Harmonic Dual-Band Diode Mixer for the X- and K-Bands

Article information

J. Electromagn. Eng. Sci. 2021;21(1):64-70

Publication date (electronic) : 2021 January 31

doi : https://doi.org/10.26866/jees.2021.21.1.64

Jeong Hun Park, Moon-Que Lee

School of Electrical Engineering and Computer Science, University of Seoul, Korea

^*Corresponding Author: Moon-Que Lee (e-mail: mqlee@uos.ac.kr)

Received 2020 July 14; Revised 2020 September 17; Accepted 2020 October 15.

Abstract

This paper presents a new dual-band diode mixer for the X- and K-bands. The proposed mixer consists of a pair of series-connected diodes and a frequency-dependent delay line that operates at 180° and 360° at the X-band of 10.525 GHz and at the K-band of 24.15 GHz, respectively. Without reconfigurable devices such as switches, the proposed mixer operates as a single-balanced diode mixer at the X-band and a subharmonically pumped antiparallel diode mixer at the K-band simultaneously. The designed circuit was implemented in a hybrid microwave integrated circuit using discretely packaged RF components on a microwave printed circuit board. The measurement results showed conversion losses of 6.5 dB and 16.6 dB at the X- and K-bands, respectively.

Keywords: Diode Mixer; Dual-Band; Radar

I. Introduction

A radar detector is a passive device that receives the microwave emission signals of a speed measuring or warning radar. It can also be used to help prevent speed-related car accidents. The frequency of these radars ranges at a variety of wavelength bands, usually at the X-, K-, and/or Ka-bands. The X- and K-bands at 10.525 GHz and 24.15 GHz, respectively, are the most common frequencies for speed measuring or warning [1].

Various microwave mixers in radar detector architectures have been studied to detect multi-band radar signals effectively. One simple method is to use two mixers for each band reception, but this approach has the disadvantages of a large circuit size and high cost. Common radar detectors usually adopt the architecture of a multi-band mixer. A gate FET mixer with a tunable gate bias voltage for the X-, K-, and Ka-bands has been explored [2]. This circuit detects only one RF band with respect to the optimized gate voltage for one band among the X-, K-, and Ka-bands. In addition to these approaches, some mixer schematics can be applied to a multi-band operation. A monolithic microwave integrated circuit (MMIC) mixer using a differential pair amplifier and a Gilbert cell mixer in a cascode configuration has been studied for multi-band wireless applications [3]. A dual-band subharmonic mixer making use of the second and fourth subharmonics of the local oscillator (LO) signal has been reported [4]. As a low-cost circuit, a dual-band self-oscillating mixer employing both the fundamental and harmonic signals has been proposed for the C-and X-bands [5].

This paper proposes a novel dual-band mixer without reconfigurable devices, which behaves as a single-balanced mixer at the X-band and a subharmonically pumped antiparallel diode mixer at the K-band simultaneously.

II. Mixing Operation and Circuit Design

Fig. 1 presents a schematic diagram of the proposed dual-band mixer for the X- and K-bands. The RF port receives dual-band signals at the X-band of 10.525 GHz and the K-band of 24.1 GHz. The LO frequencies are 11.275 GHz and 11.285 GHz for the X- and K-bands RF signals, respectively. The proposed mixer consists of a frequency diplexer for the isolation between the LO and IF (intermediate frequency) ports, a pair of series-connected diodes, a compact delay line with frequency dependency, and an RF matching circuit including a DC path. For the dual-band RF operation, the DC path was designed to have an infinite or high impedance at the X- and K-bands.

Fig. 1

Schematic diagram of a harmonic dual-band mixer for the X-and K-bands.

The key component of the proposed mixer is the frequency-dependent delay line connected between the cathode of diode 1 and the anode of diode 2. The transmission phase of the delay line is designed to have approximately 180° at the X-band RF and LO signals and 360° at the K-band RF signal of 24.1 GHz simultaneously.

1. X-Band Operation

In the X-band RF operation, the transmission phase of the delay line is approximately 180° at both the RF and LO signals. The voltage v_1,_X between the anode and the cathode of diode D1 shown in Fig. 1 is denoted as

(1) v1,X=vLO-vRF,X¯=vLO+vRF,X,

where the overbar of the symbol v_RF_,_X is the phase reversal of v_RF_,_X that occurs due to the delay line at the X-band. Similarly, the voltage v_2,_X between the anode and cathode of diode D2 can be described as

(2) v2,X=-vLO+vRF,X.

The V-I characteristics of a diode can be expressed as a power series.

