm at the resonant frequencies of 3.14, 4.34, 5.4 and 6.4 GHz, respectively, thus both the distributed-elements model and the lumped-elements model together should be used [38-40]. In the lumpedelement model, there will be capacitance formed by the shunt capacitance between the ML and the substrate, series capacitance formed between segments of the ML, inductance formed by the series inductance along the ML plus shunt inductance formed between the segments of the ML, and inductance formed by the via [41], so the models are extremely complicated [35, 42-44]. These models will have different resonant modes of operation. In the fundamental mode, only the largest capacitances and inductances are in effect and form an *LC* resonator which will have the fundamental resonant frequency *r f* proportional to 1/ *eq eq L C* , i.e.,

$$f\_r \approx \frac{1}{\sqrt{L\_{eq}C\_{eq}}}\tag{3}$$

where *Leq* and *Ceq* are the equivalent inductance and capacitance, respectively, resulted from the self inductance and self capacitance of the ML.

For the PCF MLs, at resonance, the signals will be electrically coupled from the feed line to MLs #1 and #2 via a mutual coupling capacitor *Cm* between them [38]. This coupling will detune the resonant frequency as will be shown later. For the DCF MLs, the signals will be directly fed to MLs #3 and #4. Since it is not easy, if not impossible at all, to relate *Leq* and *Ceq* to the dimensions of the MLs, full-wave simulation needs to be used for the design.

#### **4.4. Setting the notch center frequencies and bandwidths**

Parametric study of the quadruple band-notched antenna is carried out using computer simulation to explore how the dimensions of the MLs affect the characteristics of the band notches.

For the PCF resonators, ML #1 is used for studies. The smallest dimension we can make for our antenna using the prototype-machine in our laboratory is 0.1 mm. So for convenience in our design process, we fix the segment width *d1* and segment spacing *d2* of the ML to be the same value. Simulation results show that, with *d1* = *d2* < 0.2 mm, the notch bandwidth is too large (more than 1 GHz). Thus for having a low percentage of tolerance and compact size, we fix *d1* and *d2* to a slightly larger value of 0.3 mm. The segment length *d4* and distance *d3* between the ML and the feed line are then used for parametric studies using computer simulation. Results show that *d4* and *d3* affect the notch frequency and bandwidth, respectively. The effect of *d4* on the notch frequency is shown in Figure 28(a), indicating that *d4* is inversely proportional to the notch frequency. This is because increasing the segment length *d4* increases the series inductance and capacitance along the ML and hence lowering down the resonant frequency through (3). With *d4* increased from 2.8 to 3.2 mm, the resonant frequency shifts from 2.85 to 3.23 GHz, which is quite significant. ML #1 is parallelcoupled fed via the mutual capacitance between the feed line and the ML. At the resonant frequency, the signal travelling along the feed line is coupled to the ML. When *d3* is increased, the coupling effect (or the mutual capacitance) between them is reduced, leading to a lower reactance and hence a lower quality factor *Q*. For a given resonant frequency *fr*, the bandwidth is given by *fr/Q*. Thus *d3* is inversely proportional to the notch bandwidth and so can be used to adjust the notch bandwidth. The effect of *d3* on the notch bandwidth is shown in Figure 28(b). With *d3* increased from 0.1 to 0.5 mm, the 10-dB bandwidth changes from 0.31 to 0.11 GHz. It should be noted that the notch frequency is dominated by the ML's equivalent self-capacitance *Ceq* and inductance *Leq* given by (3) and so *d3* will only slightly affect the notch frequency, as can be seen in Figure 28(b).

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 259

close to the feed line, e.g. *w3 =* 2 mm, the notch bandwidth will be too wide and, together with the adjacent notches, form a very wide stopband. Moreover, the small distance *gap* is very critical for impedance matching of the antenna. Placing the ML too close to this gap will affect the matching performance and reduce the impedance bandwidth, as evident in

**Figure 28.** Return loss with different values of (a) *d4* and (b) *d3* for ML #1, and (c) *d8* and (d) *w3* for ML

first spurious response always occurs at three times the resonant frequency [46]. ML #1 is a parallel-coupled fed resonator at around 3 GHz. Figures 28(a) and 28(b) show that it has a spurious response at about 8.5 GHz, slightly less than three times the resonant frequency. In this respect, ML #1 again behaves like a parallel-coupled fed resonator. Note that ML #2 also has the first spurious response at about three times the resonant frequency, which is not

These results also reveal that when the values of *d4*, *d3*, *d8* and *w3* are changed, the return loss in the rest of the UWB band remains about the same. This provides the designers with a

The return loss, efficiency and peak gain across the UWB, and the radiation patterns at the passband and also the notch frequencies of all the four band-notched antennas are studied

great freedom to select the notched-band frequency and bandwidth for the antenna.

*g*/4-resonator implemented using a straight microstrip line, the

Figure 28(d).

#3 of the quadruple band-notched antenna

shown in Figure 28(a) due to the small scale.

**4.5. Results and discussions**

*4.5.1. Frequency-domain performance*

λ

For a parallel-coupled fed

For the DCF resonators, ML #3 in Figure 28(d) is used for parametric studies. Again, for convenience, we fix the segment width *d6* and segment spacing *d5* of the ML to have the same value. Simulation results show that a smaller value of 0.2 mm for the segment width *d6* and segment spacing *d5* can be used without having a too large notch bandwidth, so we fix *d6* = *d5* = 0.2 mm for having a smaller size. The segment length *d8*, the distance *d7* between the ML and the ground, and the distance *w3* between the center of the feed line and the ML are used for parametric studies. Simulation results show that *d8* affects the notch frequency, for the same reason as described for the PCF resonators. The effect of *d8* on the notch frequency is shown in Figure 28(c). With *d8* increased from 2.3 to 2.7 mm, the notch frequency shifts from 5.71 to 5.04 GHz.

Simulation results show that both *d7* and *w3* in ML #3 affects the notch bandwidth, with *w3* having significantly higher effects, so *w3* is used for studies and results are shown in Figure 26(d). MLs #3 and #4 are λ*g*/4-resonators with DCF. There is series inductance on the ground plane between the feed line and the ML. This inductance is connected in series with the ML and increases with the current flowing through it [45]. Since the current density is higher in the region closer to the feed line than far away from it, the inductance is larger with a shorter distance *w3*, leading to a larger reactance and a higher quality factor *Q*. For a given resonant frequency *fr*, the bandwidth given by *fr/Q* is therefore smaller. This is confirmed by the simulation results of Figure 28(d) which shows that, with *w3* increased from 4.6 to 5.8 mm, the 10-dB bandwidth changes from 0.74 to 0.28 GHz. Thus *w3* can be used to adjust the notch bandwidth. Similar to the case for the PCF resonators, the notch frequency is dominated by the self-capacitance and inductance of the ML, so *w3* will only slightly affect the notch frequency as can be seen in Figure 28(d). It should be noted that, if ML #3 is too close to the feed line, e.g. *w3 =* 2 mm, the notch bandwidth will be too wide and, together with the adjacent notches, form a very wide stopband. Moreover, the small distance *gap* is very critical for impedance matching of the antenna. Placing the ML too close to this gap will affect the matching performance and reduce the impedance bandwidth, as evident in Figure 28(d).

