A Reflection-Type Dual-Band Phase Shifter with an Independently Tunable Phase

Abstract

This paper presents a design for a dual-band tunable phase shifter (PS) with independently controllable phase shifting between each operating frequency band. The proposed PS consists of a 3-dB hybrid coupler, in which the coupled and through ports terminate with the same two reflection loads. Each reflection load consists of a series of quarter-wavelength (λ/4) transmission lines, λ/4 shunt open stubs, and compensation elements at each operating frequency arm. In this design, a wide phase shifting range (PSR) is achievable at each operating frequency band (f_L: lower frequency; f_H: higher frequency) by compensating for the susceptance occurring at the co-operating frequency band caused by the λ/4 shunt open stub. The load of f_L does not affect the load of f_H and vice versa. The dual-band tunable PS was fabricated at f_L = 1.88 GHz and f_H = 2.44 GHz, and testing revealed that achieved a PSR of 114.1° with an in-band phase deviation (PD) of ± 8.43° at f_L and a PSR of 114.0° ± 5.409° at f_H over a 100 MHz bandwidth. In addition, the maximum insertion losses were smaller than 1.86 dB and 1.89 dB, while return losses were higher than 17.2 dB and 16.7 dB within each respective operating band.

1. Introduction

The phase shifter (PS) is one of the most important elements in wireless communication systems, as it is widely used in beam-forming, phased array, harmonic distortion, and multiple-input multiple-output (MIMO) systems [1,2,3,4,5,6,7,8]. Tunable PSs are used with along/digital attenuators in phased array beam-forming networks where insertion loss (IL) and phase deviation (PD) must be as small as possible to steer the lobes and nulls of antennas. Tunable PSs are classified as transmission type [9,10] and reflection type [11,12,13,14,15,16,17,18,19,20]. Reflection-type PSs can provide continuous phase shift, as well as excellent return loss (RL) due to their use of a 3-dB hybrid coupler and identical reflection loads at the coupler’s through and coupled ports. Since the DC power consumption of a varactor diode is much smaller than that of a PIN diode or a microwave FET, varactor diodes are widely used in PSs.

In [13], a PS with wide PSR was presented using L-type and π-type circuits, which provided a PSR of 201° for L-type and a PSR of 385° for π-type. Similarly, a reflection-type tunable PS using an impedance transforming quadrature coupler was presented in [14], in which a PSR of 234° was achieved at the center frequency. In [15], modifying the structure of [14] to cascading structure resulted in a PSR of up to 407°. A compact tunable PS which achieved a PSR of 407° was presented in [16] using a vertical planar structure. Likewise, a tunable reflection-type PS at X-band was presented in [17] using a coupled line. This PS achieved a PSR of 392° with an IL of 2.1 ± 1.3 dB over the operating band. However, the in-band maximum RL was always smaller than 10 dB. A wideband tunable PS based on a coupled line was demonstrated in [18,19]. The coupled line compensated for the parasitic elements of the varactor diode, resulting in a wide PSR with small in-band PD and IL error across an extensive bandwidth. By using the series-shunt matching technique in a reflection-type PS, a wide PSR with minimum IL was achieved in [18].

Multi-band RF circuits and systems have recently been in the spotlight. The multiple functions they perform are the key to next-generation wireless communication, sensing, and radar applications. Such multi-functional systems are designed to operate concurrently across multiple frequency bands. However, the traditional PSs can operate only on a single band. It is more effective to implement a multi-band PSs rather than rely on multiple single-band PSs. In [21], the PS operating in dual-band was present. However, in this paper, there is no tunable characteristic, and there is a disadvantage that only an arbitrary phase difference is implemented. A dual-band 90° PS using band-pass and band-stop designs was presented in [22]. Similarly, a dual-band PS that combined two single-band PSs was developed in [23]. In [24], a multi-band PS was included a distributed amplifier for loss compensation and an LC network for compact chip size. Likewise, a dual-band PS using a two-stage dual-branch phase tuning network topology was demonstrated in [25]. However, none of these previously developed conventional dual-band PSs possess an independent controllable phase shift at each operating frequency, except the PSs proposed in [25].

