Design of 12-phase , 2-stage Harmonic Rejection Mixer for TV

A two-stage 12-phase harmonic rejection mixer (HRM) for TV tuners is proposed in order to reject the local oscillator (LO) harmonics up to the ninth order. The proposed 12-phase weighing scheme can eliminate the third and ninth harmonic rejection (HR) sensitivity to the amplitude error caused by irrational numbers such as 3 . To verify this HR, the 2-stage HR circuit is designed with baseband gm scaling in order to save power and improve the HR ratios without calibration. The proposed HRM achieves the third to ninth worst HR ratios, more than 55 dB, according to Monte Carlo simulations. It consumes 6.5 mA under a 2.5 V supply voltage.


Introduction
For wideband analog/digital TV tuners covering VHF and UHF bands, harmonic rejection (HR) is a challenging issue because the radio frequency (RF) signals and unwanted signals around the local oscillator (LO) harmonics are translated into the same baseband.
The required HR ratios for TV are 60-70 dB for LO harmonics [1].In order to suppress the unwanted harmonic mixing, various HR techniques have been introduced [1][2][3][4]; however, HR ratios are degraded due to the amplitude and phase errors that result from device mismatch [2].In order to reduce the sensitivity of the HR to mismatch, 2-stage HR techniques [5], [6] have been presented.The 2-stage harmonic mixing has two merits: amplitude error reduction and small integer numbers for root number generation.
1) In 2-stage harmonic mixing [5], the total amplitude error from the HR stages is a multiplication of the errors in the first and second HR stages: (ε 1st • ε 2nd ) / 4, where ε 1st and ε 2nd are the relative errors in the first/ second HR stages, respectively.Therefore, this 2- stage harmonic mixing can reduce the HR sensitivity to stage amplitude errors.
However, these 2-stage HR techniques use 8-phase LOs in which, particularly for VHF (54-216 MHz) band reception, the odd harmonics higher than the fifth order also down-convert unwanted signals to baseband because input RF frequencies span up to 16X range (from 54 to 860 MHz).To ease the requirements of the RF filter and to extend HR to the ninth harmonic, the number of LO phases must be increased to 12. Conventional 12-phase LO, however, has been reported with 1-stage implementation [7], of which HR ratios are vulnerable to amplitude mismatch or device mismatch.
In this paper, a 12-phase harmonic rejection mixer (HRM) with a 2-stage is proposed to desensitize HR ratios to device mismatch so that the third, fifth, seventh, and ninth HR is realized for TV tuner bands (54-860 MHz).To the extent of our knowledge, a 2-stage HRM with 12-phase LOs has not been reported before.This paper is organized as follows.Section 2 describes the 12-phase HR principle, numerical calculations of HR ratios, and circuit implementations of the HRM.The Monte Carlo simulation results are presented and discussed in Sec. 3. Finally, the paper is concluded in Sec. 4. Ratio (5th or 7th)

Design Consideration
When the number of non-overlapping LO phases is N, the LO harmonics greater than or equal to the (N-1) th order are not suppressed, which results in poor HR ratios, e.g.only 20log(n) dB for the nth harmonic.Thus, a 12-phase LO is required in order to enable the sine wave to reject the third to ninth LO harmonics, whereas the 8-phase LO [5], [6] can only reject third/fifth LO harmonics.A 12-phase HRM [7] based on LO-gating techniques [8], [9] was realized through 1-stage harmonic mixing with a weighting ratio of {6.2:10.8} to approximate 3 .This {31:54} ratio is close to 3 with a 0.57% amplitude error.However, it is not easy to implement these high integer numbers with good matching and low power consumption in 1-stage harmonic mixing particularly when transconductance (g m ) scaling [2] is used.The similar issue exists in 8-phase HRMs as well and has been overcome by 2-stage harmonic mixing [5].
To design the 12-phase 2-stage HR circuit, the static amplitude error due to the irrational number ( 3 ) limits the achievable HR ratio and should be considered.When the total weighting ratio in order to generate {1: 3 :2: 3 :1} is selected, it is not easy to find corresponding integer weighting ratios for each stage in the 2stage HR circuit.First, possible small integer weighing ratios to approximate {1: 3 :2: 3 :1} are investigated.Then, weighting ratios for each stage can be extended as follows: {2:3:4:3:2}, {3:5:6:5:3}, {4:7:8:7:4}, •••, and so on.Two selections among those can make the desired total weighting ratio for the 2-stage HR.In this paper, the {3:5:6:5:3}/{4:7:8:7:4} ratios were selected to generate {0:71:123:142:123:71}, as depicted in Fig. 1.The zero factor in this ratio is realized from the cancellation of differential circuits.As the weighting factors increase, the ratio between the first and second factors approaches 3 , but higher factors require more areas and power for the g m scaling technique.
Figure 2 depicts the effects of the relative errors, ε 1st and ε 2nd on the approximations for 3 .The relative errors of third/ninth harmonics are perfectly cancelled despite the non-zero ε 1st and ε 2nd because the total vector summation for the third/ninth harmonics becomes zero, which results from the error vectors having equal amplitude and opposite sign.The cancellation of these relative errors helps to improve the third HR ratio (HR3) and HR9.In the case of the fifth and seventh harmonics, the total relative error can be reduced to ε 1st • ε 2nd / 4. The achievable HR5 or HR7 is the sum of the HR ratios in the each HR stage.The ε 1st in a {3:5} ratio for the approximation of 3 is 3.775% and the ε 2nd in a {4:7} ratio is 1.03%.Then, the HR ratios in the first and second HR stages are 34.5 dB and 45.76 dB, respectively.The total HR ratio is 80.26 dB, when no phase error is assumed.

