**3. Multiband divider**

Since research on circuits and devices that support multiband systems is also actively conducted [20, 21], this section describes power dividers that can be matched at arbitrary three frequencies. Further, as an application thereof, it is shown that a dual-band power divider having an absolute constant bandwidth can be realized by moving the middle frequency closer to the low-frequency side among any three matching frequencies.

#### **3.1 Circuit construction and design method**

**Figure 6a** shows the circuit configuration of a power divider with three sections of LC-ladder circuits at the input port side [22]. The circuit parameters are normalized as described above. In designing a circuit using the even-/odd-mode excitation methods, consider an equivalent circuit having a onefold symmetry with respect to the plane AA' in **Figure 6b**. Each input/output port is represented as a terminal resistor. When the circuit structure is vertically symmetrical, *L*1*,*2*,*3*,*6, *C*1*,*2*,*4*,*5, and *R* are considered as two elements.

#### *3.1.1 Even-/odd-mode analysis*

Since the circuit in **Figure 6b** is also symmetric with respect to the plane AA', the even-/odd-mode analysis can be applied as in 2.2.1 and 2.2.2. **Figure 7** shows equivalent circuits at even-/odd-mode excitations. The conditional equations for obtaining the circuit parameters are as follows.

**Figure 6.**

*(a) Schematic of LC-ladder divider with three matching frequencies and (b) its equivalent circuit with onefold symmetry.*

**Figure 7.** *Equivalent circuit of Figure 6 at (a) even- and (b) odd-mode excitations.*

*Power Divider/Combiner DOI: http://dx.doi.org/10.5772/intechopen.104911*

$$\frac{1}{2R\_1} = \frac{1}{j2L\_1} + \frac{1}{\frac{2}{jC\_1} + \frac{1}{\frac{1}{jL\_2} + \frac{1}{\frac{1}{jC\_2} + \frac{1}{\frac{1}{jC\_3} + \frac{1}{\frac{1}{jC\_3} + R\_{(2,3)}}}}}}} \tag{3}$$

$$\frac{1}{R\_{(2,3)}} = jC\_3 + \frac{1}{jL\_4 + \frac{1}{\frac{jC\_4}{2} + \frac{1}{jL\_5 + \frac{1}{j2C\_5 + \frac{1}{\frac{jL\_6}{2} + \frac{1}{\frac{jL\_6}{2} + \frac{1}{\frac{jL\_6}{2}}}}}}}} \tag{4}$$

All parameters can be derived by the above operation, and an equal power divider with arbitrary three matching frequencies can be designed.

#### *3.1.2 Scattering parameters*

If the three normalized matching frequencies *f*1/*f*2/*f*<sup>3</sup> are set to 0.4/0.6/1.6, 0.4/0.8/ 1.6, and 0.4/1.0/1.6 according to the above design procedure, the circuit parameters of the equal power divider are shown in **Table 2**. The frequency characteristics of the scattering matrix for each power divider are shown in **Figure 8a**-**c**. The scattering matrix elements shown in this figure refer to reflection characteristics (*S*11, *S*22), division characteristics (*S*21), and isolation characteristics (*S*32). Good power division characteristics and reflection/isolation characteristics at the desired frequency can be confirmed for each circuit. Next, we are studying a dual-band power divider with absolute constant bandwidth in the UHF/SHF band. Here, the bandwidth of the UHF band is expanded by bringing two of the abovementioned three matching frequencies closer to each other. **Figure 9** shows the frequency characteristics when the design frequency ratio is 0.4/0.45/1.6. As shown in this graph, it can be seen that the band of the 920 MHz band is expanded. In the next section, when designing a dual-band power divider in the UHF/SHF band, the circuit pattern is examined by referring to each element value when the matching frequency ratio is 0.4/0.45/1.6 in **Table 2**.


**Table 2.** *Normalized circuit parameters for LC-ladder divider with various three matching frequencies.*

**Figure 8.**

*Scattering matrix of LC-ladder divider with three matching frequencies. (a) Reflection, (b) power division, and (c) isolation characteristics.*

**Figure 9.** *Scattering matrix of LC-ladder divider with constant absolute bandwidth.*

#### **3.2 Simulation and experiment**

Based on the circuit analysis using the even-/odd-mode excitation method mentioned above, we are studying the circuit pattern on the dielectric substrate by an electromagnetic analysis as a preliminary step to the trial production. The circuit pattern is shown in **Figure 10a**. The design frequency is 0.4/0.45/1.6 with a frequency ratio to the center frequency of 2.3 GHz, that is, 920 MHz/1.03 GHz/ 3.68 GHz, and the conditions for the electromagnetic simulation are the same as in Section 2.3. Assume the use of GRM Series and MCR series for capacitors and resistors, respectively. Assuming the influence of the self-resonant frequency of the element on the circuit characteristics, the inductor is arranged by the bending pattern of the line instead of the chip element. In **Figure 10a**, the circuit size is 7.0 9.3 mm<sup>2</sup> excluding the input/output ports. The frequency characteristics of the scattering matrix obtained by the electromagnetic simulation of the circuit pattern in **Figure 10a** are shown in **Figure 10b**. In addition to good reflection/isolation characteristics and division characteristics at the desired design frequency, the absolute constant bandwidth based on the center frequency in the UHF/SHF band is about 8.6%/7.4%. A prototype experiment is being conducted under the same conditions for the circuit pattern examined by the electromagnetic simulation above. A circuit is realized by forming a conductor pattern on a dielectric substrate using a commercially available substrate processing machine (ProtoMat S63/LPKF) and soldering each element to a predetermined position. A conductor pin is inserted into the via hole with a diameter of 0.3 mm and sintered to connect to the

**Figure 10.**

*Experiment of LC-ladder divider with constant absolute bandwidth. (a) Simulation pattern, (b) its analysis results, (c) photograph of fabricated divider, and (d) experimental results.*

ground conductor. **Figure 10c** shows a photograph of the prototype circuit. The frequency characteristics of this circuit were measured using a vector network analyzer. The results are shown in **Figure 10d**. Good characteristics are almost identical to the analysis results, and the absolute bandwidth of 5.6%/4.8% can be confirmed in both operating bands.
