Design of Compact Complex Impedance Transformer with Frequency and Terminal Impedance Tunability

Abstract

In the paper, a compact complex impedance transformer (CIT) composed of the cascading of three varactors loaded coupled lines and two variable shunt susceptances was proposed. Highly flexible tunability functions including only frequency tunable, only impedance tunable, and both frequency and impedance tunable can be achieved by tuning the capacitance of two types of varactors and the value of the susceptance. Design equations were derived using the even–odd mode analysis and examples are given for descripting the design procedures. For validation, a prototype was designed and fabricated. During measurement, three cases were exhibited. When the termination impedance was fixed, the measured center frequency can be tuned in the range of 1.1–2.1 GHz (62.5%). When the frequency was determined, different terminal impedances can be matched by the prototype. The function of frequency tunable at different terminal impedances is also trated by the measured results. After comparison, the potential of the proposed CIT for applications in radio frequency front-end were demonstrated.

1. Introduction

Impedance transformer [1,2] is an indispensable module in radio frequency front-end, wireless power transfer [3,4] and monolithic microwave integrated circuits. In recent years, because the impedances of the devices (such as mixers, power amplifiers, and crystal diodes) are always in a complex number, the research on complex impedance transformers (CITs) has received a lot of attention.

Generally, transmission lines (TLs) [5,6,7,8] are used for constructing CITs. In Ahn and Tentzeris [5], CIT with only one TL section was proposed. To solve the transforming range restrictions of the one TL section CIT, another TL and open/short stubs were added on the TL. Dual frequency CITs can also be obtained by TLs. In Manoochehri et al. [6], a Π-model dual-band CIT was presented to match two unequal arbitrary complex loads at two frequencies. Later, a dual-band CIT with selectable transmission zero was presented, which was composed of three sections of TLs and two shunt stubs [7]. In Xie et al. [8], parallel TLs were introduced for dual-frequency design. Except of TLs, coupled lines (CLs) can also be the candidate. For example, the miniaturized CIT based on modified CL [9] and the arbitrary terminated CIT based on susceptance loaded CL [10]. Although single- and dual-frequency CITs can be realized by TLs and CLs, they only work for one group of complex impedances with predefined frequency when the dimension is fixed. No tunability is found for the frequency and the terminal impedance.

Due to the recent trend of multifunctional and multistandard RF front-ends in communication systems, there is an increasing demand for controllable or reconfigurable devices. Tunable CITs or impedance matching networks (IMNs) are popular for unlimited power transmission, antenna matching [11], tunable power amplifiers [12,13], duplexers [14], and on-chip noise measurement systems [15,16].

At present, the research on tunable CITs are mainly focused on frequency tunable and impedance tunable. In EI-Nozahi et al. [17], a reconfigurable IMN was proposed by using the tunable inductor implemented by common drain configuration. However, the inductive behavior was affected by the parasitic capacitance at higher frequencies. In Zhang et al. [18], by using one pin diode, the adjustment characteristics at two frequency points were achieved. In Lee and Lin [19], a novel pin inductor was proposed and applied for tunable wideband IMN with a tuning range of 2.8 GHz to 4.4 GHz. Whereas, the transformation is limited to real impedances. By mploying pin diodes as switching components, a digitally-controlled impedance tunable IMN was introduced [20]. Although over 60% Smith chart coverage was achieved, the optimization process is complex. In Fouladi et al. [21], an 8-bit impedance switched IMN based on the distributed microelectromechanical transmission line was proposed with a maximum standing wave ratio of 11.5:1. In Hoarau et al. [22], a tunable IMN was proposed, which transformed the impedances varying from 6 Ω to 1 kΩ and tuned in a 50% bandwidth. Unfortunately, the bandwidth was narrow (<2%). In Lu et al. [23], an impedance tunable IMN based on the combination of transmission line, capacitors, MEMS-based switches, and inductors was proposed. In Tombak [24], an impedance tunable IMN based on ferroelectric capacitors was designed. In Arabi et al. [25], the coverage of the Smith chart of four commonly used IMNs, such as typical T, Pi, ladder, and hybrid Pi, was studied in depth. In Shen and Barker [26], a tunable IMN implemented with minimal-contact RF-MEMS switches was proposed, which demonstrated excellent coverage of the Smith chart out to a maximum VSWR of 12:1 and covered a broad frequency range extending from 10 to 50 GHz. In Jeong et al. [27], impedance tunable IMN using a transmission line with variable characteristic impedance was presented, where the variable characteristic impedance was achieved by using parallel combinations of multiple transmission lines controlled by the RF switch. In Suvarna et al. [28], an integrated transformer-based tunable IMN was described. The real and imaginary parts of the impedance can be tuned independently. However, the reported works in [23,24,25,26,27,28] only exhibited the function of impedance tuning; the feature of frequency tunable was unrealizable.