HR Sensitivity Analysis to Amplitude and Phase Errors
When both amplitude and phase errors are considered, the HR ratios are estimated through equations based on [5].The HR3 of a single-balanced 12-phase HRM is derived as where σ A is the standard deviation (SD) of amplitude error in percentage, σ θ is the SD of phase error in radian, and ε is the relative error due to the approximation of 3 in percentage.From (1), it is noted that σ A is not multiplied by ε since the two 3 vectors in the third/ninth harmonics are in the opposite direction as described in Fig. 2. Thus, HR3 is less sensitive to σ A and dominated by σ θ in our scheme.Similarly, the HR5 of a 12-phase HRM is written as Assuming ε = 1%, 3σ A worst-case HR ratios versus phase error are plotted in Fig. 3.When phase error is zero, the 3σ A (0.3%) worst HR3 and HR5 are 63.8 and 61.5 dB.To accomplish HR ratios over than 50 dB, 3σ A amplitude error is selected to 0.3% and σ θ should be less than 0.15°.

Implementation of HRM
Two methods are conventionally used in baseband HR circuits: the resistor weighting with OTAs and g m scaling.Although resistor matching is more accurate than g m matching, the number of OTAs and power consumption increases significantly.Unlike OTAs, which require a constant bias current, the common-source (CS) amplifier with g m scaling only passes the signal current when the LO switch is on and the branch is active, which results in less current consumption.Thus, the g m -based HR circuit was implemented in this work.The block diagram of the 2stage HR circuit for the I and Q channels is presented in Fig. 4. In the first HR stage, PMOS amplifiers have a g m ratio of {3:5:6:5:3} in order to approximate {1: 3 :2: 3 :1}.This g m ratio is implemented by scaling the total width of MOSFETs.As an instance, the device size for the factor 3 is W/L = 37.5 μm/1.2μm.But the problem is that each PMOS amplifier in the first stage has different Cgs due to their different total width, which increases path mismatch and degrades HR performances.To eliminate this mismatch, dummy cells with diode-connected NMOS The RF section of the HRM is described in Fig. 5.The CS amplifier (M CS ) generates a bias current of 1 mA in order to drive the 12-phase active mixer.The 12-phase LO switches are driven using non-overlapping 8.33% dutycycle LO signals.The lowpass filters (LPF) are connected to the mixer in order to suppress the LO feedthrough and out-of-band interferers.The mixer, LPFs, and thick PMOS loads operate under a 2.5 V supply for better linearity.