In this paper, a dual-band reflection-type tunable PS is presented, in which the phase shifts at the lower frequency band (f_L) and the higher frequency band (f_H) can be independently tuned. As an experimental demonstration, the proposed PS was designed and fabricated for a f_L of 1.88 GHz and f_H of 2.44 GHz. The design was ultimately confirmed to provide a PSR of 114° in each band.

2. Design Method of Proposed Dual-Band Phase Shifter

Figure 1 depicts the proposed structure of the dual-band tunable PS, which consists of a 3-dB hybrid coupler, where the coupled and through ports terminated in the same two reflection loads. Figure 1b shows the one-port reflection load (Γ_L) that consists of a f_L operating arm and a f_H operating arm. Each arm has series transmission lines (TLs) with characteristic impedance (Z_Ho or Z_Lo) and electrical length (θ_Ho or θ_Lo), shunt open stubs with characteristic impedance (Z_Hs or Z_Ls) and electrical length (θ_Hs or θ_Ls), parasitic compensation element (L_c and C_c), and varactor diodes (C_v). The series TL and shunt open stub is λ/4 at f_L in case of f_H operating arm, and vice versa. The λ/4 shunt open stub provides a short-circuited condition at node A/node B at the co-operatizing frequency.

The series λ/4 TL transforms the short-circuited condition into an open-circuited condition at the co-operating frequency. Accordingly, the f_L and f_H operating arms imitate an open-circuited condition at f_H and f_L, respectively.

2.1. Parasitic Susceptance Compensation

Each λ/4 shunt open stub works a short-circuited condition at node A for the co-operating band. However, the λ/4 shunt open stub acts as an additional susceptance at the operating band, which affects the PSR at the operating band. Therefore, the additional susceptance at the operating band should be compensated to achieve a wide PSR.

2.1.1. Susceptance Compensation at Low-Band Operation

In the f_L operation, the co-operating band can be represented by f_H. A λ/4 shunt open stub for f_H will provide a short-circuited condition at node A. However, a λ/4 shunt open stub will act as a capacitive component at f_L because f_L < f_H. To compensate for this additional susceptance, the shunt inductor (L_c) is connected at node A, as shown in Figure 2a. The input admittances of the λ/4 shunt open stub and L_c when observed from node A can be expressed as (1) and (2):

$$Y_{\mathrm{inA}}^{\mathrm{stub}}=j{Y}_{\mathrm{Hs}}\tan \left(\frac{\pi f_{\mathrm{L}}}{2f_{\mathrm{H}}}\right)$$

(1)

$$Y_{\mathrm{inA}}^{\mathrm{inductor}}=\frac{1}{j2\pi f_{\mathrm{L}}{L}_{\mathrm{c}}}$$

(2)

To compensate for the parasitic effect of a λ/4 shunt open stub, Equations (1) and (2) must be conjugated. The required L_c is calculated using Equation (3):

$$L_{\mathrm{c}}=\frac{1}{2\pi f_{\mathrm{L}}{Y}_{\mathrm{Hs}}\tan \left(\frac{\pi f_{\mathrm{L}}}{2f_{\mathrm{H}}}\right)}$$

(3)

2.1.2. Susceptance Compensation at High-Band Operation

Likewise, in an f_H operation, the co-operating band can be represented by f_L. The λ/4 shunt open stub for f_L provides a short-circuited condition at node B. However, a λ/4 shunt open stub will act as an inductive component at f_H because f_H > f_L. The capacitor was therefore connected in parallel to compensate the effect of the λ/4 shunt open stub, as shown in Figure 2b. The input admittances of the λ/4 shunt open stub and shunt capacitor (C_c) from the perspective of node B can be expressed using Equations (4) and (5):

$$Y_{\mathrm{inB}}^{\mathrm{stub}}=j{Y}_{\mathrm{Ls}}\tan \left(\frac{\pi f_{\mathrm{H}}}{2f_{\mathrm{L}}}\right)$$