(3) i=a0+a1v+a2v2+a3v3+⋯.

where a₀, a₁, a₂, and a₃ are the constant power series coefficients. The base band IF components in the mixer are linked to a₂ and a₃, which are related to the quadratic and cubic terms of the diode V-I characteristic, respectively. The quadratic term gives rise to the desired mixing product ω_RF − ω_LO, while the cubic term generates the subharmonic mixing component ω_RF − ω₂_LO.

The current i _IF_1,_X and i _IF_2,_X of the diodes related to mixing are

(4) iIF1,X∝v1,X2,

(5) iIF2,X∝v2,X2.

Considering the polarities, the sum current i_IF_,_X of the mixer is expressed as

(6) iIF,X=-iIF1,X+iIF2,X∝(-v1,X2+v2,X2).

After low-pass filtering, the IF component v_IF_,_X of the mixer is obtained as

(7) vIF,X∝cos{(ωRF,X-ωLO)t}.

This result is the same as the mixing component of a single-balanced diode mixer for the X-band RF signal.

2. K-Band Operation

In the case of the K-band RF operation, the voltage v_1,_X between the anode and the cathode of diode D1 can be described as

(8) v1,K=vLO-vRF,K.

Note that the RF voltage of the cathode of D1 v_X_,_RF has the in-phase through the delay line with a transmission of 360° at the K-band. The voltage v_2,_X between the anode and the cathode of diode D2 is

(9) v2,K=-vLO+vRF,K=-v1,K.

From the voltage relationship across the diodes, an antiparallel diode connection between D1 and D2 is achieved.

In the operation of the subharmonic mixer using an antiparallel diode connection, the IF components have no quadratic term because v1,K2 is identical to v2,K2 and is cancelled out.

In the subharmonic mixing, the current i_IF_1,_X of diode D1 is

(10) iIF1,K∝v1,K3.

Considering the polarity of D2, the current i_IF_2,_X is

(11) iIF2,K∝v2,K3=-v1,K3.

The sum current i_IF_,_X of the mixer is

(12) iIF,K=-iIF1,K+iIF2,K∝(-v1,K3+v2,K3)=-2v1,K3.

After low-pass filtering, the IF voltage component v_IF_,_X is obtained as

(13) vIF,K∝cos{(ωRF,K-2ωLO)t}.

In this configuration, the behavior of the proposed mixer is the same as that of a subharmonically pumped antiparallel diode mixer.

3. Delay Line with Frequency Dependency

The delay line between the cathode of D1 and the anode of D2 is implemented using a three-stepped impedance transmission line. The electrical length of the normal uniform transmission line with a phase of 360° at f_RF = 24.1 GHz has 157° at the X-band f_RF = 10.525 GHz, which is 23° away from the ideally required phase angle of 180°. This phase imbalance yields a poor LO to RF isolation (Fig. 2). To compensate for the phase imbalance at the dual-band RF signals, the authors propose the three-stepped transmission line, which has the required phase values at the X-and K-bands by adjusting the characteristic impedances and lengths of the three-stepped lines.

Fig. 2

Delay line (a) the conventional and (b) the proposed compact delay line.

The voltage and currents on both sides of the proposed delay line can be expressed using the ABCD matrix:

(14) [V1I1]=[ABCD] [V2I2],

where

(15) [ABCD]=[cos θ1jZ1 sin θ1jY1 sin θ1cos θ1]·[cos θ2jZ2 sin θ2jY2 sin θ2cos θ2]·[cos θ1jZ1 sin θ1jY1 sin θ1cos θ1].

Among the ABCD, the trans-impedance parameter “A” is given by

(16) A=cos θ2 cos 2θ1-(Z1Y2+Y1Z2)2 sin θ2 sin 2θ1.

The phase delay of each line section is given by

(17) θX1,2=θK1,2fXfK,

where θ_X_1,2 and θ_X_1,2 are the phase values at the X-band f_X and K-band f_X, respectively.

Fig. 3 shows the ideally required delay line at the X- and K-bands, where Z_X and Z_X are the characteristic impedances at the X- and K-bands, respectively. Their ABCD matrices are as follows:

Fig. 3

Ideally required equivalent delay line at (a) the X-band and (b) the K-band.

(18) [ABCD]X=[cos θXjZX sin θXjYX sin θXcos θX],

(19) [ABCD]K=[cos θKjZK sin θKjYK sin θKcos θK].