**Figure 28.** Return loss with different values of (a) *d4* and (b) *d3* for ML #1, and (c) *d8* and (d) *w3* for ML #3 of the quadruple band-notched antenna

For a parallel-coupled fed λ*g*/4-resonator implemented using a straight microstrip line, the first spurious response always occurs at three times the resonant frequency [46]. ML #1 is a parallel-coupled fed resonator at around 3 GHz. Figures 28(a) and 28(b) show that it has a spurious response at about 8.5 GHz, slightly less than three times the resonant frequency. In this respect, ML #1 again behaves like a parallel-coupled fed resonator. Note that ML #2 also has the first spurious response at about three times the resonant frequency, which is not shown in Figure 28(a) due to the small scale.

These results also reveal that when the values of *d4*, *d3*, *d8* and *w3* are changed, the return loss in the rest of the UWB band remains about the same. This provides the designers with a great freedom to select the notched-band frequency and bandwidth for the antenna.

#### **4.5. Results and discussions**

258 Ultra Wideband – Current Status and Future Trends

affect the notch frequency, as can be seen in Figure 28(b).

λ

from 5.71 to 5.04 GHz.

26(d). MLs #3 and #4 are

large (more than 1 GHz). Thus for having a low percentage of tolerance and compact size, we fix *d1* and *d2* to a slightly larger value of 0.3 mm. The segment length *d4* and distance *d3* between the ML and the feed line are then used for parametric studies using computer simulation. Results show that *d4* and *d3* affect the notch frequency and bandwidth, respectively. The effect of *d4* on the notch frequency is shown in Figure 28(a), indicating that *d4* is inversely proportional to the notch frequency. This is because increasing the segment length *d4* increases the series inductance and capacitance along the ML and hence lowering down the resonant frequency through (3). With *d4* increased from 2.8 to 3.2 mm, the resonant frequency shifts from 2.85 to 3.23 GHz, which is quite significant. ML #1 is parallelcoupled fed via the mutual capacitance between the feed line and the ML. At the resonant frequency, the signal travelling along the feed line is coupled to the ML. When *d3* is increased, the coupling effect (or the mutual capacitance) between them is reduced, leading to a lower reactance and hence a lower quality factor *Q*. For a given resonant frequency *fr*, the bandwidth is given by *fr/Q*. Thus *d3* is inversely proportional to the notch bandwidth and so can be used to adjust the notch bandwidth. The effect of *d3* on the notch bandwidth is shown in Figure 28(b). With *d3* increased from 0.1 to 0.5 mm, the 10-dB bandwidth changes from 0.31 to 0.11 GHz. It should be noted that the notch frequency is dominated by the ML's equivalent self-capacitance *Ceq* and inductance *Leq* given by (3) and so *d3* will only slightly

For the DCF resonators, ML #3 in Figure 28(d) is used for parametric studies. Again, for convenience, we fix the segment width *d6* and segment spacing *d5* of the ML to have the same value. Simulation results show that a smaller value of 0.2 mm for the segment width *d6* and segment spacing *d5* can be used without having a too large notch bandwidth, so we fix *d6* = *d5* = 0.2 mm for having a smaller size. The segment length *d8*, the distance *d7* between the ML and the ground, and the distance *w3* between the center of the feed line and the ML are used for parametric studies. Simulation results show that *d8* affects the notch frequency, for the same reason as described for the PCF resonators. The effect of *d8* on the notch frequency is shown in Figure 28(c). With *d8* increased from 2.3 to 2.7 mm, the notch frequency shifts

Simulation results show that both *d7* and *w3* in ML #3 affects the notch bandwidth, with *w3* having significantly higher effects, so *w3* is used for studies and results are shown in Figure

plane between the feed line and the ML. This inductance is connected in series with the ML and increases with the current flowing through it [45]. Since the current density is higher in the region closer to the feed line than far away from it, the inductance is larger with a shorter distance *w3*, leading to a larger reactance and a higher quality factor *Q*. For a given resonant frequency *fr*, the bandwidth given by *fr/Q* is therefore smaller. This is confirmed by the simulation results of Figure 28(d) which shows that, with *w3* increased from 4.6 to 5.8 mm, the 10-dB bandwidth changes from 0.74 to 0.28 GHz. Thus *w3* can be used to adjust the notch bandwidth. Similar to the case for the PCF resonators, the notch frequency is dominated by the self-capacitance and inductance of the ML, so *w3* will only slightly affect the notch frequency as can be seen in Figure 28(d). It should be noted that, if ML #3 is too

*g*/4-resonators with DCF. There is series inductance on the ground

#### *4.5.1. Frequency-domain performance*

The return loss, efficiency and peak gain across the UWB, and the radiation patterns at the passband and also the notch frequencies of all the four band-notched antennas are studied

using computer simulation. To validate the simulation results, the antennas are also fabricated on PCBs with PTFE substrate with parameters described previously, as shown in Figure 29, and measured using the antenna measurement system, Satimo Starlab.

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 261

The simulated and measured radiation patterns of the single band-notched antenna at the frequencies of 3, 5.5, 7 and 10 GHz in the two principle planes, the x-y and x-z planes, are shown in Figure 31. At 4, 7 and 10 GHz, Figures 31(a), 31(e) and 31(g) show that the antenna has approximately omnidirectional radiation patterns in the x-y plane. In the x-z plane, Figures. 31(b), 31(f) and 31(h) show that there are two nulls at the z-direction, typical for monopole antennas. At the notch frequency of 5.5 GHz, the radiation patterns in Figures 31(c) and 31(d) indicate that the gain is almost evenly suppressed in all directions by the

The simulated and measured peak gains of the single band-notched antenna are shown in Figure 32(a) and the efficiencies are shown in Figure 32(b). The average gain over the UWB, computed by excluding the notched band, is about 3.5 dBi. However, at the notched band of about 5.5 GHz, the antenna gain is suppressed from about 3 dBi to -7.1 dBi and the radiation efficiency is reduced from about 85% to 8.7%. These phenomena indicate that the MLs work

**Figure 31.** Simulated and measured radiation patterns of single band-notched antenna. (a) 3 GHz in xy plane; (b) 3 GHz in x-z plane; (c) 5.5 GHz in x-y plane; (d) 5.5 GHz in x-z plane; (e) 7 GHz in x-y plane;

(f) 7 GHz in x-z plane; (g) 10 GHz in x-y plane; and (h) 10 GHz in x-z plane

effectively to introduce a single band-notched characteristic for the antenna.

pair of MLs and the average gain drops to about -10 dBi.

**Figure 29.** Top and bottom views of prototyped (a) single, (b) dual, (c) triple and (d) quadruple bandnotched antennas

#### *4.5.2. Single band-notched antenna*

The simulated and measured return losses of the single band-notched antenna of Figure 29(a) are shown in Figure 30. It can be seen that, the antenna can operate from 2.76 GHz to over 12 GHz with return loss ≥ 10 dB which fully satisfies the UWB requirement. In the WLAN band from 4.98 to 5.93 GHz, the measured return loss is substantially lower than 10 dB.