(4)

$$Y_{\mathrm{inB}}^{\mathrm{capacitor}}=j2\pi f_{\mathrm{H}}{C}_{\mathrm{c}}$$

(5)

The parasitic compensating C_c is given as (6):

$$C_{\mathrm{c}}=-\frac{Y_{\mathrm{Ls}}\tan \left(\frac{\pi f_{\mathrm{H}}}{2f_{\mathrm{L}}}\right)}{2\pi f_{\mathrm{H}}}$$

(6)

2.2. Analysis of Phase Shifting Range

Figure 3 shows the equivalent circuits at f_L and f_H. With the exception of the series TL, none of the elements affect the PSR. By compensating for the parasitic effects of λ/4 shunt open stubs using (3) and (6), the proposed dual-band PS can achieve a PSR nearly identical to that obtained when a single alone varactor diode is used. The following sections discuss PSRs in each operating band.

2.2.1. Phase Shifting Range at Low-Band Operation

During f_L operation, the L_c is used to compensate for the unwanted effect of a λ/4 shunt open stub, as shown Figure 3a. The reflection load of the circuit at f_L (${\Gamma }_{\mathrm{L}}^{f_{\mathrm{L}}}$) can be determined using Equation (7):

$${\Gamma }_{\mathrm{L}}^{f_{\mathrm{L}}}=\frac{-X_{\mathrm{A}}{Z}_0+j{X}_{\mathrm{B}}{Z}_{\mathrm{Ho}}}{X_{\mathrm{A}}{Z}_0+j{X}_{\mathrm{B}}{Z}_{\mathrm{Ho}}},$$

(7)

in which:

$$X_{\mathrm{A}}=Z_{\mathrm{Ho}}{Z}_{\mathrm{Hs}}\cot {\theta }_{\mathrm{Hs}}-\omega L_{\mathrm{c}}{Z}_{\mathrm{Ho}}-\omega L_{\mathrm{c}}{Z}_{\mathrm{Hs}}-{\omega }^2{C}_{\mathrm{v}}{L}_{\mathrm{c}}{Z}_{\mathrm{Ho}}{Z}_{\mathrm{Hs}}\cot {\theta }_{\mathrm{Hs}}$$

(8a)

$$X_{\mathrm{B}}=Z_{\mathrm{Ho}}{Z}_{\mathrm{Hs}}+\omega L_{\mathrm{c}}{Z}_{\mathrm{Hs}}\cot {\theta }_{\mathrm{Hs}}-\omega L_{\mathrm{c}}{Z}_{\mathrm{Ho}}\tan {\theta }_{\mathrm{Ho}}-{\omega }^2{C}_{\mathrm{v}}{L}_{\mathrm{c}}{Z}_{\mathrm{Ho}}{Z}_{\mathrm{Hs}}$$

(8b)

$${\theta }_{\mathrm{Hs}}=\frac{\pi f}{2f_{\mathrm{H}}}, {\theta }_{\mathrm{Ho}}=\frac{\pi f}{2f_{\mathrm{H}}}$$

(8c)

and f is an operating frequency. From (7), the magnitude and phase of ${\Gamma }_{\mathrm{L}}^{f_{\mathrm{L}}}$ are determined using Equation (9a,b):

$$\left|{\Gamma }_{\mathrm{L}}^{f_{\mathrm{L}}}\right|=1$$

(9a)

$$\angle {\Gamma }_{\mathrm{L}}^{f_{\mathrm{L}}}={\varphi }_{f_{\mathrm{L}}}=\pi -2{\tan }^{-1}\left(\frac{X_{\mathrm{B}}{Z}_{\mathrm{Ho}}}{X_{\mathrm{A}}{Z}_0}\right)$$

(9b)

