24–40 GHz mmWave Down-Conversion Mixer With Broadband Capacitor-Tuned Coupled Resonators for 5G New Radio Cellular Applications

In this paper, a 24–40 GHz broadband millimeter-wave (mmWave) down-conversion double-balanced mixer with a dual-band local oscillator (LO) buffer employing RF and IF coupled resonators is presented for 5G new radio (NR) frequency range 2 (FR2) cellular applications. The proposed mixer comprises a transformer-coupled <inline-formula> <tex-math notation="LaTeX">$g_{m}$ </tex-math></inline-formula>-boosted common-gate (CG) <inline-formula> <tex-math notation="LaTeX">$G_{m}$ </tex-math></inline-formula>-stage, a single-to-differential current-to-current RF capacitor-tuned coupled resonator, active switching stages with dual-band three-stage LO buffers, a current-to-voltage IF coupled resonator with gain equalization, and a wideband IF buffer with a transformer-based balun. The transformer-coupled <inline-formula> <tex-math notation="LaTeX">$g_{m}$ </tex-math></inline-formula>-boosted CG <inline-formula> <tex-math notation="LaTeX">$G_{m}$ </tex-math></inline-formula>-stage improves the NF and provides broadband input power matching. RF and IF coupled resonators enable an RF operating frequency range of 24–40 GHz and IF 1 dB bandwidth of more than 0.8 GHz, respectively. The implemented mixer was fabricated using a 40 nm CMOS process and characterized primarily in the 5G NR FR2 bands. The active die area was 0.654 mm<sup>2</sup>, and the mixer drew a bias current of 16 mA from a nominal supply voltage of 1.1 V. The mixer exhibited an RF operating frequency range of 24–40 GHz, noise figure of 12.4 dB, conversion gain of 1.2 dB, IF 1 dB bandwidth of 1.1 GHz, and output-referred third-order intercept point of 6.8 dBm.


I. INTRODUCTION
Fifth generation (5G) mobile communication technology, characterized by ultra-high speed, ultra-low latency, and hyper connection, makes it possible to realize key technologies of the fourth industrial revolution, such as smart The associate editor coordinating the review of this manuscript and approving it for publication was Yiming Huo. factories, autonomous driving, and virtual/augmented reality. Several noncontiguous millimeter-wave (mmWave) frequency bands of n257, n258, n259, n260, and n261, located in the range of 24.25-43. 5 GHz, are being allocated to different countries and regions for 5G new radio (NR) frequency range 2 (FR2) communications. Ultra-wideband mmWave phased array transceivers covering all the above bands are required to support frequency diversity and international roaming. There are several 5G NR transceiver architecture options for user equipment such as RF, baseband (BB), and intermediate frequency (IF) interfaces [1]- [10]. The IF interface is the most realistic choice and widely employed in mobile platforms owing to the lower loss and ease of matching at the IF signal frequency [1], [3], [4], [6]- [9]. One chip solution, including 5G NR sub-6 GHz frequency range 1 (FR1) and mmWave IF transceiver, can also be used to implement low-cost and highly integrated IF interface option [4]. For a 5G NR mmWave transceiver with an IF ratio interface option to cover all the FR2 bands, a broadband down-conversion mixer is required.
mmWave down-conversion active mixers based on the conventional Gilbert-cell mixer are widely used in 5G NR FR2 applications. The authors of [2] and [3] employed a Gilbert mixer with current bleeding techniques in direct-conversion and sliding-IF receivers. Gilbert mixers with multiple gate transistors (MGTR) [11] or distributed derivative superposition (DS) [12] were introduced to improve linearity with low power. In addition, a 28 GHz bidirectional active mixer based on the Gilbert-cell topology was proposed to achieve both down-and up-conversion [13]. A K -band folded downconversion double-balanced mixer based on the Gilbert-cell topology was also proposed to enhance the conversion gain and noise figure (NF) [14]. A 57-66 GHz down-conversion mixer employing the current-reused LO-boosting technique was presented to achieve a high conversion gain with a low LO input power [15]. A 20-26 GHz down-conversion mixer with a bleeding path G m -boosting technique was presented in [16] to improve NF. The authors of [17] proposed a 79-110 GHz 4× quasi-subharmonic mixer to reduce the design burden of the phase shifter. A 57-66 GHz RF to 12 GHz IF down-conversion mixer employing outputmatching, noise-and distortion-cancelling active balun was introduced in [18]. The active balun enhances the linearity performance of the mixer. A 57-66 GHz RF to 8.2-9.5 GHz IF down-conversion mixer with a transformer-based IF matching network was presented in [19]. The HBT transistors were used to improve performances. A new broadband downconversion mixer topology with high performance is required to cover all the 5G NR FR2 bands.
In this paper, a 24-40 GHz broadband mmWave downconversion double-balanced mixer is proposed for 5G NR FR2 cellular applications. To obtain broadband RF and IF characteristics, the G m -stage of the mixer employs a transformer-coupled g m -boosted common-gate (CG) topology with a single-to-differential (S-to-D) current-to-current (I-to-I) capacitor-tuned RF coupled resonator. The IF stage adopts a current-to-voltage (I-to-V) coupled resonator load with gain equalization and a wideband IF buffer stage with a differential-to-single (D-to-S) transformer-based balun. The remainder of this paper is organized as follows. Section II describes the proposed broadband mmWave downconversion double-balanced mixer architecture. Section III elaborates on the circuit implementation of the mixer with a dual-band LO buffer. The experimental results are discussed in Section IV. The concluding remarks are presented in Section V. Fig. 1 shows the proposed 24-40 GHz RF to 8 GHz IF downconversion double-balanced mixer configuration. It comprises a transformer-coupled g m -boosted CG G m -stage, an S-to-D I-to-I capacitor-tuned RF coupled resonator, doublebalanced active switching stages with a dual-band LO buffer, an IF coupled resonator load with gain equalization, and a wideband IF buffer with a D-to-S transformer-based balun. To meet the 5G NR FR2 specification, the RF input operating frequencies of 24.25-43.5 GHz is required in the mixer design. To support an inter-band carrier aggregation, it is very important that a single mixer covers all 5G NR FR2 frequencies. Considering two carrier component intra-band carrier aggregation scenario, the mixer should have 1 dB IF bandwidth of more than 0.8 GHz. The IF output frequency was set to 8 GHz.

