A) System configuration

The proposed system was designed for a frequency range of 30–80 MHz (VHF Band). The phase matching is obtained by a capacitor-tuned phase shifter. We required the phase shifter to meet the following specifications: insertion loss lower than 3 dB and S ₁₁ lower than −20 dB. Therefore, we chose to implement the phase shifter design with a hybrid 90° coupler and a capacitor bank installed in each channel. In order to achieve matching between the three channels, the system is computer controlled (Fig. 1), determining the precise capacitor values. As a result, each channel is matched for a specific frequency band, while the other channels are kept isolated.

B) Coupler

The coupler was designed in a stripline structure for uniform transverse electromagnetic (TEM) wave propagation. Accordingly, the coupler can be modeled as an equivalent capacitor circuit [Reference Collin3, Reference Pozar4]. The design must take into consideration a wideband matching range and high-power transmission within acceptable dimension limitations for acceptable application. To achieve small-scale device in this frequency range, we selected meander geometry [Reference Weiss5–Reference Sugiura7]. We used electromagnetic simulations in order to design our coupler. Taking into account the contribution of even and odd modes of the coupler, we used the following equations:

(1) $$Z_{0_o} = {\eta _0} \displaystyle{1 \over {2W\sqrt {\varepsilon _r} \left[ {\displaystyle{{2B} \over {{B^2} - {S^2}}} + \displaystyle{1 \over S}} \right]}},$$

(2) $$Z_{0e} = {\eta _0}\displaystyle{{{B^2} - {S^2}} \over {4BW\sqrt {\varepsilon _r}}}, $$

where Z _{0 o} and Z _{0 e} are the approximate odd and even mode impedance expressions, respectively, B is the distance between the two ground plates, S is the distance between the two strip lines, W is the strip width, η ₀ is the characteristic impedance of free-space, and ε _r is the relative dielectric constant of the substrate. The stripline geometry and the related parameters are shown in Fig. 2. The total impedance Z ₀ of the coupler [Reference March8] can be written as

(3) $$Z_{0} = \sqrt {Z_{{0_e}}{Z_{0o}}}. $$

Fig. 2.

Stripline coupler.

In the following section, we will elaborate on several considerations which must be taken into account for design of the mentioned coupler geometry [Reference Rehnmark9]. First, line width affects both mutual coupling and impedance value. In our simulation, the line width, which was first designed to be uniform, exhibited undesired mutual coupling and high electrical fields close to the coupler ports. Second, the bending radius of the meander must be larger than the strip width [Reference Pozar4]. In our simulation, the coupler dimensions exceeded the maximum dimension constraints due to high bending radius to strip width ratio. Therefore, a correlation between W and S was introduced into the coupler design, and simulated to maintain the typical impedance and a minimal power loss. Finally, the distance between the two parallel lines must be large enough to achieve a minimal mutual coupling while retaining the compact dimensions of the coupler. Moreover, long parallel lines contribute to undesired mutual coupling along the stripline. Therefore, simulations of the power loss as a function of line length, line width, and line separation were performed (Fig. 3) in order to obtain optimal line dimensions. In addition, our coupler design was based on commercial materials in order to enable a future device fabrication. The simulation was based on the RT/duroid 6006 substrate with a relative dielectric constant of 6.15 and a thickness of 9.51 mm with 2 Oz of the copper layer. In order to obtain our device geometry, we introduced a combination of two striplines separated by the RT/duroid 6006 substrate with a thickness of 1 mm, B = 20 mm, S = 1 mm, W = 3, and L = 550 mm as defined in Fig. 2. Additional substrates were combined in order to obtain the device thickness requirements from the stripline to the ground plates. Electromagnetic simulations of the hybrid coupler show an insertion loss of ~3 dB in the transmission and coupling ports along with a reflection coefficient (S ₁₁) lower than −20 dB at the frequency range of 40–75 MHz (Fig. 4). The final structure of the coupler is shown in Fig. 5.

Fig. 3.

IL (dB) as a function of stripline length (cm).

Fig. 4.

S-parameters HFSS simulation of the coupler. Port designation: 1 for input, 2 for coupling, 3 for through, and 4 for isolation.

Fig. 5.