**Figure 30.** Simulated and measured return losses of single band-notched antenna

The simulated and measured radiation patterns of the single band-notched antenna at the frequencies of 3, 5.5, 7 and 10 GHz in the two principle planes, the x-y and x-z planes, are shown in Figure 31. At 4, 7 and 10 GHz, Figures 31(a), 31(e) and 31(g) show that the antenna has approximately omnidirectional radiation patterns in the x-y plane. In the x-z plane, Figures. 31(b), 31(f) and 31(h) show that there are two nulls at the z-direction, typical for monopole antennas. At the notch frequency of 5.5 GHz, the radiation patterns in Figures 31(c) and 31(d) indicate that the gain is almost evenly suppressed in all directions by the pair of MLs and the average gain drops to about -10 dBi.

260 Ultra Wideband – Current Status and Future Trends

notched antennas

*4.5.2. Single band-notched antenna*

using computer simulation. To validate the simulation results, the antennas are also fabricated on PCBs with PTFE substrate with parameters described previously, as shown in

**Figure 29.** Top and bottom views of prototyped (a) single, (b) dual, (c) triple and (d) quadruple band-

The simulated and measured return losses of the single band-notched antenna of Figure 29(a) are shown in Figure 30. It can be seen that, the antenna can operate from 2.76 GHz to over 12 GHz with return loss ≥ 10 dB which fully satisfies the UWB requirement. In the WLAN band

from 4.98 to 5.93 GHz, the measured return loss is substantially lower than 10 dB.

**Figure 30.** Simulated and measured return losses of single band-notched antenna

Figure 29, and measured using the antenna measurement system, Satimo Starlab.

The simulated and measured peak gains of the single band-notched antenna are shown in Figure 32(a) and the efficiencies are shown in Figure 32(b). The average gain over the UWB, computed by excluding the notched band, is about 3.5 dBi. However, at the notched band of about 5.5 GHz, the antenna gain is suppressed from about 3 dBi to -7.1 dBi and the radiation efficiency is reduced from about 85% to 8.7%. These phenomena indicate that the MLs work effectively to introduce a single band-notched characteristic for the antenna.

**Figure 31.** Simulated and measured radiation patterns of single band-notched antenna. (a) 3 GHz in xy plane; (b) 3 GHz in x-z plane; (c) 5.5 GHz in x-y plane; (d) 5.5 GHz in x-z plane; (e) 7 GHz in x-y plane; (f) 7 GHz in x-z plane; (g) 10 GHz in x-y plane; and (h) 10 GHz in x-z plane

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 263

**Figure 34.** Simulated and measured radiation patterns of dual band-notched antenna. (a) 3.5 GHz in xy plane; (b) 3.5 GHz in x-z plane; (c) 5.25 GHz in x-y plane; (d) 5.25 GHz in x-z plane; (e) 5.775 GHz in x-

The measured peak gain and efficiency of the dual band-notched antenna are shown in Figure 35. The average antenna gain over the UWB, computed by excluding the notched bands, is about 3 dBi. While at the notch frequencies, a significant gain and radiation efficiency reductions can be seen. At the notch frequencies of 5.25 and 5.83 GHz, the peak gain drops to -6 dBi and -2 dBi and the radiation efficiency reduces to below 20% and 45%, respectively. These phenomena indicate that by introducing two pairs of MLs, a dual band-

y plane; (f) 5.775 GHz in x-z plane; (g) 9 GHz in x-y plane; and (h) 9 GHz in x-z plane

**Figure 35.** Measured peak gain and efficiency of dual band-notched antenna

notched characteristic can be achieved.

**Figure 32.** Simulated and measured (a) peak gains and (b) efficiencies of single band-notched antenna

#### *4.5.3. Dual band-notched antenna*

The simulated and measured return losses of the dual band-notched antenna of Figure 29(b) are shown in Figure 33. It can be seen that, the antenna can operate from 2.95 GHz to about 11.8 GHz with return loss ≥ 10 dB. In the lower and upper WLAN bands from 5.01 to 5.48 GHz and 5.63 to 5.92 GHz, respectively, the measured return loss for the lower WLAN band is much lower than 10 dB. In the upper WLAN band, the return loss is larger. This is because the MLs are further away from the center feed line and so couple less energy compared to the MLs for the lower WLAN band.

The simulated and measured radiation patterns of the antenna at 3.5 and 9 GHz in the two principle planes, the x-z and x-y planes, are shown in Figure 34. The antenna has approximately omnidirectional radiation patterns in the x-y plane. The x-z plane patterns show two nulls at the z-direction, which are similar to that of a typical monopole antenna.

**Figure 33.** Simulated and measured return losses of dual band-notched antenna

#### Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 263

262 Ultra Wideband – Current Status and Future Trends

*4.5.3. Dual band-notched antenna*

antenna.

compared to the MLs for the lower WLAN band.

**Figure 32.** Simulated and measured (a) peak gains and (b) efficiencies of single band-notched antenna

The simulated and measured return losses of the dual band-notched antenna of Figure 29(b) are shown in Figure 33. It can be seen that, the antenna can operate from 2.95 GHz to about 11.8 GHz with return loss ≥ 10 dB. In the lower and upper WLAN bands from 5.01 to 5.48 GHz and 5.63 to 5.92 GHz, respectively, the measured return loss for the lower WLAN band is much lower than 10 dB. In the upper WLAN band, the return loss is larger. This is because the MLs are further away from the center feed line and so couple less energy

The simulated and measured radiation patterns of the antenna at 3.5 and 9 GHz in the two principle planes, the x-z and x-y planes, are shown in Figure 34. The antenna has approximately omnidirectional radiation patterns in the x-y plane. The x-z plane patterns show two nulls at the z-direction, which are similar to that of a typical monopole

**Figure 33.** Simulated and measured return losses of dual band-notched antenna

**Figure 34.** Simulated and measured radiation patterns of dual band-notched antenna. (a) 3.5 GHz in xy plane; (b) 3.5 GHz in x-z plane; (c) 5.25 GHz in x-y plane; (d) 5.25 GHz in x-z plane; (e) 5.775 GHz in xy plane; (f) 5.775 GHz in x-z plane; (g) 9 GHz in x-y plane; and (h) 9 GHz in x-z plane

The measured peak gain and efficiency of the dual band-notched antenna are shown in Figure 35. The average antenna gain over the UWB, computed by excluding the notched bands, is about 3 dBi. While at the notch frequencies, a significant gain and radiation efficiency reductions can be seen. At the notch frequencies of 5.25 and 5.83 GHz, the peak gain drops to -6 dBi and -2 dBi and the radiation efficiency reduces to below 20% and 45%, respectively. These phenomena indicate that by introducing two pairs of MLs, a dual bandnotched characteristic can be achieved.

**Figure 35.** Measured peak gain and efficiency of dual band-notched antenna

#### *4.5.4. Triple band-notched antenna*

The simulated and measured return losses of the triple band-notched antenna of Figure 28(c) are shown in Figure 36. The antenna can operate from 2.68 GHz to 11.15 GHz with return loss ≥ 10 dB. In the three desired notched bands, the measured return loss is substantially less than 10 dB.