Simulation Results
HR performances depend on both amplitude and phase errors of the effective LO waveform.In the g m -based HR circuit, the LO amplitude is realized by g m scaling that is sensitive to device mismatch.Thus, the Monte Carlo HR simulations are used to estimate their sensitivity to device mismatch and different process corners as well.In order to find the HR ratios, an RF signal (111 • N + 4 MHz, N = 1, 3, 5, 7, and 9) was applied and down-converted to 4 MHz via the N th order LO harmonics with the 111 MHz effective LO.Then, the power differences between the fundamental and harmonic tones were compared.Figure 6 illustrates that the worst-case third, fifth, seventh, and ninth HR ratios obtained by Monte Carlo simulation are 56, 55, 58, and 62 dB, respectively.This g m -based 2-stage HR circuit has ~0.1% drain current mismatch due to g m scaling according to Monte Carlo simulation.Derived from ( 1) and ( 2), the estimated 3σ worst-case HR3 and HR5 are supposed to be 63.8 and 61.5 dB, which are ~7 dB higher than the Monte Carlo simulation results shown in Fig. 6.These discrepancies result from unaccounted mismatch sources other than g m scaling mismatch, such as mixer switches and loads.
Figure 7 shows the effects of process corners and phase error in HR ratios.Figure 7(a) demonstrates that the worst-case HR ratios maintain > 50 dB in nom (27 °C), slow (120 °C), and fast (-40 °C) corners.In Fig. 7(b), the worst-case HR ratios are still better than 50 dB even with 0.3° phase error.The phase error is generated by phase shifts of the LO signal.The Monte Carlo simulation results assuming phase error of 0.15° are plotted in Fig. 8, where the worst-case HR3 of 53.6 and HR5 of 55 dB are achieved.
The wideband HR ratios of the proposed HRM are shown in Fig. 9.The RF signal at 115 MHz is down-converted to 4 MHz by the 111 MHz effective LO and the third RF interference at 335 MHz is down-converted to 2 MHz by the third LO harmonic.The third to ninth RF interferences at low frequency bands (54-95 MHz) are also down-converted to in-band by LO harmonics, thus HR3 to The HRM performances are summarized and compared in Tab. 2. Worst-case HR ratios from Monte Carlo simulations (200 runs) are reported in Tab. 2. The device size for the biggest factor 30 in the 1-stage HRM is W/L = 75 μm/1.2μm, which is the same size as the factor 6 in the proposed HRM.The 2-stage harmonic mixing improves HR3 by 4 dB compared to 1-stage harmonic mixing.Compared to the 8-phase HRM, the proposed 12-phase HRM achieves almost 40 dB improvement on HR7 and HR9, while maintaining comparable voltage gain and IIP3.Under a 2.5 V supply, the 8-phase and proposed 12-phase HRMs consumed 11.75 and 16.25 mW, respectively.Although the 12-phase HRM requires more power consumption compared to the 8-phase HRM, it can reject odd harmonics up to the ninth order.

Conclusion
A 12-phase HRM using the 2-stage g m -based HR circuit is presented for the TV tuner bands in order to suppress unwanted odd LO harmonics.Unlike conventional 8-phase HR schemes, the proposed 12-phase 2-stage HR scheme extends the maximum order of HR from the fifth order to the ninth order harmonic with small weighting factors, and rejects the third to the ninth LO harmonics between 55 to 62 dB without calibration.Although our scheme was demonstrated on the g m scaling scheme, it can be also applied to other resistor weighting schemes with transimpedance amplifiers (TIAs).
(GIST), Gwangju, in 2008.He is currently working towards the Ph.D. degree at GIST.His research interests include analog and RF IC designs for multiband and multimode wireless receivers.
Hocheol JEONG was born in 1988.He received the B.S. degree in Electronic and Radio Wave Engineering from Kyunghee University (KHU), Suwon, Korea in 2014, the M.S. degree from GIST, Gwangju, Korea in 2016.He is currently working toward the Ph.D. degree at GIST.His research areas are analog and RF IC design for wireless applications.

Fig. 1 .
Fig. 1.The effective LO waveform of the proposed HRM.

Fig. 7 .Fig. 8 .
Fig. 7. Worst-case HR ratios from Monte Carlo simulation results (200 runs) with (a) process corners and (b) phase error at the 111 MHz effective LO.
LEE was born in 1976.He received his B.Sc. and M.S. degrees both in Electrical Engineering from Seoul National University, Seoul, Korea in 1998 and 2000 respectively.He received the Ph.D. degree in Electrical Engi-neering from the University of California, Los Angeles, in 2008.In 2000, he was a consultant with GCT semiconductor, Inc., and Silicon Image Inc., designing analog circuits for wireless communication and digital signal processing blocks for Gigabit Ethernet.He joined Silicon Image Inc., Sunnyvale, CA in 2001, developing Serial ATA products.In August 2008, he joined Agilent Technologies in Santa Clara, CA, where he was involved with the development of next generation high-speed ADCs and DACs.Since 2012, he has been with the School of Information and Communications, Gwangju Institute of Science and Technology, Gwangju, Korea, where he is now an Assistant Professor.He was the recipient of the 2007 Best Student Paper Award at the VLSI Circuits Symposium in Kyoto, Japan.He received the 2015 Distinguished Lecture Award in Gwangju Institute of Science and Technology.