Meander geometry of the coupler showing six bends structure with steps in the width along the line.

C) Capacitor bank

The capacitor bank was connected to the coupling and to the through ports of the coupler, as a part of the matching unit diagram block, shown in Fig. 6. The capacitor bank, covering a phase range of 0–180°, was monitored by a phase control unit, which determines the capacitance for each channel. Each capacitance value provides a specific phase shift at a given frequency. The obtained phase shift was correlated with the two other channels to maintain a simultaneous phase match to the antenna. In order to obtain the capacitance value for each channel, the following procedure was applied, starting with equation (4), which represents the matching condition for couplers junction, in our case it was realized for three channels.

(4) $${\mathop{\rm Im}\nolimits} \left\{ {\;\sum\limits_j {{y_{ij}} + {y_{st{b_i}}}}} \right\} = \sum\limits_j {{b_{ij}} + {b_{st{b_i}}} = 0}, $$

(5) $${y_{ij}} = \displaystyle{{1 + {\Gamma _{ij}}} \over {1 - {\Gamma _{ij}}}}.$$

Fig. 6.

Matching unit diagram block.

y _ij and Γ _ij are the admittance and reflection coefficients, respectively, of channel j at the (self)-frequency of channel i. y _{stb i} is the admittance, at the (self)-frequency of channel i, of the additional stub connected between the matching unit and the junction of the three channels. By equating the imaginary part of the admittance to zero we can extract b _ij , the susceptance of channel j, at (self)-frequency of channel i and b _{stb i} , the susceptance of the additional stub at the self-frequency of channel i. By equating this part to zero, we can state that the junction is matched for all connected channels. The reflection is given by

(6) $${\Gamma _{ij}} = {\langle {{S_{11}} + \displaystyle{{S_{21}^2 {\Gamma _B}} \over {1 - {S_{22}}{\Gamma _B}}}} \rangle _{ij}},$$

where Γ _B is the reflection coefficient of the stub. The reflection coefficient is obtained from the S-parameter matrix of each channel. Using the junction equation [Reference Collin3, Reference Pozar4], and assuming a system of three channels, we can write the following matrix equation:

(7) $$\eqalign{{b_{{\rm 12}}}({C_2}) + {b_{{\rm 13}}}({C_3}) + {b_{st{b_1}}} & = 0, \cr {b_{{\rm 21}}}({C_1}) + {b_{{\rm 23}}}({C_3}) + {b_{st{b_2}}} & = 0, \cr {b_{{\rm 31}}}({C_1}) + {b_{{\rm 32}}}({C_2}) + {b_{st{b_3}}} &= 0.} $$

C _i is the capacitance value for coupler in channel i and bij(C _i ) is the susceptance as a function of the associated capacitance. This matrix is solved numerically and results in a nine capacitors bank with capacitance range of 10–500 pF. The capacitance of each channel is found derived numerically, based on prior knowledge of the other channel frequencies. A typical phase shift graph, as a function of frequency, for several capacitance values, is shown in Fig. 7.

Fig. 7.

Phase shift simulation of coupler with a capacitors bank. The figure shows different phase shift lines for capacitors ranging from 10 to 500 pF where the calculating, up line, curve are related to the highest capacitance. The phase shift is linear along the frequency and exhibits a phase of more than 180°.

A) Experimental results

Measurement was performed on the coupler and a two continuous bank capacitor, having a capacitance range of 10–350 pF. Ports 1 and 2, respectively, are the phase shifter, input, and output ports (Fig. 6). Figure 10 shows the phase shifter scattering coefficients for different capacitance values.

Fig. 10.

Matching unit scattering coefficients.

The blue graphs indicate the transfer coefficients for different capacitance values. Insertion loss (IL) measured on the device, in the relevant frequency range, was −0.5 dB. Reflectance coefficients for the input port are marked in different colors corresponding to different values of capacitance.

Figure 11 presents the capability of the phase shift unit. The graph shows a linear frequency behavior for each capacitive value, for the 35–80 MHz frequency range. The capacitor bank, with a capacity range of 10–350 pF, provides phase shift ability of 180°. This behavior facilitates the computation of the system and displays a monovalent value for channels matching.

Fig. 11.

Phase control capability for different capacitance values.