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 265

**Figure 37.** Simulated and measured radiation patterns of triple band-notched antenna. (a) 2 GHz in x-y plane; (b) 2 GHz in x-z plane; (c) 3.45 GHz in x-y plane; (d) 3.45 GHz in x-z plane; (e) 5.25 GHz in x-y plane; (f) 5.25 GHz in x-z plane; (g) 5.775 GHz in x-y plane; (h) 5.775 GHz in x-z plane; (i) 11 GHz in x-y

**Figure 38.** Simulated and measured (a) peak gains and (b) efficiencies of triple band-notched antenna

plane; and (j) 11 GHz in x-z plane

The simulated and measured radiation patterns of the antenna at the frequencies of 2, 3.45, 5.25, 5.775 and 11 GHz in the x-y and x-z planes are shown in Figure 37. At 2 and 11 GHz, Figures 37(a) and 37(i) show that the antenna has approximately omnidirectional radiation patterns in the x-y plane. In the x-z plane patterns, Figures 37(b) and 37(j) show that there are two nulls in the positive and negative z directions. The radiation patterns in Figures 37(c) and 37(d) for 3.45 GHz, in Figures. 37(e) and 37(f) for 5.25 GHz, and in Figures 37(g) and 37(h) for 5.775 GHz indicate that the gain is almost evenly suppressed in all directions in the three notched bands by the MLs and the average gain is about -10 dBi.

The simulated and measured peak gains and efficiencies of the antenna are shown in Figures 38(a) and 38(b), respectively. The measured peak gain is between 2 to 4.75 dBi over the UWB, except in the notched bands. In the three notched bands, i.e., the WiMax, lower WLAN and upper WLAN frequency bands, the peak gain is suppressed to -3.4 dBi, -2.3 dBi and -2.1 dBi, respectively. The radiation efficiency is between 55% - 99%, but substantially reduced to 14.6%, 15.2% and 22.8%, respectively, in these frequency bands. These results indicate that the MLs work effectively to introduce a triple band-notched characteristic for the UWB antenna.

**Figure 36.** Simulated and measured return losses of the triple band-notched antenna

*4.5.4. Triple band-notched antenna*

substantially less than 10 dB.

the UWB antenna.

The simulated and measured return losses of the triple band-notched antenna of Figure 28(c) are shown in Figure 36. The antenna can operate from 2.68 GHz to 11.15 GHz with return loss ≥ 10 dB. In the three desired notched bands, the measured return loss is

The simulated and measured radiation patterns of the antenna at the frequencies of 2, 3.45, 5.25, 5.775 and 11 GHz in the x-y and x-z planes are shown in Figure 37. At 2 and 11 GHz, Figures 37(a) and 37(i) show that the antenna has approximately omnidirectional radiation patterns in the x-y plane. In the x-z plane patterns, Figures 37(b) and 37(j) show that there are two nulls in the positive and negative z directions. The radiation patterns in Figures 37(c) and 37(d) for 3.45 GHz, in Figures. 37(e) and 37(f) for 5.25 GHz, and in Figures 37(g) and 37(h) for 5.775 GHz indicate that the gain is almost evenly suppressed in all directions

The simulated and measured peak gains and efficiencies of the antenna are shown in Figures 38(a) and 38(b), respectively. The measured peak gain is between 2 to 4.75 dBi over the UWB, except in the notched bands. In the three notched bands, i.e., the WiMax, lower WLAN and upper WLAN frequency bands, the peak gain is suppressed to -3.4 dBi, -2.3 dBi and -2.1 dBi, respectively. The radiation efficiency is between 55% - 99%, but substantially reduced to 14.6%, 15.2% and 22.8%, respectively, in these frequency bands. These results indicate that the MLs work effectively to introduce a triple band-notched characteristic for

in the three notched bands by the MLs and the average gain is about -10 dBi.

**Figure 36.** Simulated and measured return losses of the triple band-notched antenna

**Figure 37.** Simulated and measured radiation patterns of triple band-notched antenna. (a) 2 GHz in x-y plane; (b) 2 GHz in x-z plane; (c) 3.45 GHz in x-y plane; (d) 3.45 GHz in x-z plane; (e) 5.25 GHz in x-y plane; (f) 5.25 GHz in x-z plane; (g) 5.775 GHz in x-y plane; (h) 5.775 GHz in x-z plane; (i) 11 GHz in x-y plane; and (j) 11 GHz in x-z plane

**Figure 38.** Simulated and measured (a) peak gains and (b) efficiencies of triple band-notched antenna

#### *4.5.5. Quadruple band-notched antenna*

The return losses of the reference and quadruple band-notched antennas are shown in Figure 39. The simulation and measurement return losses agree well and are larger than 10 dB across the UWB. In the notched bands, the return loss is substantially smaller than 10 dB. In the rest of the UWB, the return loss is larger than 10 dB, indicating good radiation performance. Figure 39 also shows that ML #1, being a parallel-coupled resonator at 3.14 GHz, has a spurious response at about 8.65 GHz, which is caused by the harmonic responses of the resonator. The measured results in Figure 39 show that the four notches at the frequencies of 3.14, 4.34, 5.4 and 6.4 have the bandwidth of 178, 374, 495 and 862 MHz, respectively.

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 267

**Figure 40.** Simulated and measured (a) peak gains and (b) efficiencies of quadruple band-notched

level is quite low, except at the highest frequency of 11 GHz, as can be seen in Figure 41.

notches, but also the bandwidths and locations of the notches.

For comparison, the studies of time-domain performances are carried out as described in previous sections on the single, dual, triple and quadruple band-notched antennas and results are all plotted in Figure 42. The single, dual and triple band-notched antennas have notches at 5.5 GHz, 5.25 & 5.775 GHz, 3.5 & 5.25 & 5.775 GHz, respectively, while the quadruple band-notched antenna has notches at 3.14 & 4.34 & 5.4 & 6.4 GHz. It can be seen that, as the number of notches increases, more late time ringing (distortion) and lower powers are observed in the received pulses. To evaluate the quality of the received pulses, the fidelity *F* is used. The calculated fidelities *F* for the four band-notched antennas are shown in Table 9. It can be seen that the fidelities in the face-to-face and side-by-side arrangements are about the same, which should be the case for monopole antennas. As expected, the reference UWB antenna has the fidelity of more than 97%, the best among the antennas tested. With quadruple notches, the proposed antenna has the fidelity of more than 85%. It was expected that the fidelities *F* would drop when the number of notches increased. However, Table 9 shows that the fidelity of the single band-notched antenna is less than that of the dual band-notched antenna. This is because the dual band-notched antenna has the two notches in the lower and upper WLAN bands of 5.15-5.35 GHz and 5.725-5.825 GHz, respectively. While the single band-notched antenna has the single notched-band from 5.15 GHz to 5.825 GHz, which is larger than the total of the two notches in the dual band-notched antenna. Thus the fidelity depends not only on the number of