From Eqs. (16) and (18), for θ_X = 180°, the trans-impedance parameter “A” of the ABCD matrix should satisfy the following equation:

(20) cos θX2 cos 2θX1-(Z1Y2+Y2Z2)2sin θX2 sin 2θX1=-1.

Similarly, the required phase θ_X = 360° for the K-band is applied as

(21) cos θK2 cos 2θK1-(Z1Y2+Y1Z2)2sin θK2 sin 2θK1=1.

With the aid of the commercially available software Keysight ADS, Z₁, Z₂, θ_X₁, and θ_X₂, which satisfy Eqs. (20) and (21), were extracted as 50 Ω, 82 Ω, 100°, and 165°, respectively.

Fig. 4 shows the phase characteristics of the conventional uniform and the proposed delay lines. The proposed line yields a more optimized performance of phase reversal in the X-band RF and LO frequency compared with the conventional one.

Fig. 4

Transmission characteristics of (a) the uniform and (b) the proposed compact delay lines.

III. Measurement Results

Fig. 5 shows the equivalent circuit model of the Schottky diodes SMS7621-006LF used in the design [6].

Fig. 5

Equivalent circuit model of SMS7621-006LF.

Two Schottky diodes are series connected in a surface-mount plastic package, which has parasitic effects of lead inductances of 1 nH, stray capacitance of 0.07 pF between leads, and bond wire inductance of 0.3 nH. The intrinsic Schottky diode is expressed as the SPICE parameters: parasitic series resistance R_S = 12 Ω, zero-bias junction capacitance C_j₀ = 0.10 pF, and junction potential V_j = 0.51 V. Fig. 6 shows a photograph of the designed mixer fabricated on a Teflon substrate (TLC-30) of ɛ_r = 3.0 and h = 0.5 mm.

Fig. 6

Photograph of the proposed mixer.

Fig. 7 illustrates the simulated and measured performance of the mixer operating at the X-band RF signal. The conversion loss for the different LO input power from −10 dBm to +15 dBm is shown in Fig. 7(a). The saturated conversion loss of 6.5 dB is measured at an LO power level of 10 dBm. Fig. 7(b) presents the conversion loss of less than 7.6 dB over the X-band RF frequency at a range of 10.025–11.125 GHz at a fixed LO power of 10 dBm.

Fig. 7

Simulated and measured responses for the X-band RF input: (a) conversion loss with respect to the LO power and (b) conversion loss vs. RF frequency at f_LO = 11.275 GHz and LO power of 10 dBm.

Fig. 8 shows the simulated and measurement results in the K-band RF operation. The saturated conversion loss of 16.6 dB was measured at the LO power level of 0 dBm. The conversion loss ranged from 15.5 to 22.2 dB over the RF frequency range of 23.6–24.5 GHz at the optimal LO power of 0 dBm. The measurement shows that conversion loss increases when driven by LO power of over 0 dBm. This is attributed to the higher order mixing components generated in an overdriven diode.

Fig. 8

Simulated and measured responses for the K-band RF input: (a) conversion loss with respect to the LO power and (b) conversion loss vs. RF frequency at f_LO = 11.285 GHz and LO power of 0 dBm.

The proposed mixer has a single balance characteristic to the LO signal because of the traveling phase of 180° in the proposed compact delay line. Therefore, LO leakage in the RF port is canceled out. The LO-RF isolation was measured above 15.6 dB. The measured 1-dB compression points for the dual-band RF signal were 2 dBm and −9 dBm at 10.525 GHz and 24.1 GHz, respectively, as shown in Fig. 9.

Fig. 9

Simulated and measured responses for the X- and K-bands: (a) IF power with respect to the X-band RF power and (b) IF power with respect to the K-band RF power.

The performance of the designed dual-band mixer is compared with other published single-band passive mixers at the X-and K-bands in Table 1. According to the summary, the designed mixer shows acceptable performance in conversion loss at the X-band operation. Moreover, the conversion loss at the K-band seems acceptable, considering that the implementation uses packaged RF devices with a series lead inductance of 1 nH, which operates as a high impedance of j151 Ω at the K-band. The conversion loss and LO-RF isolation can be improved if we use the flip chip device with low parasitics or fabricate using the MMIC process.

Table 1

Performance summary of the published mixers at the X- and K-bands

IV. Conclusion

A new topology for a dual-band diode mixer has been proposed. The proposed harmonic dual-band mixer operates as a single-balanced mixer and a subharmonically pumped antiparallel diode mixer at the X- and K-bands, respectively. The validity of the proposed mixer was demonstrated by measurement results showing acceptable conversion loss and LO-RF isolation at both the X- and K-bands. The proposed dual-band mixer without reconfigurable devices, such as switches, has the advantages of simplicity, circuit size, and cost over conventional ones.

Acknowledgments

This work was supported by IITP grant funded by the Korea government (MSIT) (No. 2018-0-01658, Key Technologies Development for Next-Generation Satellites) and KIAT grant funded by the Korea Government (MOTIE) (No. N0001883, The Competency Development Program for Industry Specialist).

References

1. Martinson GD, Burin MM. Radar detector technology. Applied Microwave 2:68–85. 1990;

2. Kang SY, Yun Y, Jung JW, Go MH, Park HD. Study on improving sensitivity of multi-broadband receivers. Electronics Letters 43(25):1438–1439. 2007;

3. Wang RL, Su YK, Chien HH, Chuang CC, Hsiao HF, Tu CH, Juang YZ. A concurrent dual-band folded-cascode mixer using a LC-tank biasing circuit. Microelectronics Journal 43(12):1010–1015. 2012;

4. Pushpa K, Mondal P, Singh A. A dual-band subharmonic mixer with high RF-IF isolation. In : Proceedings of 2017 Progress in Electromagnetics Research Symposium-Fall (PIERS-FALL). Singapore; 2017; p. 1183–1189.

5. Jackson BR, Saavedra CE. A dual-band self-oscillating mixer for C-band and X-band applications. IEEE Transactions on Microwave Theory and Techniques 58(2):318–323. 2010;

6. Nguyen NTP, Van Tran S, Nguyen DB, Mai L. Design and implement a single-balanced mixer at S band. In : Proceedings of the 2015 International Conference on Advanced Technologies for Communications (ATC). Ho Chi Minh City, Vietnam; 2015; p. 637–641.

7. Begemann G. An X-band balanced fin-line mixer. IEEE Transactions on Microwave Theory and Techniques 26(12):1007–1011. 1978;

8. Bose C, Pal R, Mandai MK. Design of a wideband down-conversion mixer in X-band. In : Proceedings of the 2018 3rd International Conference on Microwave and Photonics (IC-MAP). Dhanbad, India; 2018; p. 1–2.

9. Mei L, Yao C. Low conversion loss mixers design using reflector networks. In : Proceedings of the 2018 12th International Symposium on Antennas, Propagation and EM Theory (ISAPE). Hangzhou, China; 2018; p. 1–4.

10. Mohyuddin W, Kim IB, Choi HC, Kim KW. Design of a compact single-balanced mixer for UWB applications. Journal of Electromagnetic Engineering and Science 17(2):65–70. 2017;

11. Deng KL, Wu YB, Tang YL, Wang H, Chen CH. Broadband monolithic GaAs-based HEMT diode mixers. In : Proceedings of the 2000 Asia-Pacific Microwave Conference. Sydney, Australia; 2000; p. 1135–1138.

12. Lin C, Lai Y, Chiu J, Wang Y. A 23-37 GHz miniature MMIC subharmonic mixer. IEEE Microwave and Wireless Components Letters 17(9):679–681. 2007;

13. Wei HJ, Meng C, Wu PY, Tsung KC. K-band CMOS sub-harmonic resistive mixer with a miniature marchand balun on lossy silicon substrate. IEEE Microwave and Wireless Components Letters 18(1):40–42. 2008;

Biography

Jeong Hun Park received his B.S. and M.S. degrees in electrical and computer engineering from the University of Seoul, Seoul, South Korea, in 2007 and 2020, respectively. He is currently working toward his Ph.D. degree in the school of electrical and computer engineering at the University of Seoul. His research interests include RF/microwave circuits and systems, radar systems, and retro-directive systems in satellite applications.

Moon-Que Lee received his B.S. degree in electrical engineering from the Korea Advanced Institute of Technology, Daejeon, South Korea, in 1992, and his M.S. and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, South Korea, in 1994 and 1999, respectively. From 1999 to 2002, he worked as a research engineer at the Electronics and Telecommunications Research Institute. Since 2002, he has been a professor of the school of electrical and computer engineering at the University of Seoul, Seoul. Since 2015, he has worked as a creative planner for radio and satellite at the Ministry of Science, ICT and Future Planning, Korea Government. He is the author of over 53 international journals, 17 domestic/international patents, and nine RF and microwave engineering books. His research interests include microwave/millimeter wave circuits, monolithic microwave integrated circuits, hybrid circuits, wireless communication, and radar systems. He was a recipient of the 7th IEEE International Conference on RFID Best Paper Award in 2013.

Article information Continued

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.