Using (9b), the PSR of the proposed structure at f_L can be expressed as the result of Equation (10), in which subscript V represents the bias voltage that changes the capacitance of C_v by varying V_min to V_max:

$${\Delta {\varphi }_{f_{\mathrm{L}}}|}_V=\{\begin{array}{l}{{\varphi }_{f_{\mathrm{L}}}|}_V-{{\varphi }_{f_{\mathrm{L}}}|}_{V\min }\hspace{1em}\mathrm{if}{{\varphi }_{f_{\mathrm{L}}}|}_{V\min }<{{\varphi }_{f_{\mathrm{L}}}|}_{V\max }\\ {{\varphi }_{f_{\mathrm{L}}}|}_V-{{\varphi }_{f_{\mathrm{L}}}|}_{V\max }\hspace{1em}\mathrm{if}{{\varphi }_{f_{\mathrm{L}}}|}_{V\min }>{{\varphi }_{f_{\mathrm{L}}}|}_{V\max }\end{array}$$

(10)

Table 1. Calculated PSR and in-band PD with Z_Ho, Z_Hs, and C_v.

ZHo [Ω]	ZHs [Ω]	PSR [°] (fL/fH)	PD [°] (fL/fH)
30	120	56.3/0	±1.19/±3.04
40		84.21/0	±4.69/±2.15
50		107.74/0	±10.69/±1.4
60		124.9/0	±18.45/±0.98
70		136.31/0	±27.22/±0.72
50	100	107.74/0	±13.07/±0.92
	110	107.74/0	±11.77/±1.14
	120	107.74/0	±10.69/±1.4
	130	107.74/0	±9.76/±1.69
	140	107.74/0	±8.97/±2.01

shows the calculated values of PSR and PD according to Z_Ho and Z_Hs. For demonstrations, f_L = 1.88 GHz, f_H = 2.44 GHz, and BW was 100 MHz. The value of L_c was calculated using (3), while C_v was implemented using a SMV-1231 from SKYWORKS, which provided variable capacitance by varying the bias voltage from 0 V to 16 V. PSR and PD at the f_L band increased along with Z_Ho. The PSR of the f_L band was remained constant, even though Z_Hs increased. However, the PD of the f_L band decreased and the PD of the f_H band increased as Z_Hs increased. These results highlight that an appropriate Z_Ho and Z_Hs must be selected to achieve the desired PSR and PD depending on the requirements of a specific application.

The design goals were specified as PSR > 100° at the f_L band, PD < 15° at the f_L band, and PD < 1.5° at the f_H band. For these specified design goals, the circuit parameters selected were Z_Ho = 50 Ω and Z_Hs = 120 Ω. Figure 4 shows the calculated PSR according to C_v variation.

Figure 5 depicts the PSR with and without compensation of for the λ/4 shunt open stub. The proposed PS achieved a PSR of 114° at the f_L band when the effect of the λ/4 shunt open stub was compensated for. However, PSR was reduced to 40° in cases where compensation was absent.

2.2.2. Phase Shifting Range at High-Band Operation

During f_H operation, the unwanted effect of a λ/4 shunt open stub was compensated by C_c, as shown in Figure 3b. The reflection load at f_H (${\Gamma }_{\mathrm{L}}^{f_{\mathrm{H}}}$) is determined using Equation (11):

$${\Gamma }_{\mathrm{L}}^{f_{\mathrm{H}}}=\frac{-X_{\mathrm{C}}{Z}_0+j{X}_{\mathrm{D}}{Z}_{Lo}}{X_{\mathrm{C}}{Z}_0+j{X}_{\mathrm{D}}{Z}_{Lo}},$$

(11)

in which:

$$X_{\mathrm{C}}=Z_{\mathrm{Lo}}+Z_{\mathrm{Ls}}\cot {\theta }_{\mathrm{Ls}}+2\pi f\left(C_{\mathrm{v}}+C_{\mathrm{c}}\right)Z_{\mathrm{Lo}}{Z}_{\mathrm{Ls}}\cot {\theta }_{\mathrm{Ls}}$$

(12a)

$$X_{\mathrm{D}}=Z_{\mathrm{Lo}}\tan {\theta }_{\mathrm{Lo}}-Z_{\mathrm{Ls}}\cot {\theta }_{\mathrm{Ls}}+2\pi f\left(C_{\mathrm{v}}+C_{\mathrm{c}}\right)Z_{\mathrm{Lo}}{Z}_{\mathrm{Ls}}$$