The simulated and measured radiation patterns of the quadruple band-notched antenna at the notch frequencies of 3.14 and 6.4 GHz and passband frequencies of 2.5, 7 and 11 GHz in the x-y and x-z planes are shown in Figure 41. At all the frequencies tested, Figures 41(a), 41(c), 41(e), 41 (g) and 41(i) show that the radiation pattern for co-polarization is approximately omnidirectional and stable in the x-y plane. While Figures 41(b), 41(d), 41(f), 41(h) and 41(j) show two nulls occurring in the positive and negative z-directions, which is typical for monopole antennas. At the notch frequencies of 3.14 and 6.4 GHz, Figures 41(c), 41(d), 41(e) and 41(f) show that the gain is almost evenly suppressed in all directions. The cross-polarization

antenna

*4.5.6. Time-domain performance*

The simulated and measured results on the peak gain and radiation efficiency of the antenna are shown in Figures 40(a) and 40(b), respectively. A relatively flat peak gain and constant efficiency are observed over the UWB, except in the notch bands. At the notch frequencies of 3.14, 4.34, 5.4 and 6.4 GHz, the measured gain is suppressed to -5.4, -4.1 and - 3.7 and -2.5 dBi, respectively, with the corresponding efficiency substantially reduced to 13.2%, 26.5%, 26.8% and 35.4%. Thus the MLs work effectively to generate a quadruple band-notched characteristic for the UWB antenna. Comparing the PCF MLs to the DCF MLs in terms of peak gain and efficiency reduction, the PCF MLs perform better than the DCF MLs. This is because the PCF MLs are closer to the feed line and thus couple more energy. There are discrepancies between the simulated and measured peak gains and efficiencies, especially in the lower frequency bands. This is mainly due to the small ground plane of the antenna, which results in current flowing back from the ground plane to the outer conductor of the feeding coaxial cable [21, 22].

**Figure 39.** Simulated and measured return losses of reference antenna and quadruple band-notched antenna

**Figure 40.** Simulated and measured (a) peak gains and (b) efficiencies of quadruple band-notched antenna

The simulated and measured radiation patterns of the quadruple band-notched antenna at the notch frequencies of 3.14 and 6.4 GHz and passband frequencies of 2.5, 7 and 11 GHz in the x-y and x-z planes are shown in Figure 41. At all the frequencies tested, Figures 41(a), 41(c), 41(e), 41 (g) and 41(i) show that the radiation pattern for co-polarization is approximately omnidirectional and stable in the x-y plane. While Figures 41(b), 41(d), 41(f), 41(h) and 41(j) show two nulls occurring in the positive and negative z-directions, which is typical for monopole antennas. At the notch frequencies of 3.14 and 6.4 GHz, Figures 41(c), 41(d), 41(e) and 41(f) show that the gain is almost evenly suppressed in all directions. The cross-polarization level is quite low, except at the highest frequency of 11 GHz, as can be seen in Figure 41.

#### *4.5.6. Time-domain performance*

266 Ultra Wideband – Current Status and Future Trends

respectively.

antenna

*4.5.5. Quadruple band-notched antenna*

conductor of the feeding coaxial cable [21, 22].

The return losses of the reference and quadruple band-notched antennas are shown in Figure 39. The simulation and measurement return losses agree well and are larger than 10 dB across the UWB. In the notched bands, the return loss is substantially smaller than 10 dB. In the rest of the UWB, the return loss is larger than 10 dB, indicating good radiation performance. Figure 39 also shows that ML #1, being a parallel-coupled resonator at 3.14 GHz, has a spurious response at about 8.65 GHz, which is caused by the harmonic responses of the resonator. The measured results in Figure 39 show that the four notches at the frequencies of 3.14, 4.34, 5.4 and 6.4 have the bandwidth of 178, 374, 495 and 862 MHz,

The simulated and measured results on the peak gain and radiation efficiency of the antenna are shown in Figures 40(a) and 40(b), respectively. A relatively flat peak gain and constant efficiency are observed over the UWB, except in the notch bands. At the notch frequencies of 3.14, 4.34, 5.4 and 6.4 GHz, the measured gain is suppressed to -5.4, -4.1 and - 3.7 and -2.5 dBi, respectively, with the corresponding efficiency substantially reduced to 13.2%, 26.5%, 26.8% and 35.4%. Thus the MLs work effectively to generate a quadruple band-notched characteristic for the UWB antenna. Comparing the PCF MLs to the DCF MLs in terms of peak gain and efficiency reduction, the PCF MLs perform better than the DCF MLs. This is because the PCF MLs are closer to the feed line and thus couple more energy. There are discrepancies between the simulated and measured peak gains and efficiencies, especially in the lower frequency bands. This is mainly due to the small ground plane of the antenna, which results in current flowing back from the ground plane to the outer

**Figure 39.** Simulated and measured return losses of reference antenna and quadruple band-notched

For comparison, the studies of time-domain performances are carried out as described in previous sections on the single, dual, triple and quadruple band-notched antennas and results are all plotted in Figure 42. The single, dual and triple band-notched antennas have notches at 5.5 GHz, 5.25 & 5.775 GHz, 3.5 & 5.25 & 5.775 GHz, respectively, while the quadruple band-notched antenna has notches at 3.14 & 4.34 & 5.4 & 6.4 GHz. It can be seen that, as the number of notches increases, more late time ringing (distortion) and lower powers are observed in the received pulses. To evaluate the quality of the received pulses, the fidelity *F* is used. The calculated fidelities *F* for the four band-notched antennas are shown in Table 9. It can be seen that the fidelities in the face-to-face and side-by-side arrangements are about the same, which should be the case for monopole antennas. As expected, the reference UWB antenna has the fidelity of more than 97%, the best among the antennas tested. With quadruple notches, the proposed antenna has the fidelity of more than 85%. It was expected that the fidelities *F* would drop when the number of notches increased. However, Table 9 shows that the fidelity of the single band-notched antenna is less than that of the dual band-notched antenna. This is because the dual band-notched antenna has the two notches in the lower and upper WLAN bands of 5.15-5.35 GHz and 5.725-5.825 GHz, respectively. While the single band-notched antenna has the single notched-band from 5.15 GHz to 5.825 GHz, which is larger than the total of the two notches in the dual band-notched antenna. Thus the fidelity depends not only on the number of notches, but also the bandwidths and locations of the notches.