II. PROPOSED BROADBAND MMWAVE DOWN-CONVERSION MIXER ARCHITECTURE
The G m -stage of the mixer employs the proposed wideband S-to-D I-to-I capacitor-tuned RF coupled resonator load to cover the 5G NR FR2 bands. Fig. 2(a) shows a conventional two-port I-to-V transformer-based RF coupled resonator. Unlike LC loads, the I-to-V coupled resonator load has transimpedance Z 21 with two resonant peaks, tuned at two VOLUME 10, 2022 different frequencies. The two resonant frequencies can be expressed as: where L, C, and k are the inductance, capacitance, and magnetic coupling coefficient, respectively [20]. To simplify the analysis, a symmetric transformer structure is assumed. In other words, L 1 = L 2 = L, C 1 = C 2 = C, and R 1 = R 2 = R. Z 21 at the resonant frequencies can be expressed as: where R is the parasitic resistance of the inductor L.
From (1), the separation between f L and f H can be tuned using k. Fig. 2(d) shows the simulated Z 21 magnitude response versus different k. As k increases, the frequency separation increases. To connect the G m -stage and I-to-I double-balanced active switching stages of the mixer, a modified I-to-I RF coupled resonator, shown in Fig. 2(b), is proposed. The transfer function of the I-to-I RF coupled resonator can be derived using the input impedance R SW of the following switching stages, expressed as (3), as shown at the bottom of the page. From (3), we find that R SW changes the frequency response of the I-to-I RF coupled resonator compared with the conventional I-to-V RF coupled resonator. The two resonant frequencies and Q-factors of the proposed I-to-I RF coupled resonator can be expressed as: Assuming R/R SW 1 for a simple analysis, H I at the resonant frequencies can be approximately expressed as: and As known from (4) and (5), the separation between f L and f H and Q 1 of the proposed I-to-I RF coupled resonator are lower than those of the conventional I-to-V RF coupled resonator. Consequently, the proposed I-to-I RF coupled resonator has wider frequency response. Fig. 2(e) shows the simulated H I magnitude response of the proposed I-to-I RF coupled resonator. R SW makes the magnitude response wider. If the capacitance C of the coupled resonator is tuned appropriately, the proposed I-to-I RF coupled-resonator can provide sufficient current gain to cover the required 5G NR FR2 bands, as shown in Fig. 2(e). Because the conventional capacitortuned I-to-V RF coupled resonator cannot support all 5G NR FR2 bands due to the narrowband characteristic, the proposed capacitor-tuned I-to-I RF coupled resonator has a great advantage. Moreover, it performs S-to-D conversion. The required 1 dB IF bandwidth in the mixer output is > 0.8 GHz. To meet this specification, a magnetically and electrically I-to-V IF coupled resonator load with low k, shown in Fig. 2(c), is employed after switching stages. It provides broadband and gain flatness characteristics. The capacitance C C between the primary and secondary windings of the transformer can reduce the difference between the Z 21 peak values at the two resonant frequencies [20]. Z 21 of the magnetically and electrically coupled resonator load at the resonant frequencies can be expressed as: and Fig. 2(f) shows the simulated Z 21 of the I-to-V IF coupled resonator with and without C C . C C helps perform gain equalization. A parasitic capacitance between the two windings of the transformer was used to enhance the gain equalization of the IF coupled resonator through a thorough electro-magnetic (EM) simulation with the EMX tool. To drive a 50 load, a wideband IF buffer with a transformer-based D-to-S balun was also used.