In the paper, a novel frequency and terminal impedance tunable CIT is proposed with compact structure and enhanced bandwidth. It is composed of the cascading of three varactors loaded lines, and two variable shunt susceptances. By tuning the capacitance of two types of varactors and the value of the susceptance, highly flexible tunability can be obtained, including only frequency tunable, only impedance tunable, and both frequency and impedance tunable. The content of the paper is as follows: Section 2 derives the mathematical analysis of the proposed tunable CIT through even and odd mode analysis. Section 3 gives the parameter analysis and design procedure. A prototype is designed and implemented in Section 4 for validation, followed by a conclusion in Section 5.

2. Design Methodology

Figure 1 shows the schematic diagram of the tunable CIT, which is composed of the cascading of three varactors loaded coupled lines and two variable shunt susceptances. It can realize the transformation from real impedance to complex impedance. The even- and odd- mode characteristic impedances of the coupled lines with electrical length of θ₁ are Z_1e, and Z_1o, respectively. The varactors C₁ are shunt between the center of the first and third coupled line sections, whereas the varactor C₂ is shunt between the center of the second coupled line. The susceptance defined as B is connected in parallel in the middle of the second coupled line. Let Z_g be the impedance at port 1, and Z_L (Z_L = R_L + jX_L) be the impedance at port 2.

To simplify the analysis, equivalization was applied. When considering the proposed CIT as a four-port network, it can be equivalent to a parallel coupled line with the electrical length of θ₀, the even-mode characteristic impedance of Z_0e, and the odd-mode characteristic impedance of Z_0o, as shown in Figure 1. Then, using the even–odd mode analysis, the relations of the circuit parameters for the two four-port networks can be firstly expressed, as shown in Equations (1)–(4). Here, the condition of θ_1e = θ_1o = θ₁ is applied for simplification. Detailed derivations can be found in Appendix A.

$$Y_{1\mathrm{e}}=Y_{0\mathrm{e}}\frac{\cot \left(\frac{{\theta }_{0\mathrm{e}}}{2}\right)}{\cot \left(\frac{{\theta }_1}{2}\right)}$$

(1)

$$B=\frac{2Y_{1\mathrm{e}}\left({\tan }^2\left(\frac{{\theta }_{0\mathrm{e}}}{2}\right)-{\tan }^2\left(\frac{{\theta }_1}{2}\right)\right)}{\tan \left(\frac{{\theta }_1}{2}\right)\left({\tan }^2\left(\frac{{\theta }_{0\mathrm{e}}}{2}\right)+1\right)}$$