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 269

**Figure 42.** Measured transmit pulses with spectrum from 3.1 to 10.6 GHz and received pulses of (a)

*Face-to-Face 0.9825 0.9444 0.9590 0.9184 0.8918 Side-by-Side 0.9744 0.9463 0.9557 0.9281 0.8538*

In this chapter, the designs of band-notched characteristics for compact UWB antennas have been presented. The single, dual, triple and quadruple band-notched UWB antennas using

have been designed and studied using computer simulation. For verification of the simulation results, these antennas have been fabricated and measured using the antenna measurement system, Starlab. The bandwidths and center frequencies of all these notches can be controlled independently by adjusting the dimensions of the resonators. In the frequency domain, the simulated and measured return losses of the antennas agree well. The UWB monopole antennas have approximately omnidirectional radiation patterns with

*Dual Band-Notched Antenna*

*Triple Band-Notched Antenna*

λ

*Quadruple Band-Notched Antenna*

/4-resonators and the MLs

*Single Band-Notched Antenna*

single, (b) dual, (c) triple and (d) quadruple band-notched antennas

**Table 9.** Calculated Fidelity For Different Band-Notched Antennas

different resonator structures including the CPW resonators, the

*Reference Antenna*

**5. Conclusions**

**Figure 41.** Simulated and measured radiation patterns of quadruple band-notched antenna. x-y plane: (a) 2.5 GHz, (c) 3.14 GHz, (e) 6.4 GHz, (g) 7 GHz and (i) 11 GHz. x-z plane: (b) 2.5 GHz, (d) 3.14 GHz, (f) 6.4 GHz, (h) 7 GHz and (j) 11 GHz

**Figure 42.** Measured transmit pulses with spectrum from 3.1 to 10.6 GHz and received pulses of (a) single, (b) dual, (c) triple and (d) quadruple band-notched antennas

**Table 9.** Calculated Fidelity For Different Band-Notched Antennas

#### **5. Conclusions**

268 Ultra Wideband – Current Status and Future Trends

6.4 GHz, (h) 7 GHz and (j) 11 GHz

**Figure 41.** Simulated and measured radiation patterns of quadruple band-notched antenna. x-y plane: (a) 2.5 GHz, (c) 3.14 GHz, (e) 6.4 GHz, (g) 7 GHz and (i) 11 GHz. x-z plane: (b) 2.5 GHz, (d) 3.14 GHz, (f) In this chapter, the designs of band-notched characteristics for compact UWB antennas have been presented. The single, dual, triple and quadruple band-notched UWB antennas using different resonator structures including the CPW resonators, the λ/4-resonators and the MLs have been designed and studied using computer simulation. For verification of the simulation results, these antennas have been fabricated and measured using the antenna measurement system, Starlab. The bandwidths and center frequencies of all these notches can be controlled independently by adjusting the dimensions of the resonators. In the frequency domain, the simulated and measured return losses of the antennas agree well. The UWB monopole antennas have approximately omnidirectional radiation patterns with good band-notched characteristics. The simulated and measured results have shown that substantial reductions in efficiency and peak gain can be achieved at the notch frequencies. In the time domain, the pulse responses of these notched antennas have been measured inside the quiet zone of the anechoic chamber in The University of Hong Kong. Fidelity has been used to evaluate the time-domain performance of these antennas. Results have shown that all these band-notched antennas designed have the fidelities of more than 85%, compared to 97% for the reference UWB antenna.

Creating Band-Notched Characteristics for Compact UWB Monopole Antennas 271

[14] Y. J. Cho*, et al.*, "A miniature UWB planar monopole antenna with 5 GHz band-rejection

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**7. Computer simulations and sea trials**

The proposed path-planning method can be tailored to a specific vehicle or operational domain by modifying the performance index *J* to incorporate vehicle or actuator dynamics (feasibility constraints) and mission objectives such as OA or underwater rendezvous. This section presents simulated and in-water experimental results for four different applications which use the proposed trajectory optimization framework for UMV guidance: i) underwater docking of a UUV with a mobile underwater recovery system (MURS); ii) optimal exploitation of a terrain-relative feature map to improve UUV self-localization accuracy; iii) 2D or 3D OA in cluttered environments; and iv) specific USV implementations for sonar-based OA in riverine operations.


Federated Learning Hyper-Parameter Tuning for Edge Computing

*Xueying Zhang, Lei Fu, Huanle Zhang and Xin Liu*

## **Abstract**

Edge computing is widely recognized as a crucial technology for the upcoming generation of communication networks and has garnered significant interest from both industry and academia. Compared to other offloading models like cloud computing, it provides faster data processing capabilities, enhanced security measures, and lower costs by leveraging the proximity of the edge servers to the end devices. This helps mitigate the privacy concerns associated with data transfer in edge computing, by reducing the distance between the data source and the server. Raw data in typical edge computing scenarios still need to be sent to the edge server, leading to data leakage and privacy breaches. Federated Learning (FL) is a distributed model training paradigm that preserves end devices' data privacy. Therefore, it is crucial to incorporate FL into edge computing to protect data privacy. However, the high training overhead of FL makes it impractical for edge computing. In this study, we propose to facilitate the integration of FL and edge computing by optimizing FL hyperparameters, which can significantly reduce FL's training overhead and make it more affordable for edge computing.

**Keywords:** edge computing, federated learning, hyper-parameter tuning, system overhead, internet of things

#### **1. Introduction**

As machine learning (ML) and hardware manufacturing technologies continue to advance, training and deploying ML models have become increasingly ubiquitous in our daily lives, from smart-home voice assistants to widely deployed camera surveillance systems. Edge computing is becoming more and more popular due to its advantages, such as fast data processing and analysis, security, and low cost [1]. By placing the edge servers near to the end device, which is the fundamental principle of edge computing, the border of an edge computing system is constrained and manageable.

However, even with the shorter distance between the end device and the edge server, typical edge computing systems still suffer from a significant data privacy issue, as user data is frequently transmitted from the end device to the edge server for training a centralized ML model.

Federated Learning (FL) [2] is a method of model training that is distributed and has been utilized in various applications, including mobile keyboard and speech recognition for mobile devices and IoT. It is naturally suited for edge computing since data is kept on the end devices. **Figure 1** illustrates the combination of FL and edge computing in training a distributed model. First, the model parameters are transferred from the edge server to the end device. After that, the end device trains the model locally and then transfers the model parameters from the end device to the edge server. At the end of this iteration, the edge server aggregates the received model parameters and updates the model parameters. The above procedure will be repeated until the entire training process converges or reaches a predetermined number of epochs.

Unfortunately, FL training incurs significant system overhead, making it difficult for edge computing systems equipped with FL to operate without appropriate acceleration or optimization. Therefore, we propose the integration of FL hyper-parameter tuning in edge computing to reduce the system overhead of FL training and make it more feasible. The FL tuning algorithm should focus on optimizing the four essential system overheads:

#### **Figure 1.**

*An illustration of combining FL with edge computing. The model training process incorporates four steps: Model parameter download from the edge server to the end devices, local training on the end devices, model parameter upload from the end devices to the edge server, and model aggregation on the edge server.*

computing load is beyond the reach of some low-profile devices (e.g., IoT nodes) with few computing resources.

• *Transmission Load (TransL)*. It is the total data size transmitted between the clients and the server. If the cost of data transfer is high (e.g., data transfer is expensive), the benefits of reducing the total amount of data transferred can be considerable.

Different application scenarios have distinct preferences for training parameters in terms of CompT, TransT, CompL, and TransL. For example, (1) detecting attacks and anomalies in computer networks, as shown in Ref. [3], requires quick adaptation to malicious traffic and is therefore time-sensitive (CompT and TransT); (2) smart home control systems for indoor environment automation [4], such as HVAC, have limited computation capabilities and therefore prioritize computation efficiency (CompT and CompL); (3) traffic monitoring systems for vehicles [5] rely on cellular communications and therefore emphasize communication efficiency (TransT and TransL); (4) precision agriculture based on IoT sensing [6] does not require urgent response but necessitates energy-efficient solutions, with emphasis on CompL and TransL; (5) healthcare systems, like fall detection for elderly individuals [7], require both quick response time and small energy consumption, and therefore prioritize all four training parameters (CompT, TransT, CompL, and TransL); and (6) human stampede detection/prevention systems, as discussed in [8], need efficient systems for time, computation, and communication.