(12b)

$${\theta }_{\mathrm{Ls}}=\frac{\pi f}{2f_{\mathrm{L}}},{\theta }_{\mathrm{Lo}}=\frac{\pi f}{2f_{\mathrm{L}}}$$

(12c)

From (12), the magnitude and phase of ${\Gamma }_{\mathrm{L}}^{f_{\mathrm{H}}}$ can be determined using (13):

$$\left|{\Gamma }_{\mathrm{L}}^{f_{\mathrm{H}}}\right|=1$$

(13a)

$$\angle {\Gamma }_{\mathrm{L}}^{f_{\mathrm{H}}}={\varphi }_{f_{\mathrm{H}}}=\pi -2{\tan }^{-1}\left(\frac{X_{\mathrm{D}}{Z}_{\mathrm{Lo}}}{X_{\mathrm{C}}{Z}_0}\right)$$

(13b)

Using (13b), the PSR of the proposed structure can be expressed using Equation (14), in which subscript V represents a bias voltage of varactor:

$${\Delta {\varphi }_{f_{\mathrm{H}}}|}_V=\{\begin{array}{l}{{\varphi }_{f_{\mathrm{H}}}|}_V-{{\varphi }_{f_{\mathrm{H}}}|}_{V\min }\hspace{1em}\mathrm{if}{{\varphi }_{f_{\mathrm{H}}}|}_{V\min }<{{\varphi }_{f_{\mathrm{H}}}|}_{V\max }\\ {{\varphi }_{f_{\mathrm{H}}}|}_V-{{\varphi }_{f_{\mathrm{H}}}|}_{V\max }\hspace{1em}\mathrm{if}{{\varphi }_{f_{\mathrm{H}}}|}_{V\min }>{{\varphi }_{f_{\mathrm{H}}}|}_{V\max }\end{array}$$

(14)

Table 2. Calculated PSR and in-band PD with Z_Lo, Z_Ls, and C_v.

ZLo [Ω]	ZLs [Ω]	PSR [°] (fL/fH)	PD [°] (fL/fH)
30	120	0/141.08	4.11/4.93
40		0/135.7	2.55/4.55
50		0/121.82	1.68/9.30
60		0/106.67	1.18/12.75
70		0/92.58	0.87/14.58
50	100	0/121.82	1.11/11.36
	110	0/121.82	1.38/10.24
	120	0/121.82	1.68/9.30
	130	0/121.82	2.02/8.51
	140	0/121.82	2.39/7.83

shows that the calculated PSR and PD values as Z_Lo and Z_Ls varied. Consistent with f_L band operation, f_L = 1.88 GHz, f_H = 2.44 GHz, and BW was 100 MHz. The value of C_c that compensated for the effect of a λ/4 shunt open stub was calculated using (6), while C_v was implemented using a varactor SMV-1231 from SKYWORKS, which provided a variable capacitance of 4.7 pF to 0.3 pF by varying the bias voltage from 0 V to 16 V. The PSR at the f_H band decreased as Z_Lo increased, however, PD at the f_H band increased. Similarly, PSR remained constant as Z_Ls increased. PD, however, increased at the f_L band while PD decreased at the f_H band. Therefore, appropriate Z_Lo and Z_Ls values should be selected to achieve the desired PSR and PD, keeping in mind the specific application.

Like the f_L operation, the design goals were specified as PSR > 100° at the f_H band and PD < 2° and 10° at the f_L and f_H band, respectively. To achieve these design goals, the circuit parameters were selected as Z_Lo = 50 Ω and Z_Ls = 120 Ω. Figure 6 shows the calculated PSR according to C_v variations.

Figure 7 depicts the PSR with and without compensation for the λ/4 shunt open stub. A PSR of 116° at the f_H band was achieved with compensation. However, the PSR increased to 203° in the absence of compensation. In the event that a wider PSR was desired, a circuit lacking compensation would be appropriate. We, however, assessed a circuit with compensation in order to obtain the same PSR as the varactor diode.