(2)

$$C_1=\frac{\left[\begin{array}{l}{Y}_{1\mathrm{o}}^2\left(\tan \left(\frac{{\theta }_1}{6}\right)-\cot \left(\frac{{\theta }_1}{3}\right)\right)\\ +Y_{1\mathrm{o}}{Y}_{0\mathrm{o}}\cot \left(\frac{{\theta }_{0\mathrm{o}}}{2}\right)\left(1+\cot \left(\frac{{\theta }_1}{3}\right)\tan \left(\frac{{\theta }_1}{6}\right)\right)\end{array}\right]}{4\pi f_0\left(Y_{0\mathrm{o}}\tan \left(\frac{{\theta }_1}{6}\right)\cot \left(\frac{{\theta }_{0\mathrm{o}}}{2}\right)-Y_{1\mathrm{o}}\right)}$$

(3)

$$C_2=\frac{m{Y}_{1\mathrm{o}}-Y_{1\mathrm{o}}\tan \left(\frac{{\theta }_1}{3}\right)-\frac{B}{2}\left(m\tan \left(\frac{{\theta }_1}{3}\right)+1\right)}{2\pi f_0\left(1+m\tan \left(\frac{{\theta }_1}{3}\right)\right)}$$

(4)

where:

$$m=\frac{\left[\begin{array}{l}{Y}_{1\mathrm{o}}{Y}_{0\mathrm{o}}\tan \left(\frac{{\theta }_{0\mathrm{o}}}{2}\right)\\ -4\pi f_0{C}_1{Y}_{0\mathrm{o}}\tan \left(\frac{{\theta }_1}{6}\right)\tan \left(\frac{{\theta }_{0\mathrm{o}}}{2}\right)\\ -4\pi f_0{C}_1{Y}_{1\mathrm{o}}-Y_{1\mathrm{o}}^2\tan \left(\frac{{\theta }_1}{6}\right)\end{array}\right]}{Y_{1\mathrm{o}}^2+Y_{1\mathrm{o}}{Y}_{0\mathrm{o}}\tan \left(\frac{{\theta }_{0\mathrm{o}}}{2}\right)\tan \left(\frac{{\theta }_1}{6}\right)}$$

(5)

It is observed from Equations (1)–(4) that by using the equivalization method, the analysis of the proposed tunable CIT can be changed to the analysis of a parallel coupled line. Thus, the input port impedance is expressed according to Jensen et al. [29].

$$Z_{\mathrm{in}}=\frac{V_1}{I_1}=\frac{Z_{11}{Z}_{\mathrm{L}}+\left|Z_{11}{Z}_{22}-Z_{12}{Z}_{21}\right|}{Z_{\mathrm{L}}+Z_{22}}$$

(6)

where:

$$Z_{11}=Z_{22}=\frac{1}{2\mathrm{j}}\left(Z_{0\mathrm{e}}\cot {\theta }_{0\mathrm{e}}+Z_{0\mathrm{o}}\cot {\theta }_{0\mathrm{o}}\right)$$

(7)

$$Z_{12}=Z_{21}=\frac{1}{2\mathrm{j}}(Z_{0\mathrm{e}}\cot {\theta }_{0\mathrm{e}}-Z_{0\mathrm{o}}\cot {\theta }_{0\mathrm{o}})$$

(8)

$${\theta }_{0\mathrm{e}}={\theta }_0={\theta }_{0\mathrm{o}}-\left(2n+1\right)\pi$$

(9)

In order to achieve an ideal match, the condition of Z_in = Z_g should be satisfied. Then, the even- and odd-mode characteristic impedances (Z_0e and Z_0o) of the equivalent parallel coupled line can be derived, as shown in Equations (10)–(11).

$$Z_{0\mathrm{e}}=\left\{\begin{array}{cc}\frac{\left[\begin{array}{l}\sqrt{Z_{\mathrm{g}}{R}_{\mathrm{L}}{(R_{\mathrm{L}}-Z_{\mathrm{g}})}^2+X_{\mathrm{L}}^2}\sin {\theta }_0\\ -Z_{\mathrm{g}}{X}_{\mathrm{L}}\tan {\theta }_0\end{array}\right]}{R_{\mathrm{L}}-Z_{\mathrm{g}}}& \left(Z_{\mathrm{g}}<R_{\mathrm{L}}\right)\\ -\frac{\left[\begin{array}{l}\sqrt{Z_{\mathrm{g}}{R}_{\mathrm{L}}{(R_{\mathrm{L}}-Z_{\mathrm{g}})}^2+X_{\mathrm{L}}^2}\sin {\theta }_0\\ +Z_{\mathrm{g}}{X}_{\mathrm{L}}\tan {\theta }_0\end{array}\right]}{R_{\mathrm{L}}-Z_{\mathrm{g}}}& \left(Z_{\mathrm{g}}>R_{\mathrm{L}}\right)\end{array}\right.$$

(10)

$$Z_{0\mathrm{o}}=\frac{-2Z_{\mathrm{g}}{X}_{\mathrm{L}}}{\left(R_{\mathrm{L}}-Z_{\mathrm{g}}\right)\cot {\theta }_0}-Z_{0\mathrm{e}}$$

(11)

$$C_3=\frac{B}{2\pi f_0}+\frac{1}{{\left(2\pi f_0\right)}^2{L}_1}$$

(12)

Equations (1)–(4), (10) and (11) indicate that the frequency and impedance of the proposed CIT can be tuned by changing the varactors C₁, C₂, and the susceptance B when other parameters are fixed. For example, when the operating frequency is changed from f₀ to f₁, the electrical length θ₁ is changed to θ₁·f₁/f₀. Thus, the values of θ₀, Z_0e, and Z_0o are varied accordingly. Then, the corresponding values of B, C₁, and C₂ for the new operating frequency f₁ can be obtained using Equations (2)–(4), which result in frequency tunable. Here, the changing of the susceptance B can be realized by Figure 2, which is composed of a fixed inductance L₁ paralleled with a varactor C₃. Equation (12) lists the relations between B, L₁, and C₃. Similar rules can also be found for the tuning of impedance. In the following, an example is designed in detail and procedures are given.

3. Design Procedures

In this section, a prototype was designed to validate the equations in Section 2. Detailed steps are listed below.

Step 1: Obtain the initial values of the circuit parameters.

In this design, the initial frequency f₀ was assigned as 1.5 GHz, the impedances Z_g and Z_L were set as 50 Ω and (60 − j10) Ω, respectively. According to Equations (10) and (11), the curves of Z_0e and Z_0o versus θ₀ can be plotted, as shown in Figure 3. Proper values of Z_0e and Z_0o can be determined by choosing θ₀. Here, θ₀ is chosen as 56°, Z_0e = 138.3 Ω, and Z_0o = 9.9 Ω. Substituting the obtained values in Equations (1) and (2), the values of Z_1e and B are calculated by choosing a proper value of θ₁. In the design, θ₁ is selected as 60°, and the calculated values of Z_1e and B are 127.4 Ω and −1.1 mS, respectively. From Equations (3) and (4), the curves of C₁ and C₂ versus different values of Z_1o can be plotted, as shown in Figure 4. Here, the value of Z_1o is selected as 80 Ω, and the initial values of C₁ and C₂ are calculated as 3.4 and 0.7 pF, separately.

Step 2: Obtain the corresponding values of C₁, C₂ and C₃ when the frequency is tuned.

When the frequency was tuned from f₀ to f₁ with fixed terminal impedance Z_L, the electrical length θ₁ (60°) changed to θ₁·f₁/f₀ (60°·f₁/1.5 GHz). According to Equation (10), Y_0e is a function of Z_g, Z_L, θ₀. Substitute Equation (10) into Equation (1), and the novel value of θ_0e (θ₀) at f₁ can be recalculated with the initial value of Z_1e (Z_1e = 127.4 Ω). The Z_0o corresponding to the novel value of θ₀ can be calculated by (11). Then, the novel values of B, C₁, and C₂ at f₁ can be obtained using Equations (2)–(4). Figure 5 shows the curves of capacitor C₁, C₂, and C₃ changing with the tuning frequency f₁. It is seen that when the tuning frequency f₁ is less than 1 GHz, the value of the capacitor C₁ is less than 0 pF, which is unrealizable. Similarly, the value of C₂ is less than 0 pF when the tuning frequency f₁ is larger than 2.28 GHz. Thus, the theory frequency tuning range of the designed prototype is 1.0–2.28 GHz.

Table 1. Calculated values of B, C₁, C₂, and C₃ corresponding to different tuning frequency f₁.

f1 (GHz)	C1 (pF)	C2 (pF)	B (mS)	C3 (pF)
1.1	13.8	2.2	1.3	2.7
1.3	5.5	0.2	0.1	1.8
1.5	3.4	0.7	−1.1	1.3
1.7	2.3	0.5	−2.3	0.9
1.9	1.7	0.3	−3.6	0.6
2.1	1.2	0.2	−4.9	0.3

shows the detailed calculated values of B, C₁, and C₂ corresponding to different tuning frequency f₁ in consideration of the realizable capacitance. Because B is composed of an inductor L₁ in parallel with a varactor C₃, the values of C₃ corresponding to different frequencies can be obtained with Equation (12) when choosing a fixed inductor. Here, L₁ is chosen as 8.2 nH, and the corresponding values of C₃ are illustrated in Table 1. In practice, the tuning fractional bandwidth of the proposed transformer is determined by the calculated realizable capacitance values of the three varactors.

Table 2. Parameters of the designed tune impedance transformer.

Zg (Ω)	50	Z1o (Ω)	80
ZL (Ω)	60–j10	θ1 (°)	60
f0 (GHz)	1.5	L1 (nH)	8.2
Z0e (Ω)	138.3	f1 (GHz)	1.1–2.1
Z0o (Ω)	9.9	C1 (pF)	1.2–13.8
θ0 (°)	56	C2 (pF)	0.2–2.2
Z1e (Ω)	127.4	C3 (pF)	0.3–2.7

illustrates the circuit parameters obtained by the procedures of Steps 1 and 2. Based on the parameters, a model is established in ADS for simulation. The theory results are shown in Figure 6, which includes the tuning center frequencies of 1.1, 1.3, 1.5, 1.7, 1.9, and 2.1 GHz. It is observed that a frequency tuning range of 1.1–2.1 GHz (62.5%) is achieved by changing the values of C₁, C₂, and C₃. In each tuning state, the |S₁₁| is below −30 dB at the center frequency. Under the criterion of |S₁₁| < −15 dB, the fractional bandwidths (FBWs) are 19.1%, 44.5%, 34.5%, 38.1%, 36.3%, 9.8%, respectively.

Step 3: Obtain the corresponding values of C₁, C₂, and C₃ when the terminal impedance is tuned.

When the terminal impedance (Z_L) is varied with fixed center frequency (f₀ = 1.5 GHz), the novel value of θ_0e (θ₀) at f₀ can also be recalculated with the initial value of Z_1e (Z_1e = 127.4 Ω) after substitute Equation (10) into Equation (1). The novel Z_0o can also be obtained through Equation (11). Then, the novel values of C₁, C₂, and C₃ can be obtained using Equations (2)–(4) and (12).

It is noted that for the determined Z_g and Z_L (R_L + jX_L), the range of its terminal complex impedance can be determined using the following limitations:

◆

The initial impedance R_L is larger than Z_g:

(1)

When the real part of the transformed complex impedance is greater than Z_g, the imaginary part has the same sign as X_L.

(2)

When the real part of the transformed complex impedance is smaller than Z_g, the imaginary part has the opposite sign to X_L.

◆

The initial impedance R_L is smaller than Z_g:

(1)

When the real part of the transformed complex impedance is smaller than Z_g, the imaginary part has the same sign as X_L.

(2)

When the real part of the transformed complex impedance is larger than Z_g, the imaginary part has the opposite sign to X_L.

Figure 7 shows the allowed and forbidden regions in the Smith chart according to the above limitations. The region which is colored yellow in Figure 7a corresponds to the situation of R_L > Z_g and X_L < 0, whereas the blue region in Figure 7a is for R_L > Z_g and X_L > 0. In Figure 7b, the blue and yellow regions represent the condition of R_L > Z_g/X_L > 0 and R_L > Z_g/X_L < 0, respectively.

For validation, several Z_L examples were selected among the realizable impedance range shown in Figure 7.

Table 3. Calculated values of C₁, C₂, and C₃ corresponding to different terminal impedance Z_L.

ZL (Ω)	C1 (pF)	C2 (pF)	C3 (pF)
80 − j30	7.88	0.99	1.22
70 − j20	4.41	1.01	1.24
60 − j10	3.40	0.70	1.30
40 + j20	2.33	0.80	0.99
30 + j25	2.32	0.82	1.23

illustrates the calculated C₁, C₂, and C₃ values corresponding to different terminal impedances. The theory results are plotted in Figure 8. It is observed that the FBWs of 23.8%, 36.5%, 34.5%, 6.0%, and 4.6% are obtained when Z_L equals with 80 − j30, 70 − j20, 60 − j10, 40 + j20, and 30 + j25 Ω, respectively, under the criterion of |S₁₁| < −15 dB. At the center frequency, the |S₁₁| is always below −28 dB.

4. Implementation and Measurements

To validate, the designed prototype was fabricated using the F4B substrate with a relative permittivity of 3.0, a loss tangent of 0.003, and a thickness of 1.5 mm. Figure 9 shows the layout and photograph of the fabricated prototype with an overall size of 35 mm × 24 mm. After optimization, the final dimensions were l₁ = 5.6 mm, w₁ = 0.95 mm, s₁ = 1.0 mm, l₂ = 6 mm, w₂ = 3.76 mm, w₃ = 1.5 mm, w₄ = 1.2 mm, w₅ = 1.5 mm, and the inductor L₁ was 5.6 nH. The DC blocking capacitor C_block was 33 μF, realized by Murata GRM-1885 series capacitors. Consider the variable capacitance C₁, the SMV1281 from Skyworks Solutions, Inc., was utilized, which can provide a capacitance range of 0.69–13.3 pF with the bias voltage between 0 and 20 V. Similarly, for C₂ and C₃, the SMV2019 from Skyworks Solutions, Inc., was utilized, which can provide a capacitance range of 0.23–2.3 pF with the bias voltage between 0 and 20 V. The resistor R_bias with a value of 9.1 kΩ was used for biasing. Measurement results were obtained using an Agilent N5230A microwave network analyzer. The results for only frequency tunable, only impedance tunable, both frequency and impedance tunable are given.

4.1. Frequency Tunable

Figure 10 plots the measurement results of different tuning frequencies under the bias voltage conditions shown in

Table 4. Bias conditions for different tuning frequencies.

Freq. (GHz)	Biasing Conditions
1.1	V1 = 1.3 V, V2 = 2.7 V, V3 = 1.1 V
1.3	V1 = 2.7 V, V2 = 4.1 V, V3 = 2.2 V
1.5	V1 = 4.4 V, V2 = 5.0 V, V3 = 3.7 V
1.7	V1 = 7.1 V, V2 = 7.3 V, V3 = 6.4 V
2.0	V1 = 9.4 V, V2 = 8.6 V, V3 = 8.5 V
2.1	V1 = 12.9 V, V2 = 10.2 V, V3 = 12.6 V

. The results indicate that the frequency of the fabricated prototype can be continuously adjusted from 1.1 to 2.1 GHz (62.5% tunability) by varying the bias voltages on the varactor diodes C₁, C₂, and C₃ without changing the circuit dimensions. It is seen from Figure 10a that for 15 dB return loss, the measured FBWs are 5.0%, 7.7%, 9.8%, 15.9%, 14.3%, and 13.0% for the tuning center frequencies of 1.1, 1.3, 1.5, 1.7, 2.0, and 2.1 GHz, respectively. While at each tuning center frequency, the measured |S₁₁| is less than −18 dB. As seen from Figure 10b, the measured insertion loss is in the range of 2–4 dB during the tuning of the frequency.

4.2. Terminal Impedance Tunable

Figure 11 plots the measurement results of different terminal impedances under the bias voltage conditions shown in

Table 5. Bias conditions for different terminal impedances.

ZL (Ω)	Biasing Conditions
35 + j25	V1 = 5.5 V, V2 = 4.7 V, V3 = 1.8 V
40 + j20	V1 = 5.2 V, V2 = 6.4 V, V3 = 1.8 V
60 − j10	V1 = 4.4 V, V2 = 5.0 V, V3 = 3.7 V
75 − j15	V1 = 5.4 V, V2 = 5.8 V, V3 = 4.4 V

. It is revealed that without changing the circuit dimensions, the terminal impedance of the designed CIT can be tuned by adjusting the bias voltages on the varactor. It is observed from Figure 11a that for each terminal impedance, the measured |S₁₁| at the center frequency is less than −20 dB. While under the criterion of |S₁₁| < −15 dB, the measured FBWs are 5.3%, 10.0%, 15.9%, and 10.3% for Z_L equals with 35 + j25 Ω, 40 + j20 Ω, 60 − j10 Ω, and 75 − j15 Ω, respectively. During the tuning, the measured |S₂₁| was in the range of −3 dB–−4.2 dB, as shown in Figure 11b.

4.3. Both Frequency and Terminal Impedance Tunable

Figure 12, Figure 13, Figure 14 and Figure 15 show the measurement results of different tuning frequencies corresponding to four different terminal impedances (Z_L = (35 + j25) Ω, (40 + j20) Ω, (75 − j15) Ω, and (80 − j30) Ω) under the bias voltage conditions shown in

Table 6. Bias conditions for different tuning frequencies and terminal impedances.

ZL (Ω)	Freq. (GHz)	Biasing Conditions (V)
35 + j25	1.5	V1 = 5.5, V2 = 4.7, V3 = 1.8
	1.8	V1 = 7.1, V2 = 5.8, V3 = 3.1
	2.0	V1 = 8.7, V2 = 7.2, V3 = 4.4
	2.2	V1 = 10.6, V2 = 8.5, V3 = 5.8
	2.3	V1 = 13.2, V2 = 10.0, V3 = 7.6
40 + j20	1.3	V1 = 3.9, V2 = 4.6, V3 = 0.9
	1.5	V1 = 5.2, V2 = 6.4, V3 = 1.8
	1.8	V1 = 6.7, V2 = 7.1, V3 = 3.1
	2.1	V1 = 8.2, V2 = 8.7, V3 = 4.4
	2.2	V1 = 9.6, V2 = 12.4, V3 = 6.1
75 − j15	1.1	V1 = 1.7, V2 = 3.4, V3 = 1.5
	1.3	V1 = 3.5, V2 = 4.4, V3 = 2.7
	1.5	V1 = 5.4, V2 = 5.8, V3 = 4.4
	1.7	V1 = 6.8, V2 = 7.2, V3 = 5.9
80 − j30	1.4	V1 = 4.7, V2 = 6.4, V3 = 4.9
	1.7	V1 = 6.2, V2 = 8.0, V3 = 6.9
	1.9	V1 = 8.4, V2 = 9.9, V3 = 10.7
	2.1	V1 = 10.6, V2 = 12.2, V3 = 13.8
	2.3	V1 = 11.9, V2 = 13.6, V3 = 16.0

. As seen from Figure 10, the measured frequency tuning range is from 1.5 GHz to 2.3 GHz (42.1%) when the terminal impedance is changed to (35 + j25) Ω. During the tuning, the FBWs are in the range of 5.2–7.7% under 15 dB return loss.