In this chapter, we explore the problem of supporting FL in edge computing from the perspective of FL hyper-parameter tuning. FL hyper-parameters significantly affect the system overhead of FL training, and thus, optimizing FL hyper-parameters is greatly valuable for resource-constrained edge computing. We organize this chapter as follows. Section 2 provides related work on edge computing and FL hyperparameter tuning. Section 3 explains the challenges of supporting FL in edge computing, and Section 4 presents some preliminary results. Last, Section 5 concludes this chapter.


*Edited by Thomas Heinbockel and Robert Weissert*

The recent and ongoing COVID-19 pandemic has changed societies and research around the world. As such, this new book examines the latest developments in the field of neuroscience related to these changes. It includes six chapters in two sections: "COVID-19 Effects: Neurology, Neuroimmunology, Neurogenesis" and "Molecular and Cellular Neurochemistry." The first section includes chapters that address such topics as COVID's effect on adult neurogenesis, neurological manifestations of COVID-19, and COVID-19 and seizures. Chapters in the second section discuss peripheral biomarkers in multiple sclerosis, amino acids as neurotransmitters, advancements in RNA sequencing technologies, and more.

ISBN 978-1-80355-030-5

COVID-19, Neuroimmunology and Neural Function

Published in London, UK © 2022 IntechOpen © 100 / iStock


**7. Patent information**

About 40 patent information on agriculture related matter including all necessary agenda are presented in **Table 4**, which deal with, synthesis of various flavonoids in plant and their analogs, method for increasing the flavonoids content, pest control and pesticidal activity of plant and plant protection.


**Author details**

Yasuhiko Minokoshi1,2

1 Department of Homeostatic Regulation, Division of Endocrinology and Metabolism, National Institute for Physiological Sciences, Okazaki, Japan

2 Department of Physiological Sciences, School of Life Science, The Graduate University for Advanced Studies SOKENDAI, Okazaki, Japan

\*Address all correspondence to<EMAIL_ADDRESS>
© 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.

**17**

*Neural Control of Homeostatic Feeding and Food Selection*

2017;**4**:217-226. DOI: 10.3233/

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10.1016/j.celrep.2017.11.102

[11] Andermann ML, Lowell BB.  Cell Metabolism. 2014;**19**:293-301. DOI:

[13] Farooqi S, O'Rahilly S. Genetics of obesity in humans. Endocrine

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understanding of appetite control. Neuron. 2017;**95**:757-778. DOI: 10.1016/j.neuron.2017.06.014

NHA-170027

*DOI: http://dx.doi.org/10.5772/intechopen.93413*

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*Neural Control of Homeostatic Feeding and Food Selection DOI: http://dx.doi.org/10.5772/intechopen.93413*


**2. Biomechanical basic concepts**

#### **2.1 Strain**

Strain is a local deformation parameter expressed as units of length per length, usually expressed as a percentage, and is therefore dimensionless when the bone is loaded with different force vectors.

The mathematical definition (Eq. (1)) of strain is the change in length divided by the original length.

Formula for strain calculus:

$$\text{Strain} \left( \% \right) = \frac{\text{Change in length (mm)}}{\text{Original length (mm)}} \tag{1}$$

Due to the dimensionless characteristic of this parameter, strain provides a clinically useful scaled measure of the displacement of bone fragments and can compare strain values in bones of different lengths. For example, a 1 mm fracture gap displacement is more significant in a 10 mm rat (strain 10%) femur than in a 300-mm dog femur (strain 0.3%) [1, 2].

#### **2.2 Stress**

One of the main functions of the appendicular skeleton is to support the body weight in rest or during movement, and consequently, bone is the tissue that supports more mechanical loads. When a force is applied to a bone, this will cause a stress situation [1, 2].

By definition, like pressure, stress is a local force expressed in units of force per unit area (Eq. (2)). The SI unit of force is the Newton, and force is often expressed as N/m2 or Pascal (Pa) [1, 2].

Formula for stress calculus:

$$\text{Stress} \left( \frac{\text{N}}{\text{mm}^2} \text{or} \text{Pa} \right) = \frac{\text{Load (N)}}{\text{Cross} - \text{sectional area } (\text{mm}^2)} \tag{2}$$

The damage that the load will cause depends on the area over which it is being distributed: a large force applied over a small area will result in greater stress, the contrary not being true. For instance, that is what happens when a skeletally immature dog falls from a height and supports all the weight on the hind limb. In these cases, the load will be equally distributed proximally and distally to the knee; however, due to the minor dimension of the distal part (tibial crest) of the tibial tuberosity, the fracture is normally located in this point due to stress concentration in a small area [3].

Bone tissue is constantly submitted to mechanical loads, comprehending forces/ loads of compression (axial), torsion, tension, bending, and shearing. Usually, these forces act in combination; however, they can be more predominant in an isolated way in certain locations of bones. Conceptually, it is considered that the deformation occurs in the bone tissue when small animals move and will vary between 0.04 and 0.3%, hardly exceeding 0.1%. This interval characterizes the elastic deformation of the bone, which is conceptually an initial response to the establishment of a load in the bone. In this scenario, the deformation/length of the bone returns to the initial dimensions/shape once the load is removed. It is a natural and important process for the homeostasis of bone tissue. An interesting characteristic of bone tissue is related to bone deformation according to the mechanical load that is applied. There are materials conceptually defined as isotropic, which respond to mechanical load regardless of the orientation of the material. By contrast, a material is considered anisotropic if the response to mechanical load varies with orientation. Bone is an example of an anisotropic material with mechanical properties that depend on the orientation of the bone lamellae. Thus, the mechanical properties are not equal in all directions and depend on the direction of the load applied. Long bones are stronger in longitudinal orientation than in tangential or radial orientation, since osteons have a longitudinal orientation in cortical bone. The maximum load that the bone will support is directly related to the direction in which the force is being applied. An illustrative example of this statement is that the appendicular bone supports a greater axial (compressive) load if compared to the transverse load. This difference between maximum strength in different directions emphasizes the anisotropic characteristic of bone. An example of an isotropic material is the stainless-Steel 316L (metallic alloy commonly used in the production of plates, which presents a similar behavior regardless of the direction of the load that is applied, with a similar resistance [3].

From a mechanical point of view, bone is also considered a viscoelastic tissue. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Practically, this represents the ability of the bone to resist deformation without loss of definitive structural integrity. Viscoelasticity of bone is dependent on several factors including water, mineral, and collagen type I content [4].

This concept justifies the resistance of bone to sudden loads/impacts like jumps or falls: if there is some degree of deformation, there is later a return to the original form.

However, bone tissue is not always capable of withstanding all the loads that are applied to it, and this failure occurs when the imposed force exceeds the elastic deformation capacity, which may cause a complete or incomplete fracture. In this last situation, permanent deformation occurs in the tissue even after the load is removed, triggering microfractures and trabecular disruption and preceding macroscopic rupture [3].