3. Simulation and Measurement Results

The proposed dual-band tunable PS was designed and fabricated at f_L = 1.88 GHz and f_H = 2.44 GHz with an operating bandwidth of 100 MHz, using a substrate RT/Duroid 5880 with a dielectric constant (ɛ_r) of 2.2 and a thickness (h) of 0.787 mm. The simulation was performed by using advanced design system (ADS) simulator. The variable capacitance C_v was implemented using a varactor diode SMV-1231 from SKYWORKS. A 3-dB hybrid coupler S03A2500N1 from ANAREN was also used. Figure 8 shows a layout and photograph of the designed dual-band tunable PS.

Figure 8a defines the transmission line width, length, and components in the entire circuit, and their values are listed in

Table 3. Physical dimensions and component value of fabricated PCB.

W1 = W2 = W5 = 2.4 mm	W3 = W4 = 0.5 mm	L1 = 22 mm
L2 = 29 mm	L3 = 23 mm	L4 = 30 mm
L5 = 13.6 mm	Lc = 5R4||5R4 (Part no.)/3.82 pF (@ fH)	Cc = 0R8 (Part no.)/1 pF (@ fL)
DC block capacitor: 120 J	RF choke inductor: 3R9	Bypass capacitor: 8R2
56.6 pF (@ fL)/216 pH (@ fH)	76.02 nH (@ fL)/223.8 nH (@ fH)	12 pF (@ fL)/29.01 pF (@ fH)

. The part number and measured value of DC block capacitor, RF choke inductor, bypass capacitor, L_C, and C_C at f_L and f_H are also listed. The overall size of the fabricated circuit was 85 mm × 52 mm.

3.1. Results of Low-Band Operation

Figure 9 presents out simulated and measured results achieved by varying the bias voltage of the varactor diode in the f_L band and fixing the bias voltage to 0 V in the f_H band. Figure 9a shows the simulated and measured PSRs. The phase at f_L band tuned, while the f_H band was maintained constantly. Based on our experiment, we determined that the PSR of the f_L was 114.194° ± 8.2615° within a bandwidth of 100 MHz, a result that was achieved by varying the bias voltage from 0 V to 16 V. While varying the phase at the f_L band, the phase of f_H remained at 0.225° ± 0.936° within the bandwidth. Figure 9b shows the simulated and measured IL and input/output RLs. The measured ILs at the f_L band and the f_H band were smaller than 1.867 dB and 1.897 dB, and the input/output RLs were higher than 19.674 dB and 16.684 dB, respectively.

Table 4. Measured results of the dual-band PS achieved by varying the bias voltage of the low-band while fixing the bias voltage of the high-band.

Bias Voltage [V] (fL/fH)	PSR [°] @ fL	Phase [°] @ fH	PD [°] (fL/fH)	Max. IL [dB] (fL/fH)	Min. RL [dB] (fL/fH)
0 to 16/2.5	114.067	60	±8.396/±0.342	1.580/1.989	19.669/21.077
0 to 16/16	114.494	114	±9.465/±0.667	1.414/1.419	19.695/25.047

@: means operating center frequency.

provides the measured results after varying the bias voltage of the varactor diode at the f_L band and fixing the bias voltage at 2.5 V and 16 V at the f_H band. As seen from Table 4, the f_L band achieved almost the same PSR and the phase of the f_H was constantly maintained. The measured ILs were smaller than 2 dB, and RLs were higher than 19.6 dB.

3.2. Results of High-Band Operation

Figure 10 shows the simulated and measured results of the dual-band PS achieved by varying the f_H band bias voltage from 0 V to 16 V and fixing the bias voltage at 0 V in the f_L band. The PSR of the f_H band was 114.097° ± 6.076°, and the phase at the f_L band was maintained at 0.360° ± 1.035°. The measured ILs were smaller than 1.867 dB and 1.983 dB, and RLs were higher than 22.550 dB and 16.833 dB within the two bands.

Table 5. Measured results of the dual-band PS achieved by varying the bias voltage of the high-band while fixing the bias voltage of the low-band.