III. CIRCUIT IMPLEMENTATION
This section describes the detailed circuit design of the broadband down-conversion double-balanced mixer for 5G NR FR2 applications. Fig. 3 shows the schematic of the proposed mmWave down-conversion mixer with a dual-band LO buffer.
A. TRANSFORMER-COUPLED g m -BOOSTED COMMON-GATE G m -STAGE A transformer-coupled g m -boosted CG configuration is used to boost the effective transconductance of the mixer G m -stage. Transformer TF1 provides anti-phase operation between the gate and source terminals. A cascode transistor is not used to improve the noise performance at the cost of reverse isolation [21]. The input impedance and overall transconductance of the transformer-coupled g m -boosted CG G m -stage are analyzed using the small-signal model introduced in [22], which is shown in Fig. 4. For an intuitive and simple analysis, the effects of C gs and channel-length modulation of M N 1 are considered, while other parasitics and body effect are ignored.
Using the Kirchhoff current law and Kirchhoff voltage law, the following equations can be derived.
V gs1 = − I S1 sC gs1 (11) V OUT = −Z L I OUT (12) Here, V gs1 , g m1 , r o1 , and C gs1 are the gate-to-source voltage, transconductance, output impedance, and gate-to-source capacitance of M N 1 , respectively. Z L is the load impedance. L P1 , L S1 , and M 1 are the self-inductances of the primary and secondary windings, and mutual inductance of transformer TF1, respectively. I P1 and I S1 are the currents flowing into the primary and secondary windings, respectively. From (8)- (13), the input admittance of the G m -stage can be given as: where k 1 is a coupling coefficient (k 1 = M 1 / √ L P1 L S1 ), and n 1 is the turns ratio (n 1 = √ L P1 L S1 ). When it is assumed that g m1 r o1 1, Z L /(r o1 + Z L ) 1, ω 2 (1 − k 2 1 )L S1 C gs1 1, the input admittance of the G m -stage can be simplified to The overall transconductance of the G m -stage is The transformer-coupled configuration increases the effective transconductance by (1 +n 1 k 1 ).

B. SWITCHING STAGE WITH DUAL-BAND LO BUFFER
The double-balanced active switching stage, where the transistors of M N 2 , M N 3 , M N 4 , and M N 5 are switched between the saturation and cut-off regions, are driven by a dualband LO buffer. The required operating frequency range of the LO buffer is 16.25-35.5 GHz because the mixer has 24.25-43.5 GHz RF and 8 GHz IF. Since it is difficult to design a broadband amplifier that covers such a wide frequency range, the LO buffer is designed to be divided into two bands to obtain sufficient voltage gain stably. Fig. 3 shows the proposed dual-band LO buffer. In each band, a three-stage LO buffer is employed, which is composed of a cross-coupled CG amplifier, and two common-source amplifiers. All the amplifiers adopt cascode transistors to enhance the voltage gains. Because adjacent inductors can influence each other, L Deg , L L1 , L L2 , and L L3 were co-designed through a thorough EM simulation. Low-band and high-band LO signals are selected through the MUX and supplied to the switching transistor.
The simulated voltage gains of the LO buffers including the routing line and MUX exceed 18 dB for all operating frequencies. When an LO input signal with P LO = −10 dBm is applied, the LO buffer can stably drive the switching stages to achieve the maximum conversion gain and minimum NF of the mixer.

C. RF AND IF COUPLED RESONATORS
The k of the transformer for the I-to-I RF coupled resonator was set to 0.38 to provide a broadband frequency response. Fig. 5 Fig. 5(c). The designed RF coupled resonator covers all 5G NR FR2 operating bands. Fig. 6(a) and (b) show the layout and simulated parameters of the transformer for the I-to-V IF coupled resonator load, respectively. To obtain a low k, the overlap between the primary and secondary windings is minimized. The EM simulated L P , L S , Q P , Q S , and k at 8 GHz are 1.23 nH, 1.21 nH, 11.9, 11, and 0.13, respectively. A parasitic capacitance between the two windings of the transformer was used as C C to enhance the gain equalization of the IF coupled resonator. The optimal transformer was designed through numerous trials and errors through a thorough EM simulation by adjusting the width, layer, and spacing of the metal and overlapping area of the two windings of the transformer. Fig. 6(c) shows the simulated Z 21 magnitude response of the IF coupled resonator employing gain equalization with the 4-bit capacitor array. When k = 0.13, the IF load has the 1 dB bandwidth of more than 0.8 GHz. C 31 and C 32 can be tuned using 4-bit digitally controlled signals to compensate for the center frequency variation due to the process, voltage, and temperature variations.

D. WIDEBAND IF BUFFER WITH BALUN
A wideband IF buffer with a transformer-based 1:1 balun is used to drive the single-ended 50 . As shown in Fig. 3, the topology of the IF buffer involves a CS amplifier and crossstacked source-follower [23]. The gain of this combined topology can be expressed as: where g mi and r oi are the transconductance and output impedance of M i , respectively, and R L is the load impedance of the buffer, which is close to 50 . When g m1 = g m3 = g mBF , r o1 = r o3 = r oBF , g mBF r oBF 1, the gain is simplified to 2g mBF R L /(2 + g mBF R L ). From (17), we find that the gain of the current-reused IF buffer is almost twice than that of the conventional source follower.

E. CONVERSION GAIN
Considering the source resistance R S and input impedance matching condition of (1 +n 1 k 1 )g m1 R S = 1, the conversion gain of the proposed down-conversion mixer can be approximated as where Z 21IFCR = L P3 (1 + k 3 )/2R LP3 C 31 , A VBF = 2g mBF R L /(2 + g mBF R L ), and R LP3 is the parasitic resistance of L P3 in TF3.

F. NOISE ANALYSIS
The noise sources were assumed to be uncorrelated to each other. For simplicity, the body effect, channel-length modulation, and induced gate noise were also ignored. When a voltage source V S with a source impedance R S is applied to the source of M N 1 , the total noise factor of the proposed down-conversion mixer can be expressed as: (19) where EF is the excess noise factor used to quantify the noise contribution of each sub-block to the overall noise factor F, k is the Boltzmann's constant, T is the absolute temperature, A VMixer is the conversion gain from the voltage source V S VOLUME 10, 2022 to the output V OUT ,IF , and V 2 GM , V 2 SW , V 2 IFCR , and V 2 IFBF represent the output-referred noise voltages generated by G m -stage, switching stages, IF coupled resonator load, and IF buffer, respectively [24]. To simplify the analysis, the parallel parasitic resistance of the I-to-I RF coupled resonator seen to the following switching stages is assumed to be much higher than the input impedance of the switching stages. The RF coupled resonator can remove the white noises in the image band and all its odd harmonics to some extent; therefore, their effect is ignored. The excess noise factors with an input impedance match condition of (1 + n 1 k 1 )g m1 R S = 1 can be derived as follows: where A is the LO amplitude, and I B is the dc bias current of the switching stage [25]. From (20)-(23), the noise factor of  the proposed down-conversion mixer can be expressed as: Fig. 7 shows the simulated excess noise factor of the mixer sub-block at 28 GHz RF and 8 GHz IF under the condition of input impedance match, g m1 = 35 mS, n 1 = 0.63, k 1 = 0.47, n 2 = 1, k 2 = 0.38, n 3 = 1, k 3 = 0.13, n 4 = 0.94, k 4 = 0.71, g mBF = 40 mS, and R L = 50 . As expected, the excess noise factor of the switching stages has the most dominant effect in determining the overall NF performance. Fig. 8 shows the simulated NFs of the mixer with the transformer-coupled g m -boosted CG G m -stage and basic CG G m -stage. By employing the transformer-coupled   g m -boosted CG G m -stage, the mixer achieves 0.7-1.7 dB NF improvement.

IV. EXPERIMENTAL RESULTS
The proposed mmWave broadband down-conversion doublebalanced mixer with the dual-band LO buffer for 5G NR FR2 applications was implemented in a 40 nm CMOS process.   The chip photograph is demonstrated in Fig. 9. The effective active areas of the mixer and LO buffer without the bond pads are 0.36 and 0.294 mm 2 , respectively. The power consumptions of the mixer and dual-band LO buffer are 17.6 and 10.7 mW with a nominal supply voltage of 1.1 V, respectively. The power consumptions of the G m -stage, double-balanced switching stages, and IF buffer in the implemented mixer are 5.83, 2.07, and 9.7 mW, respectively. The measurement of the mixer was performed using an on-wafer probing. The RF input and IF output of the mixer were probed with groundsignal-ground (GSG) RF probes, and the LO signal was provided through a bonding wire on the test PCB board. Supply voltages and SPI control signals were also provided from the PCB board. The measured and simulated S 11 and S 22 of the downconversion mixer are depicted in Fig. 10 and 11, respectively. The measured S 11 is less than −6.5 in the entire frequency range of 24-40 GHz, and the measured S 22 is less than −10 dB at an IF frequency of 8 GHz. When it is actually used in the receiver, the S 11 characteristic is expected to improve because there is no test pad for measuring the mixer input. Fig. 12 shows the measured and simulated conversion gains of the down-conversion mixer. The measured conversion gain in the 24-30 and 37-40 GHz frequency bands are obtained from −2.5 to −0.46 dB and −4.1 to 1.2 dB, respectively. The frequency response of the mixer in the IF frequency range is illustrated in Fig. 13. The measured 1 dB bandwidth of the mixer IF output is more than 1.1 GHz. The proposed IF coupled resonator load with gain equalization improves the gain flatness and bandwidth. As shown in Fig. 14, the measured NF in the 24-30 and 37−40 GHz frequency bands are obtained from 13.8 to 15.3 dB and 12.4 to 13 dB, respectively. Fig. 15 depicts the measured and simulated OIP3. The two-tone test conditions for the IIP3 are f 1 = f IMD3 + 10 MHz and f 2 = f IMD3 + 20 MHz, where f IMD3 is the third-order intermodulation distortion (IMD3) frequency. The measured OIP3 in the 24-30 and 37-40 GHz frequency bands are obtained from 5.73 to 6.8 dB and 4 to 5.2 dB, respectively. The proposed down-conversion mixer can also support n259 (39.5-43.5 GHz) based on the simu-lation results with parasitic extraction. However, it has been measured up to 40 GHz because of the limitation of the measurement equipment. Table 1 summarizes and compares the performances of the implemented mmWave down-conversion mixer with previous state-of-the arts. This work achieves the best performance in terms of the operating frequency range. It can cover all 5G FR2 bands.

V. CONCLUSION
A broadband mmWave down-conversion double-balanced mixer employing RF and IF coupled resonators with a dualband three-stage LO buffer was implemented for 5G NR FR2 applications through a 40 nm CMOS process. In the proposed mixer architecture, the transformer-coupled g m -boosted CG G m -stage improved the noise performance, and the I-to-I capacitor-tuned RF coupled resonator and I-to-V IF coupled resonator with gain equalization provided broadband frequency characteristics such as an RF operating frequency range of 24-40 GHz and a 1 dB IF bandwidth of more than 0.8 GHz. The proposed wideband down-conversion mixer topology can serve as an effective candidate in 5G NR FR2 transceivers employed in mobile phones.