At each tuning center frequency, the measured |S₁₁| is less than −20 dB with less than 5 dB insertion loss. When the terminal impedance is tuned to (40 + j20) Ω, the frequency can be tuned from 1.3 GHz to 2.2 GHz (51.4%) with more than 20 dB return loss and less than 4 dB insertion loss at each tuning center frequency. In addition, the measured FBWs for |S₁₁| < −15 dB are in the range of 5.1–9.3%. For Z_L = (75 − j15) Ω and (80 − j30) Ω, the measured tuning center frequencies are in the range of 1.1–1.7 GHz (42.9%), and 1.4–2.3 GHz (48.6%), respectively. At each tuning center frequency, the measured return losses are more than 20 dB return loss and the measured insertion losses are less than 3.5 dB.

Table 7. Performance comparisons among the proposed and reported representative CITs.

Ref.	Technology	Tuning		Insertion Loss
		Frequency	Impedance
[17]	Tunable inductor	Δf/f0 = 23.3% (Continuous)	NO	--
[18]	Pin diodes	0.9 GHz, 2.0 GHz	NO	--
[19]	Pin inductor at RF breakdown	Δf/f0 = 44.4% (Continuous)	YES (Discrete)	2–3.5 dB
[20]	Pin diodes	NO	YES (Discrete)	--
[21]	Switched MEMS capacitors	NO	YES (Discrete)	0.4–7.55 dB
[22]	Varactor	Δf/f0 = 50% (Continuous)	YES (Continuous)	2.5–3.5 dB
[23]	MEMS-based switches	NO	YES (Discrete)	0.7–2.1 dB
[24]	Ferroelectric capacitors	NO	YES (Continuous)	1.4–2.5 dB
[25]	Varactor	NO	YES (Continuous)	--
[26]	RF-MEMS varactors	NO	YES (Continuous)	2.5–5 dB
[27]	Pin diodes	NO	YES (Discrete)	About 0.2 dB
[28]	NMOS switches	NO	YES (Discrete)	1.8–4 dB
This work	Varactor	Δf/f0 = 62.5% (Continuous)	YES (Continuous)	2–4.5 dB

summarizes the performance comparisons among the proposed and reported representative CITs. In Zhang et al. [18], the CIT was operated at two certain frequencies. For the CITs in EI-Nozahi et al. [17] and Lee and Lin [19], the frequency was tuned continuously with fixed terminal impedance. However, the tunability was less than 50%. In references [19,20,21,23,27,28], the terminal impedance was reconfigured at a certain fixed center frequency. Due to the using of switch diodes, the changing of terminal impedance was discrete. By using ferroelectric capacitors [24] and varactors [25,26], the terminal impedance can be tuned continuously. Although the work in [22] showed a frequency and impedance tuning ability, the bandwidth was narrow (<2%). d with the reported work, the proposed CIT exhibited higher flexibility including a larger frequency tuning range of 62.5% and a continuous tuning of the terminal impedance with enhanced bandwidth (>5%). The insertion loss of the designed prototype was slightly higher than other structures. Because a high Q-factor corresponds to low insertion loss, the loss of the CIT can be reduced by choosing varactors with a high Q-factor. In summary, the progress of the proposed CIT indicates that it can serve as a good candidate for microwave applications.

5. Conclusions

In this paper, a compact CIT with tunable frequency and terminal impedance was presented. The tunable characteristic was achieved by changing the capacitance of the three types of varactors shunt on the coupled lines. To demonstrate, an example was designed and fabricated. The measurement results verified the functions, including only frequency tunable, only terminal impedance tunable, and both frequency and terminal impedance tunable. The progress of the proposed structure indicates that it has the potential for applications in radio frequency front-end and monolithic microwave integrated circuits.