Bias Voltage [V] (fL/fH)	Phase [°] @ fL	PSR [°] @ fH	PD [°] (fL/fH)	Max. IL [dB] (fL/fH)	Min. RL [dB] (fL/fH)
2/0 to 16	60	113.947	±1.035/±5.555	1.485/1.851	20.670/16.710
16/0 to 16	114	114.242	±0.168/±5.897	1.514/1.735	19.662/16.724

@: means operating center frequency.

presents the measured results when the bias voltage of the varactor diode at the f_H band was varied and fixing the bias voltage was fixed at 2 V and 16 V at the f_L band. As seen from Table 5, the f_H band achieved a nearly identical PSR while the phase of the f_L was constantly maintained. The measured ILs were smaller than 1.9 dB, and RLs were higher than 16.7 dB.

3.3. Simultaneous Dual-Band Operating Results

Figure 11 shows the simulated and measured results of the dual-band PS in the circumstance where the bias voltages of the f_L and f_H bands were simultaneously shifted. As seen in Figure 11a, the PSRs of the f_L and f_H bands were 114.134° ± 8.43° and 114.017° ± 5.409° within the bandwidth, a result achieved by varying the bias voltage from 0 V to 16 V. The ILs were smaller than 1.867 dB and 1.897 dB, and the input/output RLs were higher than 19.695 dB and 16.833 dB within bandwidth of the f_L and f_H bands.

A comparison of the performance of the proposed dual-band PS against previously reported PSs is provided in

Table 6. Performance of the proposed design against state-of-art alternatives.

References	Freq. [GHz]	BW [GHz]	Number of Varactors	IL [dB]	RL [dB]	PSR [°]	PD [°]	Dual-Band	Size [mm × mm]
[13]	2	0.2	6	<1.56	>13.4	385	NA	X	81 × 117
[14]	2	0.2	2	<4.6	>12	234	NA	X	49 × 51
[15]	2	0.2	4	<4.6	>14	407	NA	X	69 × 51
[16]	1.5	1	4	<5.8	>14	350	±100	X	52 × 32
[17]	10	2	4	<3.4	>10	392	NA	X	NA
[18]	2.2	0.8	2	<3.2	>10	360	±15	X	19.4 × 17
[19]	2.5	0.5	4	<1.28	>15.76	146.9	±5.79	X	NA
[20]	10	2	2	<2.3	>10	190	±10	X	NA
[24]	3.5	0.02	NA	<3.7	>10	360	±3	Yes	2.3 × 1.2 (IBM 180-nM RF CMOS)
	5.8	0.02		<4.5	>10	360	±3
[25]	5.9	0.2	12	<2.8	>10	106	NA/±7	Yes (independently)	0.92 × 1.06 (0.25 um GaAs process)
	16	0.4		<3.5	>10	108	±2/NA
This work	1.88	0.1	4	<1.867	>19.695	114.1	±8.43	Yes (independently)	85 × 52
	2.44	0.1		<1.897	>16.833	114.0	±5.40

. Although the previous PSs perform very well, in as much as they achieve a wide PSR and low in-band PD, these designs are single-band operation only. The proposed design, in contrast, is of a dual-band PS with independently controllable phase shifts in each band. In addition, unlike previously published papers, using a transmission line with an electrical length of λ/4 without a band-pass filter or a band-stop filter has the advantage of being able to fabricate more easily without using a compound process and can operate independently without affecting the co-operating frequency. This proposed design had a higher RLs, lower in-band PDs, and used fewer varactor diodes than previous PSs.

4. Conclusions

This paper presents an independently controllable dual-band tunable reflection-type PS. The proposed dual-band PS uses compensation elements to deal with the unwanted parasitic elements of a co-operating band with a shunt open stub and achieves wide PSRs at two operating bands. In the event that the ratio of two operating frequencies is greater than two and less than three, the inductor could be used as the same compensation element for both operating bands. The proposed dual-band PS was verified by fabricating the circuit at 1.88 GHz and 2.44 GHz. Furthermore, the proposed dual-band PS is easy to manufacture and would be useable in a number of diverse dual-band RF circuits and systems.