*Biomechanical Basis of Bone Fracture and Fracture Osteosynthesis in Small Animals DOI: http://dx.doi.org/10.5772/intechopen.112777*

**Figure 1.**

*Graphic representation of the stress/strain curve, and the biomechanical concepts of young modulus, yield, and fracture point.*

When a supraphysiological force is applied, the bone will be deformed. The mechanical properties of bone are well represented by the load/stress-strain curve (**Figure 1**). The load/stress response of the bone directly depends on the length, thickness, density, shape, and type of bone (cortical vs. cancellous), so the stressstrain curve represents the structural properties of the object. Bone is characterized by a stress-strain curve with initially a linear response, the so-called elastic deformation. From the point at which the response ceases to be linear to the load and starts to express a curve (physiological limit point), plastic deformation appears and microfractures occur at the structural level, which can culminate in macroscopic fractures if the load is not interrupted or maximum force is reached (fracture point) [3].

#### **2.3 Strength and stiffness**

Strength denotes the ultimate load a material can withstand before a catastrophic failure, which is also designated as the fracture point (**Figure 1**) when this concept is applied to bone [1–3].

The stiffness of a biomaterial or bone tissue is the mechanical property that characterizes and quantifies the changes in the original shape when a force vector or a load is applied to it. A graphic that represents stiffness is called a load/displacement curve, and the relationship between stress and strain for materials, or load and displacement for structures, can help us understand these properties better. The slope of the straight part of the curve that ascends represents the elastic modulus or stiffness. The steeper the slope of this part of the curve, the stiffer the material. The strain (or change in shape) in this part of the curve is elastic, which means the material can return to its original shape after the force is removed. There is a point on the curve, called Y, known as the yield point or yield load where the curve stops being nonlinear (**Figure 1**). At this point, the strain exceeds the material's ability to recover from its

original shape, and the material gets a permanent change in shape if the load is removed. This point shows where the material changes from elastic to plastic deformation. This point is important for clinical reasons because it means that the bone acquires a different shape from its original [2].

This permanent change in shape, called plastic (instead of elastic) deformation, occurs when covalent bonds break at a molecular level. The point on the curve where the material breaks or fails is called U, or ultimate failure/fracture point (**Figure 1**). The curve also shows how much energy the material can absorb during the loading process [2]. This is called toughness, and it is represented by the area under the curve [2].

#### **2.4 Elastic modulus of young**

The elastic modulus, also called the modulus of Young (Y), represents the relationship between stress and strain and is one of the most useful parameters for mechanically comparing biomaterials. It is calculated by applying the formula represented by Eq. (3), where the slope of the stress is plotted versus the strain curve (**Figure 1**). It has the same units as stress (N/mm2 ) because strain does not have any units [3]. It quantifies the relationship between tensile/compressive stress. Young's moduli values are normally so large that this parameter must be expressed in gigapascals (GPa) instead of in Pascals. The components of the formula for Young's modulus calculation are: σ (force per unit area) and axial strain, ε (proportional deformation) in the linear elastic region of a material and is determined using the formula (Eq. (3)):

Young modulus formula:

$$E = \frac{\sigma}{\varepsilon} \tag{3}$$

The elastic modulus of Young is a measure of the linear elasticity of a material. This parameter allows grading materials in two categories: flexible and rigid. Materials with higher Y values are considered rigid. The bone tissue, for example, is included in the rigid category with a value of 15 GPa but is less rigid when compared to materials used in the manufacture of orthopedic implants. The elastic modulus of stainless-steel implants is usually 188 GPa, pure titanium is 116 GPa, and titanium alloy (Ti-6Al-4 V) is 113 GPa. A single value of Y assumes a linear relationship, which is true for metals (until their yield point) [3].

#### **2.5 Area moment of inertia (AMI)**

The area moment of inertia is a geometric parameter to be considered when the mechanics of implants are studied. The AMI is a measure of the resistance of materials exclusively related to flexion loads. This parameter is only influenced by the geometry and not by the composition of materials. Implants manufactured with bigger AMI have the least probability of structural collapse when submitted to higher flexion loads (higher stiffness to flexion loads). AMI does not take into account material properties, and for that reason, AMI must be only used to compare different constructs of the same material. AMI is a geometric parameter that is calculated based on the dimensions of the structure in the direction of bending. For a circular implant (e.g., a pin or interlocking nail), the direction is not relevant, and the formula used for this particular type of implant is the following (Eq. (4)):

AMI formula for circular implant:

$$\frac{1}{4.p.r4} \tag{4}$$

In Eq. (4), the radius is raised to the fourth power, so a small increase in the diameter of a pin or other circular implant has a large impact on its bending stiffness.

This concept can be illustrated by the following example: if the AMI of a 2.4 mm pin (3/32 inch) is 1.6 mm4 and for a 3.2-mm (1/8 inch) pin is 5.1 mm4 , an increase of 33.3% of the pin diameter results in an increased AMI value, 3 times larger than an original pin.

For solid rectangular structures, AMI is calculated using a different formula (Eq. (5)):

AMI formula for solid rectangular structures:

$$\frac{1}{3.b.h3} \tag{5}$$

In the AMI formula, *b* is the width, and h is the height in the direction of bending. Plate thickness is an important parameter because this dimension is cubed. However, for bone plates, the presence of the screw holes adds complexity to this calculus. At the screw holes, the AMI is usually less than half the value that would be calculated from its external dimensions [5].

#### *2.5.1 The impact of plate orientation on AMI*

If the direction of the bending force of a fracture is known or the vector force can be simplified to a craniocaudal direction, the orthopedic surgeon can also use this concept of AMI to consider alternative plate locations. The classic example of this concept is for distal radius fractures. In this type of fractures, the primary direction of bending is considered to be in the craniocaudal plane; if a 2.7-mm LC-DCP (Limited Contact-Dynamic Compression Plate) is placed on the medial aspect, a higher AMI value (solid section of approximately 111 mm4 ) will be measured when compared to a 3.5 mm LC-DCP placed on the cranial aspect (AMI of 30 mm4 ), because the height of the 2.7 mm plate in the direction of bending is 8 mm (almost 3 times greater), compared with 3.3 mm for the 3.5 mm plate [2].

Another variant that influences the AMI is the position of the implant regarding the neutral axis of the bone, which is represented by the medullary canal of the bone. If the implant is positioned more distant from the neutral axis, the implant is less efficient to resist the bending forces. For the mentioned reason, the interlocking nail is the most mechanically favored implant to resist bending forces [3].

The use of AMI helps the decision-making process for choosing the osteosynthesis method but is not exclusively based on this parameter. Every long bone has a tension side and a compression side when axial loading is applied to the bone that will cause deformation, promoting bending. When the axial loading is applied and the bone bends, one side will experience tension and the cortices suffer traction. At the same time, the opposite side of the bone and the bone cortices will experience compression. Every long bone has a neutral axis that corresponds to the medullary cavity and that does not suffer compression or traction forces, and also has a tension and compression sides [1–3].

By using the AMI and tension/compression sides defined for each bone, in the decision-making process of orthopedic surgery, two premises must be fulfilled to succeed: